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Here is another post about a book I've read recently. This time, I'm writing about the book "Making Number Talks Matter" by Cathy Humphreys and Ruth Parker.

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In Cathy and Ruth's words, number talks are "a brief daily practice where students mentally solve computation problems and talk about their strategies". I had heard people talk about them before and how they are a powerful way to help students come to a better understanding of how numbers fit together and to develop their confidence. So I read this book in the hope of finding out more about what they are and how to implement them. My goal was to eventually use number talks to help make a difference to Science and Health Science students, especially those with little maths experience or only painful maths experiences.

I have to admit to you now that I've been trying to write this post for a couple of weeks now and I've been having real trouble. I think it's because I had mixed feelings about the book at the time, but that looking back several months after reading it I have different feelings now than I did back then. I think the easiest way to write the post is to talk about some of those feelings first.

While reading the introductory chapters, I had such hope for the power of Number Talks. Cathy and Ruth talked about how much students need to talk about numbers and make sense of things, rather than follow algorithms without making sense, and inside I was saying "Yes!" and I was inspired to keep reading. When I got to the next chapter where they described the standard routine for Number Talks, I felt a bit let down. The directions said to get students to put away all paper and pens, to ask them not to talk and to put up thumbs to say when they've got an idea, then to share answers before asking for strategies. My knee-jerk reaction was to feel very restricted by these directions. Looking back later, I am drawn much more to the rationales about each step: that no paper helps to focus away from algorithms and towards sensemaking; that no talking helps students to form their own ideas; that answers before strategies helps to get answers out the way to focus more clearly on strategies later. Focussing on the rationales helped me imagine how I might decide to change some of these to match the needs of the students I might be working with.

On that note, the next chapter on Guiding Principles for Number Talks was I think the most useful chapter in the whole book. I kept coming back to it while reading the rest of the book to ground myself again. Indeed, the later chapters on specific strategies for specific operations got me a bit bogged down and made me feel a bit like I'd lost my vision of what we were trying to do here. I needed the touchstone of the Guiding Principles to pull me out of that feeling of slogging through. I'm going to come back to this chapter and talk about it in more detail because I want to end with the best bit!

The next several chapters talk about various operations and number types and the various strategies that we might hear students using or encourage them to use. I found this a bit heavy-going, partly because some of the strategies were not natural to me and so I couldn't think to try to recommend them to anyone! In hindsight I think it's really good that I read this before trying any number talks because I am pre-prepared in order to not be surprised too much when students do some interesting stuff. Also, as I flick through them now, I am somehow more able to see how each strategy might apply to my current students. I think maybe having all those strategies floating in my mind while I've spent a few months helping my students make sense of algebra and calculus has helped me see where these strategies for operations tie in with the later maths concepts. I do need to say that even upon first reading, a useful thing about these middle "operations" chapters were the many vignettes of number talks in action that slowly gave me a better idea of how the discussion part of the routine is implemented.

My very favourite part of all of the middle chapters were the special number talks that appeared in the chapter on fractions, decimals and percentages. These ones had students not calculate an answer but decide which of two numbers was bigger, decide if a number was closer to 1/2 or 1, or to place a fraction on a number line. These really gave me a better idea of the possible ways of using number talks to promote sensemaking than any of the previous calculation number talk ideas. I suddenly felt free to consider more options and therefore free to give it a go.

And then the book finished off with a chapter called "Managing Bumps in the Road". This was another chapter that was really useful for helping me be brave to try it myself eventually. Based on the roadbumps mentioned here, I reckon one of the major dangers is losing sight of the important goals of number talks outlined in those guiding principles at the start. This chapter helped refocus my attention on what's important and gave some ideas for how to refocus this attention on the fly too.

Which brings me to the end of the book. It was in some ways not the easiest book to read, but I did learn a lot about sensemaking and strategies and managing discussions. And as I said, the guiding principles mentioned early on were a very excellent thing I was able to take away from the book. Most of them are applicable to most of my maths teaching and not just to the specific routine of number talks. As promised, here they are:

Guiding Principles for Number Talks

from "Making Number Talks Matter" by Cathy Humphreys and Ruth Parker

1. All students have mathematical ideas worth listening to, and our job as teachers is to help students learn to develop and express these ideas clearly.
2. Through our questions, we seek to understand students' thinking.
3. We encourage students to explain their thinking conceptually rather than procedurally.
4. Mistakes provide opportunities to look at ideas that might not otherwise be considered.
5. While efficiency is a goal, we recognise that whether or not a strategy is efficient lies in the thinking and understanding of each individual learner.
6. We seek to create a learning environment where all students feel safe sharing their mathematical ideas.
7. One of our most important goals is to help students develop social and mathematical agency.
8. Mathematical understandings develop over time.
9. Confusion and struggle are natural, necessary and even desirable parts of learning mathematics.
10. We value and encourage diversity of ideas.

Number 2 and Number 5 in particular shone out to me at the time as my guiding lights for day-to-day teaching even outside of number talks. (Though looking through them now, 6, 7 and 8 are right up there too.) Two specific quotes from this chapter make these more real to me and are a good place to finish:

These comments were left on the original blog post:

Mark Pettyjohn 25 May 2017

Your post reminded me of some conflicted thoughts I’ve previously had. The nature of which were about:

Number Talks (TM) vs. number talks

Four or five years ago I became aware of Number Talks via Sherry Parrish’s book. I got an overview and then dove in with my class. The results were amazing, for me and for them. I think the principles of what I saw happening were highly aligned with the principles outlined by Humprheys and Parker.

Then something peculiar happened. I wanted to share with others the good things happening, so I went back to my Number Talks book (again, Parrish not Humphreys), and it all looked so stilted. I watched the accompanying videos and they looked little like what was happening in my classroom. It was more a teacher driving strategies to students rather than principles 1-7, 9, and 10 outlined here.

So as I was reading your reticence to write this post, I was feeling my own reticence back then about sharing Number Talks (TM) with colleagues because I didn’t feel like it captured in practice or in spirit what we were doing in my classroom. There’s enough confusion around terms in education that I was hesitant to add to it.

That’s partially why I asked on Twitter if you had seen or done any yourself. I’ve found that a number talk is not always a Number Talk (TM) and I would imagine that extends to what Humphreys and Parker have here.

But I really like the principles outlined in your post, and I think that if you can look back at a number talk (with your own kid or with other students) and see those principles reflected, then you done good.

Susan Jones 25 May 2017

I share the reaction to restrictions. I remind myself that it’s only for that chunk of time and…. I think I’d break it every once in a while for people like me who think wth their pencils. I see that obsession with algorithms on our 5-math-question survey at the beginning of our “transitions” course for students, which asks what 4 and a half x 2 is. In several years we’ve seen 1 or 2 students answer it correctly while half the students attempt an algorithm (many leave it blank).

David Butler 26 May 2017

Interestingly, in the book they do do some number talks where they suggest to let the students have pencil and paper. I think you really need to be looking at what message you are sending today and whether not having paper is going to help.