Reasoning and proving in school mathematics curricula: An analytic framework for investigating the opportunities offered to students

Stylianides, G.J., & Silver, E.A.

ABSTRACT. There is widespread agreement that reasoning and proof should be a central feature of all students' mathematical experiences. Yet, research shows that students often have serious difficulties acquiring competency in this domain. Students are unlikely to develop proficiency in reasoning and proving on a large scale unless attention to this mathematical practice is woven into curriculum materials. Too little is known about the opportunities mathematics curricula offer students for reasoning and proving; a curriculum analysis is needed to illuminate the nature of the opportunities provided so they can be further developed. This study seeks to provide needed knowledge by: (a) conceptualizing reasoning and proving in a way that is sensitive to the mathematical discipline and promising to push forward the conceptual work on the nature of this activity in school mathematics; and (b) using this conceptualization to develop and validate an analytic framework that provides a reliable and comprehensive way to analyze the opportunities mathematics curricula provide students to engage in reasoning and proving.