As a graduate student in Math Elementary School, I will study this semester how teaching algebra in elementary school.

As you may remember, I grew up in France. In middle school/high school, I had math classes, several times a week, but they were not referred as Algebra, or Calculus. They were just referred as … Math. Some days, we did Geometry, others Algebra, etc. Although I do remember starting struggling with math in 11^{th} and 12^{th} grade, I did not recall it to be on a specific branch of math. Now, here, in the US, I can tell that people may have a much stronger opinion about Algebra ! So I have to admit that I am pretty excited to learn more about how to teach this fearful branch of math.

I just started reading 2 of the required books, and I am hooked.

The first one, Carpenter *et al*, 2003, got all my attention even before I started. Indeed, Carpenter is one of the authors of a book I often refer too in this blog, *Children’s Mathematics : Cognitively Guided Instruction*, and its approach of teaching mathematics based on developing mathematical thinking.

The second one, Blanton, 2008, got me within the first few pages with “*all* children can learn to think algebraically”.

First interesting fact I am noticing: early algebra, or algebra taught in elementary classrooms, should not be seen as a simplified version of an Algebra curriculum that may be taught in High School. Rather, it should be focused on helping students start using their understanding of arithmetic as a foundation of algebra, and, more specifically on :

- “building generalizations about operations on and properties of numbers” (Generalized Arithmetic). For instance, children may start noticing that numbers can be added in any order (a + b = b + a)
- “looking for patterns in how quantities varies in relation to each other” (Functional Thinking).

When you know that “algebra often serves as a gatekeeper that prevents students from continuing the study of mathematics, thereby limiting their access to college majors and careers that require knowledge of mathematics beyond simple arithmetics” (Carpenter *et al*, p6), it is never too early to start building up strong foundations, don’t you think?

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References:

- Blanton, M. L. (2008).
*Algebra and the elementary classroom*. Heinemann: Portsmouth, NH, pp1-8. - Carpenter T. P., Franke, M. L., & Levi, L. (2003).
*Thinking mathematically: Integrating arithmetic & algebra in the elementary schoo*Heinemann: Portsmouth, NH, Ch. - Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014).
*Children’s Mathematics, Second Edition: Cognitively Guided Instruction*. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.

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