# Building up foundation in algebra in elementary school

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 11th and 12th 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?

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.