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How a standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable

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Abstract

Analyzing the important features of different curricula is critical to understand their effects on students’ learning of algebra. Since the concept of variable is fundamental in algebra, this article compares the intended treatments of variable in an NSF-funded standards-based middle school curriculum (CMP) and a more traditionally based curriculum (Glencoe Mathematics). We found that CMP introduces variables as quantities that change or vary, and then it uses them to represent relationships. Glencoe Mathematics, on the other hand, treats variables predominantly as placeholders or unknowns, and then it uses them primarily to represent unknowns in equations. We found strong connections among variables, equation solving, and linear functions in CMP. Glencoe Mathematics, in contrast, emphasizes less on the connections between variables and functions or between algebraic equations and functions, but it does have a strong emphasis on the relation between variables and equation solving.

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Notes

  1. The research reported here is part of a large project designed to longitudinally compare the effects of the Connected Mathematics Program (CMP) with the effects of more traditional middle school curricula on students’ learning of algebra (Cai & Moyer, 2006). In the large project (Longitudinal Investigation of the Effect of Curriculum on Algebra Learning, LieCal Project), we investigate not only the ways and circumstances under which the CMP and other curricula like Glencoe Mathematics can or cannot enhance student learning in algebra, but also the characteristics of the curricula that lead to student achievement gains. In 2006 and 2009, the authors published revised editions of the CMP curriculum under the name CMP2. This article is based on the CMP curriculum because the students in the LieCal project used CMP, and not CMP2. LieCal Project is supported by a grant from the National Science Foundation (ESI-0454739). Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.

  2. As we indicated before, this article is based on the CMP curriculum, because the students in the LieCal Project used CMP, and not CMP2. Furthermore, we can accomplish our purpose, which is to examine how a representative NSF-funded Standards-based middle school curriculum differs from a representative traditional curriculum, using either CMP or CMP2 as the Standards-based curriculum.

  3. In CMP2, this unit is categorized as a geometry unit. Nonetheless, like the CMP curriculum, the CMP2 curriculum has seven algebra units because the CMP2 authors added a new eighth grade algebra unit (See Lappan et al., 2006).

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Authors and Affiliations

  1. University of Delaware, Newark, DE, USA

    Bikai Nie & Jinfa Cai

  2. Marquette University, Milwaukee, WI, USA

    John C. Moyer

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  1. Bikai Nie
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  2. Jinfa Cai
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Correspondence to Jinfa Cai.

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Nie, B., Cai, J. & Moyer, J.C. How a standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable. ZDM Mathematics Education 41, 777–792 (2009). https://doi.org/10.1007/s11858-009-0197-1

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