If you’re just joining us, we’re reading and discussing Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, by Margie Pearse and K. M. Walton.
This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.
Use the links below to read previous posts. Last week’s conversations were lively and thought-provoking!
- Preface and Introduction
- Critical Habits 1 & 2
- Critical Habits 3 & 4
- Critical Habits 5 & 6
- Critical Habit 7
- Critical Habits 8 & 9
- Essential Components 1, 2, & 3
- Essential Components 4 & 5
Habit 3: Identify Similarities and Differences, Recognize Patterns, Organize and Categorize Ideas, Investigate Analogies and Metaphors
“Math is a science of patterns; it is much more than arithmetic”
I have a little secret for you…I never set out to be a math teacher. When I left the business world to pursue teaching, I thought for sure that I would be a reading teacher, because I loved reading (still do…). I interviewed at a well-respected elementary school in Houston ISD that was also very close to my home, and I really wanted a job there! The principal and I hit it off, and before I knew it, she was offering me a job…as a 3rd-grade math/science teacher. Wait, what? I smiled, graciously accepted the job, and the rest is history. Why do I tell that story? Because I think it is directly connected to the quote I used to introduce this section. When I was in school, I was taught arithmetic, and I did not find it at all interesting. It was only when I began teaching math, and studying how to teach math, that I saw the beauty in the patterns and became hopelessly hooked! For example, follow the evolution of a simple number bond and see how the concept of decomposing numbers connects so many different skills–skills we typically teach in isolation.
Referring to work by Marzano, Pickering, and Pollock (2001), Pearse lists four highly effective forms of identifying similarities and differences: comparing, classifying, creating metaphors, and creating analogies. I’d love to hear comments about how each of those looks in your classroom. I think I regularly incorporate comparing and classifying activities, but I’m not so sure about metaphors and analogies.
I had the pleasure of hearing Jana Hazecamp present a session on building mathematical vocabulary last week, and she shared an activity that is both simple and powerful. Perfect for this chapter!
Habit 4: Represent Mathematics Nonlinguistically
“Nonlinguistic representations are necessary to students’ understanding of mathematical concepts and relationships. Representations allow students to convey mathematical approaches, arguments, and conceptual understandings.”
With my love of the concrete, representational, abstract (CRA) sequence of instruction, this chapter was music to my ears! I heard a lot about CRA this past week at the National Conference on Singapore Math Strategies. They call it CPA, with the P standing for pictorial, and it’s at the heart of how math is taught in Singapore.
The research on nonlinguistic representations is compelling, and I think we’ve all experienced what happens when students are rushed to the abstract stage of learning. My experience with struggling students is that they have no pictures in their heads for the math they are trying to do, which fits perfectly with the authors’ statement that “For every symbol that students write, there must be a concrete referent in their heads of what that symbol refers to.” (p 38) I think this gets back to the problem of focusing on quantity over quality in our classrooms. I’d rather have students work on one great problem–build it, draw it, talk about it–than ten routine problems.
So many great, practical ideas in this chapter! I particularly like the list of Good Questions to Ask When Incorporating Visual Representations (p 42). How about taping a copy of that in your lesson plan book as a reference for planning?
Finally, what a great list of math read alouds (p 49-52). I’ve always used literature to engage students, but I didn’t think about how powerful read alouds are for helping students visualize. You might want to check out this blog post for additional online resources for literature for teaching math.
I’m looking forward to another lively discussion about this week’s reading!