Developing mathematical thinking and reasoning skills for 4th graders through teaching fraction operations

Abstract

This study designs and analyzes teaching activities for fraction operations in grade 4 to develop students’ mathematical thinking and reasoning skills. Based on theories of mathematical thinking and reasoning, the zone of proximal development, and the difficulties students face when learning fractions, the study proposes principles for organizing teaching activities that integrate cognitive processes such as analysis, comparison, synthesis, generalization, analogical reasoning, and critical reasoning. Illustrative activities include teaching rules for fraction operations and fraction exercises, enabling students to observe, predict, test, compare, discuss, and justify their solutions. The results show that teaching guided by analogical reasoning and the zone of proximal development not only reinforces knowledge and skills but also promotes mathematical thinking and reasoning, creating an active learning environment and cultivating logical and critical thinking.