University of South Wales

University of South Wales

2064711

A MA THEM A TICS ASSESSJVCEJNTT

SOHEIVIE FOR LESS ABLE

by

Lynn Davies

A Thesis submitted for the degree of

Master of Philosophy, C.N.N.A. London

Department of Mathematics and Computing,

The Polytechnic of Wales,

Pontypridd,

in collaboration with the Welsh Joint Education Committee

August 1990

DECLARATION

THIS IS TO CERTIFY that an advanced course of reading has been

undertaken and that this thesis has neither been presented, nor is

being concurrently submitted, for any degree at any other academic

or professional institution.

Candidate : Lu \j^ I)

V

CERTIFICATE OF RESEARCH

THIS IS TO CERTIFY that, except where specific reference is made,

the work described in this thesis is the result of the investigation of

the candidate.

Candidate

Supervisors :

Director of Studies

CONTENTS

Page

Acknowledgements (i)

List of Tables (ii)

Abstract (iii)Introduction *"t/'

CHAPTER 1 : PERSPECTIVES 1

1.1 Numerical Competency 1

1.2 The Mathematics Curriculum 7

1.3 How Children Learn Mathematics 9

1.4 Assessment 19

CHAPTER 2 : THE CERTIFICATE OF EDUCATION 29

2.1 Background 29

2.2 Course Structure 36

2.3 Pattern of Assessment 39

2.3.1 Written Assessment 43

2.3.2 Oral Assessment 45

2.3.3 Practical Assessment 46

2.3.4 Project 47

2.4 Mark Weighting 48

CHAPTER 3 : SCOPE OF THE STUDY 50

3.1 Suggestions for Change 50

3.2 The End of Module Tests 51

3.3 The Practical Assessments 52

3.4 The Oral Assessments 52

3.5 The Project 53

Page

CHAPTER 4 : THE END OF MODULE TESTS 56

4.1 Introduction 56

4.2 Research Method 57

4.2.1 Administration of Tests 58

4.2.2 Scrutiny of Results 59

4.2.3 Analysis of Scrutiny of Test Results 61

4.2.4 Conclusions 62

4.3 Testing the Hypothesis 75

4.3.1 Research Method 75

4.3.2 Analysis of Results 76

4.4 Conclusions and Recommendations 76

CHAPTER 5 : THE PRACTICAL ASSESSMENTS 85

5.1 Introduction 85


5.3 Findings and Recommendations 90

5.4 Conclusions 94

CHAPTER 6 : THE ORAL ASSESSMENT 97

6.1 Introduction 97


6.2.1 Informal Teacher Survey 102

6.2.2 Comparison of Marks 102

6.3 Analysis of Results 108

6.3.1 Results of Teacher Survey 108

6.3.2 Analysis of Comparison of Coursework Scores 109


CHAPTER 7 : THE PROJECT 112

7.1 Introduction 112

7.2 Investigation 118

7.3 Conclusions 119

Page

CHAPTER 8 : ATTENDANCE 126

8.1 Introduction 126


8.3 Analysis of Results 129


CONCLUSIONS 148

REFERENCES 152

QUOTATIONS 155

APPENDIX I - CERTIFICATE OF EDUCATION SYLLABUS

APPENDIX II - NOTES OF GUIDANCE FOR TEACHERS

APPENDIX III - END OF MODULE TESTS

ACKNOWLEDGEMENTS

I would like to thank the staff and pupils of the five schools

in Mid Glamorgan who took part in this investigation; the Welsh Joint

Education Committee who allowed access to their examination archives,

and Mr. Roger Scott of the Polytechnic of Wales, who advised on

statistical procedures.

My very grateful thanks are also extended to my supervising

tutor, Dr. George Ball, of the Polytechnic of Wales, without whose

consistent support this study would not have been completed; and

to Suzanne for her help in typing the finished result.

Figure 1.1

ur i

Weighing Scale Dial

Page

23

Table 2.1

Table 2.2

Table 2.3

Table 4.1

Table 4.2

Table 4.3

Tables 4.4-4.8

Table 4.9

Table 4.10

Tables 4.11-4.15

Table 4.16

Table 4.17

Table 4.18

Tables 4.19-4.23

Tables 4.24-4.28

Table 5.1

Table 5.2

Table 6.1

Tables 6.2-6.6

Table 6.7

Table 6.8

Table 8.1

Table 8.2

Tables 8.3-8.7

Tables 8.8-8.12

Table 8.13

Table 8.14

Course Structure for the Certificateof Education, Numeracy 37

Assessment Structure for the Certificateof Education, Numeracy 43

Mark Weighting 49

Written and Aural Tests undertakenby each Sample 58

End of Module Test Scores forCandidate 5.32 60

End of Module Test Scores forCandidate 4.5 60

End of Module Test Results for Sample 63-67

Median Total Scores for each Sample 68

Median Total Scores for each Sample 68

End of Module Paired Test Resultsfor Sample 69-73

Median Total Scores using Paired Tests 74

Median Total Scores using Paired Tests 74

Median Difference in Total Scores onAural and Written Tests 76

Sign Tests of the Median Difference inTotal Scores for the Sample 78-80

Sign Tests of the Median Difference inPaired Total Scores for the Sample 80-82

List of Practical Tasks 86

Summary of Written Assessments 95

Breakdown of Oral Marks per Section 99

Percentage Coursework Marks for Sample 104-107

Distribution of Highest Coursework Marks 109

Distribution of Highest Coursework Marks of Candidates who Completed all Elements of Coursework 110

Number of Candidates in each Examination Category 130

Number of Candidates in each Coursework Category 131

Raw Coursework and Final ExaminationMarks for Sample 133-137

Weighted Coursework and ExaminationMarks for Sample 138-142

Pattern of Attempted Assessments for Candidates who failed the Coursework Assessments 143

Number of Assessment Categories Attemptedand Number with Scores in Excess of 40% 144

11

ABSTRACT

This study is concerned with the assessment framework used

within the W.J.E.C. Certificate of Education Numeracy Course.

A sample of 193 candidates, drawn from 5 large Comprehensive

Schools in Mid Glamorgan, was tested using written, aural, oral, and

practical assessment procedures, and the results obtained were analysed.

The data collected refers to the 1986-1988 cohort of entrants, while the«

schools were chosen to reflect a variety of catchment areas and

management structures.

A variety of research techniques were used to interpret the

results. These included statistical analysis, teacher interviews and

reasoned argument. The following conclusions were drawn:

Pupils score significantly higher marks when End of Module tests

are administered aurally rather than in written form.

A higher mark-weighting should be attached to the practical

assessments in order to reflect more fully the practical ethos of

the course. More detailed assessment criteria are suggested to

enable positive achievement in this area to be rewarded.

The oral assessment merits a higher mark-weighting than is

presently allocated. However, in view of the relatively high level

of absence for this component, it is noted that such a change

could have a significant effect on the overall pass rate for the

course.

There is little support among teachers for the retention of an

individual extended piece of work. However, a directed project,

with a detailed marking scheme, would be a viable alternative.

CCi.

INTRODUnTTDKT

The Certificate of Education Numeracy Course is a mathematics course

designed for pupils of secondary school age for whom a G.C. E. or C.S.E.

syllabus and examination is considered inappropriate. The course was

developed in Mid Glamorgan and is recognised for examination purposes by

the Welsh Joint Education Committee.

During the two-year period of study, pupils undertake a variety of

coursework activities which are assessed by the class teacher. This form of

continuous assessment, together with an end of course written examination,

is intended to provide an assessment structure which is comprehensive in

both breadth and depth for the target population.

The Certificate of Education Working Party, who were responsible for

formulating both the syllabus and assessment structure, decreed that the

course should run for an initial period of five years (1981-1986) without

any amendments; but that during this period close monitoring of the

effectiveness of the course content and the assessment procedures should

take place.

During this monitoring process it has become clear that the practical

ethos of the course should be more clearly reflected in the assessment

structure generally, and in the mark weightings attached to various

assessment elements specifically.

The purpose of the present research is therefore to clarify the

assessment procedures within the Certificate of Education course, and to

determine a more appropriate allocation of marks for each assessment

module. The study uses data collected from five large comprehensive

schools during the period 1986-1988, and the author, who is a member of

the Certificate of Education Working Party, and also its Chief Examiner,

addresses five major concerns:

i) Consideration is given to the proposal that the End of Module Tests,

which form a significant part of the present assessment scheme,

should be administered in an aural rather than a written form.

ii) The possibility of providing more detailed guidelines for administering

the practical tasks, and increasing the marks associated with these, is

examined.

iii) The relative importance of the oral assessment, and the suggestion

that this component should merit greater importance is investigated.

iv) The future inclusion, or otherwise, of an extended individual study is

considered.

v) The extent to which the assessment structure is affected by non-

attendance is examined.

The conclusions reached are to be presented to the Examination

Board, with a view to incorporating any recommended changes into the

Certificate of Education course.

CHAPTER 1

PERSPECTIVES

1.1 NUMERICAL COMPETENCY

"Few subjects in the school curriculum are as important to the future of the nation as mathematics; and few have been the subject of more comment and criticism in recent years".

(Mathematics Counts, 1982)

Standards of numerical competency among young people is

an issue about which a great deal of concern has been expressed.

"Mathematics Counts" [1] states that:

"the word "numerate* should imply the possession of two attributes. The first of these is an at- homeness with numbers and an ability to make use of mathematical skills which enables an individual to cope with the practical mathematical demands of everyday life. The second is an ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables, or by reference to percentage increase or decrease."


As early as 1964, a study carried out by the DES with less

able pupils [2] in secondary schools, found that at least 10% of the

group were significantly 'backward in number'. They concluded that,

as a matter of urgency, a mathematics curriculum suitable to their

abilities and particular difficulties should be formulated.

Lochhead 13], Clement 14], Alderman 15] and Johnson [6],

amongst others, have studied the mathematical ability of professional

adults, and have shown that many have in fact failed to understand

rudimentary aspects of the subject. In all cases the adults

interviewed had, throughout their lives, hidden their inadequacies by

using the human ability to imitate and learn by rote. This had

allowed them to pass formal examinations without acquiring the

assembled experiences which would give meaning and understanding

to mathematics.

During the background research to their report

"Mathematics Counts", the Cockloft Committee built up a firm

impression that functional innumeracy, i.e. the inability to apply

mathematics to problem-solving, was more widespread than they had

previously believed. As a result of this belief the DBS were asked to

commission a study [7] in an attempt to discover the extent of this

apparent deficiency in groups of working adults.

The most striking feature of the study was the extent to

which the need to undertake even a simple and straightforward piece

of mathematics could induce feelings of anxiety, helplessness, and

fear. No connection was found between this mathematical anxiety and

occupational group. People of widely different mathematical

competences were found in all occupational groups', and there did not

appear to be any connection between educational qualification and the

extent to which mathematics was used. Some very highly educated

people used little or no mathematics, while some with few or no

qualifications displayed a high level of mathematical competence.

One group who were able to perform the calculations which

they normally required considered themselves inadequate because they

did not use what they termed "proper methods" - standard classroom

techniques.

A second group appeared to have only one method for

solving a given problem. If this failed, or if the calculation proved

too cumbersome, they lacked the ability and confidence to try a

different approach.

Another feature revealed by the study was a widespread

inability to understand percentages. Nor was there any realisation

that the introduction of a decimal currency system had made it easier

to calculate a percentage of an amount of money. The reading of

charts and timetables was also an area revealed as causing a high

level of anxiety.

Many strategies were encountered for coping with the

mathematical demands of everyday life. These included always buying

£10 worth of petrol, or always paying by cheque. There was

frequent reliance on other family members to check or pay bills, to

measure or read timetables, and also much "learning by rote" from

past experience. It was also clear that lack of mathematical ability-

had become a deterrent to applying for jobs or promotion, and had

proved a very real handicap to many throughout their lives.

Employers, teachers and young people themselves, all agree

on the importance of a basic level of numerical competency. It is

universally felt that:

"If school leavers are to play their proper role in society, then proficiency in the basic skills is essential".

(Davies, 1977)

Low attainment in mathematics has been ascribed to many

specific causes. Denvir, Stolz and Brown [8] conducted interviews

with people who regarded themselves as having 'failed' at mathematics

at school in that they had not achieved any formal qualification in the

subject. Among the reasons cited for failure were:

a limited grasp of language;

no encouragement or support at home;

no grasp of relationships;

not very bright;

no practical experience at infant level;

too fast a teaching pace;

everything marked wrong;

The Cocko-oft Committee also found that failure and

consequent dislike of mathematics was often ascribed to a specific

cause when young. Such causes included change of teacher or

school, absence through illness, being promoted to a higher class and

thus being 'left behind', having an unsympathetic teacher, and even

over-expectation on the part of parents.

Laurie Buxton [9J found that most adults interviewed

related feelings of uncertainty and anxiety about mathematics to

specific unpleasant experiences at school, or to over-anxious cramming

on the part of their parents.

For any individual pupil it is unlikely that there is one

specific cause of low attainment. More likely there are several

contributory factors which interlink to form a downward spiral of

cause and effect that is difficult to identify, and even more difficult

to separate into its component parts.

Some of these causes of low attainment in mathematics may

be wholly or partly beyond the control of the school. However, this

is not to say that a pupil cannot be helped at school to overcome or

minimise their difficulties. No school can change a pupil's home

background, but a knowledge of specific problems and an

understanding of emotional difficulties can do much to create a non-

stressful working environment.

Pupils may be influenced by their own parents' attitudes

to mathematics. Some parents may themselves have experienced

difficulty in mathematics and pass on their own anxiety or negative

attitude to their children. In such cases an understanding teacher

(and school) can, by careful choice of subject matter and learning

experiences, do much to influence both pupils' and parents' attitudes.

Many causes of low attainment are, however, within the

control of the school. Denver [10] lists these contributory factors as

being:

inappropriate teaching methods and content;

lack of suitable materials;

lack of teacher time to reflect on pupils' difficulties

and plan suitable work;

teachers' lack of detailed knowledge of the

mathematics being taught;

teacher's inability to motivate and involve pupils

and organise work efficiently.

Teachers of low attainers in mathematics should therefore keep under

constant review their teaching methods, use of materials and

resources, and selection of mathematical content in relation to the

needs of the particular pupils being taught.

The identification of the causes of low attainment will not,

however, lead to any simple remedies, but will serve to increase

teachers' awareness of the pupils' difficulties and hence of the

suitability of different approaches and content.

1-2 THE MATHEMATICS CURRICULUM

The question of what mathematics should be taught to

pupils has been considered by many writers. Amongst these,

Maclaughland [11], Hart [12] and Dean [13J argue that the mathematics

taught to pupils should not only be of a sufficiency in itself, but

should influence and support all the areas of experience that a pupil

- of any ability - is likely to encounter. It should contribute

aesthetically by developing a sense of order through an emphasis on

pattern in number and shape, and by fostering an appreciation of

symmetry in shape and form. It should contribute creatively by

encouraging pupils to provide their own methods of solution and

devise their own problems, not simply imitating the work of others.

It should contribute linguistically by helping to refine and make

precise the descriptive language that children use. Similarly a

reciprocal relationship should exist within science, for scientific

methods are used in the learning of mathematics and mathematics is

frequently applied in science. Social, political and ethical issues can

be clarified by the use of statistical and other forms of mathematical

argument.

Finally, mathematics requires neatness and accuracy, clear

logical thinking, and precise and concise expression and

communication. These are valuable personal skills which help to

prepare pupils for the world of work and their place in society.

Denvir, Stolz and Brown [14] acknowledge that for low

attaining pupils the amount of mathematics needed in daily life is

small, but some aspects of number, time and money are fundamental.

However, even for low attaining pupils, the mathematics curriculum

cannot be considered as a separate entity. At school, pupils are

helped by their mathematical understanding to make progress in other

subjects. An understanding of shape is necessary for the

interpretation of drawings in the workshop, an appreciation of

population trends in history requires an appreciation of the relative

magnitude of large numbers. Sorting experiences are a prelude to

scientific classification of plant and animal life, using a filing system,

or even organising storage space in a kitchen.

Outside school, facility with mathematical skills can enhance

the quality of many aspects of life. At work some jobs require

specific mathematical skills. Most jobs, at the very least, require

employees to plan logically and follow ordered procedures.

In considering the needs of society, it is important to

remember that pupils will be consumers as well as workers. Low

attainers in mathematics are open to exploitation if unable to manage

their own affairs. The ability to handle money, estimate the amount

of decorating material required, plan a holiday, score in a game of

darts, are all useful social skills which make living in society a

comfortable experience rather than a threatening one.

The Cocl^roft Committee published a "foundation list" of

topics which should be present in the mathematics curriculum of all

mainstream secondary school pupils. Their report, which has

probably had more effect on the teaching of mathematics in schools

than any previous work, recommends that:

"the mathematics course (for less able pupils) needs to be specifically designed to build up a network of simple related ideas and their applications ... at all levels it (the mathematics course) should not be based simply on computational skills but should relate to all sections of the foundation list."


Finally, the National Curriculum [15] can be seen to

endorse the recommendation of the Cocl^roft Committee by demanding a

'broad balanced mathematics curriculum' containing aspects of number,

algebra, measures, shape and space, probability and data handling for

all pupils.

1.3 HOW CHILDREN LEARN MATHEMATICS

Any attempt to state definitively how children learn

mathematics is doomed to failure. Despite the vast amount of past

and present research, surprisingly little is known about the complex

activity of learning. However, virtually all those who have made

studies in this field are agreed that it is an active rather than a

passive experience, and should be based firmly on the child's past

and present experiences of the real world.

Piaget [16] believes that activities are vital. He argues

that pupils learn from two types of experience using the term

'physical experience' to mean an actual activity, with real objects,

undertaken in order to discover the properties of the objects

themselves; and the term 'logico-mathematical experience' to describe

the mental activity relating to the physical activity in which the child

is engaged. Piaget suggests that a child's logico-mathematical

thinking had three distinct stages of development:

'pre-operational' - when a child is incapable of consistent

reasoning.

'concrete-operational' - when a child is capable of reasoned

thinking about objects of which he has had actual

experience.

'formal-operational* - when a child has the capacity for

abstract thought.

Piaget believes that most children remain at the pre-

operational stage until about seven years of age; are in the

concrete-operational stage until about twelve years of age, and from

then onwards are in the formal-operational stage. He further

maintains that a child cannot learn logical concepts until he or she

has reached a certain stage of readiness.

10

Piaget's views are by no means universally accepted.

However, most researchers would agree with him in his belief that a

child's previous experiences are of paramount importance on his

present learning.

The sequential stages of intellectual development which

Piaget claims are necessary, are similar to those proposed by Bruner

[17J:

"We would suggest that learning mathematics reflects a good deal about intellectual development. It begins with instrumental activity, a kind of definition of things by doing them. Such operations become represented and summarised in the form of particular images. Finally, and with the help of a symbolic notation that remains invariant across transformations in imagery, the learner comes to grasp the formal or abstract properties of the things he is dealing with."

(Bruner, 1973)

These three stages, which Bruner calls enactive, iconic and

symbolic, are stages in the function of learning which, though similar,

cannot be translated directly into Piaget's age-related stages of

cognitive development. Bruner's stages can be experienced at any

age by both children and adults while they are learning some new

piece of mathematics. Another important aspect of Bruner's theory is

that children should learn through discovery. In this way, he

11

believes they will not only assimilate a body of mathematical

knowledge, but also begin to think like mathematicians.

At all levels of ability, pupils have been found to display

weaknesses in their conceptual thinking. In pupils of low ability,

these weaknesses have been observed to be more pronounced than in

their more able peers. Each individual has to construct his or her

own conceptual system. Pupils of different ability levels require very

different lengths of time and very different experiences to do this

effectively.

Lovell 118J states that it is essential to allow children time

to develop an understanding of the concepts and processes which

form the basis of mathematical thinking. He concludes that children

who demonstrate a lack of understanding of these concepts through

insufficient time being spent at each stage of their development, could

be severely handicapped in their mathematical development.

Shayer, Kiichemann and Wylan 119] also considered that

sufficient time was crucial to the development of conceptual thinking.

They infer that the stages of development proposed by Piaget actually

occur much later in most children than had been thought. This

implies that slow learning children are likely throughout the whole of

their formal schooling, to be working within the 'pre-operational' and

'concrete-operational' stages.

12

Gulliford 120) notes that children are often assumed to

have understood a mathematical concept when in fact they are simply

mimicking and repeating previously encountered operations. When,

later, an attempt is made to present the operations within a word

problem, children fail because they have no understanding of how the

operation relates to the problem. To distinguish between learning

with understanding and learning without understanding, Skemp [21J

uses the term 'relational understanding' to mean 'knowing both what

to do and why'. The acquisition of skills purely by rote learning he

labels 'instrumental understanding' or 'rules without reasons', and

acknowledges that instrumental understanding can appear to offer

many short term advantages. It is both easier and quicker to

acquire, while the rewards are immediate and apparent. It can allow

pupils to achieve the correct answer to a routine question presented

in a familiar way, thus giving a feeling of instant success. However,

in the longer term, relational understanding will prove a more

worthwhile investment. It is adaptable to new tasks - pupils do not

have to acquire a new method for each type of problem; it is not

dependent on memory, and although harder to . acquire, the

relationships once made, are more permanent. ' Constructing

relationships is more satisfying than having to memorise meaningless

procedures and is therefore more motivating. Perhaps most

importantly, each idea grasped is a growth point for further

relationships to be developed. Without forming relationships, which are

the essence of relational understanding, pupils can neither deduce

new ideas nor reconstruct old ones. The heavy reliance on memory

13

vvhich results creates severe learning difficulties for many low

attaining pupils who have a poor memory.

The advantages of relational understanding do not however

imply that the memorising and recall of basic facts and skills is

unimportant. It is important. Rather, it illustrates the need for

skills to be explicitly related to concepts which the child has already

established. Skemp 122] described a concept as:

"a way of processing data which enables the user to bring past experience usefully to bear on the present situation."

(Skemp, 1971)

He considers a variety of ways in which concepts can be interrelated

and the resulting mental structures formed. These structures he

terms 'schemas 1 . He believes that the very foundation of learning

mathematics is built around the study of the mental structures

themselves; the ways in which they are built up, and the ways in

which they function.

The Mathematics Association in considering the teaching of

mathematics states:

"it is necessary that pupils fully understand what they are doing at each stage ... pupils who are taught only the procedures (for solving mathematical problems) may feel insecure when placed in a new situation and previous stages have not been fully understood."

(Mathematical Association, 1979)

14

Hart [22) concurs with this in her own research on a

hierarchy of understanding in mathematics. She believes that

children have to pass through each 'stage' of understanding and will

be unable to acquire 'higher order' concepts unless 'lower order'

concepts are thoroughly assimilated and understood. She also

acknowledges the importance of a 'number readiness' and asserts that:

"a less able pupil would be unlikely to assimilate that which is essentially abstract until far later than more able peers."

(Hart, 1981)

Indeed, in many cases she believes that less able children may never

be ready to assimilate the more abstract type of mathematics which is

their usual diet in the upper secondary school.

In conjunction with other previously mentioned research

findings, Hart believes that the most important consideration in

deciding what mathematics activities should be presented to pupils is

the 'knowledge base' and previous relevant experience that a pupil

has. She maintains:

"As teachers we have expectations of what a child 'should' know, very often based on intuition and usually very different from the actuality."

(Hart, 1981)

Verngnaud [23] also believes that children make progress

in their conceptual thinking only when new experiences are firmly

15

built around previously assimilated ideas. However, he does not

completely agree with Hart in her research on hierarchical thinking.

He believes that mathematics is not strictly hierarchical in structure

in the sense that an idea at any given level is defined uniquely in

terms of those at a lower level. Instead he argues that hierarchies

exist on a 'local level' with interconnections and 'chains' of definitions

and arguments within, and across, the network of concepts which

make up mathematics. He states:

"the hierarchy of mathematical competencies does not allow a total order organisation, as the theory of stages unfortunately suggests, but rather a partial order one. Situations and problems that students master progressively; procedures and symbolic representation that they use, from the ages of two or three up to adulthood and professional training, are better described by a partial order schema in which one finds competences that do not rely on each other; although they may all require a set of more primitive competencies, and all be required for a set of more complex ones."

(Verngnaud, 1983)

When considering ways in which children build up a

network of interrelated concepts, no study can be complete without

giving consideration to the importance of language in this

development. Brissenden [24] mentions the work of Vygotsky and

Halliday as being of particular importance in this field. Vygotsky

argues that the relation of thought to word is a continual moving

interdependent process; that thought is not merely expressed in

words, but also comes into existence through them. Thus it seems

16

reasonable to suppose that the complicated meanings and thought

processes involved in mathematics will be dependent on the level of

language development which children are acquiring. If this is the

case, discussion of mathematical ideas is vital in order to allow

children to develop and negotiate a particular meaning for themselves,

and also to communicate this meaning to others.

The Cockjroft Committee acknowledges the importance of

discussion in the development of mathematical thinking:

"the ability to 'say what you mean and mean what you say' should be one of the outcomes of good mathematics teaching. This ability develops as a result of opportunities to talk about mathematics, to explain and discuss results which have been obtained, and to test hypotheses."


Both the National Curriculum Council and the Curriculum

Council for Wales endorse the importance of language and discussion

to mathematical development. The Non Statutory Guidance produced

by these bodies suggests that:

"talking about ideas and findings are essential to the development of mathematical understanding."

and further states that:

17

"the range of learning modes should include... talking - describing, explaining or clarifying ideas; giving examples; making predictions; asking and answering questions; reporting outcomes; discussing .... ."

(National Curriculum - Non Statutory Guidance for Mathematics, 1989)

When implications are drawn for the teaching of

mathematics in schools, it does appear that although we do not know

exactly how children learn, there are some general principles upon

which researchers agree. One such principle is that pupils should

not pass through an invariant system of skill and process 'learning'.

Instead, pupils should be subjected to a network of possible

sequences of ideas which might be viable. No one sequence will be

the optimum one for all pupils, but various chains will have more, or

less, relevance for differing groups of pupils.

Another is that mathematics is an active learning process.

Pupils need to be engaged in activities which offer opportunities for

experimentation and investigation, not merely subjected to a passive

process of rote learning of facts and skills.

Finally, if mathematics is to be a powerful and succinct

means of communication, pupils need to develop these communication

skills throughout their mathematics learning by becoming involved in

talking about the activities in which they are engaged.

cIndeed, the Cock/Sroft Committee considered that:

18

"Mathematics teaching at all levels should include opportunities for

exposition by the teacher;discussion between teacher and pupils andbetween pupils themselves;appropriate practical work;consolidation and practice of fundamentalskills and routines;problem solving, including the application ofmathematics to everyday situations;investigational work."


1.4 ASSESSMENT

For more than a decade there has been considerable

interest and discussion concerning the assessment of mathematical

ability in schools. During this period a considerable amount of money

and resources have been invested in developing schemes to assess

pupils' achievement in mathematics. Much of the current interest is

undoubtedly externally instigated and can perhaps be traced initially

to the work undertaken by the Foundation for Educational Research

on behalf of the Assessment of Performance Unit at the Department of

Education and Science. This work is continuing with the

development of graded assessment schemes and records of

achievement.

Pupils are assessed to determine their 'present state of

knowledge'. However, the value of the assessment lies in the use

which is made of the information which it reveals.

Most of the externally instigated schemes of assessment are

essentially concerned with evaluating and grading children's

19

achievements for the purpose of 'sorting and selecting'. This type of

summative assessment is essentially public - the results being made

available to interested bodies in order that judgements may be formed

about the pupils and schools, and selections may be made. In this

type of assessment, comparisons may be made between pupils, and a

rank order established; alternatively, pupils may be measured against

a pre-ordained 'standard' where no comparison with other pupils is

made. This type of assessment has, in the past, been generally the

province of agencies outside the classroom - examination boards and

commercial agencies. However, with the advent of the National

Curriculum, summative assessment is becoming partly the

responsibility of the teachers in the form of Teacher Assessments

which will stand alongside nationally produced Standard Assessment

Tasks as a measure of what children know, can do, and understand.

Although summative assessment is primarily concerned with

measuring a pupil's attainment, it is important that it is not seen as a

separate entity completely divorced from the curriculum, but that it

should reflect the teaching of the curriculum in terms of its aims,

objectives, criteria for content and approaches.

Another form of assessment - an essentially private one

between pupil and teacher - is carried out for diagnostic purposes to

develop an awareness of a child's progress and in order to aid

learning.

20

Brenda Denvir 1251 includes the following list as major

uses of formative teacher assessment:

to identify pupils in need of extra help;

to allocate pupils to classes or groups, and

sometimes to indicate what forms of organisation

may be appropriate;

to help the teacher plan appropriate work; either

by selecting particular activities, or by allocating

pupils to particular courses;

to evaluate the effectiveness of the teaching;

to aid continuity when pupils transfer to a new

teacher or school;

to motivate pupils;

as a way of controlling the curriculum.

This type of assessment is and always has been a

necessary part of teaching. Diagnostic assessment of this kind can

encompass both formal (examinations, tests) and informal (observation

of pupils) procedures; but in order that improved learning is

21

achieved, follow-up action must be a recognised part of the

assessment procedure.

The above list is certainly not exhaustive, nor are the

items mutually exclusive. Indeed, there is a great deal of common

ground between some points, while others can be seen to be in

conflict. For example, the assessments which are most suitable for

allocating pupils to classes or groups are those which result in a

wide range of marks. However, such a range implies a number of

pupils will obtain very low marks - doing little for self esteem and

even less in the way of motivation. Formal end of course

examinations are the assessments which generally carry most weight

with parents and employers, and indeed can provide a focus for

study for many pupils. However, by their very nature they cannot

be used for diagnosing learning difficulties, monitoring progress and

evaluating the effectiveness of learning or teaching experiences. To

serve this purpose, continuous in-course information is required.

The implication therefore is that the purposes for which

the assessment is used must be clear and in any assessment system

there should not be an over-emphasis on one purpose at the expense

of others.

The different modes of assessment can also be used in

different ways to reveal a candidate's strengths and weaknesses and

depth of understanding.

22

For example, answering correctly the 'pencil and paper'

question "What weight is shown by the weighing scale dial?" (see

Figure 1.1) will give some information about a candidate's ability to

read a weighing scale, but will give very little information about a

candidate's ability to weigh an object, as it ignores many elements of

the weighing process.

FIGURE 1.1 - WEIGHING SCALE DIAL

For example, can the candidate identify the correct

instrument to use for the task? Can the candidate use the

equipment effectively - e.g. zero the scale before weighing? Can the

candidate weigh out a given amount? These are important aspects of

being able to 'weigh' accurately, which are impossible to assess by

pencil and paper methods.

Thus not only is it important to identify the purpose of

assessment, but also the mode of assessment which will most

accurately measure that which is to be assessed.

23

Traditionally, good teachers have always been involved in

assessment for diagnostic purposes. With the advent of G.C.S.E. they

are now involved in the assessment of pupils for public examinations.c

The Cockroft Committee states:

"... we believe that provision should be made for an element of teacher assessment to be included in the examination of all pupils, at all levels of attainment."

and also that:

"Examinations in mathematics which consist only of timed written papers cannot, by their nature, assess ability to undertake practical and investigational work or ability to carry out work of an extended nature. They cannot assess skills of mental computation or ability to discuss mathematics, nor, other than in very limited ways, qualities of perseverance and inventiveness. Work and qualities of this kind can only be assessed in the classroom, and such assessment needs to be made over an extended period".


Cornelius [26] also makes the point that mathematical

examinations would have to offer a coursework element for the

effective assessment of a pupil's ability to discuss mathematical ideas

and carry out mental calculations and practical work.

Isaacson [27] suggests that there should be two

fundamental principles governing any assessment in mathematics, viz.,

24

(i) Examination papers and other methods of assessment should

enable candidates to demonstrate what they know rather

than what they do not know.

(ii) The examinations should not undermine the confidence of

those who attempt them.

This has been interpreted as both the provision of

differentiated examination papers tailored to specific ability levels,

and a coursework requirement which pupils can fulfil by carrying out

work appropriate to individual capabilities.

The needs of adult life and employment would also point to

the necessity of the classroom teacher becoming involved in the

assessment of pupils for other than diagnostic purposes. Coaker 128]

makes the point that employers not only require all children to be

proficient in the basic skills, but also require the ability to use these

skills in practical ways and to describe how and why they have

performed a particular activity.

Coaker also makes the point that the actual skill

requirements of many employees are relatively limited. This would

appear to imply that the syllabus covered should be of restricted

content; but that time should be made available for as wide a

diversity of applications as possible, including examples from the

pupil's own environment and experience as well as from industry and

commerce.

25

It is patently obvious therefore that any mathematics

examination catering for pupils in secondary schools must be

differentiated to allow pupils of all ability levels to approach the

assessment with the confidence of knowing they will have the

opportunity to demonstrate what they know. It must contain a

variety of modes of assessment - practical, oral and written - so that

knowledge, understanding and applications can be assessed in the

most natural and useful way possible. Furthermore, there should be

an extended piece of work in order that pupils can demonstrate

perseverance, interest and inventiveness - qualities not readily

assessed by any short term tests.

Finally, for less able pupils, the Coclaroft Committee

suggests that:

"...it is likely to be more helpful to lower attaining pupils to be offered a series of short terra targets, success at each of which provides evidence of achievement, rather than to have to wait for a one-off test when they are about to leave school."


