CURRENT TRENDS IN MATHEMATICS EDUCATION: QUALITIES OF

AN EXPERIMENTAL MATHEMATICS TEACHER

BY

NNEAMAKA ONAIFOH

DEPARTMENT OF ADULT AND NON-FORMAL EDUCATION

FEDERAL COLLEGE OF EDUCATION (TECHNICAL), ASABAamakacharles1@yahoo.com

\

A PAPER PRESENTED AT THE MAIDEN NATIONAL ACADEMIC

CONFERENCE OF SCHOOL OF SCIENCE EDUCATION FEDERAL

COLLEGE OF EDUCATION (TECHNICAL), ASABA, DELTA STATE.

6TH - 10TH MAY, 2013

Abstract

This paper articulated who an experimental mathematics teacher is. A teacher who istrained to teach mathematics and who has the skills and competence needed to carryout the task effectively. Unfortunately the department has been saturated withunqualified teachers who are specialists in other disciplines like chemistry, physics,economics, engineering etc. The paper however, describes the dimensions of anexperimental mathematics teacher as teacher’s personality, knowledge of the subjectand methodology which play a role in the teaching and learning of mathematics. Thepaper also identified and explained the modern methods of teaching mathematics.These are problem solving, cooperate/group, computer assisted instruction, andinteractive method. It recommended, among others, that government and schoolauthorities should engage the services of qualified teachers of mathematics andprovide appropriate teaching and learning equipment/facilities. Also, it is important forteachers to identify with professional organizations so as to meet the challenges of thefast growing trends.

INTRODUCTION

Research findings have confirmed the dearth of mathematics

teachers at all level of education in the country. Obioma (2005)

has drawn attention to the depreciating capacities of mathematics

teachers, observing that the old generations of mathematics

experts were fast disappearing and where there were any

replacements at all, younger persons who had little or no

guidance in the profession and research generally dominated the

skyline. The lack of enough teachers to handle the subject

particularly at the secondary level has led to borrowing teachers

who are specialists in other disciplines like chemistry, physics,

economics, engineering etc. to teach mathematics. In many cases,

such borrowed teachers are not professional teachers because they

are not trained teachers. Hence, they lack the skills, competence

and the teaching methods required to teach mathematics

effectively. Usually, such teachers avoid the teaching of some

topics which they find difficult to handle. In essence, it means

that short supply of qualified teachers leads to mathematics

teaching been handled by incompetent hands who in turn can only

produce poorly bred mathematics students. The students therefore

become victim of poor teaching. This trend confirms the assertion

by Fakuade (1973) that a shortage of suitably qualified teaching

staff will result in poor teaching which invariably will result

in a production of another generation of poor students.

Freudenthal (1991) maintained that to learn mathematics means to

engage in the process of mathematising through which mathematics

is re-invented. His emphasis on mathematising carries a strong

evolutionary stance and is further elaborated subsequently by

Wittmann (2001) who proposed that mathematics education should be

viewed and studied as a ‘systemic evolutionary design science’.

He also proposed that the study of teaching units called

substantial learning environments should form the core of

mathematics education. “The design of substantial learning

environments around long-term curricular strands should be placed

at the very centre of mathematics education. Research,

development and teacher education should be consciously related

to them in a systematic way (Wittmann, 2001).

Experimental Mathematics Teacher

From research evidence, econometric analyses have equivocally

demonstrated that, some teachers are dramatically more effective

than others and that these differences have lasting effects on

student learning (Rivkin, Hanusahek, and Kain, 2005). The teacher

is the most indispensable factor in effective administration of

any educational system. Also, it has been established that no

amount of resources put into the nation educational system,

without adequately prepared and motivated teachers, nothing

tangible can ever be achieved from the system. The role of

teachers at all levels of education is emphasized in the National

Policy on Education (FRN, 2004) that no educational system may

rise above the quality of its teachers. This declaration in the

policy document underscores the need for teachers’ effectiveness

in teaching and learning. Eso (1998) conceptualized teachers’

effectiveness as the managerial skills essential for enhancing

classroom control and discipline. It is the teachers’ competence,

ability, resourcefulness, and ingenuity through effective

utilization of appropriate language, methodology and available

instructional materials that could bring out the best from the

learners in term of academic achievement. But what makes a great

teacher? Some people are of the opinion that teachers are born.

