PROOF Project

Although there is abundant literature focusing on various aspects of proof in school mathematics, to date, little systematic information about how students acquire and develop their understandings of what constitutes evidence and justification in mathematics and how such understandings can be extended and refined exists. The purpose of this 5-year longitudinal study is to trace the development of middle school students' competencies in justifying and proving and to identify conditions that influence that development. This study will follow a group of 6th grade students through the completion of 8th grade, using written assessments, semi-structured interviews, and classroom observations to document and analyze changes in their competencies and to understand classroom practices that influence these changes. In addition, these students' teachers will participate in concurrent professional development activities designed to enhance their understandings of middle school students' development of mathematical reasoning and classroom practices that promote that development.

The objectives of this project are threefold: (1) to understand the development of students' competencies in justifying and proving; (2) to understand the conditions and pedagogy necessary to promote the development of those competencies; and (3) to develop teacher preparation and professional development materials designed both to enhance teachers' understandings of proof and to support them in fostering the development of students' competencies in justifying and proving.

Three primary research questions guide this study:

  1. What is the conceptual landscape of middle school students' competencies in justifying and proving?
  2. What are plausible trajectories for the development of students' competencies in justifying and proving?
  3. What are conditions and pedagogy that might foster the development of students' competencies in justifying and proving?