Thus in addition to the criteria discussed above,

examinations for less able pupils should contain a substantial element

of continuous assessment. Indeed, the Task Group on Assessment

and Testing Report [29] commissioned by the Department of Education

and Science, recommends that assessment for all pupils should contain

a substantial element of continuous assessment by the class teacher.

26

Information gathered should in the main be formath e in that its

purpose is to provide information about how a pupil's future learning

programme should be structured, but will also be summative in that it

should give a comprehensive picture of a pupil's overall achievement.

It is important however that if normal classroom activity is

extended into certified assessment where it is important for pupils to

"score well', then this should not be allowed to undermine the

essential teacher/pupil relationship whereby the learning support role

of the teacher is subtly altered in the eyes of the pupils to that of

an assessor.

As Noss et al. [31] states:

"There have been moves recently towards a negotiation of mathematical meanings between pupil and teacher, the adoption of a more exploratory approach, and a readiness on the part of many teachers to see participation in (and enjoyment of) mathematical activity as a primary goal in the classroom".

(Noss et al., 1988)

There is a strong belief that it would be catastrophic if

this trend were reversed and mathematics teaching once more became

the transmission of 'facts' and 'rules' in order to "do well" at a test.

If teachers are to become involved in external assessment,

the scheme in operation must provide them with a means of

objectively assessing each pupil's knowledge and understanding as

27

well as allowing them to retain their learning support rolv in u

classroom which remains a stimulating, investigative area for all

pupils.

28

CHAPTER 2

THE CERTIFICATE OF EDUCATION

2.1 BACKGROUND

In recent years, the apparent differences in examination

achievement of pupils in England and Wales has given rise to considerable

concern. Nowhere has this apparent difference been more pronounced than

in Mid Glamorgan. This disparity of performance was a constant feature of

the sixties, but became even more pronounced after the school leaving age

was raised in 1972/73, suggesting that the problem was concentrated at the

lower end of the ability range. Indeed, it is clear from an analysis of

examination statistics that the greatest disparity occurrs in the levels of

achievement in the C.S.E. examinations.

One of the more significant factors contributing to this disparity

must be the numbers of pupils in Wales, and more significantly in Mid

Glamorgan, who were not entered for any public examination. While some

schools undoubtedly offered these pupils valuable educational experiences,

specifically tailored to their needs, many schools subjected non-examination

pupils to 'watered down' examination courses which were neither meaningful

nor useful; and which only succeeded in adding to the sense of failure and

frustration already experienced throughout most of their schooling.

Such was the concern in Mid Glamorgan that several key subject

working parties were brought together, under the aegis of the Adviser for

Curriculum Development, to study ways of providing for pupils who were, at

that time, not entered for any formal examinations.

29

The Mathematics working party, which included the author, first

met early in 1981 with the following broad aims:

to devise aims and objectives for a mathematics

curriculum for low attaining pupils;

to devise a content list for pupils for whom the C.S.E.

content list proved too taxing;

to evaluate and appraise the various examination courses

already in existence and to consider their possible

suitability for the target group in terms of content,

approach and assessment structure.

Initially the belief of the working party was that one or several

of the examination courses on offer from examination boards outside Wales

would prove suitable for Mid Glamorgan pupils, and that guidance and

support material would be developed to aid teachers in their delivery of the

curriculum for these courses. However, as meetings progressed the feeling

grew that none of the existing courses would completely meet the needs of

the specified target group without involving the class teacher in an

overburdensome administrative and assessment structure.

It was decided therefore to attempt to design a completely hew

course aimed specifically at the target group for whom G.C.E. and C.S.E.

examinations were proving inappropriate. It was further resolved that the

30

course developed would be submitted to an examination board for

ratification.

When formulating the criteria which would be reflected in the

course structure and pattern of assessment, the working panel were very

aware of previous research undertaken into the needs of less able pupils.

For example, Hart [22] makes the point that:

"less able pupils would be unlikely to assimilate the type of mathematics which is essentially abstract in nature."

(Hart, 1981)

Thus it was accepted from the outset that skills and concepts

would need to be presented to pupils in a wide variety of relevant,

interesting and accessible contexts.

Smith [31] identifies specific problems encountered by children

with learning difficulties. These include:

difficulty in differentiating between similar signs;

being unable to keep several things in mind at any one

time;

. having poor rote memory;

being handicapped by reading difficulties;

having poor hand/eye coordination.

31

Maclaughland [32] found that many children with learning

difficulties lacked confidence because their best efforts were always

considered unacceptable by comparison with their more able peers. This

lack of confidence often manifested itself in an expressed dislike of a

subject and an unwillingness to attempt anything which could result in

failure.

Gulliford [33] refers to the difficulties which less able children

experience in differentiating, both verbally and in written form, between

similar signs. He found that some children failed to assimilate even a

rudimentary understanding of place value, and had little realisation that the

number system is based on ten.

Denvir, Stolz and Brown [34] list several difficulties identified by

low achievers in mathematics, viz., an inability to understand relationships,

number bonds and number operations. Contributing factors to these

difficulties are believed to be insufficient practical experience, insufficient

time spent at each stage of development, too early presentation of ideas in

the abstract form, lack of continuity, and the pupil's general slowness in

assimilating ideas.

When considering the structure of the Certificate of Education

Course, the working panel made every effort to take into account these

major research findings. The following criteria were eventually formulated:

there would need to be a restricted mathematics content

list, which would be accessible and relevant to pupils of

very limited ability;

32

practical work would form a major element of the course,

with a strong emphasis on the practical skills needed for

employment and for everyday life;

pupils should be given every opportunity to discuss the

meaning of mathematical concepts and ideas;

pupils would be encouraged to develop their own ideas

and interests via individual projects and assignments;

the mathematics content would appear in contexts relevant

and pertinent to pupils' experiences.

Working within these criteria, it was considered imperative that

the finalised course should offer opportunities for pupils to engage in

practical, oral and written work, both individually and in groups.

Opportunities should be provided for practice of basic skills and concepts

in a wide variety of relevant contexts; while problem solving using

practical apparatus should be a major factor of the course.

The content list finally decided upon (Appendix I) corresponded

almost exactly with the foundation list detailed in "Mathematics Counts"

published later that year. A nucleus of practical skills, the mastery of

which was thought to be particularly important to this target group, was

identified and specified in the syllabus. It was decided that comprehensive

teachers' notes should be provided, giving ideas for realistic contexts for

33

the mathematics taught, and examples of suitable activities which would

emphasise the practical ethos of the course (Appendix II).

Presenting information in a variety of contexts and modes can

help to overcome difficulties associated with confusion or non-recognition of

mathematical terms or symbols and unfamiliar situations. For example,

research carried out by the Assessment of Performance Unit (A.P.U.) 135J

has shown that the same mathematical operation embedded in different

settings has dramatically different facilty levels. In particular if a money

context is used, pupils are more likely to obtain correct answers than in

any other context.

Among examples reported by the A.P.U. is the question

"4.5 + 0.5 =

which was answered correctly by 63% of a sample of fifteen year olds, and

the "word problem"

"John saved £4.50 and his mother gave him £0.50, how much did he have

altogether?"

which was answered correctly by 82% of the same sample - this despite the

additional reading skills needed in the latter.

Lave et al. [36J compared calculations based around 'shopping at

a supermarket'. When carried out in a practical way using actual money

the calculations were performed with almost 100% success. When repeated

34

using pencil and paper and with the aid of a calculator, the success rate

fell to 66%.

Thus, in the Certificate of Education course, it was decided that

calculations would be presented to pupils in contexts with which they were

familiar, or in situations with which they would need to become familiar to

cope successfully in adult and working life. In almost every context the

necessary practical apparatus would be made available to pupils - the

underlying philosophy being "try it and see."

Also built into the course structure would be opportunities for

discussion of mathematical ideas, and an element of time during which pupils

could engage in an extended piece of work of their own choosing.

When designing the course, the working party also paid

particular attention to research findings detailing non-academic problems of

low attaining pupils. Gulliford [37] and Schonell [38] considered emotional

factors to be of more importance than intellectual factors on pupil

attainment. Impulsive, careless, over-emotional or quick children are

thought to experience some degree of disability at mathematics whatever

their level of intelligence. Children who dislike making a positive

commitment to any situation are also believed to be handicapped by the

precise nature of mathematics. Emotional difficulties of this type are likely

to lead to behavioural problems, and thus it is important that more teacher

time be made available to these pupils than to their more able peers. This

may be achieved not only by overall increase of the teacher-pupil ratio, but

also by more flexible allocation of teacher time. To achieve this, it is

recommended throughout the Certificate of Education course, that the pupil-

35

teacher ratio is no more than sixteen to one, and that where there is more

than one class in a school following the course, there should be 'block

timetabling' so that team teaching may take place wherever possible.

2.2 COURSE STRUCTURE

A wide variety of courses within the framework of the Certificate

of Education have been designed for secondary shcool pupils who would not

demonstrate sufficient positive achievement at G.C.S.E. The syllabuses are

designed to motivate such pupils and give them the opportunity to

demonstrate what they know and can do.

The Certificate of Education Numeracy course is intended not

only to stand as a component in its own right - providing the mathematics

necessary for everyday life - but also to provide the background to enable

pupils to deal confidently with the mathematical content of the other

Certificate of Education courses.

Throughout the course pupils are encouraged to read, write and

talk about mathematics in a wide variety of ways. Emphasis is placed on

oral and practical work, and the placing of mathematics in realistic contexts.

The teaching element of the course consists of eleven modules

(as outlined in Table 2.1) which contain the breadth of the mathematics

curriculum to be followed (see Appendix 1). The depth of study to be

attempted will vary according to the individual needs and abilities of the

pupils themselves. However, the minimum depth to be covered is exemplified

within each teaching module.

36

TABLE 2.1 - COURSE STRUCTURE FOR CERTIFICATE OF EDUCATION,

NUMERACY

Spring Autumn Term Term

H0)

1 ^3 V

tt> H

YEAR 1MODULES 1-8

1Whole numbers Fractions

Imperial measures Conversion graphs

7EstimationUse of acalculator

2Division of number RatioFractions

5

Percentages

8

Area

3Place value Metric system of weights, measures

6

Time

YEAR 2MODULES 9-11

9Money

in the

home

10

Geometry

11Directed Number Algebra Statistics Probability

Project Revision

In addition to the specified content, pupils are encouraged to

develop their skills in estimation, mental arithmetic and the efficient and

effective use of a calculator.

Throughout the course pupils are given every opportunity to

undertake practical activities. A practical element forms a significant and

natural part of each teaching module, and a specified list of practical

activities is detailed in the syllabus (see Appendix 1). It is believed that

pupils of this ability will need a wide variety of practical work in order:

to help them develop necessary practical skills and

concepts;

37

to enable them to become familiar with everyday practical

apparatus and measuring equipment.

to help them solve problems;

In this respect, pencil and paper exercises are entirely inappropriate.

Pupils need frequent and natural access to practical equipment to develop

the necessary skill and confidence in using it in a variety of appropriate

contexts.

Mathematics is a powerful means of communication. The

development of communication skills therefore forms a significant part of a

pupil's classroom experiences. Pupils are given every opportunity during

the course to undertake oral work including:

pupil/pupil discussion - whereby pupils are encouraged

to share and compare their ideas;

pupil/teacher discussion - whereby pupils are encouraged

to explain their own understanding of a variety of

mathematical concepts;

oral mental exercises.

At any convenient time during the course, pupils are required to

undertake an extended individual piece of work. This can be undertaken as

one single project or broken down into smaller units of work undertaken at

various times during the two years - depending on the level of commitment

38

and concentration of individual pupils. An individual piece of work is of

significant value as a learning experience for pupils in whatever form it is

undertaken. However, the School Council [39] has reported that pupils

produce the best individual studies in circumstances where:

a manageable problem is defined;

a hypothesis or generalisation is advanced or model

formulated;

data is collected;

data is analysed and presented;

conclusions are reached which enable the hypothesis,

generalisation or model to be evaluated.

In the Certificate of Education course, teachers are recommended

to follow this model as far as possible. However, it is recognised that less

able pupils will need considerable guidance as to the structure they should

follow if the project is to prove a worthwhile experience for pupils.

2.3 PATTERN OF ASSESSMENT

When designing the scheme of assessment for the Certificate of

Education Numeracy course, the panel were very anxious that both the

ethos of the course structure should be reflected in the pattern and modes

of assessment, and also that the needs of the target group should be a

39

prior concern. Hence the following aims for the assessment structure were

formulated:

all assessment should be completed by Easter of the fifth

year;

the modes of assessment should include written, oral and

practical elements;

the course should contain a substantial element of

continuous assessment;

a major part of the assessment should be conducted by

teachers during the course - but must not be

over burdensome.

Once again, the aims of the working panel agree closely with

those in "Mathematics Counts" which states:

"If assessment at 16+ is to reflect as many aspects of mathematical attainment as possible, it needs to take account not only of those aspects which it is possible to examine by means of written papers, but also of those aspects which need to be assessed in some other way.

... we believe that provision should be made for an element of teacher assessment to be included in the examination of pupils of all levels of attainment."


It is clear that based on these aims the pattern of assessment

should contain practical, oral and written elements; should give the teacher

40

an ongoing picture of a pupil's progress, and should provide diagnostic

information upon which remediation may take place.

The panel decided that the pattern of assessment should include:

short term 'achievable goals' in the form of short written

tests at the end of each content module;

longer written assessments encompassing several modules;

practical assessments which would be conducted during

normal classroom lessons when and where the relevant

skill applications occur naturally during the course;

an oral assessment which would take place towards the

end of the course and which would include discussion

about the understanding of various mathematical concepts;

an extended piece of work;

an end of course examination.

This range of assessment techniques, it was felt, would provide

ample opportunity to assess pupils':

mastery of skills and concepts specified in the content

list;

41

mastery of the specified practical skills;

ability to solve simple, realistic problems;

involvement and commitment in developing an extended

piece of work;

ability to discuss mathematics in relevant contexts.

It was also decided that at no time would pupils be compared

with other pupils. Their success would not be measured against that of

their peers but against a 'standard' of basic mathematical competence

designated by external moderators.

While firmly convinced of the desirability of continuous teacher

assessment forming a substantial part of the assessment structure, both for

diagnostic purposes and as a means of motivating pupils, it was essential

that the requirements should not prove overburdensome to teachers. It was

decided therefore that the end of module tests, the practical assessments

and the extended piece of work, should form the element of teacher

assessment, the remainder of the assessments being undertaken by external

agencies.

The final pattern of assessment is detailed in Table 2.2.

42

TABLE 2.2 - ASSESSMENT STRUCTURE FOR CERTIFICATE OF EDUCATION,

NUMERACY

AutumnTerm

Spring/SummerTerm

AutumnTerm

SpringTerm

Y

E

A

R

1

Y

E

A

R

2

End of module tests 1-3

Practical assessments





Project Oral

Progress Test 1

Progress Test 2

Progress Test 3

Final Examination

2.3.1 Written Assessment

The written assessments take the form of:

(a)

(b)

(c)

End of module tests.

Progress tests.

Final examination.

43

(a) End of Module Test:

These tests at three to four week intervals, provide pupils with

short term 'achievable goals'. They are presented as written tests but can

be read to pupils if so desired - thus minimising reading difficulties and

presenting mathematical symbols in written and spoken form. The tests are

intended to serve two purposes, viz.,

(i) to provide diagnostic information for the class teacher which may

be required for any necessary remedial action;

(ii) to assess the pupils' short-term retention of information and

techniques.

If it is found that the pupil lacks sufficient understanding of

any particular 'parcel' of work, remediation can take place and the test

deferred to a later date.

(b) Progress tests:

These tests are intended to assess the pupils' understanding of

basic mathematical skills and processes presented in a written form in

contexts which are familiar to pupils. The language level is kept as simple

as possible and questions are illustrated with helpful diagrams. However,

reading difficulties are minimised still further as questions can be read to

pupils if so desired.

44

(c) Final Examination:

The National Criteria for Mathematics stipulates that any syllabus

at G.C.S.E. level entitled 'Mathematics' must contain an end of course written

examination. Although the Certificate of Education is not intended for

pupils of G.C.S.E. ability, it was still felt by the majority of the panel, and

a large body of teachers, that an end of course examination was desirable.

In view of this an end of course examination is part of the assessment

structure.

2.3.2 Orftl Assessmept

An oral assessment is conducted by the class teacher during the

final term of the course. The class teacher can use the flexibility of an

oral assessment to:

discuss mathematical ideas with a pupil;

probe a seemingly obscure or incomplete statement;

discuss the reason for an answer;

minimise reading and/or writing difficulties.

In an oral situation, pupils are not subjected to the 'one off

form of a written examination. Understanding and reasoning can be

assessed in the fullest sense while allowing teachers to adjust the level of

questioning to the level of each individual pupil - a task almost impossible

in any other assessment situation.

45

2.3.3 Practical Assessment

The practical tasks are intended to be an integral part of the

Certificate of Education course. They are designed to assess a pupil's

dexterity in the use of basic practical equipment, knowledge of the

equipment required for a specific task, and the way in which it should be

used. During a practical assessment it is important that the class teacher

recognises exactly what is being assessed, i.e. the product (the finished

task) or the process (the method of working). Ideally, all aspects which

can be adequately tested by other means should be eliminated and the

practical assessment only used to test a pupil's performance of a task.

However, there is still a definite hierarchy in the successful undertaking

and completion of a task, viz., effective performance is based on adequate

knowledge and an ability to identify and use materials and equipment.

Vernon [40] recognises the possible unreliability of a practical

assessment when it is assessed solely on a written record of the experiment

- was the experiment carried out correctly and a mistake made during

recording, or was the recording a sanitised version of a badly conducted

experiment? Thus in the Certificate of Education, when a practical task is

being assessed, it is the performance of the task - the actual process

through which the pupil works - upon which the class teacher focuses. In

order to do this, the assessment is carried out in a 'one-to-one' situation

during normal classroom time at a point in the syllabus where the task

would occur naturally. If help is needed, it is given and the actual

assessment completed on another occasion.

An example of a practical task is given below:

46

Practical Task - Using a Weighing Scale

A range of practical equipment - kitchen scale, thermometer, ruler, etc., is

displayed in the classroom.

(a) The pupil is asked by the class teacher to fetch the equipment

to weigh an object.

(b) the pupil is told to use the scales to weigh the object.

(c) the pupil is given a bag of beans and told to measure out a

given weight of beans.

To gain a mark, the pupil must complete every part of this assessment.

2.3.4 Project

An individual extended piece of work is valuable as a learning

and teaching experience whether or not a formal assessment is made of the

finished article. However, the majority of the panel believed that if a

significant amount of time was spent in undertaking a project it should

merit inclusion in whatever final assessment a pupil receives. Furthermore,

any assessment should not be made solely on the final written account but

should reflect the commitment shown by the pupil, and the skills and

abilities developed while undertaking the work. The class teacher should

therefore base the majority of the assessment given on these criteria rather

than on the final account.

47

2.4 MARK WEIGHTING

The decision as to how great an emphasis should be placed on

each assessment element caused the greatest difference of thought among

the panel, ranging from a reluctance to accept anything other than the final

examination result as 'evidence' of success, to a belief that the final

examination should merit only a nominal inclusion - the majority of a pupil's

final mark being based on in-course assessment.

During their discussions, the panel considered the following

issues:

(1) An important criterion was that pupils should follow the

whole course. The ethos of the Certificate of Education is based around the

suitability of a highly practical, relevant, mathematics course for this target

group. If too significant a weighting is given to the final examination, then

pupils could achieve a 'pass' mark without having to demonstrate their

levels of practical and oral ability.

(2) Again if too significant a weighting were placed on the final

examination, a certificate from this course could be regarded as a 'safety

net" for the more able but less committed pupils in G.C.S.E. classes who,

simply by attending the final examination, could gain sufficient marks to

'pass'.

(3) The wishes of the teachers. It is undoubtedly true that the

vast majority of teachers consulted were in favour of a significant

weighting for the final examination. Perceived reliability, fairness and

familiarity with the system were the main reasons cited for favouring the

48

end of course written paper. However, other reasons were mentioned. The

unfamiliarity of teachers and pupils with a system of continuous assessment

of a practical and oral nature was one such reason. Secondly, many

teachers see the end of module tests and practical assessments as 'one off

occasions which, if missed by a pupil would result in a significant loss of

marks. Thirdly, a significant number of teachers appeared to lack

commitment to the project. Many expressed the feeling that the time spent

giving the help and guidance needed by the majority of this target group

could more constructively be spent in 'revising' certain aspects of the

mathematics content. As such, the teachers themselves would not offer

pupils the opportunity to undertake a project - again with a significant

loss of marks.

The mark weighting for each element finally arrived at is shown

in Table 2.3. However, a constraint was also built into the assessment

system in that pupils had to attain a minimum standard in both the overall

coursework element (though no single coursework assessment was

compulsory) and also in the final examination.

TABLE 2.3 - MARK WEIGHTING

Pattern of Assessment Mark Weighting

End of module testsProgress testsOral assessmentPractical tasksProjectFinal examination

11% (11 x 1%) 15% ( 3 x 5%)

7% 12% (12 x 1%)

5% 50%

49

CHAPTER 3

SCOPE OF THE STUDY

3.1 SUGGESTIONS FOR CHANGE

It was agreed by the examination panel and those teachers

entering candidates for the course, that the pattern of assessment decided

upon should remain in place for an initial five year trial period. It was

also agreed that during this trial period frequent meetings would be held at

which staff from participating centres could discuss progress and monitor

the effectiveness of the teaching and learning programme.

As a result of these meetings, several suggestions for change

within the course - some of them contradictory - were discussed. In the

majority of cases no concensus of opinion was reached, bringing to mind

the principle "you can never please all of the people all of the time".

However, there were four specific areas, notably within the

assessment structure, which did appear to cause concern to the majority of

the panel. It is these areas which form the basis for the research work

undertaken during this study.

50

3.2 THE END OF MODULE TESTS

PROPOSAL: These tests (which are currently presented to

candidates as part of the written assessment) should be undertaken in an

aural form.

Three main reasons have been highlighted for this proposed

change:

(1) The low level of reading ability of the target group might

result in candidates achieving a lower success rate in a written test than

their mathematical ability would merit. The end of module assessments,

which are set and marked by the class teacher, would appear to be a part

of the assessment structure which would lend itself readily to aural

presentation, being neither too time consuming nor too unwieldy to

administer in this way. Indeed, teachers have always been at liberty to

'read' these tests to pupils. However, very few of them appear to do so.

(2) The low level of concentration and perseverance of the target

group often results in candidates 'giving up' at the first sign of difficulty

- often with much of a question paper left unread. If these questions are

administered aurally, one question at a time, it is felt that this tendency

might be overcome to some extent.

(3) It is generally felt that the pattern of assessment is

overweighted in favour of written assessments.

51

3.3 THE PRACTICAL ASSESSMENTS

PROPOSAL: The marks awarded for the practical assessments

should be considerably increased.

Two main reasons were mentioned for this:

(1) For this target group, the ability to use equipment to

perform simple practical tasks is thought to be of significant importance.

This should be reflected in the marks awarded to the practical tasks within

the pattern of assessment. It is generally felt that, at present, the

obtainable marks do not reflect this perceived importance.

(2) The successful completion of a practical task involves the

mastery of several related skills. The system at present in operation,

whereby candidates are either awarded one mark - for successful completion

of the whole task - or no marks, even if part of the task is completed

successfully, does not accord with the desirable practice of rewarding

positive achievement. Consequently it is felt that a structure whereby

mastery of the separate skills can be rewarded should be developed.

3.4 THE ORAL ASSESSMENTS

PROPOSAL: This assessment, during which candidates have a

unique opportunity both to discuss mathematics and to question the

examiner if a point is unclear, should merit a greater weighting in the

assessment structure.

It was generally felt that this is the part of the assessment where

candidates, unhampered by reading skills or pressure of time, can attempt

52

longer more realistic mathematics questions, and also have the opportunity

to demonstrate, in a one-to-one situation, their depth of understanding of a

mathematical concept or process.

3.5 THE PROJECT

PROPOSAL: An individual, extended piece of work should no

longer form part of the assessment structure.

Four reasons were highlighted for this suggestion:

(1) The concentration and commitment of pupils in this target

group is such that they are not able to develop a piece of work for

themselves, with the result that any developments are largely teacher-

initiated and directed. Consequently, submitted projects vary widely in

both content and development, as teachers are unsure how much guidance

is permissible or even desirable for a piece of work which is being assessed

as the candidate's own.

(2) Many teachers are themselves unsure of what form an

individual study in mathematics should take.

(3) The time and effort required by both staff and pupils is not

reflected in the final mark obtainable.

(4) A significant number of candidates (for a variety of reasons)

do not submit a project.

53

Various remedies have been suggested which might overcome some

or all of these problems, viz.,

offer more detailed advice, guidelines, exemplars to

teachers on project work;

increase the number of marks awarded for the project;

abandon the project.

It must be admitted that the majority of the working panel and

the teachers following the course were in favour of this last suggestion.

However, this was resisted strongly and a possible compromise will be

discussed during the study.

It is therefore proposed to undertake research into the above

mentioned areas in order to decide whether some, or all of the suggested

changes should be incorporated into the pattern of assessment. If such

changes are deemed desirable in the light of evidence collected, then it is

intented to suggest a new assessment structure incorporating these

amendments.

In particular, the following issues will be addressed:

(1) a comparison of the relative performance of candidates when the

end of module tests are set in (a) written, (b) aural form;

(2) an investigation of a possible marking structure for the practical

assessments which

54

(a) allows candidates to be rewarded for positive achievement of

each related skill within a task;

(b) increases the total marks available for this assessment;

(3) the feasibility of increasing the available marks for the oral

assessment;

(4) consideration of the future role of the project within the

Certificate of Education assessment schedule.

In addition to the above mentioned issues, an analysis of results

will be undertaken in an attempt to define to what extent the assessment

structure is affected by pupil attendance.

Five comprehensive schools in Mid Glamorgan have agreed to

participate in the research. The schools were selected on a subjective

basis in an attempt to reflect a variety of socio-economic backgrounds and

divergence of teaching styles, and hopefully to represent a broad cross-

section of the comprehensive schools in the County.

55

CHAPTER 4

THE END OF MODULE TESTS

4.1 INTRODUCTION

These tests are intended to serve two purposes:

(1) to provide diagnostic information for the class teacher, upon

which remedial action may be taken and future teaching based;

(2) to assess the pupils' short term retention of the skills and

concepts encountered in each module.

The tests are devised and assessed by the class teacher using

guidelines laid down in the "Notes of Guidance for Teachers" (see

Appendix II).

Pupils undertake these short assessments at the end of each

module of work. Although the tests are primarily intended as written

assessments, it has always been made clear to teachers that the tests

could be read to individual pupils, or the whole class, if any reading or

comprehension difficulties were suspected. However, it appears very

few teachers take advantage of this opportunity, citing 'fairness' or

'pressure of time' for not doing so. There is now a feeling, however,

among a significant number of teachers, that for the reasons previously

56

stated these assessments should be undertaken in aural rather than

written form.

The null hypothesis put forward for the purpose of this

research is:

Pupils score comparable marks when a series of questions are

asked singly, in an aural form by the class teacher, and when all

questions are presented together in written form.

4.2 RESEARCH METHOD

To undertake this research, two series of tests were devised,

A and B (see Appendix III) consisting of very similar questions and

involving apparently comparable numerical data. Each pupil would thus

sit two similar end of module tests - one aural and one written - the

marks of which would be compared.

When making comparisons in this way, it is recognised that the

results could be affected by a number of variables, viz.,

unperceived differences in the degree of mathematical

difficulty of the tests;

rogue or 'odd' questions;

difference of language levels in the questions;

differences in the ability of the cohorts' undertaking

Certificate of Education courses in the schools.

57

It was decided, therefore, that the tests would be administered

in a way which as far as possible would minimise the above-mentioned

variables, and also that a scrutiny of results would be undertaken in

order to attempt to identify any variables which did exist.

4.2.1 Administration of Tests

The tests in set A were undertaken by pupils in schools 1 and

2 in written form, and presented aurally to schools 3, 4 and 5.

Similarly series B was undertaken in written form by pupils in schools

3, 4 and 5, and aurally by pupils in schools 1 and 2 (see Table 4.1).

Table 4.1: Written and Aural Tests Undertaken by Each Sample

Schools

School number

No. in Sample

Aural test sat

Written test sat

Sample

1

P

2

55 44

B

A

B

A

Sample Q

3

19

A

B

4 5

41 34

A A

B B

As a further safeguard, class teachers were required to vary

the order in which the written and aural tests were given for different

modules.

58

4.2.2 Scrutiny of Results

In order to undertake a scrutiny to determine any apparent

differences in the tests or the cohorts undertaking them, the median

total mark for each sample in both the written and aural versions of the

tests was calculated. The differences in these marks was then analysed.

This analysis was undertaken in two ways:

METHOD 1 - Total mark comparison:

The marks awarded for all written and aural tests taken by

each pupil were totalled and compared.

METHOD 2 - Paired test comparison:

Only the marks awarded for tests where a pupil was present

for both the written and aural versions of the test were totalled and

compared.

The 'paired test comparison' was undertaken for two reasons.

Firstly in order that a comparison of 'like with like' could be made. It

can easily happen that a pupil's attendance pattern is such that only a

few modules of work have been assessed by both the written and aural

version of the End of Module Test. Indeed, this is the case with

candidate No. 5.32 whose scores on the end of module tests are shown in

Table 4.2.

59

Table 4.2: End of Module Test Scores for Candidate 5.32

Module

Written test score

Aural test score

1

-

2

2

3

_

3

3

3

4

5

6

5

-

_

6

5

_

7

-

2

8

6

_

9

3

6

10 11

8

- 10

If a straightforward total mark analysis is undertaken in this

case, the comparison is being made on work covering different

mathematical content - hardly a 'fair' comparison.

Secondly, attendance patterns are such that pupils frequently

sit significantly unequal numbers of written and aural tests. An

example of this is shown in Table 4.3.

Table 4.3: End of Module Test Scores for Candidate 4.5

Module

Written test score

Aural test score

1

8

_

2

9

10

3

4

_

4

6

8

5

10

10

6

9

_

7

7

_

8

6

9

9

4

9

10

5

7

11

6

6

Again, in the above case it would be misleading to make a total mark

comparison. In the analysis of results, therefore, statistics calculated

using both the above detailed methods will be analysed.

60

4.2.3 Analysis of Scrutiny of Test Results (a comparison of the median total scores of each sample in the aural and written tests)

The marks achieved by pupils in the End of Module Tests,

both written and aural, are shown in Tables 4.4-4.8. If the only marks

recorded are those where pupils sat both versions of the End of Module

Tests, the results are as shown in Tables 4.11-4.15.

Using a total mark comparison (Method 1) the results shown in

Tables 4.4 and 4.5 were combined to give the total scores for schools 1

and 2 (sample P) and the results from Tables 4.6-4.8 were combined to

give the total scores for schools 3, 4 and 5 (sample Q).

In each case, the median total scores for the written and aural

tests were calculated. The results are shown in Tables 4.9 and 4.10.

The paired test comparison (Method 2) which uses only those

results where the candidate was present for both the written and aural

versions of the test shows a similar pattern (Tables 4.16 and 4.17).

The results obtained would appear to indicate two trends:

Pupils in sample Q consistently scored higher marks than

those in sample P (both versions of the tests). This would

appear to indicate that pupils in sample Q are of higher

ability than those in sample P. This could indeed be the

case, as schools often operate different policies with regard

61

to the entry of pupils for Certificate of Education

examinations.

. Although the samples appear to differ in regard to ability

levels, there is a marked degree of consistency between

differences in performance in the written and aural versions

of the tests. This appears to indicate that sets A and B of

the tests are of a comparable degree of difficulty.

4.2.4 Conclusions

As the above results do not provide conclusive evidence of

either ability level or comparability of tests, it has been decided that

the end of module tests for each school will be analysed separately

using both a total mark comparison, and a paired test comparison.

In each case the hypothesis that the median difference in

marks is zero is tested against the alternative hypothesis that the

median difference in marks is not zero.

