MATHEMATICAL BELIEFS AND PROBLEM SOLVING (SYSTEMS, ANXIETY, MOTIVATION, GIFTED)
Abstract
The purpose of this study was to investigate the role of students' mathematical beliefs in problem solving. The subjects were four junior high school students participating in Purdue University's STAR program, a two-week intensive summer program for the mathematically and verbally talented. These subjects were enrolled in a Beginning Math Problem Solving with Computers class. The four subjects were individually interviewed throughout the program. In the interviews, the students were questioned about their classroom experiences in mathematics and were encouraged to discuss their beliefs about mathematics. However, most of the interview time was spent with the students using the "think-aloud" technique to solve problems. The interview data were analyzed qualitatively. At the time that this study was designed and implemented, the focus was on the role of mathematical beliefs in problem solving. Five general categories of mathematical beliefs were distinguished based on analysis of the interview data. These categories were: beliefs about one's ability to do mathematics, beliefs about mathematics as a discipline, beliefs about where mathematical knowledge comes from, beliefs about solving mathematics problems, and beliefs about how mathematics should be taught and learned. Each type of belief was found to influence problem solving behavior. After preliminary analysis of the interview data it became apparent that other factors in addition to beliefs would have to be considered when explaining why these students did what they did when they solved problems. Mathematical problem solving, for these students at least, was conceptualized as being part of a larger framework. Components of this framework include the individual's prior experiences in mathematics, his mathematical knowledge, and his mathematical beliefs, needs, and motivations. Mathematics myths (societal beliefs) are also part of the framework, since they influence the individual's view of mathematics.
Degree
Ph.D.
Subject Area
Mathematics education
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