Research on organization of mathematics knowledge in good mathematical cognitive structure

Abstract

This research adopted the method of network data analysis, chose 31 senior high school first-grade outstanding students as participants and 44 concepts about trigonometric function as materials, analyzed the organization of mathematics knowledge in good mathematical cognitive structure (GMCS) with the help of software Ucinet. The results indicated: (1) The connections between the concepts in GMCS were more extensive, especially those connections with higher tightness degree. (2) Most connections in GMCS were direct. (3) There were more abstract concepts as accumulation points connecting with others. (4) There were a number of concrete and frequently used concepts connecting with others directly. Therefore, the mathematics teachers should help students to construct extensive and direct connections between mathematics knowledge in their mind. These new findings expanded and deepened the current research about mathematical cognitive structure(MCS), pointed out the direction and target for educators helping their students form GMCS. Meanwhile, this research demonstrated the network data analysis method was feasible and valuable to analyze mathematics psychological issues.