Understanding authority in small-group co-constructions of mathematical proof

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI:10.1016/j.jmathb.2022.101015
Sarah K. Bleiler-Baxter , Jordan E. Kirby , Samuel D. Reed
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Abstract

Authority becomes shared in mathematics classrooms when perceived sources of valid mathematical knowledge extend beyond the teacher/textbook and allow both students and disciplinary modes of reasoning to hold authority. The goal of this research is to better understand classroom situations that are intended to facilitate shared authority over proof, namely small-group episodes where students are granted authority (Gerson & Bateman, 2010) to co-construct mathematical proofs. We sought to better understand the content of undergraduate students’ attention during group proving and the sources of legitimacy for students. Using Stylianides’ (2007) definition of proof as an analytical frame, we found that student discourse focused primarily upon the mode of argumentation, followed by the mode of argument representation, and then the set of accepted statements. We identified four themes with respect to the sources of authority students relied upon in their group proving: (1) the course rubric, (2) peers’ confidence, (3) form and symbols, and (4) logical structure. Implications for research and practice are presented.

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理解数学证明的小组共建中的权威性
当有效数学知识的感知来源延伸到教师/教科书之外,并允许学生和学科推理模式都掌握权威时,权威就在数学课堂上共享。这项研究的目的是更好地理解旨在促进共享权威而非证明的课堂情况,即学生被授予共同构建数学证明的权力的小组事件(Gerson&;Bateman,2010)。我们试图更好地理解本科生在群体证明过程中的注意力内容以及学生合法性的来源。使用Stylianides(2007)对证明的定义作为分析框架,我们发现学生话语主要关注论证模式,其次是论证表示模式,然后是可接受的陈述集。关于学生在小组证明中所依赖的权威来源,我们确定了四个主题:(1)课程准则,(2)同伴的信心,(3)形式和符号,以及(4)逻辑结构。提出了对研究和实践的启示。
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来源期刊
Journal of Mathematical Behavior
Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
2.70
自引率
17.60%
发文量
69
期刊介绍: The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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