This study examined the effect of problem-based instruction (PBI) on undergraduate students and prospective secondary mathematics teachers’ perceptions of mathematical proof and pedagogical views. Quantitatively, the Mathematical Proof Survey (MPS) was developed and used to assess the views of mathematical proof held by undergraduates in lecture-based and PBI mathematics courses. Qualitatively, research interviews examined the way teacher candidates’ experiences as mathematics learners in the courses affected their conceptions of mathematical proof and views of learning and teaching mathematics and proof. Findings from quantitative analysis of MPS data and qualitative analysis of interview data are presented, and results from the comparative analysis are discussed for implications. The results of the study suggest that experiences with proof and instruction in such PBI courses provide opportunities for undergraduates and prospective mathematics teachers to develop more humanistic perspectives of proof and process-oriented pedagogical views than do lecture-based courses. / text

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

Although proof has long been viewed as a cornerstone of mathematical activity, incorporating the mathematical practice of proving into classrooms is not a simple matter. In this dissertation I aim to advance research on proof by addressing this issue. In particular, I explore the role proof might play in promoting the learning of mathematics in the classroom. I do this in a series of three articles (organized as three chapters), which are preceded by an introductory chapter. The introductory chapter situates the remaining chapters in the context of mathematics education research. In the second chapter I explore what the literature on proof tells us about what role proof might play in the promotion of learning in the mathematics classroom. In this chapter I also compare the ways in which proof is purported to promote learning in the mathematics classroom with the roles it is purported to play in the field of research mathematics. In the third chapter I look at empirical data to explore ways engaging in proof and proving might create opportunities for student learning. In particular, my analysis led me to focus on how identifying and reflecting on the key idea of a proof can create opportunities for learning mathematics. The final chapter is an article for a practitioner journal and discusses implications for practice based on the two preceding articles.