62

Table 4.4 End of Module Tests - Results for School 1

Hi

H ̂

H3

H4

H5

H6

H7

H8

H9

H10

Hll

H12

H13

H14

HIS

H16

H17

HIS

H19

H20

H21

H22

H23

H24

H25

H26

H27

H28

H29

H30

H31

H32

H33

H34

H35

H36

H37

H38H39

H40

H41

H42

H43

H44

H45

H46

HI 7

H48

H49ucn nju

H51

H52

H53

H54

H55

Wl

4

8

6

10

9

6

7

9

9

9

8

6

8*

10

7

9

7

10

8

8

6

6

9

6*

8

10

9

6

8

6

7

8

9

8

98

10

10

8

9

4

9

10

10

6

9

8

8

6A

7

Al

4

9

6

10

10

5

9

10

8

10

10

7

5A

10

10

9

6

10

10

10

7

8

10

7*

10

9

9

5

10

8

7

8

10

10

1010

10

10

9

9

6

9

10

9

6

10

9

10

10

7A

10

W2

8

6

C

9

9

8

7

3

10

5

9

6

8

3

10

5

10

8

9

7

1

6

3

A

A

4A

9

4

3

8

6

4

8

4

65

6

7

9

7

4

6

6

8

5

5

7

7

5

7A

5

A2

9

6

2

10

9

6

10

10

10

3

9

5

9

9

4

10

8

10

6

4

9

3

A

A

5

A

10

2

5

9

6

6

7

7

79

5

7

10

8

4

6

7

10

1

4

5

10

6

10A

4

W3

5

5

4

8

7

7

2

3

5

3

6

3

3

4

1

5

7

6

5

1

5

3

A

A

1

A

7

5A

9

2

2

9

6

55

3

8

7

4

3

6

5

9

5

5

4

6

5

4

8

A3

7

1C

3

9

7

6

4

3

5

6

5

4

2

5

7

4

8

9

7

3

6

6

A

A

3

10

6A

10

4

1

10

7

55

4

8

10

5

4

7

4

10

6

6

6

5

6

7

6

W4

*

8*

6

6

4

6

6

6

7

6

6

7

5

6

5

7

1

7

9

6

5

5

6

6

7

8

5

5

6

7

4

5

6A

5

8

7

5A

7

6

5

6

1

4

5

6

8

6

A4

4

9

A

8

6

5

7

7

10

6

9

6

6

6

5

6

7

3. 7

10

7

4

5

8

7

10

9

5

4

7

8

7

4

66

6

4

8

8A

7

6

6

7

4

6

4

6

10

7

W5

*

5A

4

4

4

2

4

6

3

3

5

A

6

6

4

4

A

4

7 *

5

4

2

7

8

3

7

4

0A

3

4A

4

4

9

5

2

4

5

2

5

A

5

5

7

7

6

A5

A

6A

4

3

5

3

6

4

1

4

7

A

7A

5

6

A

A

9A

6

5

4

10

9

1

8

7

2A

6

3A

5

4

10

5

4

9

5

1

6

A

6

4

9

10

6

we

7T

6

9A

7

6A

10

7

9

8

8

9

9

7

a7

2

5

6

7

7

9

5A

A

9

7A

4A

5A

A

5

6

3A

*

6

5

7

6

6

8

5A

6

A6

9

7

7

A

7

7A

7

8

6

6

8

10

9

10

4A

6

8

9

7

8

7

9

6A

A

10

9A

8A

6A

A

4

6

6A

A

7

3

10

6

7

7A

7

W7

A

3

4

7

4

4

A

A

A

4

8

6

A

5

4

3

3

7A

A

3

4

A

6A

4

5A

5

6A

45

6

6

6

3A

4

5.3

6

8

7

6

9

6

A7

jk

4

5

8

3

4A

A

A

2

8

7

A

6

4

4

6

6A

A

4

7

A

4A

9

4A

5

6A

35

7

6

6

5A

7

5

4

7

9

8

7

6

10

5

W8

c

6

8

4

8

4

5

7

3

7

5

7

7

2

6

5

7

2

6

4

3

3

3

1

6A

2

2

3

5

66

6

4

8

1

6

5

2

8

5

2

2

8

8

4

4

3

A8

8

6

6

8

5

7

6

6

8

5

7

6

8

10

5

7

6

7

4

6

6

2

4

4

1

7A

4

5

5

4

6

9

6

6

6

7

5

4

6

9

4

5

9

7

4

6

5

W9

9*

*

*

5*

9

8

4

aA

A

6A

7

9

A

A

A

9

5

8

5A

7

5

3

2

9

5

6

A

4

8

5

6

6

6

3

8

A9

1 U

*

*

6

6

4

10

10

3

9A

A

7A

4

10

A

A

A

10

7

10

6A

10

8

5

5

5

7

7

A

6

10

9

8

6

8

6

9

W10

6

4

9

5

6

2

7

9

7

7

8

8

4

5

1

8

7

10

6

5

6

5

8

6

4A

6

4

6

5

5

9

8

A

6

8

8

4

7

8

9

6

AID

-r

^

;

4

7

1

8

10

10

8

10

9

3

5

5

3

6

10

6A

4

7

2

10

5

4A

5

3

7

6

6

10

10

A

7

9

10

6

7

10*

7

wi:

p***8

0A

4

4

1

*

A

3A

6

5

A

A

A

A

A

7

*

7

8

6

9

5

6

4

8

7

5

6

6

7

6

6

8

6

6

8

8

All

9

*

A

A

9

2A

6

6

3A

A

4A

6

6

A

A

A

A

A

9

A

9

10

4

10

4

7

5

9

8

6

7

A

9

7

10

10

7

6

7

9

63


01

02

03

04

06

07

08

09

010

Oil

012

013

014

015

016

017

018

019

020

021

022

023

024

025

026

027

029

030

031

032

033

034

035

036

037

038

039

040

041

042

043

044

045

046

Wl

9

7

5

3

6

10

6

7

7

9

9

9

9

5

5

8

6

10

10

6

9

8

5

8

5

7A

9

10

8

10

10

6

10

8

9

7

8

8

8A

8A

10

Al

9

9

9

4

10

4

6

10

10

9

A

10

8

7A

9

10

10

5

9

5

5A

6A

A

10

10

7

9

9

6

7A

7

7

6

10

6A

9A

8

W2

7

0

4

1

7

7

7

9A

6

9

8

7

3

6

6

6

8

5

9

6

5

7

1

10

7

8

7

6

8

9

7

7

6

7

7

8

6

1A

5A

8

A2

7

3

5

2

7

/

9

8A

7

10

10

10

4

7

7

6

9

7

5

10

10

4

10

9

10

8

10

6

6

6

10

9

7

9

7

10

10

6

4

A

6A

9

W3

7

1

0

2

4

4

0

3

2

7

7

5

7

4

1

. 7

7

8

3

7

6

1

6

8

3

4

7

6

3

2

2

5

4

4

6

5A

4

3

3A

5A

3

A3

7

4

7

3

5

4

5

4

1

7

7

8

2*

5

5

9 *

A

A

2

4

9

1A

5A

4

0

3

4

2A

7

5A

4

2

3A

7A

4

W4

A

7

6

6

7

8

8

9

9

9

6

8

6

8

2

6

9

7

7

8

10

4

5

8

4

8

8

3

6

7

7

4

7

7

7

6

5

8

7

5A

6A

A

A4

A

9

10

4

5

9

10

10

10

9

6

9

10

6

4

6

10

9

3

7

9

7

9

9*

5

10A

4

7

6

7

10

9

10

7

6

9

7

10A

9A

A

W5

7

3

4

2

4

6

3

5

7

9

4

6

8

7

7

7

9

10

6

7

8

4

4

6

2

7

5

7A

3

5

6

5

3

1

5

6

6

3

3A

6*

*

A5

8

5

5

4

5

7

5

6

8

9

8

4

10

6

6

7

10

10 *

10

10

6

7

7

5

7

6

9*

4

5

6

9

5*

7

7

9

5

2*

10*

*

W6

2

6

1

9

9

3

9

10

8

5

2

6

7

10

8

9

10

3

9

9

8

10

4

8

7

8

10

8

6

8

7

7

9

8

7*

7

9

3

8

A6

4

10

7

3

10

10

5

10

7

4

4

4

9

4

10

10

9

9

5

10

9

9

6

7

8

9

9

10

9

6

10

6

10

10

7

10 *

6

9

5

9

y7

10

5

5

4

4

7

5

0

5

3

2

3

4

6*

7

5*

2

2

6

0

6

5

4

6

3

6

7

4

4

8

2

4

4*

4*

7

3

4

A7

10

6

6

5

9

6

6

4

5

6

5

5

4

7

10

8

10*

7

6

6

4

7

4*

6

4

7

8

4

4

9

9

4

5*

6*

8

5

8

W8

10

6

2

5

6

9

2

9*

8

7

6

6

9

6

6

8*

6

7

8

6

8

6

6

2

9

8

4

2

6

7

9

7

6

6A

5

2*

A8

10

7

5

4

7

10

5

10A

9

6

6

6

10

10

10

9A

7

9

9

5

9A

9

9

10

5

4

4

10

7

10

6

6*

4

7*

W9

10

5

2

7

10

10

8

10

10

9

5

7

9

9

7

9

6*

4

9

4

8A

8

6

8

5*

7

8

9

9

3*

8

7

6

A9

10

7

4

8

10

9

9

10

8

10

6

8

10

10

8

9

7A

5

10

5

8

8

9

9

10

4*

10

10

8

10

5*

10

6

6

W10

9

4

2

8

8A

9

. 8

7

6

9

7

9

10

6

10

10*

6

10

7

8

7

7

8

6

3

8

7

9

6

7

7A

8

9

6

A10

10

5

7

8

7A

10

10

8

8

10

6

6

9

7

10

5A

7

9

10

10

8

7

9

10

5

10

7

10

7

7

9A

8

10

6

Wll

10

7

4

A

10A

9

10

2

7

6

7

5

9

6

8

10

4

7

8

5

9

8

6

7

8A

8

6

9

8

6

6A

7

8

6

Al

10

7

7

A

10It

9

9

5

10

7

8*

10

7

9

10

7

6

9

9

10

10

9

7

4A

10

7

9

10

7

A

A

9

8

10

64


Wl Al W2 A2 W3 A3 W4 A4 W5 A5 W6 A6 W7 A7 W8 A8 W9 A9 W10 A10 Wll All

1112

13

14

15

16

17

18

19

noin112

113

114

115

116

117

118

119

120

6

6

8

3

7

5

9

10

9

10

8

10

7

8

4

7

9

10

10

9

7

10*

5

7

7

8

10

9

8

10*

9

3

10

10

9

10

10

6

9

1

7

6*

7

6

9

6

10

4

8

3

6

8

8

8

8

7

9

0

2

6*

4

7*

4*

4

7

2

5

7

10

10

10

3

4

1

3

4

3

4

3

5

1

8

1

6

2

2

6

9

10

7

7

5

2

8

5

2

5

6

6' 3

10

2

7*

9

9

9

10

6

7

5*

4

3

10

3

2

7

3

3

3

3

5

5

6

8

9

7

9

*

*

5

7

9

4

4

8

6

6

4

4

5

4

7

9

8

8

1

8

9

4

3

6

5

7

7*

5

3

8

3

1*

9

10

9

3

9

10

5

5

4

6

7

6*

7

7

10

4

0*

10

10

10

5

6

2

5

7

7

5

5

7

7

7

3

8

9

8

9

9

9

9

7

7

4

7

4

7

7

6

6

10 *

5

9

9

9

9

10

9

9

6

8

0

5

2

8

6

3

4

5

2

8

3

2

10

7

10

6

7

9

2

7

4

10

9

5

4

5

5

9

4

5

10

8

9

7

4

4

1

6

3

4

5

4

4

8

6

7

3

2

4

4

9

5

8

6

5

3

3

3

9

5

5

10

7

6

7

3

4

5

10

5

8

7

5

3

9

10

9

4

10

8

7

8

10

9

10

7

5

8

9

10

5

10

9

9

8

10

6

9

6

8

6

9

8

9

8

8

6

7

9

9

9

10

10

4

10

10

10

8

9

5

4

9

7

8

5

8

7

9

6

5

4

8

6

3

9

6

10

4

10

8

10

4

6

5

10

9

78

65


Cl

C2

C3 C4

C5

C6

C7

C8

C9

CIO

Cll

C12

C13

C14

C15

C16

C17

C18

C19

C20C21

C23

C24

C25

C26

C27

C28

C29

C30

C31

C32

C33

C34

C35

C36

C37

C38

C39

C40

C41

Wl

10

10

10

8

8

10

9

9

10

8

10

10

9

10

6

10

8

10

1010

10

9

9

8

9

10

9

10

10

9

10

9

4

7A

6

10

7

A

9

8

Al

9

9

10

10A

10

9

10

10

10

10

10

9

9

9

8

10

7

7

10

10

6

5

3

*

6

10

10

5

5*

10

3

6A

9A

6A

A

10

W2

6

10

9

6

9

7

7

7

10

5

8

9

8

9

7

5

9

8

53

5A

4

0

9

8

7

7

4

5

7

1

4

7

10

9

6A

7A

A2

7

10

9

10

10

8

7

8

10

7

7

10

10

9

6

9

9

3

66

5

2

2

A

5

5

6

1

2*

0

6

6A

6A

*

7

8

W3

9

8

4

9

4

8

7

1

9

8

8

9

6

6

9

10

8

4

36

6

2

2

7

7

3

3

4

6

7

9

1

5A

5

5

5A

4

4

A3

*

9

3

7A

7

4A

8

5A

7

5

5

7

9

8

8

57

7

5

5A

A

4

4

9A

A

6

4

4

4

7

4

A

4

4

W4

7

4

6

4

6

7

5

8

8

6

7

7

3

5

8

7

5

7

77

5

8

4

5

8

9

6

9

6

7

6

4

6

7

4

8

6

5

7

9

A4

6

8

8

S

9

5

10

9

7

6

8

5

5

9

6

7

8

7

8

6

10

3

7

7

10

10

9

5

9

9

5

6

6

7

9

9

8

10

10

W5

7

6

9

10

9

9

8

9

6

9

10

7A

6

9

10

7

7

5

5

3

6

6

6

4

7

3

4

3

5

5

7

8A

5

6

A5

8

7

10

10

9

8

10

9

9

10

10

8A

6

10

9

6

9

6

6

6

9

10

4

5

7

3

6

9

6

6

9

4

8

10A

7A

W6

9

9

10A

9

9

7

8

8

10

10

10

5

9

6

8

9

7

7

6

6

9

7

9

8

9

7

6

3

6

7

5

7A

A

10

10

e

9

:o*

9

97

8

8

10

10

10

5

9

6

8

9

7

5A

64

a

5

5

9

3~

-

3

9

7

5

6

10

10

W7

5

4

7

A

6

9

8

3

5

6

7

7

9

8

6

3

4

6

5

5

9

3

4

8

5

4

7

6

4

3

7

7

5

10

8

A7

A

5A

A

6A

10

5

6

9A

9

9

6

6

6

5

7

5

5

A

5

6

7

9

5

9

9

4

8

10

8

6

10

6

W8

3

6

6

8

6

10

9

8

9

9

6

9

9

9

10

5

7

7

8

6

10

7

7

10

7

7

9

9

5

10

7

5

10

7

A8

4

A

9

9

9

9

10

9

10

5

7

10

9

10

7

6

8

8

8

6

10

8

8

10

7

*

10

9

3

9

8

9

10

9

W9

7

4

9

5

9

8

7

9

9

7

*

10

10

9

7

3

4

5

5

8

3

6

9

6

6

6

4

4

9

3

1

10

5

A9

9

9

7

6

10

10

10

10

10

9

*

9

9

8

8

7

3

7

9

10

5

7

10

2

4

*

7

2

10

5

5

10

7

W10

7

5

7

7

7

7

7

8

8

7

6

10

8

8A

9

4

6

4

6

2

3

9

6

8

5A

2

6

3A

10A

A;; wi;

e 75

1C 8

5

7

6 8

1C 10

9 8

9 8

5 7

5 6

10 8

9 9

9 *

* 5

* 10

5 6A A

7 5

5 8

7 6

1 ** *

9

* 7

8

9 5A A

0 1

9 5

4 *A A

9 10A A

66


Wl Al W2 A2 W3 A3 W4 A4 W5 A5 W6 A6 W7 A7 W8 A8 W9 A9 W10 AiO Wll All

01

D2

03

04

05

06

07

08

09

010

Oil

012

013

014

015

016

D17

018

019

020

D21

022

023

024

025

026

027

028

029

030

031

032

033

034

035

7

6

9

8

9

9

9

10

10

9

10

10

9

9

10

8

9

9

7

7

8

8

5

8

5

7

8

10

9

9

5A

9

10A

9

8

4

8

10

10

9

9

10

10

8

9

6*

*

*

10

7

10

6

9

6

9

10

10

10

9

10

2

10

10A

7

5

9

8

4

7

8

6A

8

7

3

6

9

7

7

7

5A

3

3

7A

7

7A

A

A

6

3

7

9A

10

6

10

10

7

4

9

5A

9

9

4

10

6

7

9

10

4

1

7

5

4

6

7

6

4

4

8

8

3A

6*

A

7

8

6A

3

7A

A

7A

5

7A

8

5

5

8

3

5

2

5

4

3

3

8

5

9

7

3

7

3A

6

9

9

4

7A

A

9A

9

6

6X

3

4

1

1

2

5

4

3A

6

5

8

3

3

3

4A

9

8

6-

7A

8

6

9

6*

7

9

6

7

7

A

4

5

7

6

7

6A

A

7

5

5

8A

10

10A

5

9

7A

9

6

9

9A

6

6

7

9

9

A

5

5

8

8

7

8A

A

A

8

6

9

9A

5

4A

6

4

8

8

8

5A

3A

5

6

3

4

5

6

4

6

7

10

7

5

7

5A

8A

5

7A

6

5A

10

5

9

10

10

4A

5A

6

10

3

4

6

7

5

9

10

10

6

8

7

6A

10

A

6

aA

7

9

9

4

7

4

8

6

8

8

3

6

7

6

5

6

5

4

9

5

6

6

7

6

5

9

8A

7

5

9

8

6

7

10

8

1

8

5

9

7

9

10

4

10

8

9

9

8

7

6

10

5

8A

9

7

9

8

10 *

7A

9A

A

7

3

7

6

4

6

5

7

A

3

3

7

7

3A

6

5

8

7

7

4

5A

5

5

5

7A

9A

5

4

3

10

4

7

9

5

6

6

8A

3

9

10

9

4

6

5

8

7

8

8

4

4

A

4

8

8

8A

10

27

7

4

8

5

6

6

3

5*

7

7A

A

6

7

4

2

7

4A

5

7

5

4

3

6

6

A

6

6

7

7

6

6

6

7

6

4

9A

6

7A

A

9

10

9

5

7

1A

7

6A

7

4

6

6

A

9A

7

8

8

5

6

9

4

8

5

10

8

7

7

10

6

7

5

4

5

5

7

5

6

4A

6

5

7

A

9

3

7

5

7

6

7

7

7

7A

*

10

7

8

8A

7

9

9

8

7

10*

10

6A

6

9

9

A

7

6

9

6

7

7

A

8

6

8

8

9

5

8

4

6

10

10

8

5

6

6

10A

10

9

4

7

7

9

*

8A

9

8A

5A

9

7

9

9

10

6

10

10

7

9

8

8

7

10

7

10A

9

10

5

7

8

10

A

9A

9

10A

8

9

6

8

87

6

6

8*

7

4

10

7

7

9

7A

5

7

8

7

5A

A

9

8

8

7A

1C

1 C

7

g

7

7

-t

10

9A

9

6

10

4

7

10

8A

8

7

10A

8

6A

A

10

10

10

8A

67

Table 4.9: Median Total Scores for Each Saaple

Sample Scores

Median total score for Sample P in the written tests (set A)

Median total score for Sample Q in the written tests (set B)

Median total score for Sample P in the aural tests (set B)

Median total score for Sample Q in the aural tests (set A)

57

62

63

65

Table 4.10: Median Total Scores for Each Sample

Written

Aural

P

57 (A)

63 (B)

Q

62 (B)

65 (A)

68

Table 4.11 Paired End of Module Tests - Results for School 1

Hi

HZ

H3

H4

H5

H6

H7

H8

H9

H10

Hll

H12

H13

H14

HIS

H16

H17

HISH19

H20

H21

H22

H23

H24

H25

H26

H27

H28H29

H30

H31

H32

H33

H34

H35

H36H37

H38LJ-1Qnjy

H40

H41

H42

H43

H44

UAC. nM 3

H46

H47

H48

H49yen n ju

H51

H52

H53

H54

H55

Wl

4

8

6

10

9

67

9

9

9

8

6

8*

10

7

97

10

8

8

6

6

9

6*

810

9

6

8

67

8

9

8

9

10

10

8

9 4

9

10

10

6

9

8

8

6*

7

Al

4

9

6

10

10

5

9

10

8

10

10 7

5*

10

10

9

610

10

10

7

8

10

7A

10

9

9

5

10

8

7

810

10

1010

10

10

9

9

6

9

10

9

6

10

9

10

10

7*

10

W2

8 6

0

9

9

87

310

5

9

6

8

10

5

10

8

9

7

1

6

3

A

*

4

94

3

8

64

84

65

6

7

97

4

6

6

8

5

5

7

7

5

7*

5

A2

9

6

2

10

9

6

1010

10

39

5

9

9

4

10

8

10

64

9

3

*

*

5

10

2

5

9

6

67

7

79

57

10

84

6

7

10

1

4

5

10

6

10*

4

W3

5

54

87

7

2

3

5

36

3

3

4

1

5

76

5

1

5

3

*

*

1

7

5*

9

2

2

9

6

55

3

87

4

3

6

5

9

5

5

4

6

54

8

A3

7

10

3

9

7

64

3

5

6

5 4

2

5

7

4

89

7

3

6

6

*

*

3

106*

104

1

107

55

4

8

10

5

4

7

4

10

6

6

6

5

67

6

W4

*

8*

6

64

66

6

7

6

6

7

5

6

57

1

7

9

6

5

5

6

6

7

8

5

5

674

5

6

5

87

5*

7

6

5

6

1

4

5

6

8

6

A4

*

9*

8

6

57

7

10

6

9

6

6

6

5

67

37

10

7

4

5

87

109

5

4

7

874

6

6

4

8

8 *

7

6

67

4

6

4

6

10

7

W5

*

5A

4

4

4

24

6

3

3

5

*

6A

44

*

A

7*

5 4

2

7

8

3

7

4

0*

3

4

4

4

9

5

2

4

5

2

5

*

5

5

7

7

6

A5

*

6*

4

3

5

364

1

4

7

*

7*

56A

A

9A

6

5

4

109

1

87

2*

6

3

5

4

10

5

4

9

5

1

6

*

6

4

9

10

6

W6

7

7

6A

A

7A

A

107

9

8

8

9

97*

7

2

5

6

7

7

5A

A

97

A

4

5

A

5

6

3A

A

6

5

7

6

6

8

5*

6

A6

97

7

A

A

7A

A

8

6

6

8

10

9

104

A

6

8

9

7

8

9

6A

A

10

9A

8

6

A

4

6

6A

A

7

3

10

6

7

7*

7

W7

A

34

7

4

4A

A

A

4

8

6

A

5

4

3

3

7A

A

3

4

A

6A

4

5A

56

4

5

6

6

6

3A

4

5

3

6

8

7

6

9

6

A7

A

4

5

8

3

4A

A

A

2

8

7

A

6

4

4

6

6A

A

4

7

A

4

A

9

4A

56

35 7

6

6

5A

7

54

7

9

8

7

6

10

5

W8

7

5

6

84

84

57

37

5

7

7

2

6

57

2

6

4

33

3

16

*

2

2*

3

66

6

4

8

1

6

5

2

8

5

2

2

8

8

4

4

3

48

3

5

6

8

5

7

66

8

57

6

8

10

57

67

4

6

6

24

4

1

7A

4

5A

54

6

9

6

6

6

7

5 4

6

9

4

5

9

7

4

6

5

W9

9A

A

A

5A

9

84

8A

A

6A

7

9

A

A

A

9

5

85A

7A

5

3

2

9

5

6

4

8

5

6

6

6

3

8

A9.

10*

A

A

6A

1010

3

9A

A

7A

4

10

A

A

A

10

7

10

6A

'10

A

8

5

5

577

6

10

9

8

6

8

6

9

W10

6

4

9

5

6

27

9

7

7

8

8

4

5

1

8

7

10

6

5

6

5

864A

6A

4

6

5

5

9

8

6

8

8

4

7

8A

6

AID

•J

5

/

4

7

18

10

10

8

10A

9

3

5

5

3

6

10

6

47

210

54

A

5A

3

7

6

6

10

10

7

9

10

6

7

10A

7

Wll

8A

A

A

8

0A

4

4

1

A

A

A

3A

6

5

A

A

A

A

7

A

7

86

9

5A

6

4

8

7

5

6

7

6

6

8

6

6

8

8

A::

9*

A

A

9

2*

6

6

3A

A

*

4

*

6

6

A

A

A

A

9

A

9i;

c.

1C-«

~

5

9

867

97

10

10

7

6

7

9


01

02

03

04

06

07

08

09

010

Oil

012

013

014

015

016

017

018

019

020

021

022

023

024

025

026

027

029

030

031

032

033

034

035

036

037

038

039

040

041

042

043

044

045

046

Wl

9

7

5

3

6

10

6

7

7

9

9

9

5

5A

6

10

10

6

9

8

5A

5A

A

9

10

8

10

10

6

10A

9

7

8

8

8»

8*

10

Al

9

9

9

4

10

4

6

10

10

9

X

10

8

7A

9

10

10

5

9

5

5A

6A

A

10

10

7

9

9

6

7A

7

7

610

6A

9A

8

W2

7

0

4

1

7

7

7

9A

6

9

8

7

3

6

6

6

8

5

9

6

5

7

1

10

7

8

7

6

8

9

7

7

6

7

7

8

6

1A

5A

8

A2

7

3

5

2

7

7

9

8A

7

10

10

10

4

7

7

6

9

7

5

10

10

4

10

9

10

8

10

6

6

6

10

9

7

9

7

10

10

6

4A

6*

9

W3

7

1

0

2

4

4

0

3

2

7

7

5

7

4A

7

7

8A

A

A

1

6

8

3A

7A

3

2

2

5

4A

6

5A

4

3

3A

5A

3

A3

7

4

7

3

5

4

5

4

1

8

7

7

8

2*

5

5

9A

A

A

2

4

9

1A

5A

4

0

3

4

2A

7

5A

4

2

3A

7A

4

-4

A

7

6

6

7

8

8

9

9

9

6

8

6

8

2

6

9

7

7

8

10

4

5

8X

8

8*

6

7

7

4

7

7

7

6

5

8

7

5A

6X

X

A4

*

9

10

4

5

9

10

10

10

9

6

9

10

6

4

6

10

9

3

7

9

7

9

9A

5

10A

4

7

6

7

10

9

10

7

6

9

7

10X

9A

A

W5

7

3

4

2

4

6

3

5

7

9

4

6

8

7

7

7

9

10A

7

8

4

4

6

2

7

5

7*

3

5

6

5

3A

5

6

6

3

3A

6A

*

A5

8

5

5

4

5

7

5

6

8

9

8

4

10

6

6

7

10

10A

10

10

6

7

7

5

7

6

9*

4

5

6

9

5A

7

7

9

52A

10

A

A

W6

2

6

1

9

9

3

9

10

8

5

2

6

7

10

8

9

10

3

9

9

8

10

4

8

7

8

10

8

6

8

7

7

9

8

7A

7

9

3

8

A6

4

10

7

3

10

10

5

10

7

4

4

4

9

4

10

10

9

9

5

10

9

9

6

7

8

9

9

10

9

6

10

6

10

10

7

10A

6

9

5

9

W7

10

5

5

4

4

7

5

0

5

3

2

3

4

6*

7

5A

2Zf>0

6

5

6

3

6

7

4

4

8

2

4

4A

4*

7

3

4

A7

10

6

6

5

9

6

6

4

5

6

5

5

4

7A

8

10A

7

6

6

4

7

4

6

4

7

8

4

4

9

9

4

5*

6A

8

5

8

W8

10

6

2

5

6

9

2

9A

8

7

6

6

9

6

6

8A

6

7

8

6

8A

2

9

8

4

2

6

7

9

7

6

6A

5

2A

A8

10

7

5

4

7

10

5

10A

9

6

6

6

10

10

10

9A

7

9

9

5

9A

9

9

10

5

4

4

10

7

10

6

6A

4

7A

W9

10

5

2

7

10

10

8

10

10

9

5

7

9

9

7

9

6A

4

9

4

8A

8

6

8

5A

7

8

9

9A

3X

8

7

6

A9

10

7

4

8

10

9

9

10

. 8

10

6

8

10

10

8

9

7A

5

10

5

8X

9

9

10

4A

10

10

8

10x

5*

10

6

6

W10

9

4

28

8*

9

8

7

6

9

7

9

10

6

10

10A

6

10

7

8

7

7

8

6

3

8

7

9

6

7A

7A

8

9

6

AID

10

5

7

8

7*

10

10

8

8

10

6

. 6

9

7

10

5A

7

9

10

10

8

7

9

10

5

10

7

10

7

7A

9A

8

10

6

Wll

10

7

4

*

10*

9

10

2

7

6

7A

9

6

8

10

4

7

8

5

9

8

6

7

8A

8

6

9

8

6A

A

A

7

8

6

A:

10

7

7*

10A

9

9

5

10

7

8A

10

7

9

10

7

6

9

9

10

10

9

7

4A

10

7

9

10

7A

A

A

9

8

10

70


Wl Al W2 A2 W3 A3 W4 A4 W5 A5 W6 A6 W7 A7 W8 A8 W9 A9 W10 AID Wll All

n12

13

14

15

16

17

18

19

no111112

113

114

115

116

117

118

119

120

6

8 *

7

5

9

10

9

10

10*

8

4

7

9

10

10

9

7

10 *

5

7

7

8

10

9

10*

9

3

10

10

9

10

10

6

9

1

7

6*

7

6*

6*

4

8

3

6

8

8

8

8

7

9

0

2

6*

4

7*

4 *

4

7

2

5

7

10

10

10

3

4

1

3

4

3

4

3

5

1

8

1

6

2

2

6

9

10

7

7

5

2

8

5

2

5

6

6

3

10

21*

9

9

9

10

6

7**

*

4

3

10

3

2

7

3

3

3

3

5

5

6

8

9

7

9

*

*

5

7

9

4

4

8

6

6

4

4

5

4

7

9

8

8

1

8

9

4

3

6

5

7

7 *

5

3

8

3

1 *

9

10

9

3

9

10

5

5

4

6

7

6A

7

7

10

4

0*

10

10

10

5

6

2

5

7

7

5

5

7

7 *

3

8

9

8

9

9

9

9

7

7

4

7

4

7

7

6

6

10*

5

9

9

9

9

10

9

9

6

8

0

5

2

8

6

3

4

5

2

8

3

2

10

7

10

6

7

9

2

7

4

10

9

5

4

5

5

9

4

5

10

8

9

7

4

4

1

6

3

4

5

4

4

8

6

7

3

2

4

4

9

5

8

6

5

3

3

3

9

5

5

10

7

6

7

3

4

5

10

5

8

7

5

3

9

10

9

4

10*

8

7

8

10

9

10

7

5

8

9

10

5

10*

9

9

8

10

6

9

6

8

6

9

8

9

8*

8

6

7

9

9

9

10

104

10

10

10

8*

9

5

4

9

7

8

5

8

7

9

6

5

4*

8

6

3

9

6

10

4

10

8

10

4

6

5*

10

9

7

8

71


Cl

C2

C3

C4

C5

C6

C7

C8

C9

CIO

Cll

C12

C13

C14

C15

C16

C17

C18

C19

C20C21

C22

C23

C24

C25

C26

C27

C28

C29

C30

C31

C32

C33

C34

C35

C36

C37

C38

C39

C40

C41

Wl

10

10

10

8*

10

9

9

10

8

10

10

9

10

6

10

8

10

1010

10

9

9

8

10

9

10

10

9A

9

4

7

A

6A

7A

A

8

Al

9

9

10

10*

10

9

10

10

10

10

10

9

9

9

8

10

7

710

10

6

5

3

6

10

10

5

5A

10

3

6*

9A

6A

A

10

W2

6

10

9

6

9

7

7

7

10

5

8

9

8

9

7

5

9

8

53

5A

4

0

8

7

7

4

5

1

4

7A

9*

A

7A

A2

7

10

9

10

10

8

7

8

10

7

7

10

10

9

6

9

9

3

66

5A

2

2

5

5

6

1

2A

0

6

6A

6A

A

7

A

W3

A

8

4

9

A

8

7

*

9

8A

9

6

6

9

10

8

4

36

6

2

2A

3

3

4

*

A

9

1

5A

5

5

5*

4

4

A3

A

9

3

7

A

7

4

*

8

5A

7

5

5

7

9

8

8

57

7

5

5*

4

4

9A

A

6

4

4A

4

7

4A

4

4

W4

7

4

6

4

6

7

5

8

8

6

7

7

3

5

8

7

5

7

77

5

8

4

5

9

6

9

6

7

6

4

6

7

4

8

6

5

7

9

A4

6

5

8

9

5

10

9

7

6

8

5

5

9

6

7

8

7

8

6

10

3

7

7

10

10

9

5

9

9

5

6

6

7

9

9

8

10

10

W5

7

6

9

10

9

9

8

9

6

9

10

7A

6

9

10

7

7

5

5

3

6

6

6

4

7

3

4

3

5

5

7

8A

5A

A5

7

10

10

9

8

10

9

9

10

10

8A

6

10

9

6

96

6

6

9

10

4

5

7

3

6

9

6

6

9

4

8

10A

7

A

W6

9

9

10*

9

9

7

8

8

10

10

10

5

9

6

8

9

7

7

6

6

9

7

9

8

9

7

6

3

6

7

5

7A

A

10

10

A6

9

9

10*

9

9

7

8

8

10

10

10

5

9

6

8

9

7

5*

64

8

5

5

9

8

7

2

7

8

9

7*

*

10

10

W7

A

4

*

A

6A,

8

3

5

6A

7 '

9

8

6

3

4A

5

5

A

3

4

8

5

4

7

6

4

3

7

7

5

10

8

A;

