The Nature and Role of Algebra in the K-14 Curriculum Proceedings of a National Symposium (1998) / Chapter Skim
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Appendix D: Invited Papers
Appendix D: Invited Papers
Pages 133-144
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Appendix D Invited Papers Stating the Obvious: Mathematics Course Taking Matters (W.
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Moreover, the practice of tracking students out of college prep mathematics opportunities is akin to restricting them to the basic skills curriculum. SOME RECENT TRENDS: COURSE TAKING MATTERS The impact of restricting students to a basic skills mathematics curriculum is most apparent when studies of course taking and mathematics achievement are examined.
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One method of intervention is to mandate specific course requirements at the eighth grade andlor secondary level. To enhance policy intervention, student learning is required at the elementary level.
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The conception of the nature of algebra behind these efforts is perhaps most easily seen in Isaac Newton' s book on elementary algebra, which bore the title The Universal Arithmetic.2 Newton himself gives a clear exposition of the philosophy: "Common arithmetic and algebra rest on the same computational foundations and are directed to the same end. But whereas arithmetic treats questions in a definite, particular way, algebra does so in an indefinite, universal manner, with the result that almost all pronouncements which are made in this style of computation and its conclusions especiallymay be called theorems.
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in developing mathematical logic.5 It was not until the twentieth century that the conception of algebra as the study of manipulation of certain symbols acquired meaning. Katz notes that "it was Emmy Noether who taught the mathematicians in Gottengen in the 1920s that algebra was central to mathematics, that its ideas extended to all areas of the subject, and that an abstract approach was the way to look at algebraic concepts." 6 A REMARK OF I.M.
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The teacher (the present writer) was working on a fairly standard New York State Regents curriculum with a group of well-motivated, high-ability ninth graders.
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Learning algebra may or may not involve learning a "universal arithmetic." As Kieran and Chalouh point out, the application of algebra to arithmetic requires a different set of experiences than the acquisition of purely algebraic skills. Vignette 2 This scene took place in a small remedial class.
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Indeed, while algebra is a useful tool for the study of functions, recent literature is replete with examples of classroom work supporting the function concept in ways that avoid the use of algebraic expressions. i2 AN HYPOTHESIS CONCERNING THE TEACHING OF ALGEBRA To summarize the argument so far: (1)
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We start students on the road to algebra with its concrete applications, such as the description of number patterns or functions. Later on, the algebraic ideas are used to solve polynomial equations (where the algebraic expressions represent rational, real, or complex numbers)
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But the possibility of doing algebraic computations quickly and accurately immediately presents another opportunity; of exploring algebraic patterns. The following is an example of a classroom exploration that I have found useful where good use of symbolic manipulation software can be made.
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CONCLUSIONS The current trend in education is to unify the teaching of different areas and to create strands throughout the grades of subjects formerly taught in discrete packages. This trend has helped us to reach past mathematical techniques to mathematical concepts.
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