Teaching Numeracy, Components 4 & 5 - Math Coach's Corner

Hard to believe this is our last week of the book study! I want to thank Margie for being such an active participant and spending part of her summer with us. I know, personally, that I have made a new math friend, and we have all benefited from her interaction. It’s not too often that we have the opportunity to discuss a book with the author. Throughout the book study, you all have had wonderful praise for the book. As we wrap up, I hope you’ll take a minute to head over to Amazon, rate the book, and leave a short review. It’s the least we can do to thank Margie for being such a huge part of our book study!

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.

If you’ve just stumbled upon us, we’ve been reading and discussing Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, by Margie Pearse and K. M. Walton.  You can use the links below to check out our discussions.


Reading Schedule

Component 4: Gradual Release in Mathematics

“…teachers must spend explicit instruction time teaching students how to think rather than what to think.”

I knew two things as soon as I started reading this chapter: (1) that I was going to love it, and (2) that it was one of the most important chapters in the book. This chapter sums up the great paradigm shift that is needed for our math instruction to be truly effective. Just because we teach it, that doesn’t mean the students learn it. We simply can’t teach math in the same way that we have been and expect the results that our changing world demands. First, the authors explain the difference between teaching a lesson and thinking aloud (p 154). A think-aloud helps students see inside your mathematical thinking–to hear how you process information. That is very different than explaining a list of procedures. The example on pages 154-157 illustrates this idea beautifully.

From there, they define formative assessment and explain that it is a process not just for teachers, but for students, too (p 158). They remind us that formative assessment provides immediate feedback that determines the course of further instruction. We simply can’t wait for a quiz or test to find out that our students don’t understand a concept we’ve taught. I love the idea that students are involved in the process and that we are teaching them to be reflective.

Closely tied to the idea of formative assessment is the use of small-group instruction in math. The authors state, “It is very difficult for teachers to assess students’ knowledge without spending some time interacting directly with them.” (p 159) I confess that for many years I was primarily a whole-group teacher, and I felt that I understood my students’ needs. It was not until I began working with students in small groups during extended learning time that I realized how much more powerful small group instruction was for advancing student learning. There is no substitute for small-group interaction. If you can only make one change in your instruction this year, or you’re not sure exactly where to start, move to more small-group instruction.

Pages 161 through 165 contain excellent ideas for choosing groups. I’ve used Clock Partners (p 164), but really liked the get-to-know-you version. Perfect for back to school! I also liked the Perfect Partners method, so much so that I made a little set of the cards. Click here to download your free copy.

Component 5: Debrief

“Whenever we succumbed to the clock and skipped those moments of reflection, the cohesiveness created during the lesson did not congeal.”

The idea of this final component is the importance of allowing students time to reflect on their learning. I am Guilty, with a capital G, of losing track of time and rushing to wrap up class. Often. I love the point that the authors make on page 169 that the debrief shifts responsibility for learning to the students. The Human Continuum described on page 171 is a great way to determine understanding (formative assessment) while getting the kiddos up and moving. It’s similar to the Thumbs Up, Thumbs Down, Thumbs to the Side described on page 162.  As noted by the authors, it’s important to carefully set the stage for self-reflection done in this manner.


“In other words, we challenge you to never be satisfied with good enough, to never settle for just okay. Continue to craft and revisit and to question yourself–every single day. Continue to push yourself out of your comfort zone.”

Thank you so much for taking precious time out of your summer to pursue new learning. The beginning of school can be so hectic. Right now, before the whirlwind starts, jot down 2 or 3 ideas you plan to implement from what you’ve read this summer. Then, maybe over the winter break, revisit the book and choose 2 or 3 more ideas. Baby steps. Here are my three goals:

    • I’m going all the way back to Habit 1 and the fix-up tools. So powerful, especially for the struggling students I will be working with.
    • I want to work on my think-alouds. This was a huge theme running throughout the book.
    • I’m going to focus on helping my students think more deeply and communicate more effectively through the use of better questions.

Thank you again for making this book study so successful!  I look forward to reading your three goals.

Pin It on Pinterest

Share This