Guiding reinvention of conventional tools of mathematical logic: students’ reasoning about mathematical disjunctions
Guiding reinvention of conventional tools of mathematical logic: students’ reasoning about mathematical disjunctions
复制标题
指导数理逻辑传统工具的重塑：学生对数学析取的推理
DOI：
10.1007/s10649-016-9722-7
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发表时间：
2017
影响因子：
3.2
通讯作者：
J. Cook
中科院分区：
文献类型：
--
作者：
P. Dawkins;J. Cook
出于观察，形式逻辑回答问题的学生还没有问，我们进行了探索性的教学实验，本科生旨在指导他们的真值函数定义的基本逻辑连接词的再造。我们打算通过展示逻辑如何在学生的数学活动中出现来重新构建推理和逻辑之间的关系。这项活动需要反思和系统化他们自己的语言使用在不同的语义内容。我们提出了学生未经训练的评估数学析取的真值策略的类别。学生的初始推理严重地反映了内容特定性和语用因素，与数理逻辑的规范和惯例不一致。尽管如此，所有的学生团体都重新发明了简单析取的标准真值函数定义。我们展示了这种学习如何依赖于特定形式的逻辑推理。我们还比较了各种评估量化的析取和他们的不同启示在学生的数学活动的策略。
Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how logic emerges within students’ mathematical activity. This activity entails reflecting on and systematizing their own language use across diverse semantic content. We present categories of students’ untrained strategies for assessing the truth-values for mathematical disjunctions. Students’ initial reasoning heavily reflected content-specific and pragmatic factors in ways inconsistent with the norms and conventions of mathematical logic. Despite this, all student groups reinvented the standard truth-functional definition for simple disjunctions. We demonstrate how this learning depended upon particular forms of reasoning about logic. We also contrast various strategies for assessing quantified disjunctions and their different affordances in students’ mathematical activity.