But Ukeje (1991) is of the view that teachers may be born but a

good teacher is born and made. Maduabum (2009) explained that,

this is because teaching is both an art and a science”. Some

aspects of the art of teaching may be innate, but the science of

teaching has to be cultivated Maduabum (1986) had argued that

having knowledge and transmitting knowledge are two different

things. Some people have both abilities but many do not. The

‘born teacher’ exists but he is a rare bird! (Maduabum, 2009).

However, ability to transmit can be acquired if one is not lucky

enough to be born with it. Adepoju (1995) categorized these

teachers into four categories, they are:

a) Those who know mathematics but do not know how to teach it

b) Those who know how to teach mathematics but do not know much

mathematics

c) Those who do not know mathematics and do not know how to

teach it

d) Those who know mathematics and know how to teach it.

With these categories of teachers in the school system there is

the need for professional competence among teachers, so that

teachers can be confident in doing their job while helping

students learn mathematics.

Ezenweni (2002) define an experimental mathematics teacher as a

teacher trained to teach mathematics as a science to secondary

school students. That is, the teachers use different teaching

method to reduce the persistent problem of mathematics

abstractness and in a null shell, an experimental mathematics

teacher is a lover of mathematics.

An example will be helpful to illustrate a pedagogy -caused

student difficulty. Tanner (2000) states that teachers

generally use “fruit and salad approach” to introduce the

addition of two algebraic expressions, such as, 2a+3b in

algebra teaching. This kind of expression is often explained

to students by teachers through the use of some materials,

such as 2 apples and 3 bananas. However, Pimm (1987), as

cited in Tirosh, puts forward reservations regarding this

approach, warns against its potential role in causing

learning difficulties for students and notes that it leads

to confusion between a being apples and a being the number

of apples. The algebraic expression is not an analog of 5

apples, nor is 5 apples a possible interpretation of 5a, the

letters themselves are standing for numbers. In fact, some

studies have shown the disadvantages of using this approach

in introducing algebraic expressions. Booth (1988), for

example, shows that some students thought that the

expression 2a + 5b is equal to 7ab on the grounds that 2

apples plus 5 bananas is 7 apples-and bananas. Tirosh,

(1998) also point out that this approach may lead students

to think algebraic expressions, such as 2a and 3b, cannot be

multiplied, that is one cannot multiply apples and bananas.

All these suggest that sometimes the way materials are used and

the way the teaching is conducted can be the causes of, or at

least play a role in the emergence of student learning

difficulties for mathematical concepts.

Fennema and Franke (1992) argue that if a teacher has a

conceptual understanding of mathematics, this influences

classroom instruction in a positive way, therefore, it is

important to have mathematics knowledge for teachers. Teachers’

interrelated knowledge is very important as well as procedural

rules. They also emphasize the importance of knowledge of

mathematical representations, because mathematics is seen as a

composition of a large set of highly related abstractions. They

also stated that ‘if teachers do not know how to translate those

abstractions into a form that enables learners to relate the

mathematics to what they already know, they will not learn with

understanding’.

Traditional indicators of teacher quality, such as educational

level and certification, do not predict student outcomes (Rivkin,

Hanushek, and Kain 2005), certain aspects of teacher education

are relevant. For example, mathematics teachers who have

completed PhD course work in mathematics and an advanced

certificate course in Education are more effective than peer

teachers without such advanced training in education. An

experimental mathematics teacher should be able to use modern

methods of teaching and learning in order to bring out a

desirable outcome (Ezenweani, 2002). He outlined the

characteristics of experimental teachers to include the

following:

1. They are emotionally balanced

2. They are active and never lazy

3. They are cognitively balanced

4. They are mentally healthy and ready to find solutions to

problems

5. They are friendly to all people and see things from other

people’s point of view to learn on their part

6. They are very enthusiastic in academic work

7. They are cultured in dealing with issues affecting human

relations

8. To avoid the bad characteristics generally identified in

them, they are supposed to be neat in appearance all the

time, become more careful the way they dress and careful in

the choice of vocabulary and expression. They should avoid

being harsh to students and speak clearly not only to the

students but in public

9. They are supposed to be creative in their experimental

pursuit which should make for some originality in their

activities and findings.

Here are three dimensions of an experimental mathematics teacher

they are:

Teachers personality

Knowledge of the subject matter

methodology

Teachers Personality

The teacher’s personality is one of the characteristics to look

for in the teaching and learning of mathematics. Anybody can

become a teacher, but it takes special person to be a great

experimental teacher. He/she must rise above the crowd and make

empathy, enthusiasm, creativity, dedication, and discipline in

the process of teaching.