*

5*

A

6A

10

5

6

9A

9

9

6

6

6

5

7

5

5

A

5

6

7

9

5

9

9

4

8

10

8

6

10

6

W8

3A

6

8

6

10

9

8

9

9

6

9

9

9

10

5

7

7

8

6

10

7

7

10

7A

9

9

5

10

7

5

10

7

A8

4

A

9

9

9

9

10

9

10

5

7

10

9

10

7

6

8

8

8

6

10

8

8

10

7

A

10

9

3

9

8

9

10

9

W9

7

4

9

5

9

8

7

9

9

7

A

10

10

9

7

3

4

5

5

8

3

6

9

6

6

A

4

4

9

3

1

10

5

A9 W10

9 7

9 5

7 7

6 7

10 7

10 7

10 7

10 8

10 8

9 7

* 6

- 9 10

9 8

8 8

8 *

7 *

3 4

7 6

9 4

10 6

5 2

7 3

10

2

4 *

* 5

7 *

2 2

10 6

5 3

5 *

10 10

7 *

A10 Wll

6 7

7 5

10 8

7 5

7 7

6 8

10 10

9 8

9 8

5 7

5 6

10 8

9 9

9 *

* 5

* 10

5

7 5

5 8

7 6

1 *

4 7

A 9

* 7

* 8

9 5A A

0 1

9 5

4 *A A

9 10A A

All

A

9

6

9

6

8

10

8

6

9

10

7

4

10A

6

10A

A

9

9

5A

7

9

8

10A

5A

4

6A

A

10

A

72


Wl Al W2 A2 W3 A3 W4 A4 W5 A5 W6 A6 W7 A7 W8 A8 W9 A9 W10 A10 Wll All

01

02

03

04

05

06

07

08

D9

010

Dll

012

013

D14

015

016

017

018

019

020

021

022

023

024

025

026

027

028

029

030

D31

032

033

034

035

7

6

9

8

9

9

9

10

10

9

10

10

9

9

10X

x

A

7

8

5

8

5

7

8

10

9

9

5A

9

10A

9

8

8

4

8

10

10

9

9

10

10

8

9

6A

A

A

10

7

10

6

9

6

9

10

10

10

9

10A

10

10A

7

5

9

8

4

7

8

6A

8

7

3

6

9

7

7

7

5

3

3

7

7

7A

A

A

6A

7A

A

10

6

10

10

7

4

9

5A

9

9

4

10

6

7

9

10

A

1

5

4

6

6

4A

*

A

3A

6A

A

7

8

6A

3

7A

A

7A

5

7A

8A

5

8

3

5

2

5

4

3A

8

5

9

7

3

7

3A

6

9

9A

4

7A

A

9A

9

6X

6X

3

4

1

1

2

5

4

3A

6

5

8

3

3

3

4A

9

8A

6

4

7A

8

6

9

6A

7

9

6

7

7

A

4

5

7

6

7

6A

A

A

7

5

5

8A

10

10A

5

9

7A

9

6

9

9A

6

6

7

9

9

A

5

5

8

8

7

8A

A

A

8

6

9

9A

5

4A

6

4

8

8

8

5A

3A

5

6

3

4

5

6

4

6

7

10

7

5

7

5A

8A

5

7A

6

5A

10

5

9

10

10

4A

5A

6

10

3

4

6

7

5

9

10

10

6

8

7

6A

10A

6

8A

7

9

9

4

7

4

8

6

8

8

3

6A

7

6

5

6

5

4

9

5

6A

7

6

5

9

8A

7A

9A

A

7

10

8

1

8

5

9

7

9

10

4

10A

8

9

9

8

7

6

10

5

8A

9

7

9

8

10A

7*

9A

A

7

3

7

6

4

6

5

7A

3

3

7A

7

3A

6

5

8

7

7

4

5A

5

5

5

7A

9A

5

4

3

10

4

7

9

5

6

6

8A

3

9

10

9

4A

5

8

7

8

4

4A

4

8

8

8A

10

A

7

7

4

8

5

6

6

3

5A

7

7A

A

6

7

4

2

7

4A

5

7A

4

3

6

6A

A

6A

7

7

6

6

6

7

6

4

9A

6

7A

A

9

10

9

5

7

1A

7

6X

7

4

6

6A

A

9A

7

8

8

5

6

9

4

8

X

X

8

7

7

10

7

5

4

5

5

7A

6

4

A

6

5

7A

A

9

3

7

5

7

6

7

7

7

7A

A

10

7

8

8

7

9

9

8

7

10A

10

6A

6

9

9A

A

7

6

9

6

7

7

X

8

6

8

8

9

5

8

4

6

10

10

8

5

6A

6

10A

10

9

4

7

7

9A

A

8A

9

8*

5X

9

7

9

9

10

6

10

10

7

9

8

8

7

10A

7

10X

9

10

5

7

8

10A

A

9*

9

10A

8

9

6

8

8

7

6

6

8A

7

4

10

7

7

9

7A

5

7

8A

7

5A

A

A

9

8

8

7A

10

10

7

8

7

7

7

10

9*

9

6

10

4

7

10

8A

8

7

10A

8

6X

X

*

10

10

10

8X

73

Table 4.16: Median Total Scores using Paired Tests

Sample (using paired tests)

Median total score for Sample P in the written tests

Median total score for Sample Q in the written tests

Median total score for Sample P in the aural tests

Median total score for Sample Q in the aural tests

Scores

55.5

59

63

67

Table 4.17: Median Total Scores Using Paired Tests

Written

Aural

P

55.5 (A)

63 (B)

Q

59 (B)

67 (A)

74

4.3 TESTING THE HYPOTHESIS

As previously stated, the null hypothesis put forward for the

purpose of this research is:

Pupils score comparable marks when a series of questions are

asked singly, in an aural form by the cktss teacher, and when all

questions are presented together in written form.

4.3.1 Research Method

To test the above hypothesis, the marks scored by pupils in

the end of module written and aural tests were again analysed in two

ways:

METHOD 1:

For each pupil the marks awarded for the written and aural

tests were totalled and the difference in these total scores calculated.

The median difference in totals was then found for each school.

METHOD 2:

For each pupil, the marks awarded for the written and aural

tests where pupils were present for both versions of the test were

totalled and the difference in these scores calculated. The median

difference in scores was then found for each school.

In each case the hypothesis that the median difference in

marks is zero was tested against the alternative that the median

difference in marks is not zero.

75

4.3.2 Analysis of Results

In order to facilitate an analysis of results, a number of

statistics have been calculated and brought together in Table 4.18.

Table 4.18: Median Difference in Total Scores on Aural and Written Tests

School

Aural tests sat

Written tests sat

Number in sample

Method 1Median difference intotal scores (a-w)

Number in sample(paired tests)

Method 2Median difference inpaired total scores(a-w)

1

B

A

55

6

54

6.5

2

B

A

44

6

44

8

3

A

B

19

6

19

8

4

A

B

41

1

41

5

5

A

B

34

5

34

6.5

From the above table it can clearly be seen that in at least

four out of the five schools pupils performed significantly better when

the tests were administered aurally than when they were undertaken in

written form.

76

A more detailed analysis of the results shown in Tables 4.19-

4.23, indicates that in four out of the five cases, where the comparison

is made on a total score analysis, neither the 95% confidence interval

nor the 99% confidence interval covers the zero difference mark. For

example, in school 3, the 95% confidence interval for the median

difference of scores is (3.728, 8.136) and the 99% confidence interval is

(2, 9.3). The actual probability that the median difference of total

scores is zero is recorded as 0.0044.

If the comparison is made on paired test scores, the results

are as shown in Tables 4.24-4.28. In this instance the zero difference

score occurs outside both the 95% and the 99% confidence intervals in

all five cases.

This difference in performance would appear to be less

significant in school 4. However, when the median difference in scores

is calculated using only paired tests, the results for school 4 closely

follow the results for the other sample schools. This apparent ambiguity

can be explained by considering the individual pupil results for school

4, shown in Tables 4.7 and 4.14.

As can be seen, the pattern of attendance is such that on a

significant number of occasions pupils in this school more than any

other were present for only one version of an end of module test. In

most cases this was the written test. Thus, when a 'total mark'

comparison is used to analyse results in this school, the total marks for

the written tests are significantly higher than when a 'paired test'

77

Table 4.19 Sign Test of the Median Difference in Total Scores for School 1

Sign Test of Median

N Below 55 9

Confidence Intervals School 1

= 0.00000 versus N.E. 0.00000

Equal Above P-Value Median 1 45 0.0000 6.000

for the Median Difference in Total Scores for

95% Confidence Interval

N Median 55 6.000

Achieved Confidence 0.9848 0.9900 0.9930

99% Confidence Interval Achieved

N Median Confidence 55 6.000 0.9409

0.9500 0.9690

Confidence Interval ( 4.000, 9.000 ) ( 4.000, 9.000 ) ( 4.000, 9.000 )


Position 19

NLI 18

Position 21

NLI 20


Sign Test of Median = 0.00000 versus N.E. 0.00000

N 44

Below 8

Equal 3

Above 33

P-Value 0.0001

Median 6.000

Confidence Intervals for the Median Difference in Total Scores for School 2


N 44

Median 6.000

Achieved Confidence0.90390.95000.9512

99% Confidence IntervalAchieved

N 44

Median 6.00

Confidence 0.9774 0.9900 0.9904

Confidence Interval Position( 4.000, 9.000 ) 17( 2.089, 9.000 ) NLI( 2.000, 9.000 ) 16

Confidence Interval Position(2.00, 9.00 ) 15(2.00, 10.86) NLI( 2.00, 11.00 ) 14

78



N Below Equal Above P-Value 19 3 0 16 0.0044

Median 6.000



Achieved N Median Confidence

19 6.000 0.9364 0.9500 0.9808



0.9900 0.9956


Confidence Interval ( 2.00, 9.00 ) ( 2.00, 9.31 ) (2.00, 10.00 )

Position 6

NLI 5

Position 5

NLI 4


Sign Test

N 41

Confidence School 4

of Median = 0.00000 versus N.E. 0.00000

Below Equal Above P-value Median 18 1 22 0.6358 1.000

Intervals for the Median Difference in Total



0.9500 0.9725

Confidence Interval (-2.000, 3.000 ) (-2.181, 3.181 ) (-3.000, 4.000)

Scores for

Position 15

NLI 14


N 41

Achieved Median Confidence 1.000 0.9885

0.9900 0.9957

Confidence Interval (-4.000, 5.000 ) (-4.000, 5.000 ) (-4.000, 5.000 )

Position 13

NLI 12

79



N Below Equal Above 34 7 1 26

P-value 0.0013

Median 5.000



N 34

Median 5.000



N 34

Median 5.000




Table 4.24 Sign Test of the Median Difference in Paired Total Scores for School 1


N N* Below Equal Above P-value Median 54 1 5 2 47 0.0000 6.500


for the Median Difference in Paired Total Scores for


N N* Median 54 1 6.500



Position 21

NLI 20


N N* Median 54 1 6.500



Position 19

NLI 18

80



N Below Equal Above P-value Median 44 5 1 38 0.0000 8.000




N Median 44 8.000

Achieved Confidence

0.9039 0.9500 0.9512


Position 17

NLI 16


N Median 44 8.000



Position 15

NLI 14







N Median 19 8.000

Achieved Confidence

0.9364 0.9500 0.9808


Position 6

NLI 5


N Median 19 8.00



Position 5

NLI 4

81







N Median 41 5.000

Achieved Confidence

0.9404 0.9500 0.9725


Position 15

NLI 14


N Median 41 5.000



Position 13

NLI 12







N Median 34 6.500

Achieved Confidence

0.9424 0.9500 0.9757


Position12

NLI 11


N Median 34 6.500



Position 11

NLI 10

82

comparison is used, as a number of written test marks have been

'discarded' when calculating 'paired test' totals.

Nevertheless, even when all written test results are used,

pupils still perform marginally better when the tests are administered in

aural form.

4.4 CONCLUSIONS AND RECOMMENDATIONS

In view of the research findings detailed above, it can be

concluded that pupils will be granted greater opportunity to

demonstrate retention of the skills and concepts learned in each module,

if the end of module tests are administered aurally than if they are

undertaken in written form. As these assessments are to be used for

diagnostic as well as summative purposes, this knowledge is needed in

order that teachers may plan the most effective mathematical experiences

for each pupil.

It can also be argued that while teachers are administering

the tests aurally, they are in the position of being able to observe the

way in which pupils answer the test questions. Thus observation

during the test, and marking after the test, are being used as

assessment tools to monitor pupils' progress. Logically this must give a

more reliable diagnosis of pupils' achievements than marking alone.

In consequence therefore, it is being recommended to the

examination board that in future years the end of module assessments

should be administered aurally by the class teachers. However, teachers

83

should retain the option of setting written tests where the needs of

pupils make it more advantageous to do so - for example in partial

hearing units.

84

CHAPTER 5

THE PRACTICAL ASSESSMENT^

5.1 INTRODUCTION

These tasks are intended to assess the pupils' mastery of

elementary skills and techniques using practical equipment (see Section

2.3.3, pp.46-47).

It is intended that practical work, and use of apparatus, be an

integral part of the Certificate of Education course. As such, pupils should

have ample opportunity to familiarise themselves with everyday practical

apparatus and measuring instruments, and to develop the skills needed to

use this equipment in the undertaking of basic practical tasks set out in

the syllabus. It is essential to the ethos of the course that practical tasks

become neither 'pencil and paper' exercises, nor 'one off tests administered

towards the end of the course.

The practical assessments are intended to be undertaken on a

one-to-one basis during the course of a normal classroom lesson. It is

neither necessary nor desirable to assess all of the pupils at the same time;

nor is it necessary to set up a formal practical examination. When a pupil

fails to complete a practical task successfully, remediation takes place and

the technique is demonstrated. The pupil is then re-tested at a later date.

The over-riding criteria for awarding the permitted mark for a practical

assessment is that by the end of the course the pupils should have

mastered a particular skill.

At present, the practical tasks account for 12% of the total marks

to be awarded.

85

TABLE 5.1 - List of Practical Tasks (Certificate of Education, Numeracy Component)

Pupils will be expected to perform all of the following tasks

1. Use a weighing scale or simple balance.

2. Use a ruler to measure in cms or inches to within one tenth of a unit.

3. Use a tape measure to measure in metres to one hundredth of a unit, or in feet to within one inch.

4. Write a cheque.

5. Give the time correctly as a.m. or p.m. from an analogue display to the nearest minute.

6. Read a twenty-four hour digital display, and interpret this as a.m. or p.m.

7. Read a timetable.

8. Estimate capacity up to ten litres, to within two litres.

9. Read a thermometer in degrees Centigrade or degrees Farenheight, to within one unit.

10. Measure bearings on an eight point scale.

11. Measure distance on a map, to within ten percent.

12. Give the correct change in response to a simple bill.

86

As has been previously stated, dissatisfaction has been expressed

both as to the number of marks available for the assessments (one mark per

task) and in the way that these marks are to be awarded.

5.2 RESEARCH METHOD

To undertake this investigation, an attempt was made to identify

any common assessment objectives present in all the practical tasks. A list

of tasks is shown in Table 5.1, which is reproduced from the current course

documentation (see Appendix I). Each of these tasks was analysed to

identify possible assessment criteria, and the findings are reproduced

below.

Possible Assessment Cri

Task 1 - Use of a weighing scale

(i) Choice of correct instrument from a variety of equipment.

(ii) Familiarity in using the weighing scale, i.e. setting to zero before weighing an object.

(iii) Weighing a specified amount of material.

(iv) Reading the weight of an object in appropriate units.

Task 2 - Use of a ruler

(i) Choice of correct instrument to measure a short length.

(ii) Familiarity in using a ruler, i.e. setting one end of the object at the zero mark on the ruler.

(iii) Measuring a specified length of material.

(iv) Reading the length of an object in appropriate units.

87

Task 3 - Use of a tape measure

(i) Choice of correct instrument to measure a long length.

(ii) Familiarity in the use of a tape measure, i.e. setting the zero mark on the tape measure at one end of the length to be measured.

(iii) Measurement of a specified length of 'material'.

(iv) Reading the length of a given 'object' in appropriate units.

Task 4 - Paying by cheque

(i) Recognition of a cheque among a range of other documents.

(ii) Familiarity with the use of a cheque book.

(iii) Writing a cheque to pay a bill.

(iv) Checking the correctness (or otherwise) of a written cheque against a 'bill of sale'.

Task 5 - Telling the time from an analogue display

(i) Choice of correct instrument (digital timepiece not present).

(ii) Setting an analogue display to read a specified time.

(iii) Reading an analogue display.

(iv) Interpretation of a given time as a.m. or p.m.

Task 6 - Telling the time from a 24-hour display

(i) Choice of correct instrument (analogue timepiece not present).

(ii) Setting a digital display to show a specified time.

(iii) Reading a digital display.

(iv) Interpretation of a given display as a.m. or p.m. time.

88

Task 7 - Reading a timetable

(i) Choice of correct timetable for a specified journey from a selection of documents.

(ii) Familiarity with the use of a timetable, i.e. can identify sections for outward/return journey.

(hi) Correct selection of 'next' bus/train after a specified time.

(iv) Correct choice of bus/train to arrive at a given destination by a specified time.

Task 8 - Estimation of capacity

(i) Comparison of common measures of capacity.

(ii) Choice of appropriate container to hold a specified volume of liquid.

(iii) Estimation of the volume of liquid in a container,

(iv) The measurement of a specified volume of liquid.

Task 9 - Use of a thermometer

(i) Choice of correct instrument for measuring temperature.

(ii) Familiarity with the use of the instrument, i.e. display must settle before reading.

(iii) Reading a given temperature scale,

(iv) Finding the temperature of a liquid.

Task 10 - Use of an eight-point compass

(i) Choice of correct instrument for measuring bearings.

(ii) Familiarity with the use of the instrument, i.e. compass must be aligned to magnetic North.

(iii) Indicating a 'land mark' on a map in a given direction.

(iv) Finding the direction of a 'land mark' in the vicinity of the candidate.

Task 11 - Distance on a map

(i) Choice of sensible method of measuring a non-straight road/river on a map.

89

(ii) Measurement to a specified degree of accuracy of a given feature on a map.

(iii) Interpretation of the scale of the map.

(iv) Finding the true length of a given feature using the scale of the map.

Task 12 - Giving change

(i) Recognition of coins in current use.

(ii) Choice of correct coins to make up a given amount of money.

(iii) Giving correct change when a product is paid for with a £5/£10 note.

(iv) The ability to check the correctness of the change given.

5.3 FINDINGS AND RECOMMENDATIONS

In each task, the following four assessment objectives were

identified:

(i) Identification of the correct equipment/material needed to perform

the task.

(ii) Correct use of the equipment/material in order to gain a result,

(iii) Correct reading or interpretation of the equipment/material to a

specified degree of accuracy,

(iv) Communication of results.

It is recommended that each of the above objectives could be, and

should be, specifically assessed and, if undertaken successfully, positively

rewarded. Further, it is recommended that the specific assessment

objectives detailed above should be incorprpated into the practical

assessment in the following way:

90

Task 1 - Use of a weighing scale

Equipment : Weighing scale with which candidate is familiar, object, sand/small blocks etc.

(a) Candidate chooses weighing scale from range of equipment.

(b) Candidate zeros the scales before each weighing.

(c) Candidate weighs out a given amount of sand/blocks.

(d) Candidate weighs object correctly.

Task 2 - Use of a ruler

Equipment : Ruler, photograph, length of string, scissors.

(a) Candidate chooses ruler from range of equipment.

(b) Candidate measures from zero mark on ruler.

(c) Candidate measures and cuts a specified length of string (shorter than length of ruler).

(d) Candidate measures width of photograph correctly.

Task 3 - Use of a tape measure

Equipment : Tape measure, string, scissors, two marks on floor.

(a) Candidate chooses tape from range of equipment.

(b) Candidate measures from zero mark on tape.

(c) Candidate measures and cuts a given length of string.

(d) Candidate measures distance between two marks.

Task 4 - Paying by cheque

Equipment : Cheque (ready written from a bill but with one mistake), blank cheque, bill.

(a) Candidate chooses a cheque from a range of documents.

(b) Candidate can suggest when a cheque book could be used.

(c) Candidate writes a cheque to pay a bill (all entries correct).

(d) Candidate checks the written cheque against the bill and indicates an error.

91

Task 5 - Telling the time from an analogue display

Equipment : Analogue clock/watch.

(a) Candidate chooses clock from range of equipment.

(b) Candidate sets the clock to a given time.

(c) Candidate reads a given time correctly.

(d) Candidate interprets 'morning' or 'afternoon' time as a.m. or p.m. time.

Task 6 - Telling the time from a 24-hour display

Equipment : 24-hour display.

(a) Candidate chooses display from a range of equipment.

(b) Candidate sets a 24-hour digital display to a given time.

(c) Candidate reads a digital display set at a.m. time as 'in the morning'.

(d) Candidate reads a digital display set at p.m. time as 'in the afternoon/evening'.

Task 7 - Reading a timetable

Equipment : Local bus/train timetable.

(a) Candidate chooses correct timetable from selection of timetables.

(b) Candidate chooses correct section of timetable for specified from/to journey.

(c) Candidate correctly identifies 'next' bus/train after a specified time.

(d) Candidate correctly identifies bus/train which should be caught to arrive at a given destination by a specified time.

Task 8 - Estimation of capacity

Equipment : Selection of containers, e.g. 1 pt. bottle, 1 litre bottle, bucket, small medicine glass.

(a) Candidate is asked to compare two units, i.e. about how many of these i pt. glasses could be filled from this 1 litre bottle?

(b) Candidate is asked to select a suitable container to hold a specified amount of liquid.

92

{c) Candidate is asked to estimate the amount of liquid in a container,

(d) Candidate is asked to measure a specified amount of liquid.

Task 9 - Use of a thermometer

Equipment : Thermometer, hot/cold liquids.

(a) Candidate chooses thermometer from range of equipment.

(b) Candidate ensures gauge has 'settled' before reading displays.

(c) Candidate is asked to read a given temperature.

(d) Candidate finds the temperature of a liquid.

Task 10 - Read a bearing on an 8-point scale and use the 8 points on compass

Equipment : Compass, simple map.

(a) Candidate chooses compass from a range of equipment.

(b) Candidate 'sets' compass to magnetic North before each reading.

(c) Candidate uses compass to indicate a land mark on a map in a specified direction.

(d) Candidate uses compass to indicate the direction of an object in the vicinity of the candidate.

Task 11 - Distance on a map

Equipment : Local map with a definite non-straight road/river/railway.

(a) Candidate indicates a sensible way of measuring a non-straight road/river.

(b) Measurement of road/river.

(c) Candidate gives a sensible interpretation of the scale of the map.

(d) Candidate uses the scale to find the actual length of road/river.

93

Task 12 - Giving change

Equipment : A selection of "small change" (all current coins), a bill, a selection of priced goods.

(a) Candidate is able to select all current coins by name.

(b) Candidate is able to offer the correct amount of money for one of the priced items.

(c) Candidate is able to offer the correct change when a priced item is bought with a £5/£10 note.

(d) Candidate is able to check the correctness of the change given when buying a priced item with a £5/£10 note.

5.4 CONCLUSIONS

Identifying specific assessment objectives within a task, and

detailing the skills which pupils need to demonstrate to achieve these

objectives, make it possible for teachers to reward positive achievement

even though completion of the whole task may still be beyond some pupils.

Breaking down tasks in this way should also help the teacher to identify

the precise area in which a pupil is failing, allowing remediation to be

specific to the area of difficulty.

Having decided on the specific areas where credit may be gained,

the mark weighting for each element of the task needs to be specified. In

deciding this, consideration was given to the following points:

The relative importance of proficiency in the practical skills for

the target group.

The comparable marks available to pupils on demonstration of

achievement of a particular skill within the written assessments.

94

The time and effort required throughout the course by the

teacher in undertaking the practical activities.

It is clear that if the above points are taken into consideration,

the pupil's ability to demonstrate a practical skill should be considered of

at least equal merit to the ability to demonstrate the acquisition of a skill

on a written paper. Indeed, with the practical skills being of such

relevance to this target group, it might be argued that the demonstration of

a practical skill should command greater credit than that of a 'pencil and

paper' skill.

Analysis of the written assessments reveals that there are 275

single questions - each one offering an opportunity to demonstrate the

acquisition of a mathematical skill or simple concept. In total the written

assessments amount to 76 marks.

TABLE 5.2 - Summary of Written Assessments

Assessment

End of module tests

Progress tests

Final examination

Total

No. of separate elements

110 (11 x 10)

90 ( 3 x 30)

75 (50 + 25)

275

No. of marks

11

15

50

76

95

It follows that each correct answer is worth (on average) 0.28 of a mark. To

fulfil the criteria already mentioned, each element of a practical task should

merit at least a comparable mark, if not significantly more. It is

recommended therefore, both as a reflection of importance, and for ease of

administration, that each element of a practical task should be worth 0.5 of a

mark. In this way, each full task would be worth 2 marks and the practical

assessments as a whole would have a mark weighting of 24 marks.

96

CHAPTER fi

THE ORAL ASSESSMENT

6.1 INTRODUCTION

The oral assessment, produced by the examining board and

conducted by the class teacher on a one-to-one basis with each pupil,

takes place in the final term of the course. It is designed to give as

comprehensive a picture as possible of the knowledge, skills and

understanding a pupil has gained throughout the course.

Four oral 'packages' are sent to each participating centre.

The class teacher selects a 'package' of questions for each pupil, using

the set of four packages in rotation. An example of one such package is

given in Appendix II. Each assessment 'package 1 consists of three

sections.

Section A. - a, short mental test

This consists of 8 mental arithmetic questions involving both

non-context questions and simple problems. The pupils are asked the

questions in the way that is most familiar to them but they must be

answered without benefit of pencil and paper or calculating aids of any

kind.

Section B - a longer thematic question

This consists of a long, relatively difficult, 'real life' problem

which is divided into discrete manageable units of reasoning and/or

calculation. The question contains interdependent strands which need to

97

be identified and used, to obtain a final solution to the complete

problem.

In this section the pupils' understanding of a variety of

mathematical concepts is assessed, and their ability to solve more

complicated mathematical problems is tested.

Pupils are led step-by-step through the whole problem, with

any mistakes or misconceptions being dealt with before later stages are

developed. Pencil and paper and other calculating aids may be used

freely and pupils are encouraged to clarify points or questions not fully

understood.

Section C - interpretation of a graph, chart or table

In this final section, pupils are presented with a diagrammatic

or tabular representation of some information. The questions asked

would involve interpretation of the information shown, calculations based

on the diagram and possibly inserting extra information into the

diagram.

The pupils would be expected to display reasoning powers and

common sense inference, as well as the ability to make mathematical

calculations. There is no set time limit to an oral assessment. However,

most teachers estimate that about 20-25 minutes is spent with each

pupil.

A detailed marking scheme is provided with each oral 'package'

but briefly, the breakdown of the marks is as shown in Table 6.1.

98

Table 6.1 : Breakdown of Oral Marks per Section

Section

A

B

C

Total

Total Marks Available

2

3

2

7

As has been previously stated, a large proportion of teachers

feel that the marks for the oral assessment should be significantly

increased.

6.2 RESEARCH METHOD

The oral assessment, conducted by the class teacher using a

script provided by the examining board, offers teachers and pupils

unique opportunities not found elsewhere in the assessment structure.

For the pupil, the oral assessment offers a range of

opportunities not found in written assessments, to:

demonstrate mental dexterity;

discuss mathematical ideas;

demonstrate their reasoning;

use pencil and paper methods which are meaningful

and which reflect thought processes;

interpret charts and diagrams without the impediment

of having to use written language;

99

question the teacher to clarify a point.

During the assessment, the teacher can also make maximum use

of a variety of opportunities. For example, it is possible to:

discuss mathematical ideas with pupils;

question a pupil if a statement is unclear or

incomplete;

explain an incomprehensible word or phrase;

listen to a pupil;

observe a pupil working out a problem or performing

a calculation.

Using such a comprehensive range of assessment techniques at

any one time ensures that the teacher is in the position of being able to

assess not only the final product - the answer produced by the pupil -

but also to observe the mathematical processes through which the pupil

worked. This not only ensures a deeper understanding of a pupil's

ability, but also shows where understanding of a concept might have

broken down, and perhaps enabling a pupil to be rewarded for some

positive achievement. (This procedure also provides valuable information

for the teacher regarding the effectiveness of teaching strategies.)

Nowhere else in the assessment structures are such a range of

opportunities present for both teacher and pupil. As such, it is

generally believed that the flexibility, adaptability and comprehensive

nature of this component should be reflected in the marks available for

its assessment.

100

Although there is a very strong general feeling that the marks

for this assessment should be substantially increased, two reservations

have been expressed, namely:

(1) some children may feel threatened by the formal one-to-one

situation and consequently might not demonstrate their true

capabilities;

(2) pupils who are absent on the one day designated for the oral

assessment stand to lose a high proportion of coursework

marks.

To give due consideration to the first issue, it was decided to

pursue two lines of investigation, namely:

an informal questioning of teachers who have had

experience of conducting oral assessments; and

a comparison of marks gained in the oral assessment

against marks gained in the other coursework

elements.

By considering these two aspects, i.e. behaviour and

performance, it is felt that a clear insight will be gained into how

threatening pupils regard the oral assessment and to what extent their

performance is affected. Consideration will be given to the second issue

- that of attendance patterns - in Chapter 8.

101

6.2.1 Informal Teacher Survey

The opinion of teachers, regarding the extent to which

candidates might be disadvantaged during an oral assessment, was

sought during a Certificate of Education meeting of Mid Glamorgan

teachers currently following the course. Over 30 teachers were present

at this meeting, many of whom had taught the course since its

inauguration. Teachers outside Mid Glamorgan were also asked for their

opinion on this issue during in-service meetings in other counties.

Altogether, approximately one hundred teachers were asked to give an

opinion for the purpose of this research.

6.2.2 Comparison of Marks

The marks gained by candidates in the coursework elements of

the Certificate of Education course are given a variety of weightings for

the final assessment. For the purpose of this comparison, each

coursework mark was converted to a percentage of the total possible

mark for that element of the coursework.

The percentage scores gained by candidates in all elements of

the coursework are shown in Tables 6.2 to 6.6. From these tables a

distribution of 'highest coursework scores' was extracted. This shows

in which elements of the coursework pupils scored their highest (or

joint highest) marks.

Using these statistics, conclusions were drawn regarding the

pupils' ability to demonstrate positive achievement in the oral

assessment.

102

Table 6.2 Percentage Coursework Marks for School 1

Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module Test

2545424450579

5312485248383755536365756172635556556465654955686751141120215332634422522863153575

Intermediate Test

3834441711525149*

41414344263941533944767337511676702740524640474428*6*

54*

23116**30*3779

Practical Assessments

677567586767

100100

*100100100100100100100100100100929210067

1009275677575838392585042334275100100100100100100100

*50

100

. Oral Test

**

86***

8686

10086*

71***

10010010010086

10010086

100100100

*100100100

*******

86*

86**

29*86**

100

Project

00

800

40400000000000000

204040000000

60400

6000000

600000000000

103


Candidate No.

123456789

1011121314151617181920212223242526272829303132333435363738

End of Module Test

8744525567665371294853787172477763803167777562665385416768526779704440465565

Intermediate Test

6114634967685782135270787471678331712057327624436984327368378193224232227360


10083679210083677542506792928358100429250

1008392679217838

58755875927550587510092

Oral Test

10071

100100

*7186

100438671100100100100100718657

10086*

71100100100

**

10071100100

*868686

10086

Project

80800

608080806080

1006040606040800

800

601008020800

400

80604040600

2080808080

104


Candidate No.

123456789101112131415

End of Module Test

7154698543747552805215555

7258

Intermediate Test

593639861026632360261768146253


1009283

1007510010083

1008325

100*

100100

Oral Test

8657*

10057

1008671100574371*

8671

Project

2040402020208060206020600

4060

105


Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module Test

6559292744744755753665856858827784835752467045863

128445197545466667316077134652192085537

656658

Intermediate Test

6154*

1127763248772222736961767979862341403838189

335330*

82341747602355717*5315*

8157*

554027


1001005083751001001001009283

1001001001001001001001783

1008383

100508383

10058

1008392

10010067

1001002592

100757510010067

10083

100

Oral Test

7171*

71*

10057*

10086*

1008686

100*

10086***

100*

100***

57578679866493*

7171*

9357**

9371*

5786*

Project

000000000000000000000000000000000000000000000000

106


Candidate No.

123456789

10111213141516171819202122232425262728293031323334353637383940

End of Module Test

53757071464523555756495262748168445647697556747049557051457048517156525861556565

Intermediate Test

24648457436418664856475659728453624437797360765636248150116830708163585264476971


7592100929275588392838392929210092679283929283928375*

9283839283839283759292839283

Oral Test

**

100*****

86**

86868610086**

10010086

10010086

100*

100100

*86100100

**

10086868686

100

Project

0000

20000000

2040200000

4000000

4000

40000000

40000

2040

107

6.3 ANALYSIS OF RESULTS

6.3.1 Results of Teacher Survey

More than 30 Mid Glamorgan teachers were canvassed

regarding their views on whether or not pupils were in any way

disadvantaged during the oral assessment. Not one teacher felt that this

was the case. Replies ranged from:

'They know the teacher - it is not as if they are asked to talk

to a stranger'.

and 'Some candidates are initially nervous - but they soon get

over this. It does not appear to affect them'.

to 'They enjoy the attention - and doing something different. For

once they are important in the school'.

and 'There are no peer group distractions. They are eager to

show what they can do'.

