Mathematical Sophistication and Differentiated Emotions during Mathematical Problem Solving

Abstract

George Polya, author of Mathematical Discovery and the enduring best seller How to Solve It: A New Aspect of Mathematical Method, claims that more sophisticated people experience more differentiated emotion during mathematical problem solving, a claim that has been untested for nearly fifty years. Using instruments that measure ongoing evaluations and emotion in real time, and traits that reflect mathematical sophistication, the effect of sophistication on emotion during mathematical problem solving was investigated in this study using 209 mathematics and science majors at a technological university in the northeast. Students who were more mathematically sophisticated, as defined by Polya, were better problem solvers and had more highly differentiated emotions and on-going self-evaluations of progress towards solutions than students where were not mathematically sophisticated, just as Polya claimed. These more sophisticated students also managed their negative emotions and anxiety during problem solving better than students who were not mathematically sophisticated. It is hypothesized that these sophisticated students would be good mentors or work partners for students who were less mathematically sophisticated as they would model these meta-cognitive skills and traits for these later students helping them to learn them.