Assessing the strands of student proficiency in elementary algebra

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

Algebra and Functions In order to assess something, you have to have some idea of what that something is. Algebra means many different things in today’s schools (for a discussion, see [RAND 2003, Chapter 4]). In particular, the study of algebra is often blended with the study of functions. Although it is true that the notion of a function is lurking behind much of beginning algebra, and that there is an algebraic aspect to many of the tasks we want our students to carry out with functions, the conglomeration of algebra and functions has considerably muddied the waters in the teaching of algebra. Therefore, I’d like to spend some time clarifying my own stance before talking about how to assess proficiency. In the process, while acknowledging other possible uses, I will use the word “algebra” to mean the study of algebraic expressions and equations in which the letters stand for numbers. I include in this study consideration of the relationship between the algebraic form of expressions and equations and properties of their values and solutions. I make a distinction, however, between this study and the study of functions. In the progression of ideas from arithmetic to algebra to functions, there is an increase in abstraction at each step, and the increase at the second step is at least as large as that at the first. In the step from arithmetic to algebra, we learn to represent numbers by letters, and calculations with numbers by algebraic expressions.

Original languageEnglish (US)
Title of host publicationAssessing Mathematical Proficiency
PublisherCambridge University Press
Pages157-162
Number of pages6
ISBN (Print)9780511755378, 0521874920, 9780521874922
DOIs
StatePublished - Jan 1 2007

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Mccallum, W. G. (2007). Assessing the strands of student proficiency in elementary algebra. In Assessing Mathematical Proficiency (pp. 157-162). Cambridge University Press. https://doi.org/10.1017/CBO9780511755378.016

Assessing the strands of student proficiency in elementary algebra. / Mccallum, William G.

Assessing Mathematical Proficiency. Cambridge University Press, 2007. p. 157-162.

Research output: Chapter in Book/Report/Conference proceedingChapter

Mccallum, WG 2007, Assessing the strands of student proficiency in elementary algebra. in Assessing Mathematical Proficiency. Cambridge University Press, pp. 157-162. https://doi.org/10.1017/CBO9780511755378.016
Mccallum WG. Assessing the strands of student proficiency in elementary algebra. In Assessing Mathematical Proficiency. Cambridge University Press. 2007. p. 157-162 https://doi.org/10.1017/CBO9780511755378.016
Mccallum, William G. / Assessing the strands of student proficiency in elementary algebra. Assessing Mathematical Proficiency. Cambridge University Press, 2007. pp. 157-162
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