Knowledge of the subject

The knowledge of an experimental mathematics teacher are defined

as the skills effectively and efficiently acquired when teaching

mathematics. That is, the ability to organize and teach in

interesting and flexible ways. Knowledge of the subject matter

content is vital for the experimental teacher. It determines the

line of activity the teacher should follow to achieve the desired

objective and being acquainted with the content to be taught.

Methodology

The learning of mathematics depends on the way it is presented to

the learner, the way the learner actively interacts with the

learning experiences presented to him and the environment within

which the learning takes place. With the current increase in

scientific knowledge, much demand is placed and emphasis is laid

on the teacher, the learner and the environment in the whole

process of teaching and learning of mathematics. Today’s

mathematics teachers are experiencing major changes not only in

the mathematics content they teach, but also in the way they

teach.

Modern Method of Teaching Mathematics

Problem solving method: This approach is characterized by the

teacher in helping students to construct a deep understanding of

mathematical ideas and processes by engaging them in doing

mathematics: creating, conjecturing, exploring and testing.

Polya’s (1965) describe problem solving processes into four

stages:

1) understand and explore the problem

2) find a strategy

3) use the strategy to solve the problem

4) Look back and reflect to the solution.

Alio and Harbor-Peter (2000) recommended that polya’s problem

solving strategy should be used by secondary school mathematics

teacher to teach mathematics. The learning of mathematics in this

case proceeds from the concrete to the abstract. Approaching

mathematics through problem solving can create a context which

stimulates real life and therefore justifies the mathematics

rather than treating it at the end.

Cooperate / Group method: Cooperate learning method of teaching

is an instructional strategy that simultaneously addresses

academic and social skill learning by students. It is one way of

providing students with a well-defined framework from which to

learn from each other. Cooperate method of teaching is a team

approach where the success of the group depends upon everyone

pulling his or her weight. Group members share the various roles

and the interdependent in achieving the group learning goal.

Cooperate learning can take place in a variety of circumstance.

For instance brainstorming and tutorial group, when employed as

instructional strategy provides opportunity to develop

cooperative learning skills and attitudes

Computer Assisted Instruction: this approach uses computer as a

substitute for the teacher, that is, the students interacts with

the computer directly, usually as a terminal. Although the

teacher is involved in planning the system and supervising it’s

operation, a well-planned system frees the teacher from routine

teaching tasks, so that he may spend more time in working closely

with individual students (Odili, 2006). NCTM (2000) asserted

that educational technology (computer) can help teach content. It

can offer students a bridge from concrete to abstract thinking,

enabling them to observe and create multiple representations of

mathematical ideas. For instance, students can use geometric

instruction software to investigate the relationship between

circumference and diameter of a circle (Agwagah, 2013).

Interacting method: Interactive method of teaching includes

giving students something to do and getting what they have done,

so that you can decide what would be best to do next. If a

teacher asks questions in class, gives assignment, and check

homework then you are already teaching interactively. Interactive

instruction relies on discussion and sharing among participants

which allows for a range of groupings and interactive method.

Interactive method requires the refinement of observation,

listening, interpersonal and intervention skill and abilities by

both teachers and students

Teachers Development Programs

Effective instruction in school is defined through teacher

education program, which is the key towards understanding the

knowledge and skills of teaching and learning (Ololube, 2005a,

2005b). The education of pre-service and in-service science

teachers is meant to help individual teacher grow and develop as

a person, provide him or her with the skills and professional

abilities to motivate children to learn, assist them in acquiring

the right types of understandings, concepts, values and attitudes

to manage classroom instruction and be productive members of the

society in which they are born, grow and live (Lawal, 2003).

If mathematics teaching is to be effective, the pre-service

training of teachers must be very sound, while they also need to

be exposed to in-service training at regular intervals. Where

teacher preparation is inadequate it will lead to teaching

failure in the classroom; this is an area that needs to be

improved upon. Teacher development is considered particularly

effective, when teachers are in charge of the agenda and

determine the focus and nature of the programming offered (Ball,

1996). This concur with, the FRN (2004) National Policy on

education stipulates that teacher education shall continue to

take cognizance of changes in methodology and in curriculum.

Furthermore, that teacher shall be regularly exposed to

innovations in their profession (p 34). Fennema, Carpenter, Levi

and Franke (1998) learned that engaging teachers in current

reforms requires more than showing them how to implement

effective practices. Hence the government agencies are committed

to development and training of teachers which is aimed at

increasing the ability of the individual and groups to contribute

to organizational effectiveness.

