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

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.

Impact of curriculum reform: Evidence of change in classroom practice in the United States

“…On the other hand, non-CMP lessons emphasize the procedural aspect of instruction to a greater extent than the CMP lessons. This finding is consistent with goals and features of Standards-based and traditional curricula (Hirsch, 2007;Senk & Thompson, 2003) as well as with the findings from our analyses of the CMP and non-CMP curricula (Cai, Nie, & Moyer, 2010;Nie, Cai, & Moyer, 2009). The CMP curriculum includes more cognitively demanding problems than the non-CMP curriculum (Cai et al, 2010).…”

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

“…Nonetheless, we did an in-depth comparison of the approaches to algebra taken by the two types of curricula. We found major differences in the development of fundamental algebraic ideas, and these differences appear to be related to the differences we observed (Cai et al, 2010;Nie et al, 2009). For instance, the CMP curriculum uses a functional approach to introduce variables and equations, whereas the non-CMP curriculum uses a structural approach to introduce variables and equations.…”

“…In particular, when we conducted detailed analyses of CMP and one of the non-CMP curricula 2 , we found significant differences between them (Cai, Nie, & Moyer, 2010;Nie, Cai, & Moyer, 2009). Overall, our research revealed that the CMP curriculum takes a functional approach to the teaching of algebra, and the non-CMP curriculum takes a structural approach.…”

Searching for evidence of curricular effect on the teaching and learning of mathematics: Lessons learned from the two projects

“…An analysis of the intended curriculum took the form of content analysis (Cai, 2010;National Research Council, 2004;Stein, Remillard, & Smith, 2007), such as, the worldviews or orientations towards the subject matter, depth of coverage, ways to sequence topics, ways to present topics, and accuracy. The US project completed a detailed content analysis that compared the structural and functional treatment of algebra in the reform and non-reform curricula (Cai, Nie, & Moyer, 2010;Nie, Cai, & Moyer, 2009). The Chinese project provided a general description of the purpose and objectives of the new curriculum but did not include a detailed content analysis.…”