Investigating Mathematical Knowledge for Teaching Proof in Professional Development
Investigating Mathematical Knowledge for Teaching Proof in Professional Development
复制标题
研究数学知识以作为专业发展的教学证明
DOI：
10.21890/ijres.13913
复制
发表时间：
2016
期刊：
影响因子：
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通讯作者：
Kristin Lesseig
中科院分区：
文献类型：
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作者：
Kristin Lesseig
一项关于教师对证明的脆弱理解以及证明是如何被推进的研究表明，加强证明在学校数学中的作用将需要教师大量的学习。到目前为止，几乎没有研究详细说明哪些数学知识可以支持证明教学，或者专业发展(PD)如何支持这种学习。本文提出了一个用于教学证明的数学知识框架(MKT For Prompt)，该框架规定了跨学科和跨教学领域的证明知识。为了探索该框架的实用性，本文考察了教师和领导者在四种不同的PD情境下完成同一证明任务的数据。通过对这四种情境下的讨论的分析，揭示了在每种情境下可获得的证明知识的异同。这些发现提供了一种方法来详细说明MKT for Proof框架，并展示其作为设计、分析和评估PD中证明经验的工具的有效性。
Research documenting teachers’ fragile understanding of proof and how it is advanced suggests that enhancing the role of proof in school mathematics will demand substantial teacher learning. To date, there is little research detailing what mathematical knowledge might support the teaching of proof or how professional development (PD) might afford such learning. This paper advances a framework for Mathematical Knowledge for Teaching Proof (MKT for Proof) that specifies proof knowledge across subject matter and pedagogical domains. To explore the utility of the framework, this paper examines data from four different PD settings in which teachers and leaders worked on the same proof-related task. Analysis of discussions across these four settings revealed similarities and differences in knowledge of proof made available in each setting. These findings provide a means to detail the MKT for Proof framework and demonstrate its usefulness as a tool for designing, analyzing and evaluating proof experiences in PD.