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A small-scale study on the effects of metacognition and beliefs on students in A-level sequences and series problem-solving
Author
Teo, Oi Mei
Supervisor
Tay, Eng Guan
Toh, Tin Lam
Abstract
The main purpose of this study was to investigate the effects of metacognition and beliefs on junior college students while working on Sequence and Series problems. In order to evaluate how the students exercised their control decisions, two tests were constructed. The confidence of the students with regard to their test solutions was also analysed. This includes finding the correlation between the correctness of answer on the test items and their confidence level. A questionnaire that deals with the students' perception on how to solve mathematical problems was also analysed. Lastly, interviews were conducted with selected students to understand in more detail how the students' control decision affect their approaches.
Firstly, the findings in this study suggest that an individual's control decision affects their test performance. Inefficient control behaviour often causes the students to rush into solving the problem without much analysis. On the other hand, students who were good in accessing their resources and had good control were more successful. Secondly, it was found that students' confidence in their solutions was positively correlated with their test performance and this suggests that students generally know if they have got the answer right or not. Thirdly, the data analysis suggests that there is significant difference in the difference mean score of Test 1 and Test 2 between students in the group with Teacher Intervention and the group without Teacher Intervention at 0.10 level but not at 0.05 level. Also, the Teacher Intervention procedure was found to have medium effect (according to Cohen's criteria). Fourthly, the findings from the questionnaire suggest that the students seldom check their working nor reflect on alternative solutions. At the same time, most students believed that application of heuristics or strategies was important in mathematical problem solving.
Lastly, from the interviews, students with good control demonstrated how they approach the problems with ease. More control decisions were made when working with familiar problems. The issue of control becomes crucial to success in their attempts with unfamiliar problems. This study recommends that the students be exposed to metacognitive strategies in the classroom so as to become self-directed learners.
Firstly, the findings in this study suggest that an individual's control decision affects their test performance. Inefficient control behaviour often causes the students to rush into solving the problem without much analysis. On the other hand, students who were good in accessing their resources and had good control were more successful. Secondly, it was found that students' confidence in their solutions was positively correlated with their test performance and this suggests that students generally know if they have got the answer right or not. Thirdly, the data analysis suggests that there is significant difference in the difference mean score of Test 1 and Test 2 between students in the group with Teacher Intervention and the group without Teacher Intervention at 0.10 level but not at 0.05 level. Also, the Teacher Intervention procedure was found to have medium effect (according to Cohen's criteria). Fourthly, the findings from the questionnaire suggest that the students seldom check their working nor reflect on alternative solutions. At the same time, most students believed that application of heuristics or strategies was important in mathematical problem solving.
Lastly, from the interviews, students with good control demonstrated how they approach the problems with ease. More control decisions were made when working with familiar problems. The issue of control becomes crucial to success in their attempts with unfamiliar problems. This study recommends that the students be exposed to metacognitive strategies in the classroom so as to become self-directed learners.
Date Issued
2006
Call Number
QA63 Teo
Date Submitted
2006