Teachers outside Mid Glamorgan expressed similar views.

Among all those questioned, no reservations whatsoever have been

expressed concerning the pupil's anxiety or performance during oral

assessments.

The only concern expressed by a very few teachers was the

amount of time required to be given to the very slowest children if they

were not to be rushed into giving haphazard answers.

108

6.3.2 Anajysis of Comparison of Coursework Scores

The percentage scores gained by candidates in all elements of

the coursework are shown in Tables 6.2-6.6. To facilitate this analysis,

relevant statistics have been extracted and are displayed in Tables 6.7

and 6.8. The first of these tables shows the number of candidates from

each school who obtained their highest score (or joint highest scores) in

particular coursework elements. For example, in School 1 only one

candidate (or two percent of the sample) obtained a highest score in the

end of module test, while 17 candidates (thirty-five percent of the

sample) obtained their highest (or joint highest) scores in the oral

assessment.

Table 6.7 : Distribution of Highest Coursework Marks

School/ Sample Size

1 48

2 38

3 15

4 48

5 40

Total 189

End of Module Tests

No. 1

1 2

1 3

0

0

1 2.5

3 2

Intermediate Tests

0

0

1 7

1

0

2 1


37 77

11 29

13 87

31 65

26 65

118 62

Oral Assessments

17 35

26 68

4 27

6 13

15 37.5

68 36

Project

0

4 11

0

0

0

4 2

As can be seen from Table 6.7, a high proportion of candidates

scored their highest coursework marks in the oral assessment.

If account is taken of only those candidates who completed all

elements of the coursework, the results are as shown in Table 6.8.

109

Table 6.8 : Distribution of Highest Coursework Marks of Candidates who

completed all Elements of Coursework

School/ Sample Size

1 23

2 33

3 13

4 25

5

Total 119

End of Module Tests

No. %

0

0

0

0

0

0

Intermediate Tests

0

0

0

0

0

0


14 61

8 24

11 85

22 88

12 48

67 56

Oral Assessments

17 74

26 79

4 31

5 20

15 60

67 56

Project

0

3 9

0

0

0

3 3

As can be seen from this table, the oral together with the

practical assessemnt produced the highest coursework scores for the

greatest number of candidates, with an overall 56% of pupils scoring

highest in these elements.

The difference in results (36% to 56%) can be accounted for by

absence. It is true to say that a significant number of pupils did not

attend the oral assessment, and hence gained no marks. The effect of

absence on overall results, and recommendations regarding this, will be

discussed in Chapter 8.

110

6.4 CONCLUSIONS AND RECOMMENDATTOflg

From an analysis of the results of both the survey of teachers

and a breakdown of highest coursework scores, the following conclusions

can be drawn.

The oral assessment offers a unqiue opportunity both to

explore a pupil's understanding of mathematical concepts and

to test basic skills.

Provided sufficient time is allowed, and the assessment is

conducted by the class teacher, pupils do not appear to

regard this one-to-one situation as an ordeal.

Provided they attend the oral assessment, candidates are likely

to score higher marks on this element than on any other.

The oral assessment is undoubtedly significantly affected by

the erratic attendance pattern of the target group.

In view of the above conclusions, it would appear that the oral

assessment merits a significantly higher mark weighting in the overall

coursework assessment. However, if candidates are not to be severely

disadvantaged by non-attendance, then due consideration will need to be

given to ways of overcoming this drawback. (Further suggestions

regarding the problem of non-attendance will be discussed in Chapter

8.)

Ill

CHAPTER 7

THE PROJECT

7.1 INTRODUCTION

The project is intended as an example of the candidate's

ability to develop an individual, original piece of work over a significant

period of time. It is also intended to motivate candidates to collect and

use information and to involve them in external enquiry and sustained

thought (see Section 2.3.4, p-47).

Initially, it was intended that the area of study should be a

matter for negotiation solely between pupil and class teacher. However,

the following guidelines on the nature of a mathematical project, were

provided:

PROJECT GUIDELINES

It is suggested that the project component should adopt the following

strategy:

1. A project must be stated in the form of a question, or a

hypothesis to be tested.

2. It should take no more than 4 weeks teaching time.

112

3. All projects must be involved in a mathematical enquiry which

can be structured in the following way:

(i) A topic for study is recognised through observation,

discussion, reading or previous study. (Experience has shown

that it is helpful if the title of the study is couched in terms

of either a problem to be solved or a hypothesis or assertion

to be tested.)

(ii) The objectives of the study are defined in specific terms.

(Again experience has shown that it is helpful if the candidate

clearly recognises that the study involves a consideration of a

number of more specific problems or questions.)

(Hi) Decisions are made concerning: (a) what data are relevant to

the study, (b) how they can be collected.

(iv) Data are collected.

(v) Data are refined and recorded in the form of maps, diagrams,

etc.

(vi) Data are interpreted.

(vii) Conclusions are reached relating to the original objectives.

(In some cases these may include comments on the limitations

of the study and suggestions for further investigation.)

113

Notes for guidance on completion of

1. Copying from previously completed projects is totally

inadmissible.

2. Parental or other assistance is to be welcomed in the

gathering of material for the project; however, the actual

writing of the project should be undertaken in class to enable

the teacher to monitor the child's work.

3. Group projects are inadmissible, but children should be

encouraged to exchange information and ideas. Again the

teacher is expected to monitor carefully the work performed

by individual children.

4. Where pupils are undertaking projects on the same, or similar,

topics; it is desirable that the mathematics associated with the

topic, be unique to each pupil.

A significant number of teachers felt that these guidelines

implied the undertaking of a somewhat more ambitious individual study

than could reasonably be expected from the Certificate of Education

target group; hence the following simplified guidelines were circulated

to participating centres, together with a suggested interpretation of the

mark scheme detailed in the syllabus.

114

SIMPLIFIED PROJECT GUIDELINES

1. Pupils choose a topic of interest to them (some ideas are

given).

2. Either through discussion with the teacher, or class

discussion, mathematical ideas are associated with the topic

chosen.

3. From the above the information to be collected by the pupil is

determined.

4. The pupil then collects the information, perhaps with help from

the teacher, or other sources.

EQBMAX

Title

This is simply the title and possibly a brief written introduction.

Collected

Each item of information collected by the pupil is presented in a

suitable form, e.g. cuttings pasted into a folder, pictures drawn, a few

sentences written.

115

Mathematical Content

Associated with most items, there should be some suitable mathematical

interpretation or exercise, e.g. graph, chart, simple arithmetic problems.

It is suggested that the project is marked out of 25, and scaled

afterwards. If this is done the given mark scheme in the syllabus

would be interpreted as follows:

Mathematical content - as defined above - 10 marks

Presentation - general impression of layout - 5 marks

Originality - material collected by the pupil - 5 marks

Accuracy - accuracy of the mathematics contained in the

project - 5 marks

At present, the project accounts for 5% of the total marks.

As has been previously stated, there was significant feeling among

teachers that an extended piece of work should no longer form part of

the assessment structure (see Section 3.5, pp.53-55). This however has

been resisted strongly for the following reasons:

The mathematical activities of low attaining pupils tend to be

of a very fragmentary nature - often a series of short

experiences undertaken as discrete packages of mathematics.

An extended piece of work allows pupils to experience the

ways in which mathematical ideas are interrelated to form a

116

coherent structure, and how different areas of mathematics

are brought together to solve 'real life' problems.

An extended piece of work allows pupils to extract, appraise

and interpret mathematical information which has been

gathered from realistic situations, giving them an opportunity

not only to appreciate the necessity and usefulness of

mathematics, but also to develop their own powers of selective

thinking and reasoning.

An extended piece of work offers an ideal opportunity for

pupils to work cooperatively as well as independently. During

cooperative activities, the linguistic ability of pupils is

fostered through mathematical discussion and communication.

It allows pupils to clarify their own ideas through questioning,

explaining and discussing with other pupils, and helps develop

the ability to 'say what one means, and mean what one says'.

An in-depth study is also of potential value in terms of the

development of personal qualities such as perseverance,

commitment and confidence.

Pupils in this target group have often experienced repeated

failure in being subjected to unsuitable mathematical experiences. Hence

their enthusiasm and interest in the subject will often have diminished

accordingly. Involvement in an interesting meaningful project, involving

117

manageable mathematical activity, can do much to rekindle enthusiasm

and bring meaning to the mathematics they are studying.

Therefore, as an alternative to abandoning the project, two

positive proposals were considered:

the feasibility of increasing the marks awarded for the project

the possibility of providing more detailed advice, guidelines

and exemplars of suitable project work.

7.2 INVESTIGATION

From an analysis of project work submitted in previous years

it would not appear to be the case that candidates and/or teachers are

unwilling to devote the necessary time or effort to this undertaking.

Many of the projects submitted are 'weighty tombs', the compiling of

which has obviously taken many painstaking hours, but which lack the

necessary structure. All too often the content has little or no

mathematical relevance and has involved minimal individual or

cooperative enquiry. Such work consists for the most part of pages

copied from books, pictures cut from published material, with rarely any

conclusions being drawn.

Those centres where a significant number of candidates had

failed to submit any project work were approached for reasons why this

had occurred. Most teachers cited one or more of the following reasons:

118

Uncertainty as to the form of a project (in spite of the

guidance given).

Too great an investment in time for little mathematical gain.

Uncertainty as to how much guidance they were expected to

give. (In this case most gave none, hence no projects were

produced.)

Candidates in this ability band are unable to pursue an

extended investigation.

Hence it would appear that it is not the relatively low reward

in terms of marks that is a significant factor, but rather the

uncertainty of the teacher as to the required content and mathematical

value of an extended piece of work for the target group.

7.3 CONCLUSIONS

It would appear, therefore, that merely to increase the marks

awarded for the project would not result in the required change, namely

that candidates be encouraged to undertake relevant mathematical

enquiry of an extended nature under the guidance of the class teacher.

What would appear to be needed is that teachers appreciate both the

relevance of an extended piece of work for this group, and also that

significant relevant mathematics can be involved in its undertaking.

119

It was therefore decided that for 1 year only a selection of

'directed' projects would be distributed to participating centres.

Candidates and teachers could then select one topic of interest upon

which an extended enquiry should be based.

Each 'directed' project would include the following:

Opportunity for a mathematical enquiry to be undertaken.

A need for pictorial representation of results.

Opportunity for inference to be drawn or conclusions made

from findings.

Mathematical calculation.

Further, each 'project' would also include a detailed marking

scheme for use by the class teacher.

This 'compromise' was agreed by the examining board with the

following provisos:

For 1 year, directed projects only would be eligible for

submission for examination.

120

The following year teachers/candidates would have the choice

of either submitting a directed project or one of their own

choosing.

The position would be reviewed after two years.

An example of a directed project is reproduced here.

121

Certificate of Education

MATHEMATICS

DIRECTED PROJECT

For the 1988/1990 session, candidates may submit either one of the directed projects, or aproject of their own choice. Where candidates undertake their own project a detailed mark

scheme should be prepared and kept for moderation purposes.

122

A. School Lunch Local Shop Home

Project

School Meals

Sandwiches Other

You are going to carry out a survey to find out what the pupils in your school usually have for lunch.

Ask 30 of your friends what arrangements they make for lunch.

Use their answers to copy and complete the table below.

» Type of LunchSchool LunchLocal ShopHomeSandwichesOther

Tally Number

(ii) Show your results in a suitable graph.

(Hi) Write three sentences on your findings.

B . Choose Five main meals on offer in your school canteen.

(i) Ask 36 friends which of the meals in your list they would choose for their own lunch.

Use their answers to copy and complete the table below.

Meal Tally Number

(ii) Show your results in a suitable graph.

(Hi) Write three sentences on your findings.

C. Pasty 30p ChipsMince & Onion Pie 35p Baked PotatoPizza 35p SaladCheese & Onion Pie 30p Baked BeansSausage 30p RiceCoke 20p CurryLemonade 15pOrange Juice 20p

25p 25p 30p 15p 25p 35p

Doughnut Sponge Pudding Apple Orange

lOp 20p lOp lOp

The menu above is on offer one day in a school canteen.

Turn over

123

(i) Ask five friends to choose a full meal from the menu. Write down what each of your friends chooses.

(ii) Work out the cost of each meal.

(Hi) Work out the total cost of the five meals.

(iv) What is the average (mean) cost of a lunch?

(v) How do you feel the cost of school meals compares with the cost of meals in a local cafe?

124

Project

Mark Scheme

Sections A and B

(i) Survey undertaken and table completed with completely correct transference from Tally' column to 'Number' column. (Deduct 1 mark for each arithmetic error.)

An appropriate, completely accurate graph. (Deduct 1 mark for each error up to a max. of 4.)

(Hi) A mark should be awarded for each relevant, different, accurate sentence.

Section C

(i)

Max. 16 marks each

8 (max)

5 (max)

3 (max)

Max. 18 marks

5 (max)Survey carried out with five full meals written down. (Deduct up to 4 marks for failure to collect full information.)

(ii) Correct cost of meals. (Deduct 1 mark for each arithmetic error up 8 (max) to a max. of 5 marks.)

(Hi) Total cost of all lunches. (2XM1) 2 (max)

(iv) Correct average cost of a lunch. (2)(M1) 2 (max)

(v) Sensible relevant sentence - 1 mark. 1 (max)

Total marks for project 50 (max)

N. B. Where the marking scheme states (2)(M1) this indicates that 2 marks are awarded for a correct answer. If, however, the answer is incorrect, but evidence of a correct method is indicated, then one method mark should be awarded.

125

CHAPTER 8

ATTENDANCE

8.1 INTRODUCTION

The assessment structure of the Certificate of Education Mathematics

course contains a substantial element of coursework and continuous

assessment. In all, pupils are required to complete 28 separate activities in

7 categories, the results of which count towards their final coursework

mark. This, together with the end of course examination result, will give

the total mark upon which their mathematics grade is based (see Table 2.3,

P. 49 ).

Many of the coursework activities may be completed at any time

during the two year course. However, several assessment activities -

notably the intermediate tests and the oral assessment - are undertaken at

specific times designated by the examination board.

At present, the only compulsory assessment element is the final

examination. However, candidates are required to obtain a minimum mark in

both this and the overall coursework. (Typically, the minimum mark to

obtain a pass grade is 40% in the coursework element and 40% in the final

examination, i.e. a score of 20/50 in the coursework and 30/75 in the final

examination.) If candidates are absent for any coursework assessment

which must be completed on a specified day, they are not credited with any

marks for that assessment. If candidates fail to attend the final

examination, they are unable to gain a 'pass' certificate, whatever their

coursework mark.

126

When devising this pattern of assessment, the Certificate of Education

panel were constantly aware of two conflicting factors. Firstly, the needs

of the target group were of paramount importance. As has been previously

stated (see Chapter 2, Section 2.1, pp. 29-35 ) most educationalists are

convinced that continuous assessment by the class teacher should form a

major element of any assessment structure designed specifically for less

able pupils. In the Certificate of Education this conviction is reflected with

the inclusion of end of module tests, practical activities and an individual

extended piece of work. Each of these activities, which are undertaken

during the two year period, is assessed solely by the class teacher.

However, in addition to considering the needs of the target group,

the working panel were concerned with the status of the Certificate of

Education course in the eyes of pupils, schools, parents and employers. As

such, it was strongly felt that some of the in-course assessment should be

conducted on a more formal basis than was required by the teacher

assessed elements. Indeed, to ensure credibility, it was considered that

some assessment elements should be provided by the examination board.

The majority of teachers following the course supported this opinion.

It was generally felt that if the examination board provided some assessment

elements, then this would both ease the burden on teachers in providing

their own, and serve as a moderating factor for teacher assessments.

It was decided that the assessments which could best be provided by

the examination board were the longer Intermediate Tests (which would act

as moderators for the end of module tests) and the oral assessment (which

teachers had little experience of formulating).

127

It was further decided that the nature of these assessments, which

would be undertaken by candidates in all participating centres, were such

that they should be undertaken on specified dates to be decided by the

examination panel.

This pattern of assessment does, however, have certain implications

for candidates following the course, not least in terms of their attendance

levels. Candidates who fail to attend the final examination are automatically

excluded from receiving a certificate. Those who miss the coursework

elements designated for specific days are penalised by losing a substantial

number of marks. Even those coursework elements which can, in theory, be

undertaken at any time do, in practice, require a reasonable level of

attendance as otherwise the scheme becomes too unwielding for the class

teacher to administer.

It is apparent, therefore, that the level of attendance demonstrated

by a candidate during the two years of the course may have a highly

significant effect on whether or not a pass certificate is eventually gained.

It has been decided, therefore, that before any changes or

modifications to the assessment structure are recommended, an investigation

will be undertaken into the effect a pupil's attendance might have on the

final certificate awarded.

128

8.2 RESEARCH METHOD

To undertake this investigation into the significance of attendance the

assssment results of the sample group were analysed in the following way:

i) The examination results were subdivided into the categories 'pass',

'fail 1 , 'absent'. The number of candidates who passed or failed the

coursework element was calculated for each of these categories.

ii) The coursework results were subdivided into the categories 'pass' and

'fail'. The number of candidates who failed to attend the examination

was calculated for each of the categories.

In this way it was hoped, by cross referencing the number of

candidates in each category, to highlight the proportion of candidates who

would appear to have failed to achieve a 'pass' certificate solely as a result

of being absent for the final examination.

As a second strand to the investigation, the coursework marks of the

candidates who failed the coursework element were analysed. This was done

in order to form a picture of whether or not this failure should be

attributed to scoring insufficient marks on the assessments or being absent

for a significant number of the required assessments.

8.3 ANALYSIS OF RESULTS

Total number of candidates in the sample who were entered for the Certificate of Education examination 189 (drop out rate 2%)

Total number of passes 135

Total number of failures 54

129

Table 8.1 : Number of Candidates in Each Examination Category

Categories

Final Examination

AbsentAbsentFailedFailedPassedPassed

Coursework

PassedFailedPassedFailedPassedFailed

Number of Candidatesin each Category

2123

34

1353

Table 8.1 shows the number of candidates who either passed, failed or

did not attend the final examination and the corresponding coursework

grades.

This tabulation reveals that the total number of candidates who

passed the coursework element was 159. Of these, 135 also passed the end

of course examinaiton, 3 failed and 21 did not attend this assessment.

It would appear reasonable to suppose that at least a proportion of

these 21 non-attenders would have passed had they attended the

examination.

A guide as to what proportion might have achieved a pass can be

found from consideration of those candidates in the sample who passed the

coursework and did attend the final examination.

130

Table 8.2 : Number of Candidates in each Coursework Category

Passed coursework Failed coursework

Passed Examination

135 3

Failed Examination

3 4

Absent

21 23

Total

159 30

From Table 8.2 it can be seen that 138 candidates who passed the

coursework, also attended the final examination. Of these, 135 passed.

Thus almost 98% of those candidates who passed the coursework and went

on to attend the final examination received a pass certificate. If the same

proportional representation is applied to the sub-sample who passed the

coursework but failed to attend the final examination, then approximately 20

of these (98% of 21) would have passed.

Thus it would appear reasonable to conclude that approximately 20

candidates failed to achieve a pass certificate as a result of non-attendance

at an assessment.

To formulate a picture of whether or not attendance at coursework

assessments contributed substantially to failure rate, an analysis was

undertaken of the individual coursework results of those candidates who

failed to merit a pass certificate. Inspection of Table 8.2 reveals that of

the 30 candidates who failed the coursework component, 23 did not attend

the final examination; 4 attended and failed, and 3 candidates passed.

However, as previously stated, a pass certificate is only awarded when

candidates achieve sufficient marks in both the coursework and the final

131

examination. In view of this, none of the 30 candidates who failed the

coursework could be awarded a pass certificate.

Tables 8.3-8.7 show the raw coursework marks for the sample. As can

be seen from these tables, a substantial number of pupils failed to complete

one or more of the assessments.

Tables 8.8-8.12 show the weighted marks for each coursework element,

together with the weighted final examination mark.

Table 8.13 summarises the assessment performance of the 30

candidates who failed the overall in-course assessment. This table also

details the number of attempted assessments where the candidates scored

higher than 40% of the marks available. For example, the first candidate

listed in Table 8.13 attempted 4 of the possible 7 assessments, and obtained

a mark in excess of 40% in 3 of these, the remaining 3 assessments were not

attempted. If a frequency table is constructed from these scores, the

results are as shown in Table 8.14.

132

Table 8.3 Raw Coursework and final Examination Results for School 1

Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module

275046485563705813535753424160586972836779696162617071715460757456151222235835694824573169174182

Intermediate Test

3431401510474644*

373739402335374835406866334614686324364741.36424025*5*

49*

21105**

27*

3371

Practical Assessment

898788

1212*

121212121212121212121111128

12119899

101011765459

1212121212121206

12

Oral Assessment

**6***6676*5***77776776777*777*******6*6**2*

6**7

Project

004022000000000000012200000032030000030000000003

Final Examination

*3526*

30343136*

252629**

3530*

32413842*

36343942*

39333839*

31****

29*

33*

20**

31**

45

133

Table 8.4 Raw Coursework and Final Examination Results for School 2

Candidate No.

123456789

1011121314151617181920212223242526272829303132333435363738

End of Module

9648576074735878325358867879528569883474858268735893457475577487774844516172

Intermediate Test

5513574460615174124763706764607528641851296822396276296661337384203829206654


12108

11121089568

1111107

125

116

1210118

112

1017979

119679

1211

Oral Assessment

7577*567365777

. 7756476*5777**7577*66676

Project

44034443453233240403541402043223014444

Final Examination

48163931404127466

31364640423246274211*

314438374448**

37274346173524*

4133

134


Candidate No.

123456789

101112131415

End of Module

785976934781835788571761

67964

Intermediate Test

53323577

923572154231561135648


12111012

91212101210

312

*1212

Oral Assessment

64*747657435*65

Project

122111431313023

Final Examination

37363649264044

*47241431

*3434

135


Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module

7165323048815260824072947564908592916357517749953

139250218350517374346685145157212294588

727364

Intermediate Test

5549*

1024682943692020666255687171772137363434168

304827*

74311742542350647*

4815*

7352*

503624


12126

109

121212121110121212121212122

10121010126

1010127

12101112128

12123

111299

12128

121012

Oral Assessment

55*5*74*76*7667*76**

6.5**7***446

5.56

4.56.5*55*

6.54**

6.55*46*

Project

000000000000000000000000000000000000000000000000

Final Examination

3936*

11*

442526421538424240*

4448431336*

33*

46**

4632*

4835*

4237*

3542*

4033**

4738*

363025

136


Candidate No.

123456789

10111213141516171819202122232425262728293031323334353637383940

End of Module

58827778515025616362545768818975486252768362817754607756507753567862576467607271

Intermediate Test

22587651395816594350425053657648564033716654685032227345106127637357524758426264


91112111197

1011101011111112118

111011111011109*

11101011101011109

1111101110

Oral Assessment

**7*****6**66676**7767767*77*677**766667

Project

0000100000012100002000002002000000200012

Final Examination

37423938324131344139384034404637*

39404044*

434034*

4738*

45343642*

333237453442

137

Table 8.8 Weighted Coursework and Examination Marks for School 1

Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module Tests

355566761565446677878766677756876212264752637248

Intermediate Tests

65732887*6677466867

1111682

111146876774*1*8*421**5*6

12


898788

1212*

121212121212121212121111128

12119899

101011765459

1212121212121206

12

Oral Assessment

**6***6676*5***77776776777*777*******6*6**2*6**7

Project

004022000000000000012200000032030000030000000003

Total Course- work Mark

17202915182533329

30242923202431343334363933282936342030323224292012778

32162919162016342

1642

Final Exami nation

*3526*

30343136*

252629**

3530*

32413842*

36343942*

39333839*

31****

29*

33*

20**

31**

45

138


Candidate No.

123456789

1011121314151617181920212223242526272829303132333435363738

End of Module Tests

105667768356988597937987769578679854567

Intermediate Tests

92

107

10109

1228

1112111110135

11395

1147

10135

11106

12143653

119


12108

11121089568

1111107

125

116

1210118

112

1017979

119679

1211

Oral Assessment

7577*5673657777756476*5777**7577*66676

Project

44034443453233240403541402043223014444


4226303534363339163033404038304421401737343524362640112936253744202426273937

Final Exami nation

48163931404127466

31364640423246274211*

314438374448**

37274346173524*

4133

139


Candidate No.

123456789

101112131415

End of Module Tests

868958869626186

Intermediate Tests

956

1324

104943

10298


12111012

91212101210

312

*1212

Oral Assessment

64*747657435*65

Project

122111431313023


352925422131402738261237

43735

Final Exami nation

37363649264044

*47241431

*3434

140


Candidate No.

123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748

End of Module Tests

77335856847986999966585

10019528557737925622961776

Intermediate Tests

98*24

1157

1233

11109

11121213466

6631585*

12537948

111*82*

129*864


12126

109

121212121110121212121212122

10121010126

1010127

12101112128

12123

111299

12128

121012

Oral Assessment

55*5*74*76*7667*76***7*7***4466657*55*74**75*46*

Project

000000000000000000000000000000000000000000000000


3432102018392626392521403634403340401222243021338

2728261339262531351532366

2330131140319

322922

Final Exami nation

3916*

11*

442526421538424240*

4448431336*

33*

46**

4632*

4835*

4237*

3542*

4033**

4738*

363025

141


Candidate No.

123456789

10111213141516171819202122232425262728293031323334353637383940

End of Module Tests

6888553666567898565886885686585686667677

Intermediate Tests

4101397

103

1078789

11138976

12119

11854

1282

105

11121098

107

1011


91112111197

1011101011111112118

111011111011109*

11101011101011100

1111101110

Oral Assessment

**7*****6**66676**7767767*77*677**766667

Project

0000100000012100002000002002000000200012


19293928232412263125233235374032232429373732373228103732173527333126323234293636

Final Exami nation

37423938324131344139384034404637*

39404044*

434034*

4738*

45343642*

333237453542

142

Table 8.13 Pattern of Attempted Assessments of Candidates who Failed the Coursework Assessment

Number of assessments attempted(max. 7)

432323223327642353443413723334

Number of scores inexcess of 40%

330210112113231321220111002322

143

Table 8.14 : Number of Assessment Categories Attempted and Number with Scores in Excess of 40%

Number of differentassessments attempted

1234567

Total

Number ofcandidates

17

126112

30

Number of assessments inexcess of 40%01234567

0 1250234301320001000001000010010000

5 10 960000

As can be seen from Table 8.14, a high proportion of the 30

candidates only attempted 4 or less of the available assessments. It can be

deduced from Tables 8.3-8.12 that this non-submission of assessments

occurred largely in 3 areas, namely the intermediate tests, the oral

assessment, and the project. Of these three areas, only non-submission of

the project cannot be directly attributed to absence. However, even in this

area, absence might be a significant contributory factor. If, as is usually

the case, the project is attempted towards the end of the course, then it is

true to say that the attendance rate for this target group is considerably

lower than during the preceding months.

As regards the intermediate tests and the oral assessments, absence

is the only reason for non-submission. Consequently, non-attendance

undoubtedly has a damaging effect on the final coursework mark. Whether

144

or not this absence affects the final grade is more difficult to determine

categorically.

Candidates must achieve a maximum score in the coursework element

to achieve a pass grade. If no marks are available for certain of these

coursework assessments it is impossible to state definitively what a

candidate would have achieved had he/she attended the assessment.

Nevertheless, some tentative conclusions can be made from a study of

Table 8.14 which shows the number of attempted assessments where scores

in excess of 40% were obtained.

For those candidates who completed few assessments (1 or 2) the data

is insufficient to reach any conclusions. However, for those candidates who

attempted 3 or 4 assessments, a high proportion obtained marks in excess of

40%. Since there is no evidence to suggest otherwise, it could be argued

that, had candidates attempted the remainder of the assessments, many

scores would also have been in excess of 40%, thus giving many of these

candidates an overall pass grade in the coursework element.

Hence there is some evidence to suggest that non-attendance has

made a difference to the final grade of at least a proportion of these

candidates.

145

8.4 CONCLUSIONS AND RECOMMENDATIONS

From the analysis conducted above, it can be stated with some

certainty that non-attendance at the final examination has contributed

significantly to the failure rate in the Certificate of Education course.

If this assessment were no longer compulsory, and if the proposed

higher mark weightings for several of the coursework elements were

adopted, then it would be safe to say that many of the candidates who did

not attend the final written examination would still achieve sufficient marks

to be awarded a pass certificate.

This would appear to be a desirable situation since there is no more

credibility attached to a pupil's performance in the examination than in the

intermediate tests, the practical activities, or the oral assessment.

Therefore there does not appear to be any reason for retaining the

compulsory nature of this element. Consequently it will be recommended to

the examination board that the final examination no longer retains its

compulsory nature.

Although it is more difficult to state with conviction that non-

attendance at other assessments has affected the final grade awarded, it

woudl appear sensible to maximise, as far as possible, attendance at

coursework assessments. As such, the following recommendations will be

put to the examination board.

i) The oral assessment should take place in January rather than

February/March. Attendance by the target group is much more

146

ii) Directed projects (if they are adopted) should be distributed to

participating centres at the beginning of the two year course.

Teachers can then be encouraged to begin work on these during the

early part of the course rather than at the end when attendance is

erratic. This, together with the more detailed assistance given to

teachers, should ensure that more candidates attempt the project in

future.

iii) Within this target group, many pupils have, over their secondary

school years, formed a regular pattern of non-attendance at school

examinations. If it were school policy that any tests or examinations

missed were given when pupils returned to school, then perhaps

examination truancy would be minimised. It will be recommended

therefore that, where candidates miss Intermediate Tests for no good

reason, these tests are given to candidates as 'revision' or 'past

paper' tests when they return to school. Although none of the marks

obtained can be counted towards the final assessment, pupils will gain

nothing by absenting themselves, and indeed might possibly become

aware of an opportunity missed.

147

CONCLUSIONS

This research study has considered four major issues within the

assessment structure of the Certificate of Education Numeracy Course

and the effect of attendance on a pupil's overall performance.

The following proposals have been considered, and the following

recommendations made:

i) The end of module tests should be administered in an aural,

rather than a written form. This study has shown clearly that

pupils achieve higher marks when these tests are administered

aurally rather than when they are attempted in written form. In

consequence, recommendation has been made to the examining body

that an appropriate change be made in the pattern of assessment

of the course.

ii) The marks available for the practical assessments should be

considerably increased. During the course of this study it has

been found feasible to formulate detailed assessment criteria

within the required practical activities for which specific credit

can be awarded. It has also been demonstrated that if the

practical ethos of the course is to be reflected within the

assessment structure, the marks awarded for the practical

assessments should be greater than at present. As a result of

this, it has been recommended to the examining body that the

148

detailed assessment criteria be incorporated into the Certificate of

Education syllabus, and the marks awarded for this assessment be

doubled.

iii) The oral assessment should merit a greater mark weighting. The

research findings support this proposal and recommendation has

been made to the examining body that the marks awarded for the

oral assessment be doubled. However, evidence collected during

this investigation would also suggest that the level of absence for

this assessment is relatively high. This being the case it is

suggested that the above amendment should only be made if the

date of the oral assessment is brought forward to a time during

the course when the attendance pattern of the target group is

less erratic.

iv) An individual study should continue to be part of the course.

Interrogation of teachers during this study would appear to

suggest that there is little support for the project in its present

form. However, the suggestion that the project should be

abandoned has been strongly resisted. The recommendation put

forward to the examining board is that for a trial period,

candidates should be required to submit 'directed' projects

circulated by the examining board.

It is hoped that the provision of material upon which an

individual study should be based will result in a significantly higher

submission rate for this element of the coursework. It is further

149

recommended that the position be reviewed after the two year trial

period.

The investigation has highlighted two specific issues with regard

to the effect of attendance on a candidate's final result.

The study would certainly appear to support the belief that non-

attendance at the final examination significantly lowers the pass rate for

this course. In view of this the recommendation has been made to the

examining body that the final examination should no longer form a

compulsory element of the course.

The effect of non-attendance for coursework assessments on a

candidate's final grade is more difficult to assess. The pattern of the

assessment structure is such that candidates who are absent for

coursework assessments are certain to lose valuable marks. Whether

these lost marks would be sufficient to change the final grade cannot be

stated with any certainty. However, there is evidence to suggest that

this would be the case for at least some candidates. These findings

reinforce the recommendations made to the examining board, that in

cases where assessments must be undertaken at a specified time, due

regard should be given to the attendance pattern of this target group.

The issues highlighted in this investigation have resulted in a

number of recommendations being made for changes in the assessment

structure of the Certificate of Education Numeracy Course. The

150

monitoring of the effects of these changes is an area in which future

research needs to be undertaken.

The revised Certificate of Education Numeracy Course,

incorporating the recommended changes, has now been submitted to the

School Examination and Assessment Council for approval. Interim

approval, until 1991, has been granted.

151

REFERENCES

1. D.E.S. (1982):Mathematics Counts. Report of the Committee of Enquiry into the Teaching of Mathematics in Schools. London, HMSO.

2. D.E.S. (1968):Report of the Schools Inquiry Commission, 1968. London, HMSO.

3. Lochhead, J. (1980):Interpretations of Simple Algebraic Statements. Journal of Mathematical Behaviour, Vol. 3., No. 1.

4. Clement, J. (1982):Analogical Reasoning Patterns in Expert Problem Solving. Proceedings of the Fourth Annual Conference of the Cognitive Science Society.

