Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

Abstract

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word problems was found to have only a limited impact. Instead, removing contextual constraints from the problem goal was found to motivate students to validate their problem solving in terms of their everyday experiences. Based on these findings, what determines the authenticity and relevance of a mathematical problem seems to be whether the problem allows students to freely reconstruct the problem situation by making use of their imagination and everyday experiences. In short, the basic principle seems to be “less is more”; that is, fewer constraints in problem goals could function to help students personally associate problem solving with their everyday experiences.

ACKNOWLEDGEMENT

This report is based on the dissertation submitted to Columbia University. The author would like to express gratitude to Prof. Herbert Ginsburg, who served as dissertation advisor, and gave numerous helpful comments on an earlier version of this manuscript. Table 1, Table 2, Table 3, Table 5 and a portion of the coding system was reprinted from Learning and Instruction, 15, Inoue, N., Realistic reasons behind “unrealistic” solutions: The role of interpretive activity in word problem solving, 69–83, Copyright (2005), with permission from Elsevier.