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: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=459640
• 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，还是通过一个程序来产生“正确答案”？迄今为止的研究结果对这个问题提出了不同的答案。 不同的研究者认为，儿童首先学习概念，他们首先学习程序，然后他们学习概念和程序。 这个项目建立在一个不同的发现，这表明所有这些可能是真的，这些矛盾的说法可能是儿童使用的概念和程序知识的个体差异的结果。 换句话说，有些孩子可能更依赖于概念性理解，有些可能更依赖于程序性理解，而另一些可能同样依赖于两者。在此基础上，本研究将从三个方面深入探讨儿童概念性和程序性知识的个体差异。 首先，纵向和干预研究将着眼于个体差异随时间的进展，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。 第二，额外的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代数等更复杂数学主题的理解中。 第三，这个项目将探索分数的理解是否会受到其他研究人员所说的人们的“数感”的帮助或阻碍。 所有这些研究都是为了更好地了解不同的年轻人如何看待分数和更复杂的数学主题，并可能导致更好的方法来专注于这些不同类型的学习者的教学。