Conceptual and procedural knowledge in mathematical cognition

数学认知中的概念性和程序性知识

• 批准号: 355914-2008
• 负责人: Hallett, Darcy
• 金额: $ 1.09万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=497112
• 关键词: Conceptual; procedural; knowledge; mathematical; cognition

When faced with a mathematical problem involving fractions, do children think about the problem conceptually, or do they instead work through a procedure to generate the "right answer"? Results from research to date suggest varying answers to this question. Different researchers have suggested that children learn concepts first, that they learn procedures first, and that they learn concepts and procedures in tandem. This project builds upon a different finding that suggests that all of these might be true; these contradictory claims could be the result of individual differences in children's use of conceptual and procedural knowledge. In other words, some children may rely more on conceptual understanding, some might rely more on procedural understanding, and others might equally rely on both. Building on this previous result, this research project will delve deeper into individual differences in children's conceptual and procedural knowledge in three main ways. First, longitudinal and intervention studies will look at the progression of individual differences over time and how training in conceptual or procedural understanding can affect children with different conceptual and procedural profiles. Second, additional studies will investigate whether the individual differences evident in fractions understanding will also be present in children's understanding of more complicated mathematical topics like algebra. Third, this project will probe whether fraction's understanding can be helped or hindered by what other researchers have called people's "number sense". All of these studies are meant to better understand how different young people think about fractions, and more complicated mathematical topics, and may result in better ways to focus teaching for these different kinds of learners.

当面对一个涉及分数的数学问题时，孩子们是从概念上思考问题，还是通过一个过程来产生“正确的答案”？到目前为止的研究结果表明，这个问题的答案各不相同。不同的研究人员建议儿童首先学习概念，他们首先学习程序，他们同时学习概念和程序。这个项目建立在一个不同的发现之上，这表明所有这些都可能是正确的；这些相互矛盾的说法可能是儿童在使用概念和程序知识方面的个体差异的结果。换句话说，一些儿童可能更多地依赖于概念性理解，一些儿童可能更多地依赖程序性理解，而另一些儿童可能同时依赖这两种理解。在这一研究成果的基础上，本研究项目将从三个主要方面深入探讨儿童概念和程序知识的个体差异。首先，纵向和干预性研究将着眼于个体差异随着时间的推移而发展，以及概念或程序理解方面的培训如何影响具有不同概念和程序特征的儿童。其次，其他研究将调查分数理解中明显的个体差异是否也会出现在儿童对更复杂的数学问题(如代数)的理解中。第三，这个项目将探索分数的理解是否能被其他研究人员所说的人们的“数字感觉”所帮助或阻碍。所有这些研究都是为了更好地了解不同的年轻人对分数和更复杂的数学主题的看法，并可能为这些不同类型的学习者提供更好的集中教学方法。