Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-12-01 DOI:10.1093/teamat/hrw001

John Hannah;Sepideh Stewart;Michael Thomas

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引用次数: 17

Abstract

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall’s three worlds (embodied, symbolic and formal) of mathematical thinking, and use a framework combining these with Dubinsky’s Action, Process, Object and Schema (APOS) theory to analyse students’ resulting levels of understanding. Through interviews and analysis of test and examination scripts, we investigate students’ understanding of the basic concepts of linear algebra, their ability to use and explain these concepts and their relationship to definitional clarity. The results show that, while students tend not to learn definitions by rote and can be imprecise when expressing them in words, they seem to understand the concepts, can talk sensibly about them and are able to use their essential features in solving problems.

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通过数学思维的三个世界发展线性代数的概念理解和定义清晰度

线性代数是学生在大学里最先接触到的抽象数学课程之一。研究表明，许多学生发现定义、定理和证明的密集表述很难理解。采用案例研究的方法，我们报告了基于Tall数学思维的三个世界（具体世界、象征世界和形式世界）的教学干预，并使用将这些世界与Dubinsky的动作、过程、对象和图式（APOS）理论相结合的框架来分析学生由此产生的理解水平。通过访谈和对测试和试卷的分析，我们调查了学生对线性代数基本概念的理解，他们使用和解释这些概念的能力，以及他们与定义清晰度的关系。研究结果表明，虽然学生倾向于不死记硬背地学习定义，并且在用词表达时可能不精确，但他们似乎理解了这些概念，能够理智地谈论它们，并能够在解决问题时使用它们的基本特征。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.