Calls for a stronger focus on proof and justification in the middle grades have led to recent curricular and pedagogical changes emphasizing proof activities in algebra classrooms. These changes pose serious challenges, given the documented difficulties faced by students in understanding proof and by teachers in creating classrooms aimed at fostering students’ proof competencies in algebra. This project addresses these challenges by introducing into the ongoing investigation of the teaching and learning of proof a new strand of research—namely, research on quantitative reasoning.

An emphasis on quantitative reasoning has been found to support students’ understanding of algebraic relationships, encouraging reasoning that is flexible and general in character. This 5-year program of study will wed two previously disconnected lines of research on quantitative reasoning and proof in order to support (a) students’ developing proof skills in algebra and (b) teachers’ abilities to promote these skills in the classroom.

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