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 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.