Date of Award

12-1999

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Christian Hirsch

Second Advisor

Dr. Laura VanZoest

Abstract

Students’ conceptions of mathematics are shaped by the environment within which they learn mathematics and in turn they affect the manner in which students engage in mathematics.

This study examined students’ conceptions about learning, knowing, and doing mathematics after studying four years of a Standards-based reform high school mathematics curriculum developed by the Core-Plus Mathematics Project (CPMP). Student conceptions were examined at the end of high school (n = 2S6) and after one semester of college mathematics (n = 92). The study also provides case studies of six students as they navigated from the CPMP curriculum through college Precalculus or Calculus.

The Conceptions of Mathematics Inventory (Grouws, Howald, & Colangelo, 1996), a 56-item likert-scale survey, was used to measure student conceptions. Upon graduation from high school the students believed that mathematical concepts, principles, and generalizations were slightly more important than facts, formulas, and algorithms. They believed that mathematics was a coherent and dynamic field, that learning mathematics was more about constructing understanding than memorizing, that doing mathematics was more about making sense out of situations than just solving problems, and that mathematics was useful. Paired t-tests indicated that all but two of these conceptions were stable. After one semester of college mathematics, there was a statistically significant change in students’ beliefs about the composition of mathematical knowledge, with facts, formulas, and algorithms becoming more important, and in students’ beliefs about the usefulness of mathematics, with students seeing less use for mathematics.

Case studies of the experiences and thinking of six students, from five different high schools, were conducted and provide rich descriptions about the transition from the CPMP curriculum through the first semester of college mathematics. Using interviews, problem-solving sessions, classroom observations, and written assessments, the students’ conceptions and experiences were analyzed. The problem-solving sessions allowed for insight into how each student’s conceptions were reflected in mathematical situations. Among the six students a variety of conceptions about learning, knowing, and doing mathematics were exhibited. In addition, the case studies indicate that none of the six students had difficulty making the transition from the CPMP Standards-based curriculum to college mathematics.

Access Setting

Dissertation-Open Access

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