Effects of Engagement and the Difficulties with Figures on Mathematical Proof Problem Solving

Abstract

The purpose of the present study was to examine the effects of engagement and the difficulties with figures on proof problem solving. Junior high school students (N=162) completed questionnaires. It was found that: (a) The difficulties with figures was composed of 4 factor: “the properties of parallel lines and angles”, “plane figure measurements”, “methods of proof”, and “drawing and moving figures”; (b) the lower the methods of proof difficulties, the higher the cognitive engagement, and the better the proof solutions; (c) the lower the drawing and moving figure difficulties, the worse the proof solutions; and (d) the lower the methods of proof difficulties, the higher the engagement. It was concluded that reducing the methods of proof difficulties could promote better problem solving and better engagement.