Classification of students' creative thinking for non-routine mathematical problems

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has yet to classify their creative thinking in solving non-routine problems. This study created a new classification based on three aspects of creative thinking in solving mathematical problems. The research used a qualitative descriptive approach, employing 72 students from Indonesia as subjects in a test involving the use of the think-aloud approach in problem-solving. Data collection consisted of tests, observations, and interviews. There were three stages of data analysis: data reduction, presentation and conclusions, and verification. This study's results grouped students' creative thinking processes in solving non-routine problems into three classifications: direct, flexible, and elaborative. The three classifications differ in the strategies or steps used to solve problems. The similarities of the three classifications include using similar aspects of creative thinking, namely flexibility, fluency, and elaboration in solving non-routine problems, even though some of these aspects have yet to be realised optimally due to students' creative thinking in solving mathematical problems, especially non-routine problems, still needing improvement. Study offers a comprehensive study of creative thinking for mathematical problem-solving. Creative thinking is part of mathematical thinking, which is a crucial component of 21st century mathematics skills. Future educational challenges are very complex. For this reason, this study is here to present a classification of mathematical thinking for mathematical problem-solving. This research has never been conducted before, so the study is truly suitable to fill the gap and provide high novelty value. Hopefully, readers will be academically entertained by reading this study and gain new insights.