#### Sponsor

Portland State University. Department of Mathematics and Statistics

#### Advisor

Sean Larsen

#### Date of Award

Spring 5-15-2013

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.) in Mathematics Education

#### Department

Mathematics and Statistics

#### Physical Description

1 online resource (vi, 150 pages)

#### Subjects

Mathematics -- Study and teaching (Middle school) -- Research, Problem solving -- Mathematics -- Study and teaching (Middle school), Induction (Mathematics) -- Study and teaching (Middle school), Proof theory -- Study and teaching (Middle school)

#### DOI

10.15760/etd.1075

#### Abstract

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.

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/9884

#### Recommended Citation

Bartlo, Joanna Rachel, "Why Ask Why: An Exploration of the Role of Proof in the Mathematics Classroom" (2013). *Dissertations and Theses.* Paper 1075.

https://pdxscholar.library.pdx.edu/open_access_etds/1075

10.15760/etd.1075

#### Included in

Junior High, Intermediate, Middle School Education and Teaching Commons, Science and Mathematics Education Commons