Influence of Prior Knowledge and Teaching Approaches Integrating Non-routine Worked Examples and Virtual Manipulatives on the Performance and Attitude of Fifth-Graders in Learning Equivalent Fractions

Abstract

The objective of this study was to investigate the influence of prior knowledge and non-routine worked examples, integrated with manipulatives, on the performance and attitude of fifth-graders learning of equivalent fractions. The participants were divided into three groups based on the teaching method to which they were exposed: continuous examples paired with physical manipulatives (continuous-physical group), continuous examples paired with virtual manipulatives (continuous-virtual group), and integrated examples paired with virtual manipulatives (integrated-virtual group). The results indicate the following: (1) The integrated-virtual group displayed better performance than the continuous-physical and continuous-virtual groups in basic and advanced flexible thinking, whereas the continuous-physical and continuous-virtual groups showed no significant differences; (2) The students with high prior knowledge in the continuous-virtual group presented higher scores in learning enjoyment and mathematics anxiety than those in the integrated-virtual and continuous-physical groups, and those in the continuous-virtual group also displayed greater learning motivation than those in the integrated-virtual group; and, (3) The students with low prior knowledge in the continuous-virtual and integrated-virtual groups presented higher scores in learning enjoyment than those in the continuous-physical group. However, the students with low prior knowledge in the three groups displayed no significant differences in learning motivation and mathematics anxiety.