5. Alderman, Donald. (1979):Assessing Basic Arithmetic Skills and Understanding Across Curricula. Journal of Children's Mathematical Behaviour, Vol. 2.

6. Johnson, P.B. (1972):Mathematics as Human Communication.

7. Sewell, B. (1981):Use of Mathematics by Adults in Daily Life. Results of the D.E.S. Study into Adult Numeracy. Advisory Council for Adult and Continuing Education.

8. 10, 14, 25, 34. Denver, B., Stolz, C. and Brown, M. (1978):Low Attainers in Mathematics 5-16. Policies and Practices in Schools. School Council Working Paper 72, Methuen.

9. Buxton, L. (1981):Do You Panic About Maths? Heinemann Educational.

11. 32. Maclaughland, D. (1980):Maths for Slow Learners - An Unsolved Problem. Links, Vol. 6, No. 1.

12. 22. Hart, K.M. (1981):Children's Understanding of Mathematics 11-16. John Murray.

13. Dean, P.O. (1982):Teaching and Learning Mathematics, Woburn Press.

15. D.E.S. (1989):Mathematics in the National Curriculum. HMSO.

152

16. Piaget, J. (1952):The Child's Conception of Number. Routledge and Kegan Paul.

17. Bruner, J.S. (1965):The Process of Education. Harvard University Press.

18. Lovell, K. (1961):The Growth of Basic Mathematical and Scientific Concepts in Children. University of London Press.

19. Shayer, M., Kucheman, D. and Wylan (1976):The Distribution of Piagetian Stages of Thinking in British Middle and Secondary School Children. In: British Journal of Educational Psychology, No. 46.

20. 33, 37. Gulliford, R. (1980):Low Achievers, Some of the Issues.

21. Skemp, Richard R. (1971):The Psychology of Learning Mathematics. Penguin.

23. Vergnaud, G. (1983):Why is an Epistemological Perspective a Necessity for Research in Mathematics Education? In: Proceedings of the Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Montreal.

24. Brissenden, T. (1988):Talking about Mathematics. Blackwell.

26. Cornelius, M. (1985):The Cockroft Report: School Mathematics in the Early 1980's. In: Mathematics in School, Vol. 14, No. 5. Cambridge Educational Press.

27. Isaacson, Z. (1987):Assessment in G.C.S.E. Mathematics. In: Teaching G.C.S.E. Mathematics. Hodder and Stoughton.

28. Coaker, P.B. (1983):Reflections on the Cockroft Report. An Employer's View. In: Mathematics in School, Vol. 12, No. 4. Cambridge Educational Press.

29. D.E.S. (1988):Task Group on Assessment and Testing. Dept. of Education and Science.

30. Noss, R. et al. (1988):The Computer as a Mediating Influence in the Development of Pupils' Understanding of Variable. European Journal of Psychology of Education, 3.3.

153

31. Lester Smith, O.W. (1967):Education in Great Britain. Oxford University Press.

35. Assessment of Performance Unit (A.P.U.) (1986):A Review of Monitoring in Mathematics. 1978-1982. Dept. of Education and Science.

36. Lave, J. et al. (1984):The Dialectic of Arithmetic in Grocery Shopping. In: Rogoff, B. and Lave, J. (eds) Everyday Cognition. Harvard University Press.

38. Schonell, F.J. and Schonell, F.E. (1957):Diagnosis and Remedial Teaching in Arithmetic. Oliver and Boyd.

39. Schools Council (1975):Assessment in C.S.E.: Opinion and Practice. Evans/Methuen Educational.

40. Vernon, P.E. (1969):The Measurement of Abilities. University of London Press.

154

QUOTATIONS

Mathematics CountsD.E.S. Mathematics Counts. Report of the Committee of Enquiry into the Teaching of Mathematics in School. HMSO.

Davies (1978)Davies, R.B. Mathematics for Gifted Children. Journal of Children's Mathematical Behaviour.

Bruner (1965)Bruner, J.S. (1965). The Process of Education. Harvard University Press.

Skemp (1971)Skemp, Richard R. (1971). The Psychology of Learning Mathematics. Penguin.

Mathematical Association (1983) Interface.

Hart (1981)Hart, K.M. (1981). Children's Understanding of Mathematics 11-16. John Murray.

Vergnaud (1983)Vergnaud, G. (1983). Why is an Epistemological Perspective a Necessity for Research in Mathematics Education? In: Proceedings of the Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Montreal.

National Curriculum - Non-Statutory Guidance for Mathematics (1989) Curriculum Council for Wales.

NOBS, R. et aL (1988)The Computer as a Mediating Influence in the Development of Pupils' Understanding of Variable. European Journal of Psychology of Education 3.3.

155

CERTIFICATE OF EDUCATION SYLLABUS

MID GLAMORGAN EDUCATION DEPARIMENT IN ASSOCIATION WITH W.J.E.C.

CEETIFICATE OF EDUCATION

COURSE STUDIES

NUMERACY

COURSE COMPONENT NO. 5

^ or 6 teaching periods of 35A3 minutes duration in part or block are suggested.

RATIONALE

This course is intended for pupils who are not catered for by the present

formal examination system in mathematics. In addition to being a component

on its own right, it is also intended to provide the necessary background

to enable pupils to deal confidently with the mathematical content of the

other course modules.

Throughout the course pupils should read, write and talk

about mathematics ia a wide variety of ways. In addition, this course is

a core syllabus only. The range of work attempted should cover a wider

area than is set out, where this is appropriate. Time should be made

available each term not only to consolidate work already covered, but also

for developing practical skills, and extending those bopics in which pupils

take greatest interest.

AIMS

1. To enable pupils to achieve the basic level of numeracy necessary to

deal with mathematical situations encountered in their work and everyday

life.

2. To familiarise pupils with likely mathematical problems that they will

encounter in all aspects of life, and to give them the confidence to

apply their basic knowledge in practical situations.

3« To enable pupils to communicate mathematical ideas verbally and in

written form.

*+• To associate calculation with measurement in appropriate units, and

become familiar with the relative size of these units through practical

activities.

CONTENT

The course consists of twelve modules, each of approximately three weeks

teaching time. Suggested breakdowns of the course are set out in the

table below and shown as alternatives A and B.

YEAR 1

TEAM AUTUMN SUMMER SPRING

NUMBEROF

MODULES B

REVISION

AND ASSESSMENT

It must be stressed, however, that the above timetable is only

intended as a guide, and it is essential that this course is kect as

flexible as possible, in order that the individual needs of each school

and each pupil are catered for.

PATTERN OF ASSESSMENT

CONTINUOUS ASSESSMENT - 50%

TECHNIQUE

1.

2.

3.

Short tests completed

at the end of each module

Three intermediate

tests.

Practical test

V. Oral

5. Project

TOTAL

MARK WEIGHTING

11 x 1 11%

3x5 15%

12%

7%

5%

50%

The intermediate tests will take place in July and December each year,

on a date of which schools will be notified in advance.

FINAL EXAMINATION - 50%

It is envisaged that the final examination will take place in March of

the second year.

MODERATION

This scheme is subject to moderation by the examining body.

N.B. To be awarded a Certificate, candidates must obtain a satisfactory

mark in BOTH the coursework and the final examination.

CONIEJT

Modules

1. Addition, subtraction and

multiplication of integers.

Money

Simple vulgar fractions

Content

Multiplication tables e.g. 6 (£ doz.)

12 (doz.) 7 (days in week),

^ (weeks in 3ionth), 2 (pairs) etc.

Writing numbers in words and vice

versa. Reading meters.

Shopping, bills, bulk buying, gross

and net wage. Writing a cheque.

Idea of vulgar fractions in a

practical sense, e.g. fraction board,

paper folding.

2. Division of integers (12),

Unequal division.

Ratio

Division of money

Extension of fractions

Division up to 12. Averages (mean).

One person having more of a quantity

than another. Dividing a quantity in

a given ratio (money, compounds, alloys)

Unitary method of costing problems.

Fraction of an amount, e.g. -J Ib. bacon

costing £1.16 per Ib. ^'off in sales

etc.

3. The decimal point.

Place value.

Addition and Subtraction of

decimals.

Multiplication and division by

a whole number.

Conversion mm, cm, m, km,

go, kg.

Imperial Units.

Comparison of units of

length, weight, money,

capacity.

Conversion graphs

The point as a "separator" of whole

and parts of a whole. Comparison with

vulgar fractions.

Through idea of mm - cm, cm - m,

m - km.

Practical problems using length,

weight etc.

Decimal length, weight, divided

and multiplied (no recurring decimals).

Multiplication and division by

10, 100, 1000 etc.

Commonly used imperial units and

their comparison with metric

units of weight, length, money,

capacity, e.g. measuring self in

metres and ft in etc. Holidays,

foreign currency.

Comparisons of above through the

media of graphs. Drawing and interpretation*

Modules

5. Percentages.

Percentage - fraction

equivalence.

Percentage problems.

Contents

Idea of a percentage as "20p in the

£" etc. and also "out of 100".

Practical conversion charts, blocks

etc. showing relationship between

percentages and simple fractions.

Realistic problems e.g. H.P., discount,

borrowing money, profit, catalogue

commission etc.

6. Time.

Telling time.

Timetables

Time zones

a.m.,, p.m. and 2H hr. clock conversion.

Journey planning, reading timetables.

'Time in different countries.

7. Estimation

Use of a calculator.

Hounding off to "nearest" whole

number or nearest "convenient 10" etc.

Addition, subtraction, multiplication,

division, percentages. (Rough manual

checks always carried out).

8. Area of rectangular shapes.

Multiplication of decimal

numbers.

Area of triangle as half the area

of a rectangle or square.

Areas of floors, walls, carpets,

surrounds, etc.

Extension of above using decimal

length Cone decimal place only).

Estimating amount of decorating

materials (paint etc) needed.

Number of floor tiles and wall tiles

needed, amount of carpet etc.

9. Extension of work

on money.

Money in the home, budgeting, V.A.T.

Discussion (only) on rent, rates,

mortgages, etc. Rates of pay etc.

10. Geometry. The circle.

Scale drawings.

Angles.

Use of geometrical instruments*

Parts of circle and C = 1T d- Simple garden planning, room drawings,

placing furniture, windows, doors etc.

Use of a protractor to measure angles

and draw angles. Angle properties of

triangles and straight lines. Simple constructions.

ive numbertution in simple formulae applicable to realistic

ons. ions.

ics .bilitv.

In practical situations only, e.g. temperature.e.g. L x B = A, C = d, or similar expressed in words.

'I think of a number' type of equations, solvable by trial ancerror.Pie charts, bar charts, ideographs, weather charts, etc.Through the idea of "number of possible outcomes of aparticular event/total number of possible outcomes."

PRACTICAL WORK

Pupils will be expected to perform all of the following tasks.

1. Use a weighing scale or simple balance.

2. Use a ruler to measure in cms or inches to within one tenth

of a unit.

3« Use a tape measure to measure in metres to one hundredth of

a unit, or in feet to within one inch.

*f. Write a cheque.

5. Give the time correctly as a.m. or p.m. from an analogue display

to the nearest minute.

6. Read a twenty-four hour digital display, and interpret this

as a.m. or p.m.

7. Read a timetable,

8. Estimate capacity up to ten litres, to within two litres.

9. Read a thermometer in degrees Centigrade or degrees Farenheight,

to within one unit.

10. Measure bearings on an eight point scale 0

11. Measure distance on a map, to within ten percent.

12. Give the correct change in response to a simple bill.

ORAL

Refer to assessment section.

FINAL EXAMINATION - 50%

The final examination will consist of two written pacers of 50 minutes

and ^0 minutes duration respectively, separated by an interval of 20 minutes.

Paper 1 Section A: Simple one thought process questions.

Section 3: Multi-choice questions.

Paper 2 Longer questions in which more than one thought process

may be required and in which all calculations must be shown

on the examination paper.

The final examination will be set, and marked, externally.

ASSESSMENT

1. END OF MODULE TESTS

These tests are intended to serve two purposes:

(a) To assess the pupils' short term retention of information

and techniques learnt in each module.

(b) To provide diagnostic information for the class teacher, which

may be required for taking any necessary remedial action.

The tests are to be set and marked by the class teacher.

Each test should consist of ten short questions formulated

to test the pupils' mastery of the content of the module; and

should last for twenty minutes. The marks obtained in each

test should be recorded on the assessment sheet. Completed

scripts and a copy of each test paper are to be retained for

the purpose of moderation until the end of the course,

2. INTERMEDIATE TESTS

These tests are intended to help in the assessment of the pupils'

longer tern retention of information, and mastery of techniques.

They will also provide further diagnostic information for the class

teacher. They will be externally set, but will be marked by the class

teacher in accordance with a given marking scheme. This mark is then to

be entered on the assessment sheet. Test 1 will cover modules one to three

and will take place in December of the first year of the course.

Test 2 will cover modules four to eight, and will take place in

July of the first year of the course.

Test three will cover modules nine to eleven, and will take place

in December of the second year of the course. Schools will be notified

by the examining body of the dates on which intermediate tests are to

be conducted.

3. PRACTICAL TESTS

The practical tests are included to assess the pupils' mastery of some

elementary functions. It is suggested that the class teacher should

ask a pupil to perform a particular task at a particular time during

the course of a normal lesson. It is not necessary to test every

child in the class on the same day; neither is it necessary to set up

a formal practical examination, and test all pupils of their mastery

of each skill at the same time. However, the class teacher may conduct

practical tests in this way, during the final term of the course, if

this is thought to be desirable. A pupil who fails at a particular

task, should be retested at a later date. Such testing can take place

at any time during the course. The over-riding criterion which the

class teacher should use for awarding marks in practical tests is that

by the end of the course pupils should have mastered the skills listed,

and should have retained that mastery over a reasonable period of time.

When the class teacher is satisfied that a pupil has mastered a particular

skill, a mark can be entered on the sheet provided for assessment.

Award one mark for each skill mastered, and no mark for an unsatisfactory

performance. No fractional marks may be awarded.

Practical Work

1. Weighing scale or simple balance.

A difficult topic on which to be precise, because it will decend largely

on the equipment available in each school. If an object weighing over *k- is

to be weighed, then correct to the nearest ^COg (i.e. one decimal placed should

suffice. If an object less than 1kg. is to be weighed then correct to the

nearest 10g should suffice.

2. Ruler.

Every opportunity should be taken to discourage the practice of always

founding up or down. e.g. to the nearest whole number of centimetres.

3. Tape Measure.

Self-explanatory.

b. Cheque.

All five entries should be correct

5. Time.

Self-explanatory.

6. Time.

Self-explanatory.

7. Timetable.

The ability to read local bus and train timetables, including any changes

for Sunday operations etc., and school timetables.

When tested in examinations or intermediate tests only a small extract

of a timetable will be used.

8. Capacity.

It is hoped that by the end of the course pupils will be able to distinguish

between the capacity of containers in everyday use. Estimation should also

be judged by the use of common everyday containers e.g. large pop bottle,

ordinary household bucket, washing up bowl, oil can, or other suitable

containers.

9. Thermometer.

Self-explanatoryo

10. Bearings.

As well as reading a bearing from a given map some practical work with

a compass could be undertaken.

11. Distance on a map.

Use of a ruler to measure distance between two points 'as the crow flies'

or use of string or any other suitable device to obtain 'road distance'

between two points. Finding actual distance by using the given scale.

12. Simple bills.

Self-explanatory.

U. ORAL

The oral test is to be conducted on a specified day during the final

term of the course. It will be conducted by the class teacher on a

formal one-to-one basis with each pupil, and will consist of three

sections.

Section A - Short mental test

Section B - Longer questions where calculating aids and other mathematical equipment may be provided if required

Section C - Based on a graph, map, chart or some form of timetable

The marks for each section should be entered on the oral mark sheet

and the scaled total mark entered in the appropriate place on the

assessment sheet.

5. PROJECT

Projects will be marked by the class teacher and scaled in accordance

with the following:-

Mathematical Content 2

Presentation 1

Originality 1

Accuracy 1

The scaled mark should then be entered in the appropriate place on the

assessment sheet.

II

NOTES OF GUIDANCE FOR TEACHERS

TEACHER'S NOTES

Throughout this course the pupils should be encouraged to

compile their own reference booklet (or file) which should comprise:-

1. Multiplication tables.

2. Percentages and their equivalent vulgar and decimal fractions.

3. Weights and lengths in both the Metric and Imperial systems.

^. A -^ugh comparison of the above systems e.g. 2 Ib is slightly less

tnan 1kg.

5. Units of time.

6. Important angles and compass points.

At each stage of the course pupils should be required to deal

with written problems which they may expect to encounter in

everyday life. As an example of subtraction the reading of electricity

meters could be used. etc.

The following examples are intended to indicate depth of content,

and should not be assumed to be specimen examination questions.

MODULE 1

1. Work out k2. + 6 + 103

2. Work out 205 x 7

3. Write two thousand and thirty four in figures.

** . What is the cost of a dozen bread rolls at 7p each?

5. A coach can carry 52 people. If 18 seats are empty, how many people

ar~ on the coach?

6. Complete the following bill:-

(a) k Ib of carrots at Up per Ib ...........

(b) 2 tins of spam at 65p each ...........

(c) Total ...........

(d) How much change would you receive from a £5 note?

7. What fraction of the above diagram is shaded?

Module 2

1. 642 1 3 =

2. Divide £22.M? by 4

3. Five women share equally a bingo win of £21.50. How ouch does each woman get?

4. What is the average weekly mileage, of a salesman, if he travels 460 miles in a month? (4 weeks).

5. Fred and Robert share some money. Fred has 40p which is 10p more than Robert. How much money did they share out?

6. Two boys Bill and Ben share a paper round. If Bill delivers for 2 days and Ben for 3 days, how mich does Ben earn if they are paid £10 for the round.

7. If 4 pints of milk cost 88p, how much would

(a) 1 pint cost.

(b) 3 pints cost.

8. What is % of £2.64?

9. If a -Jib of rcast- pork costs 54p, what would 1lb of roast pork cost?

Module 3

1. What is the value of the 6 in the number

2. 0.7 expressed as a fraction is

(a) 7 (b) 7 (c) 7 (d) _i_ 10 100 7

3. How many mm in

*f. How many grams in 3kg?

5. What is the length of the line A3 in cm?

A i ife_________

em I 2 345678

6. Add together 3.5, 0.8 and 2.

7. Multiply 3.6 by k.

8. A fishing rod consists of two parts of length 0.6m and 1.7m. What

is the total length of the rod?

9. A plank of wood 3-2m long has 0.5m cut off one end. What length

of wood remains?

10. If three children have a total weight of 132.6kg, what is the average

(mean) weight of the children?

MODULE

1.

2.

3.<+.

5.

6.

7.

8.

1 km is about:-

(a) i mile (b) 1 mile (c) 5 miles

Which of the following statements is correct:-

(a) 1m is a little less than 3-t.

(b) 1m is exactly 3ft.

(c) 1m is a little mora than 3ft.

(d) 1m is exactly 1ft.

A 1kg bag of sugar weighs approximately how xaay pounds (ibs) ?

A man visiting Germany changes £20 into Marks. If £1 = 3.7 Marks,

how many Marks does he have?

£1 = 11 Francs.

A meal in France costs 55 Francs. How many pounds (£) is this?

A door is about:-

(a) 2mm high (b) 2cm high (c) 2m high (d) 2kai high).

1 litre is about:-

(a) 1 pint (b) 2 pints (c) 1 gallon (d) 2 gallons.

A woman weighing 8st. 51bs. (shown by the pointer in the diagram)

dieted to 7st 10lbs= Kow many Ibs did she Icse?

Use the above graph to change k litres into pints.

Use the above graph to change 12 pints into litres.

Module 5

1. A salesman gets 20$ of all his sales for himself. How much

does he earn on every £'s worth of goods he sells?

2. Out of every 100 cars on the road 11 have some fault with

their lights. What percentage of cars have faulty lights?

3. In an election one candidate gets ^J% of the vote. How many

people out of every hundred voted for this candidate?

^. What is 25# expressed as a percentage?

6. In a test a boy gets ^2 marks out of 50. What is the boy's

score expressed as a percentage?

7. In a class of 25 children 13 are girls. What percentage of the

class are girls?

8. What is 20# of £30?

9. What is 10# of £50?

10. A table costs £^0. If a discount of 1C# is given, how much is

the discount?

Module 6

1. How would 3«00 P« m « be shown on the twenty four hour clock?

2. What is 03.20 on the twenty four hour clock shown as on a.m.

or p.m. time?

3. How would you write 'quarter past four in the afternoon 1 ,

(a) in a.m. or p.m. time (b) on the twenty four hour clock?

k. A television play starts at 8.15 p.m. and finishes at 9.^0 p.m.

How long does the play last?

5. A train leaves Cardiff at 11.^5 and arrives in Bristol at 12.30.

How long did the journey take?

6. The time in New York is 5 hours behind the time in Cardiff. If

the time in Cardiff is 6.00 p.m0 , what is the time in New York?

7. Bus Timetable

DEPOT

High Street

Library

Bell Road

The White Swan

[a) How long does a bus take to travel from the Depot, to Bell Road?

kb) If you miss the 7.35 a.m. bus from the depot by 2 minutes, how

long will you have to wait for the next bus?

!c) If there is always the same time difference between buses leaving

the depot, what time will the ^th bus leave?

1st

7.15 a.m.

7.22 a.m.

7.30 a.m.

7.37 a.nu

7.^5 a.m.

2nd

7.35 a.m.

7.^2 a.m.

7.50 a.m.

7.57 a.m.

8.05 a.m.

3rd

7.55 a.m.

8.02 a.m.

8.10 a.m.

8.17 a.m.

8.25 a.m.

<rth

Module 7

1. What is the nearest whole number to 3.1?

2.

9.

10.

3.

5.

The calculator display shows the answer to a sum in pounds (£),

How would this be written in pounds (£) and pence?

3. What is the nearest whole number to A-,1 x 5.9?

(a) 9 (b) 20 (c) 2k (d) 25

*f. Use a calculator to work out A-.12 x 5.96

5. How would 23 be written to the nearest 10?

6. 1D# of £9.90 is about:-

(a) £1 (b) £9 (c) £10 (d) £90

7o Use a calculator to work out 10% of £9.90 exactly.

8.

3 7 . 1 2 1 6 8The calculator display drawn above, shows the answer to a sura

in pounds (£). Kow would you write the answer in pounds and pence,

to the nearest penny.

Use a calculator to work out in pounds (£) and pence, the cost of

9.5 m of carpet at £6.82 per metre.

A record costs £1.99« How many records could you buy for £12?

Module 8

1. Calculate ^.9x5

2.

What is the area of the above rectangle?

The area of the above rectangle is 50 cm . What is the area of the

shaded triangle?

One tin of paint covers 10 square metres of wall. How many tins woulc

you need to buy to paint an area of ^5 square metres?

A room is 5 m long and 3 m wide. How many carpet tiles, each of

area 1 square metre, would you need to cover the floor?

o.

/N

A

6<- icj Ul*\ ->

(a) What is the area of the part of the diagram marked A?

(b) How long is the side marked X ?

(c) What is the area of the part of the diagram marked B ?

(d) What is the area of the whole shape T \ •. '•• 3 together)

MODULE 9

1. Complete the following bill:-

(a) ...... oranges at 11p each M4p

(b) 1 Ib of butter at 64p per ^ Ib . =,..

(c) J dozen eggs at 7^P per dozen ....

(d) Total ...o

2. Tom's wage-is £12C per week. If he works for ^0 hours, how much is

this per hour?

3. A man earns £112 cer week. He spends £ of this on food. How much

does he spend on food?

^. Jane is paid £1.10 per day for a paper round. How much does she

earn a week if she works 6 days?

5. A bricklayer earns £6 per hour. He is paid overtime at time and a

half. How much does he earn for 1 hours overtime?

5. Mary earns £50 per week. She spends 10# of her wag3s on clothes.

How much does she spend on clothes?

7. In a warehouse, a stereo is marked at £200, but V.A.T. at 15# must

be added to this price. How much is the V.A.T.?

MODULE 1C

1.

Use a protractor to measure the above angle.

2. Draw an angle of 120 .

3.

What is the size -f the angle x in the above diagram?

if.

5.

Use a pair of compasses to bisect the line AB.

In the diagram, the line OA is called a

6. Draw a circle, and show on. it a TANGENT.

7.Scale:- 1 cm to 4 metres

The diagram above shows a scale drawing of a garden.

(a) Measure the line AB.

(b) what- is the actual distance from A to B?

8. N

In what direction is the line AB pointing?

9.

What is the size .of the angle a in the above diagram?

MODULE 1 1

1. Calculate 3-5

2. Simplify 5a - 8a + 6a

3. What is the probability of choosing a king from a pack of 52

playing cards?

If a king is chosen and put aside, what is the probability of

now choosing a queen?

^. Which of the following equations is the correct way of showing: -

"I think of a number, add 5 and the a-iswer is 6" '

(a) x + 1 = 6

(b) x + 6 = 5

(c) 5 x = 6(d) x + 5 = 6

What is the number?

The circumference of a circle is given by the formula C =5.

6.

7.

If Tf = and d = 3 cm, what is the circumference of the circle?

The Pie Chart above shows how the pupils in a class travel to

school. How do most pupils travel to school?

A group of children were asked which foreign countries they had

visited. Their answers are shown in the bar graph above. Use the graph

to answer the following questions.

(a) How many children had been to Italy?

(b) How many children had been to France than had been to Spain?

PROGRESS TEST 1

1. 1375 + ^7 + 99

2.

3.

6.

7.

1041 - 728

x 7

335 - 5

You spend 3&^p. How much change would you get from a

50p piece?

£5.63 + £2.07^- + £1.?2£

Which is larger, j or

8.

9.

10.

(a)

(b) MJ

(c) ^

(d)

3-

A packet of crisps costs 11-jp. Four packets would cost 8.

Find the cost of \ Ib of cheese at £1.03 per Ib. 9.

An article costs £6.23. How much change would you have

from a £10 note?

11.

12.

13.

15.

16.

17.

Write in figures, three thousand and sixty five.

How many grams are there in 1 kg?

(a) 1

(b) 10

(c) TOO

(d) 1000

J_ as a decimal is | 13- 10

(a) 0.01

(b) 0.1

(c) 1.0

(d) 10

Before a journey, the mileometer of a car shows 33S>65.

At the end of the journey it shows 3^168. Hew long is the

journey?

A salesman drives ^92 miles in *f days. What is his 15.

average (mean) daily mileage?

One day a cafe used 3^ dozen eggs. How many eggs is this? | 16.

A car travels 23 miles on 1 gallon of petrol. How many j 1?.

miles will it travel on 7 gallons of petrol?

18.:

iWhat fraction of this shape is shaded.

13.

19. Safety pins are 1p each, or 86p for a box of 100. Eow

much would you save by buying a box instead of 100 loose

pins?

19.

20. A plb bag of pork chops costs £4.90. How much is this

per Ib?20.

21. A shop is having a "half price sale". What would be the

sale price of a record player originally costing £68-50?

21.

22. What is the value of the figure 7 in the number

(a) 7

(b) 710

(c) 1

(d)100

22.

23. Change 1cm into mm. 23.

Ib of ham costs *f2p. How much would 1 Ib of ham cost? 2k.

25. Which is longer, 15cm, 150m or 1.5km ?

26. Calculate 7.82 x 10

21. At the end of October, John's bank balance was £75.37. 27.

On November 1st he paid by cheque for a pair of jeans

costing £21. kj>. What was his new balance?

28o Tom and Peter cleaned windows to earn pocket money. 28.

Tom worked for 2 hours and Peter worked for 1 hour.

They earned £6 between them. How much of this did

Tom earn?

29. To make a cake you need 2kg of flour, 0,75kg of sugar and 29.

0.6 kg of margarine. What is the total weight of the cake?

30. 5 oranges cost 'fOp. Find the cost of 9 oranges.

PROGRESS TEST 2

1. How many minutes are there in

one a.id a quarter hours? 1. T.l.li

2. What is the area of a room 8m long by 6m wide? 2.

J>., How many tee-shirts at £1.98 each can be bought

for £10?

. Cha.ige £ to a percentage.

5. A yard of material is

(a) just under 1 m

(b) exactly 1 m

(c) just over 1 a

(d) exactly J> m

6. Write down 5.8 to the nearest whole number., 6.

7. \ What is the area of the shaded triangle.

ffc/vt———»

7.

8. The exchange rate for a man holidaying

in America is £1 = 1.^2 dollars,, How

many dollars would the man have for £6? dollarso

9. "Top of the Pops" starts at 7.25 p.m.

and ends at 8.08 p.m. How many minutes

does the programme last? oons.

10. A catalogue offers commission of

How many pence commission would an agent

receive for selling goods worth £1? 10. 13.

11. BUS TIMETABLE

Mondays to Fridays

TETLEY BUS STATION

HIGH STREET

THE HOPE AND GLORY

THE LIBRARY

3AKEWELL ROAD

THE COMMON

RIDGEWAY FASM

08.30

08.37

08. ̂ 7

080 52

08.58

09.05

09.16

09.15

09.22

C9.32

09.37

39.^3

09.50

10.01

10.00 .....

10o07 .....

10.17 .....10.22 . .=,,

10.28 ..o.o

10.35 .....10.^ ...0.

Use the above timetable to answer the

following questions.11. (i)At what time should the next bus after 10 o'clock

leave Tetley Bus Station?

(a) 10.15

(b) 10.30

(c) 10.45

(d) 11.00 11. (i)

11. (ii)

How long does it take to travel from the

High Street to the Common? n.(ii)

11. (iii)

The 10.00 bus leaves Tetley Bus Station

5 minutes late. If it makes up 3 minutes

on it's journey, what time would it arrive

at Ridgeway Farm? 11. (iii)

12 0 A catalogue allows you to pay for the

goods you buy over a 30 week period. If

you bought goods worth £58 .Vj, ABOUT how

much would you pay each week?

(a) £1.50

(b) £2.00

(c) £2.50

(d) £3.0012. £

13.

It*

Use the above graph to change 5kg into

pounds.13.

Which whole number is the

nearest to 6.9 x 3>1

(a) 9

(b) 10

(c) 13

(d) 21 Ht.

In a youth club there are 50 children.

23 of them are boys» What percentage

are boys? 15.

16.k 2 . <f 3 2 7

The above calculator display shows

the answer in pounds (£) to a problem.

What is the answer to the nearest

penny? 16.

17.

A woman weighs 9 stone 3 Ibso She

decides to lose 6 Ibs. before going

on holiday. What weight would she

be if she did this?

(1 stone pounds) 17.

13. There are aoout 8 km to 5 miles. About

how many kilometers would you have travelled

if you had covered a distance of 15 miles?

19o A car travels 7 km on 1 litre of petrol.

How many complete^ litres of petrol would

you need to buy for a journey of 75 km.

19.

20. Find y$> of £20. 20,

21.

flA_

<- ^.C^l

n-^

21. (i) In the above diagram work out the area of the part marked A.

21.

21.i)

21. (ii) What is the length of the side marked L?

21. (iii) Work out the area of the part marked B.

21. (iv) What is the area of the whole shape? 21.iv)

22. A T.V. set costs £300. To buy it on hire 22.

purchase (H.P.) you would have to pay a

deposit of 15# of the cash price. How

much would the deposit be?

23. ENGLISH 62 out of 100 23.

HISTORY 1? out of 25

MATHEMATICS 32 out of 50.

The table shows some of Colin Jones'

examination results<, In which of the

three subjects did he do best?

2k. A man's watch is 7 minutes slow. A film 2k.

starts at 8.05 p.m. and he arrives at

8.02 p.m. by his watch. How many minutes

of the film has he missed?

25. A second-hand car dealer bought a car 25.

for S&OO, and made a profit of 1?# when

he sold it. How much profit did he make?

MID GLAMORGAN EDUCATION DEPARTMENT

CERTIFICATE OF EDUCATION

NUMERACY

COURSE COMPONENT NO. 5

INSTRUCTIONS FOR CONDUCT OF THE ORAL EXAMINATION

Four packages of oral questions are provided: A, 3, C, D.

Questions in package A are given to the first pupil on the list.

Questions in package B are given to the second pupil on the list etc.

N.3. Each pupil answers questions from only one package.

The examination consists of three parts.

SECTION 1

Mental Exercises

The examiner reads the questions singly to the pupil, repeating the questions

as necessary.

Questions 1 to k may be given in whatever form is commonly used to the pupil. For example (?0 + 2?, "seventy and twenty seven"/"seventy plus twenty seven, etc.)

This is a mental exercise, no calculating aids or writing materials are to be used.

A half mark is to be awarded for each correct answer.

SECTION 2

For this section calculating aids and writing materials may be used.

Pupils' answer sheets are provided for these questions.

Pupils or examiners record most answers en these sheets. In many cases, answers to the earlier questions are used later. Examiners should indicate these answers to the pupil when appropriate.

The questions may be repeated to the pupil as often as necessary.

SECTION 3

For this section pupils should be given the relevant sheet.

For this section calculating aids and writing materials may be used.

The member of staff conducting the oral examination should complete the Mark

sheet for Oral Examination for each pupil.


CoE 19/5/B

MATHEMATICS

ORAL TEST B

Question Paper Bl

EXAMINER'S SHEET

MENTAL EXERCISES

1.

1.

3.

».

39 + 7

27 - 16

4x8

18 +3

Find of 20

). John bought a record for £4.99. How much change did he have from a £10 note?

