Comparison of Two Teaching Methods Aimed at Enhancing Students’ Conceptual Understanding of Generalized Mathematical Concepts: Utilization of Prior Knowledge

Abstract

The purpose of the present study was to investigate whether differences in students' prior knowledge affected the deepening of their conceptual understanding. The study was conducted in 2 tenth-grade classes (N=25 and 26) whose curriculum aimed at deepening understanding of generalized mathematical concepts. One of the classes was taught with teaching method A, which used the topic of bouncing of objects as knowledge gained from daily experience. The other class was taught with teaching method B, which used the topic of geometric sequences as knowledge already studied in mathematics. Both classes were taught by the same teacher. The data were the students' descriptions of tasks related to exponential functions before and after these topics had been taught and their in-class worksheets. Analysis of the data revealed the following: (a) Teaching method A promoted a deeper conceptual understanding of generalized exponentials than teaching method B did, and (b) deepening of the students' conceptual understanding of generalized exponentials was especially achieved through the exploration of problems that captured the characteristics of constant ratios in exponential changes. The discussion dealt with teaching meth- ods that might promote a deepening of students' conceptual understanding of generalized mathematical concepts.