Abstract
Reasoning-and-proving is a crucial part of students’ mathematical experiences in secondary school. There is scholarly debate, however, on the extent to which proving at the secondary level needs to be formal and whether all students should be held to disciplinary standards of rigor. In this study, we investigated the notion of “proof for all” from the perspective of secondary mathematics teachers. We analyzed, using the framework of practical rationality, the justifications teachers gave for whether or not all students should learn proof. Based on interviews with twenty-one secondary teachers from a socioeconomically-diverse set of schools, we found that teachers differ in their opinions of who should learn proving but they were similar in their feelings of obligation toward individual student learning; some teachers cited obligations to individual students as a justification for teaching proving to all students and others cited those obligations as a justification for not teaching proving to some students. We also share teachers’ perspective with regard to their obligations to the discipline, educational institutions, interpersonal dynamics among students, and the worldly relevance of mathematics education.
Highlights
Motivation for Studying Perspectives on Who Should Learn ProvingReasoning-and-proving, the broad mathematical practice of conjecturing, justifying, critiquing arguments, constructing proofs and more (Stylianides, 2008), is central to the discipline of mathematics and can be a powerful process through which students learn mathematics (de Villiers, 1995; Stylianides et al, 2017)
With regard to formal proof in particular, Weber (2015) noted that it may be unnecessary at the secondary level to explicitly develop “proving” and that it may be sufficient to push for clear explanations and valid justifications, which is one of the functions of proving and may more clearly build upon students’ mathematical experiences prior to secondary school
As the ones directly responsible for enacting curricular recommendations, stand on this issue of “proof for all”? How are teachers thinking about the scope and appropriateness of proof for students? Past studies have examined teachers’ views of what proof is (e.g., Ko, 2010) and their views on mathematical processes including proof (e.g., Sanchez et al, 2015) but the question of who they think should learn proof is fundamental
Summary
Reasoning-and-proving, the broad mathematical practice of conjecturing, justifying, critiquing arguments, constructing proofs and more (Stylianides, 2008), is central to the discipline of mathematics and can be a powerful process through which students learn mathematics (de Villiers, 1995; Stylianides et al, 2017). With regard to formal proof in particular, Weber (2015) noted that it may be unnecessary at the secondary level to explicitly develop “proving” and that it may be sufficient to push for clear explanations and valid justifications, which is one of the functions of proving (de Villiers, 1999) and may more clearly build upon students’ mathematical experiences prior to secondary school. We interviewed 21 secondary mathematics teachers from an economically-diverse set of schools in Cape Town, South Africa. The question of who should experience proof is one with worldwide relevance as we broadly consider students’ mathematical experiences
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