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I'm developing a course that focuses on the transistion from arithmetic to algebraic thinking, particularly in grades 5-8. We will do this through focus on the common core. I'm also putting together a collection of suggested readings from the math education literature. I would be interested to hear your suggestions for suggested readings.

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Early algebra research necessarily deals with the development of algebraic reasoning and questions like "what is algebra" and "what counts as algebraic thinking and reasoning?" And my own readings on early algebra have helped me to focus on what about algebraic thinking are students developing, apart from the manipulation of symbols. This is where, I think, some of the early algebra research may have more general interest, since some of the authors deal with what students are capable of that is connected to algebra well before they are doing what we are familiar with in an Algebra 1 course.

A book collecting some different research on Early Algebra is:

Kaput, J. J., Carraher, D. W., & Blanton, M. L. (2007). Algebra in the early grades.

There is a review of it in JRME (Chazan & Edwards, 2010), and someone is sharing the review here as a PDF (in case you don't have access).

From the review:

In addition to these direct assaults on the rhetorical challenge posed by early algebra, one of the strengths of the volume is the richness of the presentations aimed at helping readers appreciate how early algebra is not the sort of activity that a reader might associate with a high school Algebra 1 course. In particular, the seven chapters in Part II offer theoretical arguments for children’s capacity to learn algebra early and empirical studies of children’s algebraic reasoning in a variety of different elementary-level classroom and curricular contexts. These chapters provide illustrations of what early algebra curriculum and instruction look like, as well as existence proofs of children’s capacity to do this work. (p. 204)

Even though you're not talking about algebrafying early mathematics, and depending on what sort of things you want students to consider and even argue about, this book (along with other early algebra research) may provide perspectives that spark thoughtful discussions and reflections.

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Although these two NCTM books cover K-12 (there are items specifically directed at middle school level) they have ideas related to how to develop algebraic thinking: The Ideas of Algebra, K12, 1988 Yearbook, A. Coxford and A. Shulte, editors, and Developing Mathematical Reasoning in Grades K-12, 1999 Yearbook, Lee Stiff and Francis Curcio, editors.

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