What is mathematics? Stability and change in prospective teachers' conceptions of and attitudes toward mathematics and teaching mathematics

In this study, I examined the conceptions of and attitudes toward mathematics and teaching mathematics of prospective elementary school teachers and whether they changed during the time they were in a course designed to help prepare them to teach mathematics to elementary-age students. There were 34 students in the class who served as subjects for the study. Four of those students also served as focus students, and I examined them as case studies. I used four main sources for data. The first was a mathematics inventory with Likert-type items and open-ended questions that the students took on the first day of class and again on the last day of class. The second source of data were math concept maps the students did at the first of the semester and the end of the semester. The third source were various journal entries the students wrote during the course including a "What Is Mathematics?" journal entry written at the beginning and end of the semester and a "Philosophy of Teaching Mathematics" entry written at the end of the semester. The final data source consisted of two interviews each of the four focus students. A colleague administered the first interview to the focus students during the course, and I administered the other interview to the focus students a semester after the class ended. I also developed a framework delineating different aspects of the students' conceptions of mathematics to use as a template for organizing the analysis.;The most important finding that became apparent from an analysis of the data is that during the course the students shifted their position in relation to mathematics from that of an experienced student to that of a prospective teacher. It appeared that that shift in positioning served as a catalyst for change in the students' attitudes toward and some of their conceptions of mathematics and teaching mathematics. Instead of basing their conceptions of and attitudes toward mathematics and teaching mathematics on their own experiences with mathematics, they were able to think about how they wanted to teach it. Having a new relation to mathematics (as prospective teachers) the students were able to imagine it being taught in a way that was perhaps different and much more positive than they had experienced as students, and their attitudes toward mathematics and teaching mathematics became much more positive.;I found significant and noteworthy changes in the students' conceptions of the processes of mathematics and the usefulness of mathematics as well as in their conceptions of learning and teaching mathematics. I also conjecture that dissatisfaction plays a role in change. One of the major implications of this study for mathematics teacher educators is that by being aware of the role that the shift in positioning in the relation to mathematics plays in facilitating change in conceptions and attitudes of prospective teachers, mathematics teacher educators can provide experiences for their students in which they can experience thinking of themselves as teachers of mathematics. Also, knowing which areas are more likely to change, mathematics teacher educators can emphasize those areas.;The main contributions of this study to research in mathematics education were a study that showed there could be change, a new framework for conceptualizing mathematics, ideas for using concept maps in research, and understanding the relevance that the shift of positioning the students experience in relation to mathematics has to changes in conceptions and attitudes.