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Teaching Numeracy, Components 4 & 5

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!

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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.

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  1. I just stumbled upon this book study now (too late) but I’ve gone back and re-read these comments and I’m really excited about this approach in math. I am a “language” person and we use the comprehension strategies regularly. I can’t believe I never thought about using them in math, but it will be a very easy transition for the students (or at least for me) as they already have the background knowledge in them for language. I hope to be able to get the book. Thank you for sharing all your info and the things you made together. What a rich learning experience!

    1. I agree completely. I was surprised with myself that I never thought of connecting comprehension strategies to math, but it is so obvious now!

  2. I have been reading your book study posts and comments along with you all and am very excited to get the book in my hands and read it for myself. I ordered the book from Amazon a few weeks into the study and have been waiting ever since. ( No worries though, I’ve had a stack of professional books I’ve been working my way through this summer.) I just received notification from Amazon that my book with arrive September 4th. I can’t wait! This is such an important topic I hope the book sells out again. Thanks to all of you for sharing. I will be re-reading posts as I work my way through the book.

  3. I have also found the think aloud component to be powerful – not just for the teacher, but for my students. I have begun asking my students to orally explain how they came to an answer to the class. I find many students really struggle to articulate their thinking, so I think they need practice. After one students explains, I make sure to ask who figured the answer out in a different way. This is a new step for me, but it has been very powerful. It helps me to see which strategies different students are using, and it showcases the strategies for ALL the kids. I also find that they begin to see there is not one “right” way to do things. This has been powerful assessment for me.

    My big goals are:
    1. To explicitly connect comprehension strategies between reading and math. This will help the kids to see how much they already know how to do, and help them make sense of things in new ways.

    2. To have my kids journal and keep math notebooks. I started this last week (we are in Term 3 in Australia), and I already love what it is doing! I can see their thinking, they can express their thoughts in their own way, and they are responsible for reflecting on and expressing what they know.

    3. I want to begin using more of a planned structure to my math sessions. I used to teach math as quick fifteen minute activities or games. This year my math sessions are one hour long, and so I found myself stringing several activities together. After reading this book, I want to plan the flow better (ignition, bridge, journaling, etc), to get the best bang for buck in the time period.

    Thank you for this fantastic book study! It is exactly what I needed at this time, and it has really inspired me!

  4. I get Goosebumps every Monday reading Donna’s reflections and love, love, love every response that follows. I feel like I have found a new math family. Thank you!

    I cannot say enough about the power of small group instruction in math. I have spent years investing in guided reading lessons. It wasn’t until much later that I asked myself; “Why couldn’t I do the same thing in mathematics?”

    Truthfully, it is in the more intimate moments that my students feel safe enough to show all they know and reveal what they don’t know, conceptually. And for practicality sake, I found small groups to the perfect venue for investigating with manipulatives.

    After years of consulting in higher level mathematics, however, I can see that incorporating small group instruction in math is a hard sell. It takes that leap of faith. But, once we jump, we are never quite the same.

    Meeting all of you has been one of the highlights of my summer. Let’s keep in touch.

    And thank you for the reviews! They are often the best way to get the word out there.

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