Who’s There? A Study of Students’ Reasoning about a Proof of Existence
Who’s There? A Study of Students’ Reasoning about a Proof of Existence
复制标题
谁在那里？关于学生关于存在证明的推理的研究
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Brown
中科院分区：
文献类型：
--
作者：
S. Brown
借鉴以前的研究间接证明，本文报告了一系列的探索性研究，探讨在何种程度上发现学生的推理方式的矛盾和对位表征学生的看法间接存在的证据。具体而言，研究1记录了学生的比较选择和选择的理由时，要求选择“最有说服力”的证明，给出了建设性和非建设性的存在证明。研究2通过记录新手对非建设性存在证据的信念和解释水平，进一步检验了研究1的发现。研究结果表明，当提出一个非建设性的证明，学生往往不仅发现证明令人信服，但也建设性地解释证明。此外，数据表明，学生谁表现出的非建设性结构的意识，在他们的意见，建设性或非建设性的形式是最有说服力的。讨论认为学生的反应，非建设性的存在证明和使用的务实和理论思维模式的析取结构。
Drawing on prior research on indirect proof, this paper reports on a series of exploratory studies that examine the extent to which findings on students’ ways of reasoning about contradiction and contraposition characterize students’ views of indirect existence proofs. Specifically, Study 1 documents students’ comparative selections and selection rationales when asked to choose the “most convincing” proof, given a constructive and nonconstructive existence proof. Study 2 further examines findings from Study 1 by documenting novices’ levels of conviction and interpretations of a nonconstructive existence proof. Findings show that when presented with a nonconstructive proof, students tended to not only find the proof convincing but also interpreted the proof constructively. Moreover, the data indicate students who exhibit an awareness of the nonconstructive structure were divided in terms of their views of which form – constructive or non-constructive – was the most convincing. The discussion considers students’ reactions to the disjunctive structure of nonconstructive existence proofs and use of pragmatic and theoretical modes of thought.