Category Archives: Number Talks

Decisions, Decisions

This week our Math Rocks cohort met for the fourth time. We had two full days together in July, and we had our first after school session two weeks ago. One of our aims this year is to create a community of practice around an instructional routine, specifically the number talks routine. We spent a full day building a shared understanding of number talks back in July. You can read about that here. We also debriefed a bit about them during our session two weeks ago.

This week we put the spotlight on number talks again. We actually broke the group up by grade levels to focus our conversations. Regina led our K-2 teachers while I led our 3-5 teachers. The purpose of today’s session was to think about the decisions we have to make as teachers as we record students’ strategies. How do you accurately capture what a student is saying while at the same time creating a representation that everyone else in the class can analyze and potentially learn from?

We started the session with a little noticing and wondering about various representations of 65 – 32:

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Very quickly someone brought up exactly what I was hoping for which is that some of the representations show similar strategies but in different ways. For example, the number line in the top left corner shows a strategy of counting back and so do the equations closer to the bottom right corner.

This discussion also led into another discussion about the constant difference strategy – what it is and how it works. It wasn’t exactly in my plans to go into detail about it this afternoon, but since my secondary goal for the day was to focus specifically on recording subtraction strategies, it seemed a worthwhile time investment.

After our discussions I shared the following two slides that I recreated from an amazing session I attended by Pam Harris back in May. (For the record, every session I attend with her is amazing.)

The first slide differentiates strategies from models. Basically, if you have students telling you their strategy is, “I did a number line,” and you’re cool with that, then you should read this slide closely:

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The second slide differentiates tools for building relationships from tools for computation. This slide is crucial because it shows that while we want students to use tools like a hundred chart to learn about navigating numbers within 100, the goal is to eventually draw out worthwhile strategies, such as jumping forward and/or backward by 10s and then 1s.

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The strategy on the right that shows 32 + 30 followed by 62 + 3 is totally the type of strategy students should eventually do symbolically after building relationships with a tool like the hundred chart.

After blowing their minds with those two slides, I led them in a number talk of 52 – 37. During my recording of their strategies, I stopped a lot to talk about why I chose to do what I did, to solicit their feedback, and even to make some changes on the fly based on our discussion.

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For example, in the top right corner of the board I initially used equations to represent a compensation strategy. Someone asked if this could be modeled on a number line because she thought it might make more sense, so I did just that in the top left corner. By the time we were done they were like, “Oh, hey! That ends up looking like a strip diagram!”

It was amusing that the first strategies they shared involved constant difference. They were so excited about learning how the strategy worked that they wanted to give it a try. I didn’t want to quash their excitement by telling them that the strategy tends to work better, especially for students, when you adjust the second number to a multiple of ten. I wanted to stay focused on my goals for the day. We’ll discuss the strategy more in a future session.

(Unless you’re in Math Rocks and you’re reading this! In which case, see if you can figure out why that’s the case and share it at our next meeting.)

After some great discussion about recording a variety of strategies, we watched Kristin Gray in action leading a number talk of 61 – 27.

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We talked about how she recorded the students’ strategies. We also talked about some really lovely teacher moves that I made sure to draw attention to.

We wrapped up our time together talking about what new ideas they learned that they wanted to try out with their students. I had asked one of the teachers to lead us in another number talk, but we ran out of time so I think I’m going to have her do that at the start of our next session together. Hopefully everyone will have had some intentional experiences with recording strategies between now and then to draw on during that number talk.

Oh, another thing we talked about at various points during the session was how to lead students in the direction of certain strategies. This gets into problem strings, which may or may not happen in number talks depending on whom you talk to. Regardless, here are some we came up with. Can you figure out what strategies they might be leading students to notice and think about?

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Math Rocks Redux Part 2

At the end of July, @reginarocks and I kicked off our second Math Rocks cohort – a group of 30 or so elementary educators that meets for almost 30 hours across 7 months. Our first cohort, which ran last school year, was a success, but when it came time to plan for year 2, we definitely found ourselves wondering how we could provide an even better learning experience this year.

The other day I wrote about the tweaks we made to day 1 of Math Rocks. All in all, the tweaks were minor – you can read about that session here – but day 2 was completely overhauled! That’s what I’d like to write about today.

But first, let me bring you up to speed on some things that happened to influence my decisions about day 2. Last year, Regina and I delivered a lot of PD across a wide variety of topics and audiences  – diagnostic assessments with interventionists, fraction sense with grades 3-5 teachers, developing number concepts with grades K-2 teachers, weight and liquid volume measurement with grade 3 teachers, spiral review strategies for grades 3-5 – but the topic that seemed to resonate the most with our teachers was number talks. Across four half-day sessions, we ended up delivering an introduction to number talks to approximately 150 of our elementary teachers! I wrote about the experience here if you’d like to read about it.

Last year’s Math Rocks cohort also dove into number talks. As part of our work together we joined a book study of Making Number Talks Matter led by Kristin Gray and Crystal Morey. Our group loved it, but because the book study was mostly discussed online via Twitter and Teaching Channel forums, I realized later we didn’t do enough work in person to talk about and work through issues that came up to support our teachers as they took on this new practice.

Fast forward to Twitter Math Camp this summer, and I had the opportunity to take part in an incredible PD experience with David Wees, Jasper DeAntonio, and Katilin Ruggiero in their session titled “Rehearsing Instructional Routines Together.” You can access all of the slides and materials from the session on the Twitter Math Camp wiki here. Their session focused on teaching us the Contemplate then Calculate routine – which I now love! – but the structure of the PD itself is what captured my attention most. So much so that I borrowed liberally from their work when designing day 2 of Math Rocks!