Conclusion

Experimental mathematics teachers are key determinants of

mathematics learning outcomes. The learning of mathematics

depends on the way it is presented to the learners, the way the

learners actively interact with the learning experiences

presented to them. With the current increase in scientific

knowledge, emphasis is laid on the teacher in the whole process

of teaching and learning of mathematics. The Teachers

personality, knowledge of the subject, and methodology play a

significant role in the mind-set of students towards the learning

of mathematics. All these factors could also be applicable to

mathematics learning since mathematics is regarded as the

language of science. It is on this premise that the mind-set of

the teacher’s disposition to the subject, students, and classroom

environment could make or mar the mind-set of the students

towards the learning of mathematics. Hence the mathematics

teacher should be psychologically prepared to teach the subject

efficiently.

Recommendations

It is important for mathematics teachers to identify with

professional organizations so as to meet the challenges of the

fast growing trends. Such as, Mathematical Association of Nigeria

(MAN), Science Teacher Association of Nigeria (STAN), Curriculum

Organization of Nigeria (CON), and African Mathematical Union

(AMU) etc. Government and school authorities should engage the

services of qualified teachers of mathematics and provide

appropriate teaching and learning equipment/facilities. The state

government should as a matter of urgency send mathematics

teachers for training and seminars for effective teaching of

mathematics, particularly in our primary and secondary schools.

Teachers should try as much as possible to relate their lesson to

real life situation in order to reduce abstract nature of the

subject.

REFERENCES

Agwagah, U. N. V. [2001]. The teaching of number bases in junior secondary school mathematics. The use of the base board. ABACUS. The Journal of the Mathematical Association of Nigeria [Mathematics Education Series]. 26[1], 1-7.

Alio, B.C. & Harbor – Peters, V.F. (2000). The effects of Polya’sproblem solving technique on Secondary school students’ achievement in mathematics. TheJournal of the Mathematical Association of Nigeria, 25 (i), 27-39.

Ball, D. L. (1996). Teacher learning and mathematics reforms:What do we think we know and what do we need to learn? Phi Delta Kappan, 77, 500-508

Booth, L. Algebra: Children’s Strategies and Errors. Windsor (UK): NFER-Nelson, 1984.

Fennema, E. & Franke, M. (1992). Teachers’ knowledge and itsimpact in: D.A. Grouws (Ed) Handbook of Research on Mathematics Teaching andLearning. New York Macmillan Publishing

Franke, M.L., Carpenter, T. P., Levi, L.W., & Fennema, E. (1998).Teachers as learner: Developing understanding through children’s thinking.Paper presented at the annual meeting of the AERA, San Diego, Ca

Freudenthal, H. (1991). Revisiting mathematics education : Chinalectures. Dordrecht ; Boston: Kluwer Academic Publishers.

Federal Republic of Nigeria (2004). National Policy on Education.(Revised Edition). Lagos: Federal Ministry of Education.

Eso, O.T. (1998). Assessment procedure and student locus ofcontrol as determinants of achievement in Integrated Science. An Unpublished Ph.DThesis, University of Ibadan, Ibadan.Ezenweani, U.L (2002). Experimental Mathematics Teaching. Enugu:Fulladu publishing

Company

NCTM (2000). Principles and standards for school mathematics.Reston Va: The National Council of Teachers of Mathematics inc.

Maduabum, M.A. (1986). A critical appraisal of universityteaching in Nigeria. Journal of curriculum and instruction 1 (1), 114-112.

Maduabum, M.A. (2009). Science Teacher Effectiveness and NationalGoal Attainment in Nigeria: In search and solution.11th Inaugural LectureAbia State university 1-37.

Obioma, G.O. (2005). Popularizing Mathematical Sciences forTechnological Development in S.O. Ale and L.D. Adetula (ed)Reflective and Intellective Position Papers on MathematicsEducation Issues Garki Abuja: Marvellous Mike Ventures Ltd. 102-117.

Wittmann, E. C. (2001). Developing mathematics education in asystemic process. Educational Studies in Mathematics, 48(1), 1-20.

Rivkin, S.G., Hanushek, E.A., and Kain, J.F. (2005): Teachers,Schools and Academic achievement. Econometric, 73,417-458.

Ukeje, B.O. (1991): The Education of Teachers for a new socialorder. The Nigeria teacher, 1 (1), 4-12.