Monomials and polynomials: the long march towards a definition

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-03-01 DOI:10.1093/teamat/hry015

Giorgio Bolondi;Federica Ferretti;Andrea Maffia

引用次数: 10

Abstract

The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations. In school, many practices go under the label ‘definition’, even though they can be very different from what mathematicians conceive as a formal definition, and in fact there are substantial differences between these different kinds of practices. This can create difficulties for pupils, since they may encounter non-coherent definitions of the same thing. Features of these schemes are exemplified through the analysis of some algebra high school textbooks, looking at the proposed ‘definitions’ of monomials and polynomials. We show how all these definition schemes are used in textbooks. Starting from the observed differences, we highlight some educational research problems.

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单调和多项式：迈向定义的长征

将名称与表征或特殊性质配对的过程渗透到许多数学课堂情境中。在学校里，许多实践都被贴上了“定义”的标签，尽管它们可能与数学家认为的形式定义非常不同，事实上，这些不同类型的实践之间存在着实质性的差异。这可能会给学生带来困难，因为他们可能会遇到对同一事物的不一致定义。通过对一些代数高中教科书的分析，以及对单项式和多项式的“定义”，举例说明了这些方案的特点。我们展示了所有这些定义方案是如何在教科书中使用的。从观察到的差异出发，我们强调了一些教育研究问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.