THE EFFECT OF COOPERATIVE LEARNING ON STUDENTS’ PERFORMANCE IN MATH

Conference of the International Journal of Arts & Sciences,

CD-ROM. ISSN: 1943-6114 :: 6(3):167–176 (2013)

Copyright c© 2013 by UniversityPublications.net

THE EFFECT OF COOPERATIVE LEARNING ON STUDENTS’

PERFORMANCE IN MATH

Mohamed Chabi , Mohammad Shahid Jamil

Qatar University, Qatar

In this paper we have studied the effects of group work on students’ performance in Math 4 “Pre-Calculus” course in Qatar University. The studies were examined in spring 2011 with four classes and in each class consist of 6 to 8 groups of students. The aim of the study was to determine the effect of cooperative learning on students’ performance in math 4 course. For this project the guidelines were formed for groups to follow. We have analysed the exams’ results prior and post of this study. The collected data from various exams shows that students who participated in the project improved their performance. In Cooperative and Group Work (GW) students have opportunity to think about facts and procedures to justify their answers.

Keywords: Pre-Calculus, Students’ Performance, Cooperative Learning, Facts and Procedures.

Introduction:

We have started to get some useful information to advance active learning concepts. Working with a group can provide an opportunity to discuss the mathematics in more detail with individuals in the group, it also gives an opportunity to students who are not active to participate with his/her peers sub-group and it helps them to build self-esteem.

We have examined the effects of group work on students’ performance in Pre-Calculus mathematics course. The study started four year ago. We selected four classes to participate in our study and each class divided into 7 to 8 sub-groups of students. We used in this paper subgroup and group word. Subgroup means 3 to 4 students with subgroup. So we have 6 to 8 small group and we refer them as a subgroup.

167

168 Mohamed Chabi and Mohammad Shahid Jamil

Strategy to Form Group

After first three weeks of classes we tested our students using 1st quiz and also engaged students

in the class to do activity and meet them in the office hours then we collected data and

formalized a general idea about each student. This allows us to select three to four students in a

subgroup. In each subgroup we selected very weak, average and good student so that they can

think and discuss together in one problem. We arrange the seat also so that in each class weak

student, strong student and fair or average student sit together as a subgroup in full semester.

Each subgroup has a team leader to take initiative in a problem and distribute task into different

group members. We also provided an extra class sessions and workshops to improve learning.

The group building presented in Figure 1: Group seating

Figure 1: Group seating.

Guidelines for Group Work

A carefully designed activity for subgroup work alone cannot guarantee a successful result

without a strong individual effort by students. Students need to develop the social skills that

support productive mathematical work with peers. To help with this, set of guidelines were

developed base on what will help students to perform their task in subgroup work. The purpose

was to get them familiar with their responsibilities during subgroup work. A particular action by

math students during the subgroup work is critical to the success or failure of the group effort.

Making the ground rules explicit helps to set the stage for effective interaction. The rules set for

students to follow and helps other members to create an environment of discussion for active and

exploratory learning. Student may tutor or help their peers to understand and work on a problem

[Gokhale, A.A. (1995)]. This is a level of student empowerment, which is unattainable with a

lecture format or even with a teacher-led whole class discussion. The guidelines for subgroup

work are:

• Do not miss regular lecture

• Respect the design seating and the assigned group

• Engage in sustained mathematical dialogue and do not get into off-task discussion.

• Listen carefully to each other and try not to interrupt.

The Effect of Cooperative Learning on Students’... 169

• Encourage your group’s member to participate in the group work.

• Focus on what can you work out from a given information

• When solving a given math question think about all the facts and procedures needed for

solving before sharing them with your group and explaining your reasoning

• Ask for clarification whenever someone give an answer that you are not agreed with and

check for agreement

• Do not split up the work. Everyone should focus their attention on the same problem at the

same time

• Be aware of the time constraints.

• If your group gets stuck or not agreed with some of reasoning, review the work and ask for

your teacher help.

• Attend all extra classes for the 12 workshop sessions of group work.

• Regular visit to teacher office hours to answer some the assigned group works.

• Check regularly blackboard for assigned group work outside of the class time

• Attend all extra classes for the 12 workshop sessions of group

Group Work in Classroom

During the lecture session we ask clicker question for groups to think about, to reinforce the

learning objective of that particular lecture and to link it to the previous lectures. Students were

given 5 to 10 minutes depending on the question standard. During that time we move in the class

room around the groups, checking progress, and asking questions designed to help the students

clarify the problem, and to focus on key aspects which may facilitate breakthroughs.

Example: After cover the concept of trigonometric functions I asked students to find domain

e: Af

The key objectives of this question to focus on following:

• To use the fact that which implies

• To recall on how to solve exponential equations:

• To use the fact that implies that where is any integer number

For a particular group, randomly we ask one of group member to write solution the question

on the board by listing all the facts, reasoning and procedures used, and then we ask other groups

to tell their thinking about the answer, facts and procedures to engage everyone into an active

learning. In the discussion that follows, encourage student to take a greater role in the discussion.

