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A cooperative mathematical problem solving (CMPS) programme to enhance mathematical problem solving performance among secondary three female students
Author
Ho, Geok Lan
Supervisor
Foong, Pui Yee
Abstract
The study is an attempt to investigate the use of cooperative learning in the teaching of mathematical problem solving. The main aim is find out whether the Cooperative Mathematical Problem Solving (CMPS) Programme designed for this study can improve the problem solving performance of students. The first aim is to find out if the students were able to apply specific problem-solving strategies to tackle non-routine problems as covered in the programme. Another aim is to study the metacognitive and affective behaviours exhibited by students as they worked together in a group to solve problems. The suggestions, feelings and opinions towards the CMPS programme were also gathered from the students to provide feedback for modifications and improvements for future instructional planning.
With the increase in emphasis in mathematical problem solving in the Singapore mathematics curriculum, it is necessary to study effective instructional methods which will help teachers to teach mathematical problem solving confidently in the classrooms. The use of cooperative learning can provide an alternative to both traditional whole class expository instruction and individual instruction systems. When students work in cooperating groups, they know that they have the peer support to help one another cope with demanding situations. From the interactions and experiences acquired while students were engaged in the cooperative problem solving process, it is hoped that they could gain confidence and skills to improve their own problem solving abilities. Therefore, there is a need to explore further the use of cooperative learning strategies in mathematical problem solving instructions to benefit both the teachers and students.
From this study, it was found that the CMPS programme improved the problem-solving performance of students as measured by a holistic analytic marking scheme designed for the study. Students learnt to be more systematic in organising data given in a problem through the use of diagrams such as drawing a Matrix table or Decision Tree; and they were able to apply specific problem-solving strategies (e.g. try simple cases, look for patterns and find a general rule) to handle non-routine problems. The use of pre-instructional strategies such as guess-and-check, unsystematic listing and number manipulation became less frequent. The students attempted all problems with some strategies they had learnt. No one left problems unattempted as compared to the pre-test before the programme.
It was also found that students displayed a range of metacognitive and affective behaviours when they solved problems together. The metacognitive behaviours manifested were: ask for clarification, remind problem requirement, give suggestion, evaluate exploration, self-questions, revise plan, check computation and explain solution. The students asked for clarification most frequently because the group provided them with opportunities to clarify their doubts and check for understanding. The students also displayed positive affective behaviours such as persist in task, praise and encourage, which kept the group working on the tasks in a relaxing and non-threatening environment. Naturally they also showed negative affective behaviours such as self-evaluation, complaints and emotions, when they became frustrated in the problem solving process.
On the whole, the students under study gave positive and encouraging feedback towards the CMPS programme. The results obtained from this study have some important implications for both teaching and future research in mathematics. The planning of instructional methods in mathematical problem solving should incorporate the use of cooperative learning strategies. It is important that teachers create in their students an awareness of their own metacognitive and positive affective behaviours so that such behaviours become internalised after constant practice through cooperative problem solving.
With the increase in emphasis in mathematical problem solving in the Singapore mathematics curriculum, it is necessary to study effective instructional methods which will help teachers to teach mathematical problem solving confidently in the classrooms. The use of cooperative learning can provide an alternative to both traditional whole class expository instruction and individual instruction systems. When students work in cooperating groups, they know that they have the peer support to help one another cope with demanding situations. From the interactions and experiences acquired while students were engaged in the cooperative problem solving process, it is hoped that they could gain confidence and skills to improve their own problem solving abilities. Therefore, there is a need to explore further the use of cooperative learning strategies in mathematical problem solving instructions to benefit both the teachers and students.
From this study, it was found that the CMPS programme improved the problem-solving performance of students as measured by a holistic analytic marking scheme designed for the study. Students learnt to be more systematic in organising data given in a problem through the use of diagrams such as drawing a Matrix table or Decision Tree; and they were able to apply specific problem-solving strategies (e.g. try simple cases, look for patterns and find a general rule) to handle non-routine problems. The use of pre-instructional strategies such as guess-and-check, unsystematic listing and number manipulation became less frequent. The students attempted all problems with some strategies they had learnt. No one left problems unattempted as compared to the pre-test before the programme.
It was also found that students displayed a range of metacognitive and affective behaviours when they solved problems together. The metacognitive behaviours manifested were: ask for clarification, remind problem requirement, give suggestion, evaluate exploration, self-questions, revise plan, check computation and explain solution. The students asked for clarification most frequently because the group provided them with opportunities to clarify their doubts and check for understanding. The students also displayed positive affective behaviours such as persist in task, praise and encourage, which kept the group working on the tasks in a relaxing and non-threatening environment. Naturally they also showed negative affective behaviours such as self-evaluation, complaints and emotions, when they became frustrated in the problem solving process.
On the whole, the students under study gave positive and encouraging feedback towards the CMPS programme. The results obtained from this study have some important implications for both teaching and future research in mathematics. The planning of instructional methods in mathematical problem solving should incorporate the use of cooperative learning strategies. It is important that teachers create in their students an awareness of their own metacognitive and positive affective behaviours so that such behaviours become internalised after constant practice through cooperative problem solving.
Date Issued
1997
Call Number
QA63 Ho
Date Submitted
1997