' 'Sportsview1 starts at 8.30 p.m. and ends at 9.45 p.m. How long does it last?

jib of butter costs 41p. How much is this per Ib?

Question Paper B2

EXAMINER'S SHEET

JOB ADVERTISEMENT

Give pupil relevant answer sheet.

EXAMINER

Look at the job advertisements in diagram 1 on your answer sheet. Jim sees these two advertisements for sales assistants in his local Job Centre.

He was unsure which job paid the better wages for a 40 hour week.

Q.I. How could he compare the two wages? A

EXAMINER

Q.2. If Jim takes the job in Webster's calculate how much he will earn for working a 40 hour week..1.

EXAMINER

Q.3. How much higher is the basic wage in Webster's than in Carter's? w

EXAMINER

Look at the advertisement for Webster's. It states that any overtime worked is paid at TIME AND A HALF.

EXAMINER

Q.4. What do you understand by "Time and a half?

(N£. If candidate is unable to explain, examiner gives explanation). [ £

EXAMINER

The basic wage is £2.60 per hour. (Indicate).

Q.5. Calculate the wage for 1 hour's overtime at "Time and a half." [ 1 ][M^

m's friend Peter works in Webster's. Jim asked him if he worked much overtime. Peter told Jim iat, on average, he works 6 hours a week.

1.6. What do you understand by "AN AVERAGE of 6 hours per week"? 4 (NJi. Accept any answer indicating 'about' 6 hours a week).

XAMINER

1.7. Remember the basic wage is £2.60 per hour. What would he be paid for 6 hours overtime atTime and a Half? [llfMH

2

XAMINER

(.8. What would be the total wage at Webster's for a basic 40 hour week and 6 hours overtime? [-^2

XAMINER

ook at the advertisement for Carter's.

1.9. How much would Jim earn for a basic 40 hour week and 6 hours overtime at Carter's?1,

'Jim works a basic 40 hour week and 6 hours overtime each week at Webster's, how much more 'ould he cam? L

Question Paper B2

JOB ADVERTISEMENT

PUPIL'S ANSWER SHEET

Webster's Stores

Sales Assistant Wanted basic wage £2.60 per hour

(40 hour week) Overtime • Time and a half

Carter's Stores

Sales Assistant Wanted £100 per week (40 hour week)

Overtime • £4.50 per hour

Q.2.

Q.3.

Q.5.

Q.7. 6 hours at Time and a Half

Q.8. Total wage at Webster's

Q.9. Total wage at Carter's

Q.10. Difference in wage

Question Paper B3

EXAMINER'S SHEET

TEMPERATURE CHART

Give pupil relevant answer sheet

EXAMINER

Look at the graph on your answer sheet. It shows the mid-day temperatures on 5 days during a week in June.

Q. 1. On which day was the highest temperature recorded? [1]

EXAMINER

Q.2. On which day was the mid-day temperature lowest? [l]

EXAMINER

Q.3. On which two days was the mid-day temperature about the same? [1]

EXAMINER

Q.4. The weather report on one of the days stated "today has been very much colder thanyesterday". Which day do you think this was? [1]

Question Paper B3

TEMPERATURE CHART

PUPIL'S ANSWER SHEET

,:!::: .; : . , : -

—— :^:^n^±r25'C- —— -i —— ?- -i ——— ±c

20'C if """""" 1" " "^"^ " "^

:r::x::::::::z^-

^-iillilHill!!10'C- •-• ———— r- ————— -0.1-

5*C- t-r- —— —————— ^

o-LLiiL — L] ———— I4iiMon Tue

i i i • ; 1 -4-r— -J---*- —i —— - ——— — j— —

f • 1 • ' | ' ——— [•»----• --«--L-H —— —— "-- —

—————— —— ---V- ———————— -^ ———

——— — 1-T^TfT^— —— -^

——— xnt^^feo^

Wed Thur Fri

Q.2. Lowest temperature ........................

Q.3. .................. and ..................

0.4. .........................

—— —— *— j ——— r- ——— |-M

g .' ". *^::q

_4- — i . , iii | -11. .3

•+- ———— L ±^::::

—— •!•''; • ' '-i ——— --

^^ ——

""" , + :

^t —— ——

4-- -4— p -+— 1-:-— -±^±

- -- — ̂ — — H ——— ^j — - --M_- ——— ———

±r —— i±rr_ ————

PBOJECT

It is suggested that the project component should adopt the following strategy:

1. A project must be stated in the form of a question, or a hypothesis to be tested.

2. It should take no more than k weeks teaching time.

3. All projects must be involved in a rnathematical enquiry which ca.i be structured in the following way.

A topic for study is recognised through observation, discussion, reading or previous study. (Experience has shown that it is helpful if the title of the study is couched in terms of either a problem to be solved or an hypothesis or assertion to be tested.

The objectives of the study are defined in specific terms. (Again experience has shown that it is helpful if the candidate clearly recognises that the study involves a consideration of a number of more specific problems or questions).

Decisions are made concerning: (a) what data are relevant to the study, (b) how they can be collected.

Data are collected.

5

Data are refined and recorded in the form of maps, diagrams, etc.

Data are interpreted.

7Conclusions are reached relating to the original objectives. (In some cases these may include comments on the limitations of the study and suggestions for further investigation).

Notes for guidance on completion of projects

1. Copying from previously completed projects is totally inadmissable.

2. Parental or other assistance is to be welcomed in the gathering

of material for the project; however, the actual writing of the

project should be done in class to enable the teacher to monitor

the child's work.

3. Group projects are inadmissable, but children should be encouraged

to exchange information and ideas. Again the teacher is expected

to monitor carefully the work done by individual children.

Where pupils are undertaking projects on the same, or similar,

topics; it is desireaole that the mathematics associated with

the topic, be unique to each pupil.


CoE 5/1

NUMERACY (PAPER I)

(50 Minutes)

Page

2

3

4

5

6

7

8

9

10

11

12Total Mark

For Examiner's use only.

Total mark pier page

Centre Number

Candidate's Name (in full)

Candidate's Examination Number

Date of Examination

All questions should be answered. Answers Thbuld be written in the spaces provided.

Scrap paper may be used for rough working.

No certificate will be awarded to a candidate detected in any unfairpractice during the examination.

SECTION A

7 mark will be given for each correct answer.

1. Calculate 273 + 649

2. Calculate 2429 - 671

3. Calculate 213 x 4

4. Calculate 642 r 3

5. Calculate 37p + 24p + 8p

6. Calculate £3.17 - £1.65

7. How much change should you have from 20p if you spent 15-ip.

8. Write in figures, three thousand and sixty four.

9. Seven packets of crisps cost 84p. How much does one packet cost?

10. What fraction ofthis shape is shaded?

11. There are 36 children in a class, 4 of them are girls. How many girls are there in the class?

12. How many centimetres are there in 1 metre?

Write your answers in this column.

10.

11,

12.

13. What is the length of the line AB?

1 2 3 4 5cm

13.

14. A man cuts 1*9 m off a piece of wood 3*5 m long. What length of wood remains? 14.

15. A man's gross weekly wage is i 127. Hisdeductions are *34. How much is his net wage? 15.

16. A car travels 42 miles on one gallon of petrol. How far would it travel on 5 gallons of petrol? 16.

17. Use the graph shown to convert i 15 to Francs. 17.

140

FRANCS

100

80

60

40

20

10 15

POUNDS (£)

20 25 30

/ Turn over

18. 31 out of every 100 cars tested had poor brakes. What percentage of cars had poor brakes?

18.

19. How many minutes are there in 1-i-hours? 19.

20. Calculate the size of the angle marked x.

20.

21. A coach will carry 50 people. How many simflar coaches would be needed to carry 230 people?

21,

22. Express 3»7 correct to the nearest whole number.

22.

23.

D

3m

7 m-.1

ABCD is a rectangle. Calculate its area.

24. The temperature in a deep freeze is -10*C. The room temperature is 17-C. How much warmer is the room than the deep freeze?

25. A man earns £2.35 per hour. How much would he earn in 8 hours?

23.

24.

25.

,*C

SECTION B

7 mark will be given for each correct answer.

In each of the following questions, four answers are given. However only one of these answers is correct. Choose the correct answer and write it in the space provided.

1. 880 - 44 -

(a) 836

(b) 844

(c) 846

(d) 920

2. What is the value of the figure 4 in the number 13*47?

(a) _4_ 100

(b) _4_ 10

(c) 4•

(d) 40

3. What is the answer to 3-4 x 2-1?

(a) 1.02

(b) 4-08

(c) 7«14

(d) 71-4

/ Turn over

4. Which of the graphs shown below matches the statement: "prices have not changed this year"?

(a) RRict

(b) PRICE

( c ) PRICE

(d) PRICE

TIME

TIME

TIME

TIME

5. How many grams are there in 5*1 kg?

(a) 51 g

(b) 510 g

(c) 5100 g

(d) 51000 g

6. Which of the following whole numbers is nearest to 7- 9 x 4« 1?

(a) 12

(b) 28

(c) 32

(d) 40

7. What is the cost of a dozen eggs at 4i.p each?

(a) L2p

(b) 48rp

(c) 54p

(d) 486p

8. In the diagram shown below, what fraction is shaded?

^

(a) I 5

(b)

(c)

9.

_ 12

57

5If a calculator is1 used to work out f25.14 the display shows:

T 8,

3 < , 1 4 2 5

What would the answer be to the nearest penny?

(a) 3p

(b) *3.00

(c) *3.14

JE314.25

[Turn over

10.

10.

The line AB in the above diagram is called:

(a) a tangent

(b) a chord

(c) a radius

(d) a diameter

11. How would quarter'past seven in the evening be shown on a 24 hour dock?

(a) 07.15

(b) 7.15pm

(c) 17.15

(d) 19.15

12. 1 kg is approximately equal to:

(a) 1 Ib

(b) 2 Ib

(c) 10 Ib

(d) 1000 Ib

11,

12.

13. A boy was given a mark of 42 out of 50 in anexamination. What would this be as a percentage?

(a) 21%

(b) 42%

(c) 84%

fd) 92%

13.

14. A box contains 8 balls; 5 red ones, and 3 green ones. What is the probability of picking a green ball?

(a) I 8

(b) 3 8

(c)

(d).

14.

15. There are 10-9 Francs in i\. francs are there in £5?

(a) 15'9

(b) 50

(c) 55

(d) 545

About how many

15.

Turn over

10

16. North

In which direction does the line from A to B point?

fa) NE

(b) SE

(c) SW

(d) NW

17. What is the area of a square of side 7 cm?

(a) 14 cm 2

(b) 28 cm 2

(c) 49 cm 2

(d) 77 cm 2

18. How many minutes are there from 1.35 pm to 2.15 pm?

fa) 0.80

(b) 40

(c) 50

(d) 80

17.

18.

11

19. Which is longest?t

(a) 30 mm

(b) 3 cm

(cj 300 m

(d) 3 km

19.

20. A girl earns *75 per week, wages. How much is this?

(a) fO.75

(b) 17. 50

(c) HO

(d) f750

She saves 10% of her

20.

21. The diagram below shows a ladder leaning against a wall. What is the size of the angle the ladder makes with the wall, marked x in this diagram?

Wall

21.

(a) 42-

(b) 48°

(c) 58 *

(d) 138°

[Turnover

12

22. How many films of length 17 hours each, could be recorded on a video tape which runs for 8 hours?

(a) 4

(b) 522.

(c) 6

(d) 7

23. John and William share 40p so that John haslOp more than William. How much does John have?

(a) lOp

(b) 20p23.

(c) 25p

(d) 30p

24. The total takings in a shop for 6 days during one week were £3420. What was the average (mean) daily takings?

(a) £490

(b) £57024.

(c) £3426

(d) £20520

25. 7x0=

(a) 0

(b) 725.

(c) 70

(d) 700


CoE 5/2

NUMERACY (PAPER II)

(40 Minutes)

Page

2

3

4

5

6

Total Mark

For Examiner's use only.

Total mark per page

Centre Number

Candidate's Name (in full)

Candidate's Examination Number

Date of Examination

All questions should be answered.Answers should be written in the spaces provided, all working must be shown.

Calculators may be used.

No certificate will be awarded to a candidate detected in any unfair practice during the examination .

1. (a) Complete the following bill.*

3 oranges at lip each

1 Ib of butter at 64p per \\b

-j-doz. eggs at f?6p per dozen ...............

TOmL ............... [4

(b) If the bill were paid with a iS note, how much change should youreceive? i

2. I think of number and subtract 5. The answer is 9.

fa) Write this as an equation. [1]

(b) Solve the equation to find the number. [1]

3. (a) What is the probability of choosing a TEN out of a pack of 52playing cards? [1]

(b) If a TEN were chosen AND NOT REPLACED, what is the probability thatthe next card chosen would also be a TEN? [ 1 ]

4. Use a pair of compasses to bisect the angle shown below.

5. The circumference of a circle is given by the formula C » ltd. [I] Find the circumference of a circle of diameter 6 cm. (Take IT a 3-14).

i

6. A shop has three special offers this week: ( i) SOAP POWDER reduced from 39p to 33p; ( ii) TISSUES reduced from 27p to 24p; ( Hi) TOOTHPASTE reduced from 40p to 35p. How much does a woman save if she buys all three items? [ 2 ]

(Turn over

III

END OF MODULE TEST PAPERS

WRITTEN TEST 1 (A)

ANSWER ALL QUESTIONS IN THE SPACES PROVIDED

NAME CLASS

4.

5.

6.

7.

8.

9.

10.

Work out 26+3+183

A bus was carrying 47 passengers. At the first stop 9 got off. How many were left on the bus?

Find the cost of 6 bags of crisps at 13p each.

Work out 142 - 7.

What fraction of this shape is shaded?

Work out £1.26 - 49p

Peter sold 136 raffle tickets and Jane sold 245 raffle tickets. How many did they sell between them?

Work out 64 x 7

Work out £2.85 x 4

A milk crate holds a dozen bottles. How many bottles of milk would there be in 8 full crates?

3.

4.

5.

6.

7.

8.

9.

10.

AURAL TEST 1 (A)

1. Work out 26 and 3 and 183.

2. A bus was carrying 47 passengers. At the first stop 9 got off. How many were left on the bus?

3. The bag of crisps in diagram 1 costs 13p. How much would 6 bags of crisps cost?

4. Work out 142 take away 7.

5. Look at diagram 2 on your answer sheet. What fraction of the shape is shaded?

6. Take 49p from 'one pound twenty six pence'.

7. Peter sold 'one hundred and thirty six' raffle tickets. Jane sold 'two hundred and forty five' raffle tickets. How many tickets did they sell between them?

8. Work our 64 times 7.

9. Work out 'two pounds eighty five' times 4.

10. A milk crate holds 1 dozen bottles of milk. How many bottles of milk would be in 8 full milk crates?

PUPILS' ANSWERS SHEET - AURAL TEST 1(A)

1.

2.

3. Crisps 13p 1

passengers

4.

diagram 2

raffle tickets

8.

9.

10. bottles of milk

WRITTEN TEST 2(A)


NAME ______________________ CLASS ___

1. Work out 627 + 3 1.

2. Peter and John went fishing. Peter caught 7 fish and John caught 2 more fish than Peter. How many did they catch between them? 2.

3. 4 Mars Bars cost 64p.

(a) How much would 1 cost? 3(a)

(b) How much would 7 cost? 3(b)

4. What is i of 32? 4.

5. The table shows how much Susan spent on school lunches every day for a week.

MON TUE WED THUR FRI 47p 56p 61p 54p 52p

(a) How much did she spendaltogether? 5(a)

(b) What was the average (mean)amount that she spent each day? 5(b)

6. Find the cost of ilb of cheese at£1.28 per Ib. 6. .

7. To make concrete, sand and cement are mixed in the ratio 3 to 2. How many buckets of sand would be needed to mix with 8 buckets of cement? 7 - .

8. Find the cost of ilb of ham at£1.80 per Ib. 8. .

AURAL TEST 2 (A)

1. Work out 'six hundred and twenty seven' divided by 3.

2. Peter and John went fishing. Peter caught 7 fish. John caught 2 more fish than Peter. How many fish did they catch between them?

3.

(a) 4 Mars Bars cost 64p. How much would 1 Mars bar cost?

(b) You have worked out the cost of 1 Mars bar. How much would 7 Mars bars cost?

4. 'What is "one quarter" of 32?

5. Look at diagram 2 on your answer sheet. The table shows how much Susan spent on school lunches every day for 1 week.

(a) How much did she spend altogether that week?

(b) What was the average (mean) amount she spent each day?

6. Look at diagram 3 on your answer sheet. The cheese is £1.28 per pound. How much would i Ib of this cheese cost?

7. Look at diagram 4 on your answer sheet. To make concrete, sand and cement are mixed in the ratio 3 to 2. How many buckets of sand would you need to mix with 8 buckets of cement?

8. Look at diagram 5 on your answer sheet. The ham is 'one pound eighty' per pound. How much would i Ib of this ham cost?

J9dWVH

PUBS

(q)

UJBJBBtp

U1BJ6BLP

d99anni Q3M am NOW

'9

'9

(q)(8)

is3i ivynv -.siidnd

WRITTEN TEST 3(A)


NAME _________________________ CLASSA

I iI i

BI

I

F | cm 1 2 3 * 56 7

What is the length of the line AB? 1.

2. How many grams are there in 2kilograms? 2.

3. Work out 0.8 x 3 3.

4. A carpenter has a piece of wood 10m long. He cuts 1.7m off one end. What length of wood does he have left? 4.

5. What is the value of the 6 in the number 1.672

_6 _6 _6_ (a) 6 (b) 10 (c) 100 (d) 1000 5.

6. Work out 5 - 2.8 6.

7. Mrs. Jones has to post 3 parcels of, 1.2kg, 0.75kg and 2kg. What was the total weight of her parcels? 7.

8. Work out 1.8 * 3 8.

9. To make a picture frame, Mr. Jones needs 4 pieces of wood, each 0.6m long. What length of wood does he need altogether? 9.

10. John and Sam are weightlifters. John can lift 107.1kg and Sam can lift 86.75kg. How many more .kg (kilograms) can John lift than Sam? 10-

AURAL TEST 3(A)

Look at diagram 1 on your answer sheet. What is the length of the line AB?

How many grams are there in 2 kg?

Work out 'nought point eight' times three.

look at diagram 2 on your answer sheet. A carpenter has a piece of wood 10m long. He cuts 1.7m from one end. What length of wood remains?

Look at the number 1.672 in Box 3 on your answer sheet. What is the value of the six: Is it

(a) 6 (b) six tenths (c) six hundredths (d) six "thousandths?

Work out 5 take away 2.8

Look at diagram 4 on your answer sheet. Mrs. Jones has to post 3 parcels of 1.2kg, 0.75kg and 2kg. What was the total weight of her parcels?

Work out 1.8 divided by 3.

To make a picture frame, Jane needs 4 pieces of wood each 0.6m long. What length of wood does she need altogether?

John and Sam art,welghlifters. John can lift 107.1kg, Sam can lift 86.75kg. How many more kg can John lift then Sam?

PUPILS' ANSWER SHEET - AURAL TEST 3(A)

ccm 1 2 3 4 3 6

diagram 1

2. __________ g

3. __________

4.

diagram 2

5.1.672

box 3

6.

7. [ 1.2 kg| j 0.75 kg[

diagram 4

8.

9.

10.

m

2 kg

m

kg

kg

WRITTEN TEST 4(A)


NAME CLASS

1. 1 metre Is about the same as (a) 1 foot, (b) 1 inch, (c) 1 yard, (d) 1 mile

3.

4.

st/lb

A woman who weighed 10 st. 6 Ib. dieted until she weighed 9 st. 8 Ib. How many pounds (Ib) did she lose?

If £1 = 2.24 dollars, how many dollars could I have for £7?

A bottle holds 2 litres of pop. If 0.6 litres are emptied out, how much pop is left?

Ift

99

5.»e

to

is

Use the graph to change £6 Into franco.

10.

litre jug^•jV< ft

A measuring jug is graded in pints and litres. On the scale, how many pints are the same as 2 litres? 10.

AURAL TEST 4(A)

1. Which of the following is about the same as 1 metre:(a) 1 inch, (b) 1 foot, (c) 1 yard, (d) 1 mile?

2. Look at Diagram 1 on your answer sheet. The scale shows John's weight at 10 stone 6 pounds. He dieted until he weighed 9 stone 8 pounds. How many pounds did he lose?

3. Look at Box 2 on your answer sheet. The rate of exchange from pounds to dollars is £1 to $2.24. If you changed £7 into dollars, how many dollars would you have?

4. Look at Diagram 3 on your answer sheet. The diagram shows a full 2 litre bottle of pop. If you poured out 0.6 litres of pop, how much would be left in the bottle?

5. Look at the graph in Diagram 4 on your answer sheet. It can be used to change pounds into francs. From the graph, how many francs would you have for £6?

6. Look at Diagram 5 on your answer sheet. What is the weight of the parcel on the scale in kilograms,

7. Which of the following is about the height of a door? (a) 2mm, (b) 2cm, (c) 2m, (d) 2km?

8. Look at Diagram 6 on your answer sheet. 1 Ib is about the same as 0.45 kg. What would be the weight in kg of the 10 Ib bag of flour?

9. Look at Diagram 7 on your answer sheet. The graph can be used to change degrees centigrade (Celcius) into degrees Fahrenheit. What would a temperature of 5°C be in degrees Fahrenheit?

10. The measuring jug in Diagram 8 is graded in pints and litres. On the scale, how many pints are the same as 2 litres?

PUPIL'S ANSWER SHEET - AURAL TEST 4(A)

1.

St/lb

Diagram 1 Ib

3. £1 $2.24

Box 2

V '

4.

Diagram 3 litres

FRANCS

5.

140

120

100

80

60

40

20

10 15 20

POUNDS^)

25 30

Diagram 4

Diagram 5

francs

kg g

1 Ib •• 0.45 kg

Diagram 6

V* <1«

If)o

'f*u>

It

10

r

Diagram 7

10.-f

-1

• 0-4

Diagram 8 pints

WRITTEN TEST 5(A)

1. A woman who runs a catalogue earns 12p in the pound (£) commission on everything she sells. What percentage (%) is this?

2. A man bought a box of 100 tiles. 11 of them were broken. What percentage (%) were broken?

3. Write down 0.5 as a percentage.

4. A boy scores 19 out of 50 in a test. What percentage (%) is this?

5. In a cafe 43% of the customers ordered coffee. If there were 200 customers in one day, how many of them ordered coffee? 5. ___________ %

6. Write down -r as a percentage (%). 6. __________ %

7. In a class of 25 children, 12 are girls. What percentage are girls?

(a) 12% (b) 13% (c) 24% (d) 48% 7. __________ %

8. A shop is having a closing down sale. They offer 50% off all goods. How much would you pay in the sale for a coat which costs £42 before the sale? 8. £_

9. What is 20% of £100? 9. £_

10. To buy a stereo costing £300 on H.P. Mr. Smith must pay a 10% deposit. How much is the deposit? 1°- L.

AURAL TEST 5(A)

1. A woman who runs a catalogue earns 12p in the pound commission on everything she sells. What percentage is this?

2. A man bought a box of 100 tiles. 11 of them were broken. What percentage were broken?

3. Write down 0.5 as a percentage.

4. Look at Diagram 1 on your answer sheet. John scores 'nineteen out of fifty 1 in a test. What percentage is this?

5. In a cafe, 43% of the customers order coffee. Oneday, the cafe had 200 customers. How many of these would you expect to order coffee?

6. Write down one quarter as a percentage.

Look at Box 2 on your answer sheet. In a class of 25 children, 12 are girls. Which of the figures in the box shows the percentage of girls in the class. Is it:

(a) 12%, (b) 13%, (c) 24%, (d) 48%?

8. Look at Diagram 3 on your answer sheet. A shop is having a closing down sale. They offer 50% off all goods. How much would you pay in the sale for the coat which cost £42 before the sale?

9. What is 20% of £100?

10. Look at the stereo in Diagram 4 on your answer sheet. The cash price is £300. To buy the stereo on Hire Purchase you would need to pay a 10% deposit. How much is the 10% deposit?

1.


John

Test

Smith 11319 50

Diagram 1

5.

6.

customers

12% 13% 24% 48%

Box 2

Diagram 3

10.H.P. deposit

10%

Diagram 4

Cash price £300

WRITTEN TEST 6(A)

1. How would "ten minutes past seven in theevening" be shown on a 24 hour clock? 1.

2. Write "20 minutes to five in the afternoon"as time in figures (a.m. or p.m. time). 2.

This is part of Monday 1 T.V. timetable:

3.10 p.m. Sons and Daughters3.45 p.m. Cartoon Time3.50 p.m. News4.10 p.m. Doctor Who4.45 p.m. Blockbusters

Use the timetable to answer the questions below.(a) How many minutes does Sons and

Daughters last? (a)_

(b) Which programme lasts for5 minutes? (b)

(c) Blockbusters is on for 20 minutes. What time does it end? (c)

4. 15 . 57

This is the time on John's digital watch, but it is 5 minutes slow. What is the real time?

5. DEPOT 7.14 7.44 8.14HIGH ST. 7.30 8.00 8.30FERN ST. 7.36 8.06 8.36LIBRARY 7.45 8.15 8.45TOWN HALL 7.55 8.25 8.55WHITE HART 8.10 8.40 9.10

This is part of the morning timetable for Hilltown buses. Use it to answer the questions below.

WRITTEN TEST 6(A) Continued

(a) The buses leave the Depot every 30 minutes. What time would the fourth bus leave the Depot? (a)

(b) John lives in Fern St. and works at the Town Hall. He starts work at 8.30 a.m. What is the latest time he could catch a bus at Fern St.? (b)

(c) Peter lives in High St. He catches the 7.30 a.m. bus to work and gets off at the Library. He works in a factory 8 minutes walk from the Library: What time does he get to work? (c)

AURAL TEST 6(A)

1. How would "ten minutes past seven in the evening" be shown on a 24 hour clock?

2. Write "20 minutes to 5 in the afternoon" as time in figures, Don't forget a.m. or p.m.

3. Look at Box 1 on your answer sheet. This is part of a T.V. Timetable. Look at the Timetable.

(a) How many minutes does "Sons and Daughters" last?

(b) Which programme lasts for 5 minutes?

(c) "Blockbusters" is on for 20 minutes. What time does it end?

4. Look at Box 2 on your answer sheet. It shows the time on John's digital watch. However, his watch is 5 minutes slow. What is the real time?

5. Look at Box 3 on your answer sheet. It shows part of a morning timetable for HILLTOWN buses.

(a) The buses leave the Depot every 30 minutes. The timetable shows the leaving times of the first three buses. What time would the fourth bus of the morning leave the depot?

(b) John lives in FERN ST. and works at the TOWN HALL. He starts work at 8.30 a.m. What is the latest bus he could catch at FERN ST.?

(c) Peter lives in the HIGH ST. He catches the 7.30 a.m. bus to work and gets off at the LIBRARY. He works in a factory 8 minutes walk from the Library. What time does he get to work?

1.

2.

3.


3.10 p.m. 3.45 p.m. 3.50 p.m. 4.10 p.m. 4.45 p.m.

Sons and Daughters Cartoon Time NewsDoctor Who Blockbusters

Box 1

15 : 57

(a)

(b)

(c)

mm

Box 2

DEPOTHIGH ST.FERN ST.LIBRARYTOWN HALLWHITE HART

(a)

(b)

(c)

7.147.307.367.457.558.10

Box 3

7.448.008.068.158.258.40

8.14 ....8.30

8.368.458.559.10

WRITTEN TEST 7(A)

n o u.oThe calculator display shows the answer to a sum in pounds (£). What is the answer in pence (p)?

A record costs £2.05. How many records could you buy for £10?

n o OThe .calculator display shows the answer to a sum in pounds (£). Write down this answer to the nearest penny (p).

The box shown weighs 2.976 kg. What is its weight to the nearest kg?

.83The display shows the answer to a sum in pounds (£). Write down this answer in pence (p).

At a football match, 27 152 tickets were sold. The local paper would show this number to the nearest hundred. What number would be in the paper?

The calcula a sum in p in pounds

-7 r» / . Ditor display shows the answer to ounds (£). Write down the answer (£) and pence (p). 7.

IQDQD JBOOfl

n ll

The tree is 2.9 metres high. Estimate the

g^^X height of the *\£)fS building to the

| 7 nearest metre 8 .

What is the nearest whole number to 12.8? 9.

10. Which whole number is nearest to 3.1 x 4.9?

(a) 12, (b) 15, (c) 16 (d) 20 10.

AURAL TEST 7(A)

1. Look at Box 1 on your answer sheet . The calculator display shows the answer to a sum in pounds. What is the answer in pence?

2. A record costs "two pounds and five pence". How many records could you buy for £10?

3. Look at Box 2 on your answer sheet. The calculator display shows the answer to a sum in pounds. Write down this amount to the nearest penny.

4. Look at Diagram 3 on your answer sheet. The parcel on the scale weighs 2.976 kg. What is this weight to the nearest kg?

5. Look at Box 4 on your answer sheet. The calculator display shows the answer to a sum in pounds. How many pence is this?

6. Look at Box 5 on your answer sheet. At a football match "Twenty seven thousand one hundred and fifty two" tickets were sold. The local newspaper would show this number to the nearest hundred. What number would be shown in the paper?

7. Look at Box 6 on your answer sheet. The calculator displayshows the answer to a sum in pounds. Write down this answer in pounds and pence.

8. Look at Diagram 7 on your answer sheet. The tree is 2.9m high. Estimate the height of the building to the nearest metre.

9. What is the nearest whole number to 12.8?

10. Look at Box 8 on your answer sheet. Which of the numbers shown is nearest to 3.1 'times' 4.9?

1.


0.0 8

Box 1

2. records

3.

4.

18.72165

Box 2

Diagram 3

5.

6.

0 6

Box 4

27 152

Box 5

1 9.3

Diagram 7 m

9.

10. 3.1 x 4.9_____

12 15 16 20

Box 8

WRITTEN TEST 8 (A)

1.2.

3.

D

What is the area of the above rectangle?

A tin of paint holds enough to cover 8 square metres of wall. How many tins would you have to buy-to paint a wall of area 26 square metres?

The area of the above rectangle is 28 square metres, what is the area of the shaded triangle?

1.

2.

3.

4. A room is 3m long and 2m wide.(a) What is the area of the floor(b) A carpet tile has an area of 7 square

metre, how many would be needed to cover the floor?

4a.

4b.

4m

3m

2m

DINING ROOM

(B)

LOUNGE (A)

5m

In the diagram above:(a) What is the area of part A?(b) What is the length of the side X?(c) What is the area of part B?(d) What is the area of the whole shape?

5a. 5b. 5c.5d.

What is the area of a room 3.4m long and 3m wide? 6.

AURAL TEST 8(A)

1. Look at Diagram 1 on your answer sheet. What is the area of the rectangle shown?

2. Look at Diagram 2 on your answer sheet. The tin of paint holds enough to cover 8 square metres of wall. How many tins would you have to buy to paint a wall of area 26 square metres?

3. Look at Diagram 3 on your answer sheet. The area of the rectangle is 28 square metres. What is the area of the shaded triangle?

A room is 3m long and 2m wide.

(a) What is the area of the floor of the room.

(b) A carpet tile has an area of 7 square metre.You have found the area of the floor. How many carpet tiles would be needed to cover this floor?

Look at Diagram 4 on your answer sheet. The diagram shows a room divided into parts A and B by the dotted line.

(a) What is the area of part A?(b) Look at the side marked X on the diagram.

What is its length?

(c) What is the area of part B of the diagram?

(d) What is the area of the whole room? - Parts A and B together?

6. What is the area of a room 3.4m long and 3m wide?


Diagram 1

PAINT £4.25

large tin

COVERAGE OF AREA 8m'

5.

(a)

(b)

4m

Diagram 2

Diagram 3

2

tiles

3m

2m

DINING ROOM

(B)

LOUNGE (A)

Diagram 4

5m

tins

sq. m

(a)

(b)

(c)

(d)

cm

cm

cmz

cm 2

6.

WRITTEN TEST 9(A)

Jane earns £4.80 per week doing a paper round.

(a) She spends ^ of this at the disco. How muchdoes she spend at the disco? la.

(b) She spends | of WHAT SHE HAS LEFT on a book. How much does she spend on the book? lb

(c) How much does she have left after payingfor the disco and the book? lc.

2. John is paid £2.80 per hour. If he worksovertime he is paid TIME AND A HALF. How much is he paid for 1 hours overtime?

3. A stereo is priced at £100, but VAT at 15% must be added to this price. What is the real price of the stereo?

4. Pam earns £2.61 per hour working in a cafe onSaturdays. If she works for 8 hours, how much does she earn?

5. A Man's gross wage is £154 per week. Hisdeductions are £38 per week. What is his take home (net) pay?

6. Mary earns £4.23 per hour. When she worksovertime she is paid DOUBLE TIME. How much does she earn for 1 hours overtime?

7. Mrs. Smith needs 6 rolls of wallpaper at £3.71 per roll. How much does she pay for wallpaper altogether?

8. Mrs. Jones has £72 per week housekeeping money. She spends 1/4 of this on rent. How much does she spend on rent?

AURAL TEST 9(A)

1. June is paid £4.80 per week for a paper round.

(a) She spends 1/4 of this at a disco? How much does she spend at the disco?