Day 2 of Math Rocks followed this structure:

  • Regina, Jan, and I each model a number talk
  • Math Rocks participants unpack the components of a number talk
  • Math Rocks participants plan their own number talk in pairs or trios
  • Math Rocks participants rehearse their number talks for the group

All of this work drove us toward our two goals for the day:

  1. Dive deeply into the number talks routine
  2. Develop a community of practice that can more precisely talk about our teaching

The day started with Regina, Jan, and I each modeling a number talk. This was challenging to plan. One of the key pieces of David’s session at Twitter Math Camp was instructional routines. Contemplate then Calculate is a routine that is broken down into very discrete steps. In order to bring this to our teachers in my district, I had to think about what the steps of a number talk are supposed to be.

What ends up making this challenging is that what makes up a number talk is not universally agreed upon. A big point of contention has to do with how many problems you do in a number talk. Some people say number talks should focus on one problem and all the strategies used to solve that one problem, while others say a number talk can involve multiple problems to solve and discuss. Those that disagree say that having multiple problems is called a number string, not a number talk. Yay, semantics!

For the purposes of my work with my Math Rocks cohort, I opted to say a number talk can include more than one problem for the sheer fact that Sherry Parrish’s book Number Talks, which we have 6 copies of on all 34 of our elementary campuses, does present number talks as strings of problems. The sample number talks videos on the DVD all show teachers modeling strings, and all or nearly all of the sample pre-planned number talks that are shared in the book are strings as well. Knowing my teachers will be using Sherry Parrish’s book as a resource, I opted to define the routine as having multiple problems to solve, but I did not define how many problems.

When deciding what the components of our number talks instructional routine would be, I also consulted this document from Math Perspectives. Here’s how they delineate the routine:

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Finally, I took all of that and simplified the number of steps to make the routine feel smooth and easy to follow. Here’s what I presented my teachers during day 2 of Math Rocks:

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Making the Math Rocks folks sit through three number talks might sound like overkill, but it served two purposes. First, we wanted to model number talks across grades to demonstrate that this routine is appropriate across the elementary grades. The three number talks we modeled came from mathematics in Kindergarten, 2nd grade, and 4th grade.

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Second, modeling so many number talks ensured we as a group had three shared experiences to draw upon when unpacking the routine later. We wanted the participants to really be able to unpack and analyze each of the components of the number talk, and in order to do that they needed to have seen each of the components enough times to have meaningful conversations about them.

After modeling the three number talks, we used the Ideas Carousel protocol to unpack the components of the number talks routine. (Just as a reminder, I borrowed liberally from David’s sessions. This protocol came from his session, too. )

Here’s how the protocol works. We made a poster for each of the components of the number talks routine, and participants chose a component to unpack. With their group, they recorded their understandings of the parts of that component, the rationale(s) for each of those parts, and any questions/wonderings they had.

Once the groups had a chance to dirty up their posters, they started rotating through the remaining posters. At each poster, they had to read the poster, check ideas that resonated with them, add new ideas, star ideas they wanted to discuss as a group, and circle the idea their group thought was most important on that poster.

After interacting with each poster, they took one last gallery walk through all of the posters before returning to their original poster. Once there, they read over their original comments and all of the extra things added by everyone else, and they marked anything that surprised them. Here are their completed posters:

Finally, as a group we talked through their wonderings, a-ha moments, and anything else that came up. It was such a rich conversation and demonstrated that we have a lot of interesting questions to explore this year. For example:

  • How do you do number talks in an intervention group that meets for only 30 minutes daily and is composed of students who are reluctant to participate or try out different strategies?
  • How do you modify number talks for emergent bilingual students? Sharing their strategies verbally may be too much of a challenge. What can we do to accommodate them?
  • How do you know what to record when students are talking about their strategies? How do you get better at that?

This really gets at one of our goals for this day of learning – creating a community of practice that can more precisely talk about our teaching. I don’t have all the answers for them, and how much more interesting is it that we as a group get to explore and discover our own answers through our experiences this year? We get to decide what works (and doesn’t) for our students, and we have a group of people to do that important work with.

Now that we had accomplished our other goal for the day – diving deeply into the number talks routine – we gave the participants time to plan their own number talks. We grouped them by grade levels to plan, though we did have one team composed of a special education teachers and two interventionists.

Finally, we had time for some of them to rehearse their number talks in front of the rest of the group. I reiterated a key thing David Wees said in our Twitter Math Camp session: the purpose of this rehearsal is not to coach individual teachers to be better at number talks. Rather it’s to give us as a group an experience where we can talk about the act of teaching. I like the meaning behind it, but I also think it helps take the pressure off the teachers. It’s not about any one person at the front of the room, it’s about how it gives everyone an experience and ability to talk about the very messy work of teaching.

All in all it was a very intense and focused day, but I loved it! I think this was just the right experience to kick off our time together over the next 7 months. I look forward to the conversations and support we’ll be able to provide one another going forward. What I’d like to do during the school year is have different participants plan and rehearse number talks so we can continue talking about the routine. I also want to spend some time focusing on how we record students’ strategies so that everyone can feel more confident in this area so they can be more intentional about how they are representing students’ strategies for the rest of the class to benefit from.

Thank you to David, Jasper, and Kaitlin for providing an awesome experience that I was able to take back and adapt for my teachers! Special thanks to Jasper for his elevator speech that encouraged me to attend his session instead of the one I was originally planning to attend.