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Paper presented at the annual meeting of the American Educational Research Association, New York, 2008
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
Project number: 
CRP 1/04 JH
Appears in Collections:CRPP - Conference Papers

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