At the end we ask each subgroup to summarize the key points that they have learn through the

given question [Davidson, N., & Kroll, D.L. (1991)]. Whole process can take roughly up to 10

minutes to accomplish this step.


Group Work in Workshop Sessions

We have arranged 12 workshop sessions and each session was last for 45 minutes. To encourage

and motivate students to achieve high participation, we adopt a policy to reward them one point

for each 4 consecutive workshop sessions. These marks will be added to their final course grade.

The Students enter a room in which each table with three to four chairs are arranged in Figure 2

Seating Arrangement in circle formation and facing the front.

Workshop sessions were running under my supervision with a TA and each workshop

session is divided into Introduction, Fact practice & Common errors, Guided group practice and

Summary of work in shown in Figure 3 Workshop session.

Figure 3: Workshop Session.

First TA will give the introduction and will review some of facts and properties that are

needed for the session. As an example that dealt with Functions and

Their Graphs, and point out work and understanding of the problem as follows:

• Determine whether a relation represent a function

• Find the value of a function

• Find the domain of a function

• Calculate sum, difference, product and quotient of two functions and so on.

For Fact Practice and Common Errors usually TA will give a practice question to students

where they can apply facts and learn about the common errors.

Let’s explain with an example: Given

a. Find

b. Find

c. Is

For Guided Group Practice set of direct and indirect questions were given to students to

practice on as group. These questions are challenging requires facts, procedure and critical

thinking. The questions were designed in a way to help them develop some of the learning


concepts of that particular session. The purpose was reinforcing the learning objective and

stimulating their thinking skills as group [Jan Terwel (2011)]. We have not been taught a

particular method for solving such questions, but are drawing on their general knowledge of

mathematics and problem-solving, as well as on recent class-work. In each session TA will move

around in the class to see each group, checking progress, providing help to the students when

they ask for clarification, and check for agreement whenever the group members are not agreed.

In each session students are asked to summarize of what they have learned. We also meet with

TA before the start of new session for a complete report on students’ progress.

Group Work outside the Classroom

Regularly we post old exam to review and understand problems and we also provide a new

practice tests to solve in group. Each group was assigned to do different questions. They had one

week to completed them and seeing us during the office hours for questions. The purpose was to

make sure that they worked as a group and learned from their peers [Jan Terwel (2011)]. The

type of questions usually we asked during the office hours were about on how they worked as

group, difficulties that they faced with and method used for the answers. The final answer was

not that important for us as much as reasoning and procedures in finding the answer. To enhance

student thinking skills, we also asked the reason for using a certain method than other existing

methods. This will allow students to be able to identify a suitable method for a particular

question.

Problem faced in Group Work:

• Use of Mobile and Lack of motivation: Student involved in other things during lecture such

as sending SMS, attending mobile calls and replying to e-mail messages. This creates

abstraction to complete on time. Actually this depends on the teacher also to raise their

motivation and drag their attention back to the session. Sometime there were few cases

whose behaviours were tolerated with difficulty because we do not permit them to do other

activity during the class.

• Absenteeism: Student absent in the lecture provides a variety of reasons as to why they did

not attend teaching sessions regularly so group partner get upset to work together.

• Lack of Knowledge: When a student gets absent in lecture they face problem in

understanding of the topic or next related lecture. Their performance decreases and also

unable to complete that tasks.

• Dissimilar and Contradictory views: When students solve a problem they want to relate with

earlier study from past level of class or from their private tutor. This creates difficulties to

explain them during lecture so we call them for workshop or office hours to resolve their

issue.

When a teacher is experienced then he/she can minimize the above difficulties to a greater

extent using previous knowledge [Eilisha Joy Bryson (2007)].


Results analysis

To examine the effects of group work on students’ performance in Pre-Calculus course, we collected data from exams for the students who participated in the study of the group work project versus the ones who did not. First, we investigate whether there is a correlation between number of sessions students attended in the workshop and their final exams results. Second, we compared students’ results before participating in the study of the group work project and after participating in the study. Third, we analyse whether there is a significance difference in exams ‘results between students who participated in the group work versus the ones who did not. Fourth, we compare the overall average of all students who were in the study to all Math4 “Pre-Calculus” students in the Qatar University. They were four classes who participated in the study and each class consisted of 7 to 8 groups of students and two other classes were not in the study but they received similar course materials including all works that was assigned to the other 4 classes who were in the study.

Table 1: Number of Students.

Correlation between Workshop and Exams’ Results

We have calculated correlation between Numbers of Sessions Student Attended in the Workshop and Final Exams’ Results. We have selected a class of 20 students to analyse data.

The Pearson correlation coefficient, r was calculated, we find and this indicate there is a strong correlation between number of sessions and students’ final exam results

Chart 1: Correlation between Number of Sessions and Students’ Final Exam.

Number of our Students who did participate in the Study 85

Number of our Students who did not participate in the study 41

All Math 4 students including our students at Foundation Program 450


I. Students’ Results before and after Group Work:

We have analyzed the comparison of Students’ Results Before and After Participating in the Study of The Group The purpose of comparing the two scores, to determine whether students benefit from the group work in improving their performance. After three weeks of regular classes students took the first test before participating in the group work “Test Score before GW”. At that time Students were only tested on first five sections of the first Unit. The result of the first test is compared to the final exam’s results. Unlike the first test, the final exam students were tested on all topics in the course syllabus. We find the result available in table 2.

