Context and Implications Document for: Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation
Context and Implications Document for: Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation
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上下文和含义文件：中学生的数学证明结构：书面与口头论证表达模式的作用
DOI：
10.1002/rev3.3158
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发表时间：
2018
影响因子：
2.4
通讯作者：
Andreas J. Stylianides
中科院分区：
文献类型：
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作者：
Andreas J. Stylianides
“证明”的概念是数学深度学习的基础，在许多国家，它被认为对所有教育级别的学生的数学经验都很重要，早在小学就开始了（例如，全国州长协会最佳实践中心和州首席学校官员理事会[NGA & CCSSO]，2010年;教育部，2013年）。证明的概念也很难教，也很难学，因此在过去的几十年里，它在国际上引起了数学教育领域研究人员的极大关注（有关这一领域最新技术的综述，请参见Stylianides，Stylianides和Weber，2017）。一项主要的研究集中在中学生（即小学后）对数学论点的建构上，表明许多中学生未能提出符合证明标准的论点。然而，这方面的研究往往只考虑中学生以书面形式提出他们认为的证据，主要是在调查研究的背景下。这些研究缺乏考虑中学生口头提出他们的感知证明-与学生的书面证明相同的索赔-可能会导致一个不完整或扭曲的学生构建的证据的潜力，这引起了人们对研究结果的有效性的关注。在这篇文章中，我的目的是通过探索的作用，在中学生的证明结构的论点表征模式的贡献。使用课堂数据来比较学生在两个中学数学教室中构建的书面论点（感知证明）与学生在课堂上为相同主张提出的口头论点，我得出的结果表明，
The concept of ‘proof’ is fundamental to deep learning in mathematics and in various countries it is considered to be important for students’ mathematical experiences across all the levels of education, as early as the primary school (e.g. National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010; Department for Education, 2013). The concept of proof is also hard-to-teach and hard-to-learn, and thus over the past few decades it has attracted significant attention internationally by researchers in the field of mathematics education (for a review of the state of the art in this area, see Stylianides, Stylianides, &Weber, 2017). A main research strand has focused on secondary (i.e. post-primary) students’ constructions of mathematical arguments, showing that many secondary students fail to produce arguments that meet the standard of proof. However, the studies in this strand have tended to only consider secondary students presenting their perceived proofs in written form, primarily in the context of survey studies. The lack of consideration by these studies of secondary students presenting their perceived proofs orally —in tandem with students’ written proofs for the same claims—might have resulted in an incomplete or a skewed picture of the potential of students’ constructed proofs, and this raises concern about the validity of research findings. In this article I aimed to contribute to this area by exploring the role of the mode of argument representation in secondary students’ proof constructions. Using classroom data to compare the written arguments (perceived proofs) constructed by students in two secondary mathematics classrooms with the oral arguments that the students presented in the front of their class for the same claims, I derived findings that suggest