Mathematical Creative Problem-Solving: Students’ Cognitive Flexibility in Idea Generation and Evaluation

Source abstract

Learning experiences that rely on procedural memorization are insufficient to support students’ cognitive development in solving non-routine mathematical problems, as such contexts require cognitive flexibility to generate, evaluate, and adapt multiple solution strategies. This study aims to explore students’ cognitive flexibility activities in the phases of idea generation and idea evaluation through mathematical creative problem-solving. Using a multiple case study design, eight junior high school students from two different school contexts (public and private) participated in individual problem-solving and discussion activities. The research was conducted through three stages, namely: define and design, prepare–collect–analyze, and analyze–conclude. Data collected from written problem-solving tasks, video-recorded sessions, and follow-up discussions. Data were analyzed using NVivo 15 software through data condensation, data display, and cross-case conclusion drawing. The findings show that strategic and representational cognitive flexibility occurred in both idea generation and evaluation, with the latter occurring more frequently. These results highlight the importance of emphasizing idea evaluation in mathematics instruction to enhance students’ adaptive thinking and deepen their understanding when facing non-routine problems.