Exploration of Creative Mathematical Reasoning in Solving Geometric Problems

Abstract

Reasoning that is constructed from remembering is imitative reasoning, while the opposite is creative reasoning. This study aims to explore creative mathematical reasoning in solving geometric problems. Mathematical creative reasoning is reasoning that contains elements of novelty, plausibility, and mathematical foundation. This type of research is descriptive qualitative, which is explorative. The research subjects were the first-semester student in the mathematics education study program with 32 students. The results showed that from 32 students, there was only one student identified as having creative mathematical reasoning in solving geometry problems. Creative mathematical reasoning can be identified when the subject is able to reason algorithmically but is aware of problems so they cannot be resolved algorithmically so that they must form new reasoning, which consists of novelty, plausibility, and mathematical foundation. Creative mathematical reasoning arises after students make an algorithmic reasoning process, but find no solution. Novelty is the weakest indicator of creative mathematical reasoning, so it requires scaffolding to bring it up.

Keywords

• creative mathematical reasoning
• geometry
• problem solving