The Article
In this article, professors Jon Star and Jack Smith and doctoral student Beth Herbel-Eisenmann examine a middle school’s new curricular approach to algebra to understand what is different about it and how this “newness” might affect student learning.

Discussion
The curriculum the authors examined was the Connected Mathematics Project (CMP), particularly the eighth-grade units. They compared the eighth-grade curriculum with the content of traditional algebra 1 because a substantial part of the eighth-grade material addresses algebraic themes and content. Star et.al. found that six elements captured much of the difference between CMP and traditional conceptions and teaching of algebra. The six elements were the fundamental objects in the curriculum, typical problems in the curriculum, typical solution methods, role of practice, role of technology for representing and calculating, and elements in a typical lesson. They discuss all six in depth. In terms of fundamental objects, they note that algebra was almost exclusively the study of equations and symbolic expressions. CMP and newer conceptions of algebra “present functional relationships as the fundamental objects. In contrast with equations, functional relationships specify how one quantity changes in relation to changes in a second quantity.” In CMP, those functional relationships are presented in contextual problems that describe some realistic situation. Thus, CMP places a heavy emphasis on word problems. Indeed, almost all of the problems in eighth-grade CMP materials are word problems. The typical way of solving problems is also different. In algebra 1, the solution methods involve completing the correct manipulations in the correct order. “Typical solution methods for CMP algebra are quite different. They involve working with and interpreting verbal statements, accompanying representations, or both.” The role of practice is also different. In CMP, practice plays a more limited role. The problems tend to be longer and have more parts, which means that students work on fewer problems in the course of a lesson. CMP also encourages a much wider use of technology, including calculators and computer software. Finally, algebra 1 lessons follow a fixed sequence of activities, which include reviewing homework, presenting new concepts, etc. CMP lessons are more difficult to characterize. The form of instruction in CMP seems to be much more student centered while algebra 1 more teacher centered.

What It Means to You
The authors do not make the case that one approach is better than the other. Instead, they make clear the differences between CMP and a more traditional approach. What curricular approach does your district employ? Would student learning in your district improve by using one, both or a combination of approaches?

For More Information
Star, J. R., Herbel-Eisenmann, B.A. & Smith, J.P. (2000). Algebraic conceptions: What’s really new in new curricula? Mathematics Teaching in the Middle School, 5(7), 446-451.

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