# Project Goals & Questions

The goals of the 3-year project are threefold: (a) investigate the nature of middle school and high school students’, undergraduate students’, and mathematicians’ thinking about the examples they use when developing, exploring, and proving conjectures; (b) investigate ways in which thinking about and analyzing examples may facilitate the development of students’ learning to prove; and (c) develop instructional materials designed to help teachers and university instructors foster the development of their students’ thinking about and use of examples in learning to prove.

The research seeks to address the following research questions:

- How does students’ use of examples and the nature of their thinking about the examples they use to develop, explore, understand, and prove mathematical conjectures develop as they gain mathematical expertise?
- What is the relationship and interplay among the purposes—to develop, to explore, to understand, or to prove a conjecture—and the nature of examples students use as they gain mathematical expertise?
- How do the various ways of thinking about and analyzing examples facilitate the development of secondary school mathematics and undergraduate mathematics students’ learning to prove?
- How can instruction foster students’ need and abilities to develop proofs by leveraging their strategic use of examples?
- What are the particular ways of reasoning with examples that are critical in supporting students’ transition to proof?

This joint effort is housed within the Wisconsin Center for Education Research at the School of Education, University of Wisconsin-Madison. Copyright ©2012, The Board of Regents of the University of Wisconsin System.