Category Archives: early algebra

“1+1=5”, by D. La Rochelle & B. Sexton. It is all about the units !

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Last month, I attended a presentation about units (Cipparone & Bass, 2017). When C. Danielson (“Talking Math with Kids”) mentioned the book “1+1=5”, I quickly wrote the title on a Post’It, knowing that as soon as we were back home,  I would check it out.

I am so glad I did. Such a fun support to make children think about units.

Each page presents a drawing and an equation, such as a unicorn and a goat and “1+1 = 3?”. On the next page, the equation includes the units i.e. 1 unicorn + 1 goat = 3 horns. Indeed, 1 + 1 = 3 :-)

You may have read it in some of my previous posts, I always remind my daughter Rosie, 8, to provide the unit at the end of a word problem, and even invite her to write the units in her equations. This book was just perfect to reinforce my point, and led us to an instructive talk about the importance of the units.

Rosie LOVED that book, and could not stop talking about it for a week, finding new examples on her own. In fact, if you meet a little girl who claims, with a mischiveous grin, that “1+1 = 3”, enjoy: you may have just met Rosie :-)


Reference:

Peter Cipparone & Hyman Bass, 2017. Bringing Out the “Unit” Across Mathematical Domains. Cognitively Guided Instruction. 2017 National Conference, Seattle June 26-28.


Back to pattern

My daughter used to love patterns. In Pre K, she would go to town with completing all kind of A-B patterns, A-B-C patterns, A-B-A-B-C patterns, etc, identifying patterns on clothes, in nature, etc.

Then, she kind of stopped. And I was not sure where to go from that point.

Taking my class on Algebra this semester, reviewing how patterns lead to algebra (see my previous post here), I am trying to start making patterns again. With numbers.

When we have a low key moment, I tell her a sequence of numbers. She continues it for a little while, and identify the pattern. Then, I give her another number, and she uses the pattern one more time, starting from that new number. So far, she has enjoyed it. Your child may too !

Here are a few examples of what we have been doing. Adding / subtracting 2 (e.g. 0    2     4    6     8. What comes next? How do you know?), Adding/subtracting.  Soon, we will likely move to adding/ subtracting 5, 10 and 100. I may also add a story to the pattern. I may also ask her how she would represent the pattern on a number line, one of the representation she uses at school. And move up to more complicated patterns.

It is fun, and a good way to keep kids busy when they get bored in the car,  in a waiting room, or while waiting in line somewhere. A win-win way to do math.


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?

 BlantonCarpenter


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.