Abstract

Providing adequate proof is one essential mathematical method, but it is a difficult task for many school-age students. While previous studies have revealed the cognitive factors of proving the proof, the function of affective factors and learning engagement has been largely unexplored. This study examined the effects and processes associated with math anxiety, self-efficacy, engagement, and backward reasoning on the provision of proof when solving math problems about geometric similarity. A survey was conducted on 160 junior high school students, from which it was found that: (a) self-efficacy was indirectly and directly positively associated with the provision of proof when solving math problems and was mediated by math anxiety and backward reasoning; (b) math anxiety was indirectly and negatively associated with the provision of proof when solving difficult proof problems and was mediated by backward reasoning; (c) the use of backward reasoning was positively associated with the provision of proof when solving proof problems; (d) cognitive engagement was indirectly and positively associated with the provision of proof when solving proof problems and was mediated by self-efficacy and backward reasoning. The results suggest that improving cognitive engagement, self-efficacy, and backward reasoning may be effective in the provision of proof when solving proof problems.

This work is licensed under a Creative Commons Attribution 4.0 License.