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The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir

The ability to engage in mathematical thinking and apply it to problem-solving constitutes a fundamental objective of mathematics teaching and learning. Current findings have depicted that students are grappling with significant challenges in developing these cognitive abilities skills. This necessi...

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Main Author: Md Nasir, Nurul Akmal
Format: Thesis
Language:English
Published: 2024
Subjects:
Problem-based learning
Study and teaching
Philosophy
Online Access:https://ir.uitm.edu.my/id/eprint/98700/1/98700.pdf
https://ir.uitm.edu.my/id/eprint/98700/
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spelling my.uitm.ir.987002024-08-26T03:38:28Z https://ir.uitm.edu.my/id/eprint/98700/ The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir Md Nasir, Nurul Akmal Problem-based learning Study and teaching Philosophy The ability to engage in mathematical thinking and apply it to problem-solving constitutes a fundamental objective of mathematics teaching and learning. Current findings have depicted that students are grappling with significant challenges in developing these cognitive abilities skills. This necessitates an immediate investigation to enhance students' mathematical reasoning and problem-solving abilities. Thus, the aim of this study to examines the impact of a problem-solving approach (PSA) on the development of students' mathematical thinking within the context of undergraduate programs at a public university. It aims to assess the effects of the PSA on students' achievements, cognitive-metacognitive processes, and heuristics knowledge before and after intervention. A mixed-method approach (embedded design) was employed for data collection. Firstly, a quasi-experimental design was used, involving two intact groups of first-year undergraduates (n=49), with 24 students in the experimental group and 25 students in the control group. Both groups underwent pre-tests and post-tests, with an 8-week intervention period, to assess and compare the participants' progress in mathematical thinking scores and heuristics knowledge. Secondly, three students were selected from the experimental group for interviews, using a thinking-aloud protocol before, during, and after the intervention. The aim was to examine the development progress in problem-solving and cognitive-metacognitive thinking processes. The integration of quantitative and qualitative data provided deeper insights into the participant’s experiences and the effectiveness of the intervention in enhancing their problem-solving skills. Descriptive analysis of the pretest among the 49 students indicated a low level of attainment in mathematical thinking scores (mean=6.61; SD=3.26) out of a maximum score of 40, depicting a poor performance with a percentage score of 16.5% among the participants. The main study findings revealed that the PSA had a significant impact on mathematical thinking achievement, as evidenced by test scores (F(1,47)=81.05, p<0.05). The results suggest that the intervention of the problem-solving approach enhanced participants' achievement in mathematical thinking. Similarly, the PSA had a positive effect on students' cognitive- metacognitive strategies development (F(1,47) = 36.12, p <0.05). Regression analysis further elucidated that heuristic knowledge significantly predicted mathematical thinking scores. Observations during think-aloud sessions demonstrated progress in problem-solving activities and cognitive processes among selected participants, indicating enhanced metacognitive skills, including read-analyse-explore-plan- implement-verify strategies. Implications suggest that incorporating heuristics-based approaches in mathematics instruction can improve problem-solving abilities and enhance mathematical thinking among undergraduates. This pedagogical approach fosters positive attitudes towards mathematics, supporting students' academic growth and cognitive development. 2024 Thesis NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/98700/1/98700.pdf The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir. (2024) PhD thesis, thesis, Universiti Teknologi MARA (Kampus Puncak Alam).
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Problem-based learning
Study and teaching
Philosophy
spellingShingle Problem-based learning
Study and teaching
Philosophy
Md Nasir, Nurul Akmal
The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
description The ability to engage in mathematical thinking and apply it to problem-solving constitutes a fundamental objective of mathematics teaching and learning. Current findings have depicted that students are grappling with significant challenges in developing these cognitive abilities skills. This necessitates an immediate investigation to enhance students' mathematical reasoning and problem-solving abilities. Thus, the aim of this study to examines the impact of a problem-solving approach (PSA) on the development of students' mathematical thinking within the context of undergraduate programs at a public university. It aims to assess the effects of the PSA on students' achievements, cognitive-metacognitive processes, and heuristics knowledge before and after intervention. A mixed-method approach (embedded design) was employed for data collection. Firstly, a quasi-experimental design was used, involving two intact groups of first-year undergraduates (n=49), with 24 students in the experimental group and 25 students in the control group. Both groups underwent pre-tests and post-tests, with an 8-week intervention period, to assess and compare the participants' progress in mathematical thinking scores and heuristics knowledge. Secondly, three students were selected from the experimental group for interviews, using a thinking-aloud protocol before, during, and after the intervention. The aim was to examine the development progress in problem-solving and cognitive-metacognitive thinking processes. The integration of quantitative and qualitative data provided deeper insights into the participant’s experiences and the effectiveness of the intervention in enhancing their problem-solving skills. Descriptive analysis of the pretest among the 49 students indicated a low level of attainment in mathematical thinking scores (mean=6.61; SD=3.26) out of a maximum score of 40, depicting a poor performance with a percentage score of 16.5% among the participants. The main study findings revealed that the PSA had a significant impact on mathematical thinking achievement, as evidenced by test scores (F(1,47)=81.05, p<0.05). The results suggest that the intervention of the problem-solving approach enhanced participants' achievement in mathematical thinking. Similarly, the PSA had a positive effect on students' cognitive- metacognitive strategies development (F(1,47) = 36.12, p <0.05). Regression analysis further elucidated that heuristic knowledge significantly predicted mathematical thinking scores. Observations during think-aloud sessions demonstrated progress in problem-solving activities and cognitive processes among selected participants, indicating enhanced metacognitive skills, including read-analyse-explore-plan- implement-verify strategies. Implications suggest that incorporating heuristics-based approaches in mathematics instruction can improve problem-solving abilities and enhance mathematical thinking among undergraduates. This pedagogical approach fosters positive attitudes towards mathematics, supporting students' academic growth and cognitive development.
format Thesis
author Md Nasir, Nurul Akmal
author_facet Md Nasir, Nurul Akmal
author_sort Md Nasir, Nurul Akmal
title The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
title_short The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
title_full The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
title_fullStr The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
title_full_unstemmed The effects of problem-solving approach on the development of mathematical thinking / Nurul Akmal Md Nasir
title_sort effects of problem-solving approach on the development of mathematical thinking / nurul akmal md nasir
publishDate 2024
url https://ir.uitm.edu.my/id/eprint/98700/1/98700.pdf
https://ir.uitm.edu.my/id/eprint/98700/
_version_ 1808976046854242304
score 13.211869

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