Fang, Yanping

Students’ limited view of mathematics and their strong orientation on numbers have been major hindrances in developing students’ capacity in problem solving. Our study aims to understand students’ challenges in reasoning quantitatively and gain insights on how they overcome these challenges. To this end, seven pairs of Grade 5 students and eight pairs Grade 7 were observed and videotaped when they solved one routine task and one nonroutine task. Their processes in solving these two tasks were analyzed using the method of conceptual analysis (Glasersfeld, 1995). Findings suggest that there were two major areas of difficulties that they experienced in reasoning quantitatively. Some of the major challenges behind those difficulties were the lack of quantitative understanding in whole numbers and fractions, the stronger focus on the magnitudes of quantities than the quantities themselves, and the stronger reliance on visually-perceived relationships in the model representation of situation than the quantitative relationships. A case of a Grade 7 pair is presented to discuss a context of pair collaboration that fosters the overcoming challenges in reasoning quantitatively that suggests a practical implication of using collaborative learning to support students’ development of quantitative reasoning capacity.