Table 2: Comparison of tests ‘results before GW and after GW.

Test Score before GW Test Score after GW Percentage of Increase

87% 100% 15%

92% 99% 8%

78% 95% 22%

71% 84% 18%

72% 88% 22%

83% 100% 20%

75% 97% 29%

74% 73% -1%

91% 100% 10%

56% 51% -9%

81% 99% 22%

67% 61% -9%

38% 83% 118%

73% 100% 37%

79% 79% 0%

84% 99% 18%

68% 65% -4%

67% 98% 46%

79% 91% 15%

65% 61% -6%


In general we can notice from Table 2 that students’ performance in the test after GW project participation was much better than their performance before participating in the GW. In addition we can notice from table 2 there was a student who improved her mark by 118% whereas there are some students whose grades decreased no more than 9 % in comparison to the previous test. In table 3 the overall was summarized. The mean score after group work was much higher than the mean score before the group work and overall students’ results improved by 29% data of the result available in Table 3.

Table3: Mean Test Score.

Mean Test Score After GW 86%

Mean Test Score Before GW 74%

Mean of Increase 29%

Mean of Decrease 6%

Highest Increase 118%

Lowest Decrease 9%

II. Analysis of Students Results Who Participated in the Group Work Project vs. Ones Who

Did Not

The students’ scores for those who participated in the group work project versus the ones who did not were further examined to determine there is a difference in the scores. The results of t-test are shown in the Table 4

Table 4: Analysis of Students Results.

Groups Mean (Gender)

T-test

Value

Significance

(2-tailed)

Did/ Did Not

85.42 (Female)

63.94 (Female) 5.94063 0.00000*

Did/ Did

85.42 (Female)

82.26 (Male) 0.80290 0.43251

When we analysed the data in Table 4, there is only small difference between the mean

scores of two classes who participated in the group work project (mean scores were 85.42 for the one class and 82.26 for another class, and t-value = 0.802890). On the other hand, students who participated in the group work performed much better than the ones who did not, the mean score for those who participated and those who did not being 85.42 and 63.94 respectively, and t-value = 5.94063. We have found that a strong significant difference between students’ results who participated versus those who did not.

III. Comparison of all Students’ Results:

Finally we started comparing all Students’ Final Exam’s Results of Math4 “Pre-Calculus” in

the Qatar University. The final Exam’s results and the attendance rate of about 85 for the


students who participated in the group-work were compared to all math4 students. There were around 450 students present in final exam of Math4 and data collect are available in Table 5.

Table 5: “Comparison of all Students’ Final Results”.

Mean Final

Exam

Max Final

Exam Grade

Min Final

Exam Grade

Attendance

Rate

Students who were in

the study

(85 Students) 84.6% 100% 51% 97%

All Math 4 Students

(450 Students) 73.4% 100% 32% 80%

We have found that students who participated in the group-work project with mean score

84.6% perform much better than all the Math4 students whose final exam’s mean score 73.4%. Also we noticed that attendance rate for students who participated in the group-work project “93%” was much better than all Math4 students “80%”. It seems the student shows more seriousness in the group-work.

Conclusion

Group-work project learning has an overall positive effect in the cognitive domain as well as the social and affective domain in tertiary mathematics. Students often learn more by listening to their peers than they do by listening to an authority figure like a teacher. In cooperative work students have opportunity to think about facts and procedures to justify their answers and discuss with the peers partners.

The entire focus of group work project was to actively involve students in the learning process. Whenever students attempt to solve a problem or answer a question they become involved in the process of exploratory learning. All in the group are developing problem solving skills by formulating their ideas, discussing them, receiving immediate feedback and responding to questions and comments by their partner.

Efforts among students in group-work learning project result in a higher degree of accomplishment by all participants as opposed to individual. When students work in groups, some members are listening while the others are discussing the question under investigation.

References

1. Gokhale, A.A. (1995). Collaborative learning enhances critical thinking. Journal of Technology Education, 7, No.1, Retrieved January 2007, from http://scholar.lib.vt.edu/ejournals/JTE/v7n1/pdf/gokhale.pdf

2. Davidson, N., & Kroll, D.L. (1991). An overview of research on cooperative learning related to mathematics. Journal for Research in Mathematics Education. 22, 362-365. Retrieved January, 2007 from http://links.jstor.org/sici?sici=0021-


3. Eilisha Joy Bryson (2007). Effectiveness of Working Individually Versus Cooperative Groups: A Classroom-

Based Research Project. Master Thesis. EDUC 545-631~Leadership for Middle School Science. University

of Pennsylvania

4. Jan Terwel (2011). Cooperative learning and Mathematics Education: A happy marriage?. Paper presented at

the OECD / France workshop, Paris 23-24 May 2011 ‘Education for Innovation: The role of Arts and STEM

Education’

THE EFFECT OF COOPERATIVE LEARNING ON STUDENTS’ PERFORMANCE IN MATH

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