(b) Remember she earns £4.80 altogether, and you have worked out how much she spent at the disco. She spends 1/3 of what she has left on a book. How much does she spend on the book?

(c) She earns £4.80 altogether. She spends someat the disco and some on a book. How much does she have left after paying for the disco and the book?

2. Look at John's payslip in Diagram 1. He is paid £2.80per hour. If he works overtime he is paid TIME AND A HALF. How much does he earn for 1 hours overtime?

3. A stereo is priced at £100, but VAT at 15% must be added to this price. What is the real price of the stereo?

4. Pam earns £2.61 per hour working in a cafe on Saturday. If she works for 8 hours, how much does she earn altogether?

5. Look at Mr. Smith's payslip in Diagram 2. His gross wage is £154 per week. His deductions come to £38 per week. What is his take-home (net) pay?

6. Mary earns £4.23 per hour. When she works overtime she is paid DOUBLE TIME. How much does she earn for 1 hours overtime?

7 Look at Diagram 3 on your answer sheet. Mrs. Smith buys 6 rolls of wallpaper at £3.71 per roll. How much does she pay altogether?

8 Mrs. Jones has £72 per week housekeeping money. Shespends 1/4 of this on rent. How much does she spend on rent?

PUPIL'S ANSWER SHEET AURAL TEST 9(A)

(a) £

(b) £_

(c) £

John Smith

Hourly rate overtime at TIME AND A HALF

1716130

£2.80

Diagram 1

Peter Smith

Gross Pay Deductions

1716131

£154 £ 38

Diagram 2

£3.71

8.

WRITTEN TEST 10(A)

1.

The line AB is (a) radius (b) diameter (c) tangent (d) circumference

2.

In the space above, draw an angle of

3.

Measure the size of the angle above. 3.

4. The circumference of a circle is found using the formula

CIRCUMFERENCE - ir x DIAMETER

If n is 3.14 and the diameter is 4cm. what is the circumference? 4.

5. Scale 1 cm to 2m

On a scale drawing a wall is shown as 8cm long. Ifthe scale is 1cm to 2m what is the real length ofthe wall? 5 --

6.

Measure the size of the angle above.

7.

In the triangle above, what is the size of the angle x?

8.

6.

7.x

In the diagram above, what is the size of the angle a? 8.a_

9.

What is the size of the angle marked

* 10.

In what direction is the line AB pointing?

9.

10.

AURAL TEST 10(A)

1. Look at Diagram 1 on your answer sheet. Is the line AB (a) a radius, (b) a diameter, (c) a tangent, (d) a circumference?

2. In the space on your answer sheet, draw an angle of 50°.

3. Measure the size of the angle in Diagram 3 on your answer sheet.

4. Look at the formula in Box 4 on your answer sheet. The circumference of a circle is found using the formula = n x diameter. Use the formula to find the circumference of a circle of diameter 4 cm. Use 3.14 for ir.

5. Look at Diagram 5 on your answer sheet. The scale drawing of a wall is 8 cm long. If the scale is 1 cm to 2m, what is the actual length of the wall?

6. Measure the size of the angle in Diagram 6 on your answer sheet.

7. In the triangle in Diagram 7 on your answer sheet, calculate the size of the angle x.

8. In Diagram 8 on your answer sheet, calculate the size of the angle a?

9. In Diagram 9 on your answer sheet, calculate the size of the angle marked with an arrow?

10. In Diagram 10 on your answer sheet, in which direction is the line AB pointing?

PUPIL'S ANSWER SHEET - AURAL TEST 10(a)

1.

Diagram 1

(a) radius(b) diameter(c) tangent(d) circumference

2. 50 C

Diagram 3

CIRCUMFERENCE = ir x DIAMETER

Box 4

ir = 3.14

cm

5. 1 1...' ' 11 1

1 11

1 1Scale 1 cm: 2m

Diagram m

Diagram 6

Diagram 7 x =

Diagram 8 a =

Diagram 9

10.

WRITTEN TEST llfAl

1 —

+10°-

+5°-

0-

-5s -

-10°-. i >

On a cold winter day the temperature was 3°C. In the night the temperature fell to -7°C. How many degrees did the temperature fall?

In a bag are 10 counters, 7 blue ones and 3 red ones. Jane takes out a counter without looking into the bag. What is the probability that it is blue?

The pie chart shows how the 400 pupils in a school travel to school each day.(a) How do most pupils travel to school?(b) How many of the pupils walk to school?

3a_ 3b

I think of a number x add 4 and the answer is 11.(a) Write this as an equation(b) What is the number x? 4b

The temperature of a pie is 9°C before it is put in a freezer. In the freezer the temperature drops 20 degrees. What is the temperature of the frozen pie? 5.

6.

6. rI II I

/S- -

r-i- i I l_ _i.

I '

Co/is/

The bar chart shows the number of computers sold (in thousands) by 5 firms.

(a) For what number does the 5 on the vertical scale stand?

(b) How many computers were sold by COMBI?

6a_

6b

(c) How many more computers were sold by J.B. than by ORBAN? 6c

AURAL TEST 11 (A)

1. Look at the thermometer in Diagram 1 on your answer sheet. On a cold winter day the temperature was 3°C. In the night the temperature fell to -7°C. How many degrees did the temperature fall?

2. Look at Diagram 2 on your answer sheet. In the bag are 10counters, 7 blue ones and 3 red ones. Jane takes out a counter without looking into the bag. What is the probability that it is blue?

3. Look at Diagram 3 on your answer sheet. The pie chart shows how the 400 pupils in a school travel there each day.

(a) How do' most pupils travel to school?

(b) Remember there are 400 pupils in the school altogether. How many of them walk to school?

4. I think of a number X, add 4 and the answer is 11.

(a) Write this as an equation.

(b) I think of a number X, add 4 and the answer is 11. What number did I think of?

5. Look at Diagram 4 on your answer sheet. The temperature of a pie is 9°C before it is put in the freezer. In the freezer its temperature falls 20 degrees. What is the temperature of the frozen pie?

6. Look at the Bar Chart in Diagram 5 on your answer sheet. It shows the number of computers sold in THOUSANDS by 5 firms.

(a) Look at the 5 on the vertical scale. How many computers does this 5 really represent?Remember the graph shows the number of computers sold in thousands.

(b) How many computers were sold by the firm COMBI.

(c) Remember the graph shows the number of computers sold in thousands. How many more computers were sold by J.B. than by ORBAN?

1.

2.

3.

4. (a)


+10°--

+5°--

0--

-5°--

-»

•10°- •V < - /

Diagraun 1

Diagram 2

Diagram 3

(b)

(a)

(b) pupils

5.

10'

0 -

-10; , ,

1

,.

Diagram 4

6.

I I

(a)

(b)

— I— —- — *i— —i — — ( c )

V

computers

computers

I I-H--r -

C01S/3".

Diagram 5

WRITTEN TEST KB)

1. Calculate 27 + 7 + 103 1.

2. There are 46 passengers on a bust. At the first stop12 got off. How many passengers are left on the bus? 2.

3. Find the cost of 5 Mars bars at 16p each 3.

4. Calculate 136-9 4.

5.

In the above diagram, what fraction is shaded?

6. Calculate £1.04 - 50p.

7. Peter had 104 records. Sue had 158 records. How many records did they have between them?

5..

6.

8. Calculate 58 x 6 8.

9. Calculate £2.68 x 3 9. £

10. A box holds 8 tennis balls. How many tennis balls would fill 9 boxes? 10.

AURAL TEST l(B)

Write all answers on your answer sheet.If you need rough paper use the side of your answer sheet.

1. Work out the sum of 24, 7 and one hundred and three.

2. There are 46 passengers on a bus. At the first stop 12 got off. How many passengers were left on the bus?

3. Find the cost of 5 Mars bars at 16p each.

4. Work out 136 take away 9.

5. Look at Diagram 1 on your answer sheet. What fraction of this shape is shaded?

6. Work out "one pound and four pence" take away 50 pence.

7. Peter had 104 records and Sue had 158 records. How many did they have between them?

8. Work out 58 multiplied by 6.

9. Work out £2.68 multiplied by 3.

10. A box holds 8 tennis balls. How many tennis balls would be needed to fill 9 boxes?

i.

PUPIL'S ANSWER SHEET - AURAL TEST KB)

2. passengers

3.

4.

5.

6.

7. records

8.

9.

10. tennis balls

WRITTEN TEST 2(B)

1. Calculate 595 divided by 5 1.

2. Jane had 9 birthday cards. Sarah had 4 more cardsthan Jane. How many cards did they have between them. 2.

3. 5 tins of coke cost 80p.(a) How much would 1 tin cost? 3a.

(b) How much would 3 tins cost? 3b.

4. Calculate of 48 4.

5. Find the cost of Ib bacon at £1.16 per Ib. 5.

6. To make a cake, flour and sugar are mixed in the ratio 4 to 3. How many ounces of flour would you need to mix with 9 ounces of sugar? 6. ______ ounce

7. Calculate of 76 7.

8. Calculate the cost of -| Ib fudge at £1.96 per Ib. 8. £_

9. In a shop a box of chocolates were priced at £1.86. In the market, the chocolates cost II 3rd of this price. How much did the box of chocolates cost in the market? 9. £

AURAL TEST 2(B)

1. Work out five hundred and ninety five divided by five.

2. Jane had 9 birthday cards. Sarah had 4 more cards than Jane. How many cards did they have between them?

3. 5 tins of coke cost 80p.

(a) How much would 1 tin cost?

(b) You have calculated the cost of 1 tin of coke. How much would 3 tins cost?

4. What is | of 48.

5. Look at Diagram 1 on your answer sheet. Find the cost of -j Ib of bacon at £1.16 per Ib.

6. Look at Diagram 2 on your answer sheet. To make a cake, flour and sugar are mixed in the ratio 4 to 3. How many ounces of flour would you need to mix with 9 ounces of sugar?

7. Find | of 76.

8. Look at Diagram 3 on your answer sheet. Find the cost of

I Ib fudge at £1.96 per Ib.

9. Look at Diagram 4 on your answer sheet. In a shop a box of chocolates was priced at £1.86. In the market the chocolates only cost I/3rd of this price. How much did they cost in the market?

1.

2.

PUPIL'S ANSWER SHEET - AURAL TEST 2(B)

cards

3. (a)

(b)

_P

_P

4.

5.

6.

Best bacon £1.16 per Ib

Diagram 1

Flour/A Flour U\F}ourfJ \ Flour

Diagram 2

ounces

7.

Fudge £1.96 per Ib

CHOX £1.86

Diagram 4

WRITTEN TEST 3(B)

1. How many grams (g) are in 3 kg?

2. Calculate 0.7 x 4

3. A piece of string 20m long has 1.3m cut from one end. What length of string remains?

4. 1.37164What is the value of the 7 in the above number?

(a) 7

(O 7

(d)100

71000 '• ————————

5. Calculate 10 - 1.8 5._________

6. Mrs. .Smith buys 5 kg of potatoes, 1.75 kg of flour and 0.5 kg of apples. What is the total weight of all these? 6._______ kg

7. Calculate 2.8 divided by 7 7._______

8. Peter can lift 6 weights, each weighing 3.9 kg.What is the total weight he can lift? 8._______ kg

9. Ann has made a paper chain 14.6 m long. Susan has made one 9.8m long. How much longer is Ann's paper chain than Susan's? 9._________m

10. Calculate 3m+2.6m + 0.75m 10. m

AURAL TEST 3(B)

1. How many grams are then in 3 kilograms?

2. Work out nought point seven (0.7) multiplied by 4.

3. A piece of string 20 metres long has 1.3 metres cut from one end. What length of string remains.

4. Look at the number in Box 1 on your answer sheet.The figure 7 is underlined. What is the value of the 7? Is it: 7, 7 tenths, 7 hundredths or 7 thousandths?

5. Work out 10 take away 1.8.

6. Look at Diagram 2 on your answer sheet. Mrs. smith buys a 5 kg bag of potatoes, a 1.75 kg bag of flour and 0.5 kg of apples. What is the total weight of these goods?

7. Work out 2.8 divided by 7.

8. Peter can lift six weights, each weighing 3.9 kg. What is the total weight he can lift?

9. Look at Diagram 3 on your answer sheet. Ann has made a paper chain 14.6 metres long. Susan has made one 9.8 metres long. How much longer is Ann's paper chain than Susan's?

10. Add together 3 metres, 2.6 metres and 0.75 metres.


1.

2.

3.

4.

Box 1

m

Diagram 2

8.

9.

10.

<——14.6 m

«——9.8 m

Diagram 3 m

2.

WRITTEN TEST 4(B)

1. 1 metre is about the same as:

(a) 1 inch (b) 1 foot (c) 1 yard (d) 1 mile 1.

st/lb

Before Christmas a woman weighed 9 st. 8 Ib. After Christmas she weighed 10 stone. How many pounds weight did she gain over Christmas. 2. It

The exchange rate is:

£1 2.31 dollars

If I changed £5 into dollars, how many dollars would I have? 3.$

A full petrol can contains 5 litres of petrol. If 1.75 litres are tipped out, how much petrol is left in the can? 4. litres

The height of a man is about:

(a)(b)(c)(d)

2mm 2cm 2m 2km 5.

AURAL TEST 4(B)

1. Look at the lengths in Box 1 on your answer sheet. Whichof these lengths is about the same as 1 metre: 1 inch, 1 foot, 1 yard, or 1 mile?

2. Look at Diagram 2 on your answer sheet. The dial shows a woman's weight at 9st. 81bs. After Christmas she weighed 10 stone. How many pounds weight did she gain over Christmas?

3. Look at Box 3 on your answer sheet. It shows the rate of exchange as 2.31 dollars for every £1. If I changed £5 into dollars, how many dollars would I have?

4. A full petrol can contains 5 litres of petrol. If 1.75 litres are tipped out, how much petrol is left in the can?

5. Look at the measurements in Box 4 on your answer sheet. Which of these is about the height of a man: 2 millimetres, 2 centimetres, 2 metres, or 2 kilometres?

6. Look at Diagram 5 on your answer sheet. 1 Pint is about the same as 0.55 litres. How many litres of pop could be poured into a 4 pint bottle?

7. Look at the lengths in Box 6 on your answer sheet. Which of these lengths is about the same length as a matchbox? 2 inches, 2 feet, 2 yards, 2 miles?

8. Look at Diagram 7 on your answer sheet. What is the weight shown by the arrow on the dial?

9. Look at Diagram 8 on your answer sheet. The 1 pound bag of flour is about the same weight as the 0.47 kg bag of flour. Write down the weight in kilograms of the 10 Ib bag of flour.

10. Look at Diagram 9 on your answer sheet. What is the weight in stones and pounds, shown on the scale?

1 Pint is about 0.55 litres. How many litres of pop could be poured into a 4 pint bottle?

The length of a matchbox is about:

(a) 2 inches(b) 2 feet(c) 2 yards(d) 2 miles

10.

What is the weight shown by the arrow on the above dial?

9. 1 Ib is about the same as 0.47 kg. Whatwould be the weight in kg of a 10 Ib bag of flour? 9,

What is the weight in stones and pounds shown by the arrow on the dial? 10. st Ib


1 inch, 1 foot, 1 yard, 1 mile

Box 1

Diagram 2

£1 2.31 dollars

Box 3

litres

2mm, 2cm, 2m, 2km

Box 4

6.

/ \ l pt0-951

Diagram 5

7.

8.

9.

10.

2 in, 2 ft, 2 yd, 2 miles

Box 6

DiagramFlour

lOlb

st Ib

Diagram 9

WRITTEN TEST 5(B)

1. Jamie runs a clothing catalogue. She earns 15p in the pound (£) commission on everything she sells. What percentage (%) is this. 1.

2. A shop found that out of every 100 light bulbstested, 7 were faulty. What percentage (%) werefaulty? 2.

3. Jenny found half the biscuits in a packet were broken. What percentage (%) were broken?

4. In a test Kirn scored 27/50. What percentage (%) was this?

5. In a survey, 23% of those asked said theysmoked. If 200 people were asked, how manyof them smoked? 5.____people

6. Sam had some sweets. One quarter of them weretoffees. What percentage (%) were toffees? 6.____%

7. In a class of 25 children, 9 of them wear glasses. As a percentage this is:

(a) 9%(b) 16%(c) 18%(d) 36% 7._____%

8. In a sale, a shop offers 50% off all goods. What would be the sale price of a coat which cost £46 before the sale? 8.£_____

9. 36% of a group of people were men. Whatpercentage (%) were women? 9.____%

10. ________£300 cash

HP 10% deposit

To buy this stereo on Hire Purchase (H.P.)Mr. Smith must pay a 10% deposit. The stereocosts £300. How much is the deposit? 10.£

AURAL TEST 5(B)

1. Jamie runs a clothing catalogue. She earns '15p in the pound 1commission on everything she sells. What percentage commission is '15p in the pound 1 ?

2. A shop found that out of every 100 light bulbs tested, 7 of them were faulty. What percentage were faulty?

3. Jenny found that half the biscuits in a packet were broken. What percentage were broken?

4. Look at Kirn's test score in Diagram 1. He scored 27 out of 50. What percentage score is this?

5. In a survey, 23% of those asked said they smoked. 200 people were asked altogether. How many of them smoked?

6. Sam had some sweets. One quarter of them were toffees. What percentage were toffees?

7. In a class of 25 children, 9 of them wear glasses. Look at the numbers in Box 2 on your answer sheet. Which of these shows the percentage of children in the class who wear glasses.

8. Look at Diagram 3 on your answer sheet. The shop is having a closing down sale. They offer 50% off all goods. How much would you pay in the sale for a coat which cost £46 before the sale?

9. 36 of a group of people were men. What percentage were women?

10. Look at the stereo in Diagram 3 on your answer sheet. To buy this stereo on H.P. (Hire Purchase) Mr. Smith must pay a 10% deposit. The stereo is priced at £300. How much is the 10% deposit?

1.2.

3.

4.

5.

6.


Kim Jones 27 50

Test

Diagram 1

smoked

9% 16% 18% 36%

Box 2

8. CLOSING DOWN

50% OFF ALL GOODS

10.

Cash Price£300H.P.10%

deposit

4.

WRITTEN TEST 6(B)

1. How would "20 minutes past 8 in the evening" beshown on a 24 hour clock? 1._______

2. How would 10 minutes past 4 in the afternoon bewritten in figure? (Don't forget am or pm) 2.________

3. T.V. Timetable

4.05 p.m. Young Doctors4.40 p.m. Newsround4.50 p.m. Cartoon Time5.15 p.m. Grange Hill5.30 p.m. Welsh News

(a) In the above timetable, Young Doctors startsat 4.05 p.m. How many minutes does it last 3a.____ min

(b) Write down the name of the programme whichlasts for 10 minutes. 3b.

(c) The Welsh News starts at 5.30 p.m. It lastsfor 20 minutes. What time does it end? (c)____p.m.

17 : 58

The above box shows the time on a digital clock. The clock is 5 minutes fast. What is the correct time? 4.

5. Bus Timetable

Station 9. 20 9.50 ....Main Road 9.35 10.05 ....Hill St 9.42 10.12 ....Town Centre 10.10 10.40 ....

The timetable above shows the times of the first two buses from the Station to the Town Centre. Buses leave the station every 30 minutes.

(a) What time would the third bus leave thestation? 5a.

(b) Pat has to be in the Town Centre before 10.30 a.m. What time bus should she catch from the station? 5b.

(c) Pat's mother lives 7 minutes walk from theHill St. bus stop. Pat catches the 9.50 a.m.bus from the station. What time will shereach her mother's house? 5c.

12

6. Draw 'hands'on the clock above to show "quarter past seven"

AURAL TEST 6(B)

1. Write down the way "twenty minutes past eight in the evening" would be shown on a 24-hour clock.

2. Write down "ten minutes past four in the afternoon" as time in figures - don't forget am or pm.

3. Look at the T.V. timetable in Box 1 on your answer sheet, (a) Young Doctors starts at 4.05 p.m. How many minutes does it last? (b) Write down the name of the programme which lasts for 10 minutes. (c) The Welsh News starts at 5.30 p.m. If it lasts for 20 minutes, write down the time it finishes.

4. Look at the digital time shown in Box 2 on your answer sheet. This time is 5 minutes fast. Write down the correct time.

5. Look at the Bus timetable in Box 3 on your answer sheet.(a) Buses leave the station every 30 minutes. The first

bus leaves at 9.20, the second at 9.50. What time would the next bus leave the station?

(b) Pat has to be in the Town Centre before half past ten. She catches the bus in the Station. What time bus should she catch from the Station?

(c) Ann decides to visit her mother who lives 7 minutes walk from the Hill Street Bus Stop. If Ann catches the 9.50 bus from the Station, what time will Ann reach her mother's house?

6. Draw hands on the clock in Box 4 to show quarter past seven.


4.05 p.m.4.40 p.m.4.50 p.m.5.15 p.m.5.30 p.m.

Young DoctorsNewsroundCartoon TimeGrange HillWelsh News

Box 1

IT : 58

Box 2

Box 3

(a).

(b)

(c)

StationMain RoadHill St.Town Centre

9.209.359.42

10.10

9.5010.0510.1210.40

(c)

Box 4

WRITTEN TEST 7(B)

0 3

The calculator display above shows the answer toa sum in pounds (£). Write down this answerin pence (p). 1.

A book costs £1.05. How many of these bookscould you buy for £10? 2.

6 7 1 2 3

The calculator display above shows the answer to a sum in pounds (£). Write down this answer to the nearest penny (p). 3.£

There are 1.98 litres of water in the beaker above. About how many full litres is this? 4. litres

The calculator display above shows the answerto a sum in pounds (£). Write down thisanswer in pence (p) 5.

Mary sold 1712 raffle tickets. She had towrite down this number to the nearest hundred.What number would she write down? 6.

4 1

The calculator display above shows the answer to a sum in pounds (£). Write down this answer in pounds and pence. 7.£

8. Write down the nearest whole number to 7.9. 8.

9.

10.

10 12 15

Which of the numbers in the box above is nearestto 2.9 x 4.1? 9.

AFP ~~L_m_In the diagram above, the garage is about 2m high. About how high is the house? 10. m

AURAL TEST 7(B)

1. The calculator display in Diagram 1 on your answer sheet shows the answer to a sum in pounds. Write down this answer in pence.

2. A book costs "one pound and five pence 1 . How many of these books could you buy for £10?

3. The calculator display in Diagram 2 on your answer sheet shows the answer to a sum in pounds. Write down this answer to the nearest penny.

4. Look at the picture of a beaker of water in Diagram 3 on your answer sheet. There are 1.98 litres of water in the beaker. About how many full litres is this?

5. The calculator display in Diagram 4 on your answer sheet shows the answer to a sum in pounds. Write down this answer in pence.

6. Look at Box 5 on your answer sheet. Mary sold onethousand seven hundred and twelve raffle tickets. She had to write down this number to the nearest hundred. What number would she have written down?

7. The calculator display in Diagram 6 on your answer sheet shows the answer to a sum in pounds. Write down this answer in pounds and pence.

8. Write down the nearest whole number to 7.9.

9. Look at the numbers in Box 7 on your answer sheet. Which of these numbers is nearest to 'two point nine 1 times 'four point one'?

10. Look at Diagram 8 on your answer sheet. The garage of the house is about 2 metres high. About how high is the house?


2.

3.

0 3

Diagram 1

Books

67123

Diagram 2

Diagram 3

Diagram 4

1 7 1 2

Box 5

4 1 2

Diagram 6

litres

9. 8

10

12

15

Box 7

2.9 x 4.1

10.

nDiagram 8 m

WRITTEN TEST 8(B)

o*

>K-% t »•- • -—

What is the area of the above rectangle? 1. cm'

White

Large (8 sq.m)

The large tin of paint above will cover 8m 2 of wall. How many large tins would you need to buy to cover 35 m 2 of wall? 2. tins

II

I")

(a) What is the area of the floor above? 3a.

(b) The floor is to be covered with carpet tiles. Each tile has an area of 1/4 m 2 . How many tiles would be needed to cover the floor? 3b.

4.

The above rectangle has an area of 24m 2 , What is the area of the shaded triangle? 4.

2m B

2m 2m

4m

5m

In the diagram above

(a) What is the area of Section A? 5 a(b) What is the length of the side L? 5b~(c) What is the area of section B? 5C ~(d) What is the area of the whole shape (A & B

together)? 5d

What is the area of a room 4m long and 2m wide? 6

m'

m

a 2

i2


1.

Diagram 1

tcrrr

4.

White

Large (8 sq.m)

Diagram 2

Diagram 3

Diagram 4

rtins

(b) tiles

AURAL TEST 8(B)

1. Look at Diagram 1 on your answer sheet. The rectangle is 7cm long and 3cm wide. What is its area?

2. Look at Diagram 2 on your answer sheet. The large tin of paint holds enough to cover 8 square metres of wall. How many large tins would you need to buy to cover 35 square metres of wall?

3. Look at Diagram 3 on your answer sheet. The floor of the room is 3m long and 2m wide.(a) What is its area?(b) The floor is to be covered by carpet tiles. Each tile

has an area of 1/4 square metres. How many carpet tiles would be needed to cover the floor?

4. Look at Diagram 4 on your answer sheet. The rectangle has an area of 24 square metres. What is the area of the shaded triangle?

5. Look at Diagram 5 on your answer sheet. The diagram shows the plan of an 'L shaped room' divided into two sections by the dotted line.(a) Section A is 5m long and 3m wide. What is its area?(b) Section B is also 3m long. How wide is it?(c) You have found out how wide section B is. Remember

it is 3m long. What is its area?(d) What is the area of the whole room - Sections A and B

together?

6. What is the area of a room 4m long and 2m wide?

</i ft

3m

£>.3

„

Br~3

(a) m 2

(b) m

(c) m 2

(d) m 2

Diagram 5

WRITTEN TEST 9(B)

1. Jane earns £6.80 per week baby sitting. She spends l/3rd of this on a record. How much is the record? l.£________

2. Peter earns £4.80 per week on a paper round.He spends 1/4 of this at a disco. How muchdoes he spend at the disco? 2.£_______

3. Mary spends half of her weekly pay on food. She spends £23.30 on food. How much is her weekly pay? 3.£________

4. John earns £3.35 per hour. When he worksovertime he is paid DOUBLE TIME. How muchdoes John earn for 1 hours overtime? 4.£_______

5. Mrs. Jones earns 12% commission with hercatalogue. How much commission would sheearn if she sold £100 worth of goods? 5.£_______

6. A waitress earns £2.40 per hour. Overtimeis paid at TIME AND A HALF. How much wouldbe paid for 1 hours overtime? 6.£________

7. Ann is paid £1.86 per hour for her Saturday job. If she works for 7 hours, what is her total pay for Saturday? 7.£_______

8. Mary's gross wage is £176 per week. Her net wage is £128 per week. How much are deductions? 8.£________

9. Mrs. Jones buys 5 tins of paint at £4.65per tin. What is the total amount she paysfor paint? 9.£_______

10. Peter travels 24 miles to work each day.He travels one quarter of the way by car.How many miles does he travel by car? 10._______miles

AURAL TEST 9(B)

1. Jane earns £6.90 a week baby sitting. If she spends 1/3 of this on a record, how much is the record?

2. Peter earns £4.80 a week on a paper round. He spends 1/4 of this at a disco. How much does he spend at the disco?

3. Mary spends half of her weekly pay on food. If she spends £23.30 on food, how much is her weekly pay.

4. Look at John's payslip in Diagram 1. John is paid £3.35 per hour. When he works overtime he is paid at DOUBLE TIME. How much does he earn for 1 hours overtime?

5. Mrs. Jones earns 12% commission from her catalogue. How much commission would she earn if she sold £100 worth of goods?

6. Look at the advert in Diagram 2. The pay is £2.40 per hour. Overtime is paid at TIME AND A HALF. How much would be paid for 1 hours overtime?

7. Anne earns £1.86 per hour working in a shop on Saturday. If she works for 7 hours, what is the total amount she earns?

8. Look at the payslip shown in Diagram 3. Mary's gross wage is £176 per week. Her net wage is £128 per week. How much are her deductions?

9. Look at the price of the tin of paint in Diagram 4. Mrs Jones buys 5 tins of paint at £4.65 each. How much does she pay for paint altogether?

10. Peter has to travel 24 miles to work each day. Hetravels one quarter of the way by car. How many miles does he travel by car?


John Smith

Wage £3.35 per hour

Overtime DOUBLE TIME

Diagram 1

"Waitress wanted 1

pay £2.40 per hour

Overtime: "TIME AND A HALF"

Diagram 2

Mary Jones

Gross wage Deductions

Net Wage

137161

£176

£128

Diagram 3

Gloss Paint

£4.65

Diagram 4

10. miles

1.

2.

WRITTEN TEST 10(

fi,

In the diagraun above, what is the name given to the line OB ?

In the space above, use a protractor to draw an angle of 60°.

3. The circumference of a circle is found using the formula:

CIRCUMFERENCE - n x DIAMETER

Find the circumference of a circle of diameter2cm. Use 3.14 for IT 3.________cm

4.

In the space above, draw an angle of 130 e

Scale 1cm to 5m

The diagram above shows a scale drawing of a tree. In the diagram the tree is 3cm high. Use the scale to find the actual height of the tree. 5. m

In the diagram above, what is the size of angle a? 6. a =

7.

8.

In the triangle above, what is the size of angle b? 7. b

The angle above is a right angle. What is its size? 8.

9.

10.

In the diagram above, what is the size of the angle c? 9. c =

PfM

In the diagram above, the arrow points north. In which direction would you be going if you walked from ABER to PEN? 10.

AURAL TEST 10(B)

1. Look at Diagram 1 on your answer sheet. What is the name given to the line OB?

2. In the space on your answer sheet, use your protractor to draw an angle of 'sixty degrees' (60°).

3. Look at the formula in Box 2 on your answer sheet. You can use this formula to find the circumference of a circle. Find the circumference of a circle of diameter 2cm - use IT as 3.14.

4. In the space on your answer sheet, use your protractor to draw an angle of 'one hundred and thirty degrees' (130°).

5. Look at Diagram 3 on your answer sheet. This shows a scale drawing of a tree. In the drawing the tree is 3 cm high. The scale is 1 cm to 5 m. What is the actual height of the tree?

6. Look at Diagram 4 on your answer sheet. What is the size of angle 'a'?

7. Look at Diagram 5 on your answer sheet. In the triangle, what is the size of angle 'b'?

8. Look at Diagram 6 on your answer sheet. The angle shown is a right angle. It is sometimes called a 'square corner" . What is it's size?

9. Look at Diagram 7 on your answer sheet. Work ou the size of the angle 'c' in the diagram.

10. Look at Diagram 8. The arrow points towards the north. In which direction would you be going if you walked from ABER to PEN?

1.


a

Diagram 1

2. 60 C

3.

CIRCUMFERENCE = ir x DIAMETER

Box 2

if = 3.14

4.

130°

Diagram 3

Scale 1cm to 5m

m

7.

8.

9.

Diagram 4

Diagram 5

Diagram 6

Diagram 7

10. NORTH

PEN*——4——»ABERt

a =

c =

WRITTEN TEST 11(B)

10-

o -

20-

One cold day the temperature was 5°C. During the night it fell to -4°C. How many degrees did the temperature fall? _deg,

I think of a number x, add 6 and the answer is 15.(a) Write this as an equation

(b) What is the number x?

John has 5 black marbles in his pocket and 4 white ones. He picks a marble without looking. What is the probability it is black?

One cold morning the temperature is -3°C. By noon it had risen 7 degrees. What is the temperature at noon?

f c. \30

-2O

,10

0 •

-20'

^*-—-"•

I think of a number x, double it and the answer is 24.(a) Write this as an equation.

(b) What is the number x?

2a.

2b. x =

3.

4.

5a.

5b. x

6.

The pie chart above shows how the 400 pupils in a school travel there each day.

(a) How do most pupils travel to school?

(b) How do the fewest pupils travel to school?

(c) There are 400 pupils in the school. How many of them walk to school?

6a.

6b.

6c.

AURAL TEST 11(B)

1. Look at Diagram 1 on your answer sheet. One cold day the outside temperature was 5°C. By midnight it had fallen to -4°C. By how many degrees had the temperature fallen?

2. (a) I think of a number x, add 6 and the answer is 15. Write this as an equation.

(b) I think of a number x, add 6 and the answer is 15, What is the number (x) I thought of?

3. Look at Diagram 2 on your answer sheet. John has 5black marbles in his pocket and 4 white ones. If he picks a marble without looking, what is the probability it is black?

4. Look at Diagram 3 on your answer sheet. One cold morning the temperature is -3°C. By noon it had risen 7 degrees. What is the temperature at noon?

5. (a) I think of a number x, double it and the answer is 24. Write this as an equation.

(b) I think of a number x, double it and the answer is 24. What is the number (x) I thought of?

6. Look at Diagram 4 on your answer sheet. The pie chart shows how the 400 pupils in a school travel there each day.

(a) How do most of the pupils travel to school?

(b) How do the fewest number of pupils travel to school?

(c) There are 400 pupils in the school altogether. How many of them walk to school?

PUPIL'S ANSWER SHEET - AURAL TEST 11 (B)

c30-

20 7

MOT

0 -r

-20-

Diagram 1 degrees

(a)

(b)

O OO 0

Diagram 2

10T

.120 ^

5.

Diagram 3

(a)

(b)

6.

Diagram 4 (a)

(b)

(c)

University of South Wales

Documents

Transcript of University of South Wales