The teaching of equation solving: approaches inStandards-based and traditional curricula in the United States

Abstract

This paper discusses the approaches to teaching linear equation solving that are embedded in a Standards-based mathematics curriculum (Connected Mathematics Program or CMP) and in a traditional mathematics curriculum (Glencoe Mathematics) in the United States. Overall, the CMP curriculum takes a functional approach to teaching equation solving, while Glencoe Mathematics takes a structural approach. The functional approach emphasizes the important ideas of change and variation in situations and contexts. It also emphasizes the representation of relationships between variables. The structural approach, on the other hand, requires students to work abstractly with symbols and follow procedures in a systematic way. The CMP curriculum may be regarded as a curriculum with a pedagogy that emphasizes predominantly the conceptual aspects of equation solving, while Glencoe Mathematics may be regarded as a curriculum with a pedagogy that emphasizes predominantly the procedural aspects of equation solving. The two curricula may serve as concrete examples of functional and structural approaches, respectively, to the teaching of algebra in general and equation solving in particular.

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).…”

“…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). This finding is also consistent with findings from the analysis of instructional tasks in CMP and non-CMP lessons that we have reported elsewhere (Cai, Wang, Moyer, Nie, & Wang, submitted for publication).…”

Investigating curricular effect on the teaching and learning of mathematics in a cultural context: Theoretical and methodological considerations

“…Instead, they are research projects that test fundamental hypotheses about the relations among curriculum, teaching, and learning in an international context. For example, reform curricula can be characterized as teaching mathematics through problem solving, in contrast to the more traditional curricula in both China and the US (See more detailed explanation in Cai, 2003a;Cai, Nie, Moyer, 2010;Cai et al, this issue;Ni et al, this issue;Senk & Thompson, 2003). An intent of the reform curricula is to build students' understanding of important mathematical ideas, often through explorations of real-world situations and problems.…”

Reasoning and Proving Opportunities in Textbooks: A Comparative Analysis

“…Some demonstrate that in both elementary and secondary mathematics textbooks, textbooks from Asian countries contain more challenging problems, while American standards-based (e.g., Everyday Mathematics) and traditional textbooks contain more single-step problems (Fan & Zhu, 2007;Li, 2000;Son & Senk 2010). However, other studies detected that standards-based textbooks include more problems with higher level cognitive demands than traditional American textbooks and Korean secondary textbooks (Cai et al, 2010;Hong & Choi, 2014). Results also differ by response types of problems.…”