Understanding and Cultivating the Connections Between Students' Natural Ways of Reasoning and Mathematical Ways of Reasoning

理解和培养学生自然推理方式与数学推理方式之间的联系

• 批准号: 0814710
• 负责人: Eric Knuth
• 金额: $ 74.19万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0814710&HistoricalAwards=false
• 关键词: Understanding; Cultivating; Connections; Between; Students

Many consider mathematical reasoning to be a basic mathematical skill and inseparable from knowing and using mathematics. Yet despite its importance, mathematics education research continues to paint a bleak picture of students' abilities to reason mathematically. In contrast, cognitive science research has revealed surprising strengths in children's abilities to reason in non-mathematical domains, suggesting that children are capable of developing complex and abstract causal theories, and of using powerful strategies of inductive inference. Thus, this raises something of a paradox: Why are children so good at reasoning in non-mathematical domains, yet so poor at reasoning in mathematical domains? The purpose of this study is to explore this seeming paradox. In particular, our goal is to extend the cognitive science research into the domain of mathematics education and, more specifically, into the domain of middle school mathematics. We seek to understand the strengths and weaknesses of students' reasoning in and out of mathematics, to understand the connections between students' reasoning in different domains, and, ultimately, to improve students' abilities to reason mathematically.

许多人认为数学推理是一种基本的数学技能，并且与了解和使用数学相关。尽管它很重要，但数学教育研究仍在描绘学生在数学上推理的能力的惨淡图片。相比之下，认知科学研究揭示了儿童在非数学领域中推理的能力的令人惊讶的优势，这表明儿童能够发展复杂和抽象的因果理论，并使用强大的归纳推理策略。因此，这引起了一个悖论：为什么孩子在非数学领域的推理中如此出色，而在数学领域的推理方面如此贫穷？这项研究的目的是探索这种看起来悖论。特别是，我们的目标是将认知科学研究扩展到数学教育的领域，更具体地说是中学数学领域。我们试图了解学生在数学中和范围内推理的优势和劣势，以了解学生在不同领域的推理之间的联系，并最终提高学生在数学上推理的能力。