Number Talks (@PWHarris & @SaraVanDerWerf)

When I first heard about number talks, I was SUPER excited about them. I learned about them from a great PD with Kara Imm at MfA, and I was blown away by some of the more efficient strategies that they were able to introduce me to. I’ve always used SOME patterns and “shortcuts” but I’ve never used all of them before. Over the summer, I finally read the three books by Pamela Weber Harris, Building Powerful Numeracy, and I was totally on board. I even bought Making number talks matter, and read that whole book, which suggested beginning with the dot patterns and then moving into arithmetic. I read blogs about it, including the blog and Sara Van Der Werf’s blog on it. I was thrilled when at the NYC mini-TMC, I was able to attend a session about number talks vs. number strings, and to participate in a few.

Now, I was told I should aim to do a number talk AT LEAST 3 – 4 times per week, and during the first two weeks, I should try to do one every day. I’m only in the fourth(ish) week of school, and I’m finding myself struggling with both of these already. First, 43 minute periods make it next to impossible to schedule a consistent routine daily, especially one that takes 10 – 15 minutes to do well – especially since I can’t currently envision how to do it as a “Warm-up” (unless I have photocopies of the handouts from Pam’s book and I use those as the independent warm-up and we discuss the strategies afterward – but I wanted students to have a bit of experience with them before working on the handouts).

The second thing (and this is one that I find hard to admit, which is why I’m pushing myself to make it public) – I have a lot of difficulty when I try to train myself in a new routine or activity, and I often need a lot of practice before I get good at leading it. For example, the first few times I led a number talk, I forgot to ask students what they thought the answer was, and I jumped right into the HOW or WHY they thought about the problem. I also found that for some of the student explanations, I can’t visualize how to represent their method on an open number line (we’re doing subtraction): for example, how do you represent “I switched 3 – 8 to 8-3, but then I made it negative because it’s the opposite.”

Another thing I’m struggling with is actually making it through more than two problems in one ten minute chunk OR keeping the kids’ stamina up to solve more than two problems in a string. We finally did a string the other day that had 6 problems in it, and by the last two, I saw many of my students’ body language (in 6th grade) indicating to me that their attention was spent, and they weren’t participating fully.

When I think about this longer string, I noticed in my students’ body language that they weren’t all listening to each other share out (as we only shared one strategy per problem), and there didn’t seem to be any accountability to paying attention or participating past putting your thumb up at the appropriate time so we could discuss. I don’t like to cold call students, especially in the beginning of the year when we’re still building relationships and getting comfortable with each other, but I notice I’m often hearing from the same 5 students, even with wait time (especially for explanations of their strategies or how they thought about the problems – some of the “quieter” kids are more willing to share their numerical answers to the problems, but only if they feel confident in their accuracy, it seems).

One other thing on my mind: I wish there was a way to gather my students in a circle or move my desks out of the way, because I feel like the students are TOO far away from my when we’re doing the number talks. I want them CLOSER to me so no one can “hide” because their desks. I’ve made our routine very specific to include pencils are down and knees are rotated to face the board and I wait, but the last two times I’ve done it, some students have been reticent to put their pencil down and focus OR to turn their bodies and I’m not 100% sure why.

So let’s talk about my sequence of introduction to number talks:

I began on the second week of school (first week only had two days with kids!). I introduced them to it with the quick images dot talk, and we did 6 dots and 10 dots and 11 dots on three of the four days that week. I ran out of time the fourth day. I did those with ALL of my classes, both 6th and 7th grade, but I noticed the 6th graders had more ways of seeing the diagrams than my seventh graders did.

In the third week of school (my first full week: last week!), I began my unit on integers with my 6th graders, and I began doing subtraction number talks with them. I originally planned to use those same number talks with my 7th graders, but I ran out of time the first day, and then every day after, I didn’t quite see how subtraction strings were close enough related to the current unit of study (probability and statistics), so I was unsure about taking 1/3 of class to discuss mental math skills that aren’t directly relevant to the work we’re doing RIGHT NOW. I considered doing different number talks with them, but I wasn’t sure what – I feel like fractions/decimals/percents would be most useful to them right now in their current unit, but I’m not sure exactly how to write strings for that. One thing we’ve done a bunch of so far in class is talk about the eighths as percents and the sixteenths as well. I’m wondering if there are strings I could design that would help them think about those percents more easily; I know the books don’t recommend starting there, but with my 7th graders (who seem so disaffected, honestly!), I’m worried about subtraction being seen as “too easy” by them.

At least in sixth grade, even though we’re thinking about subtraction (and we often all have only one answer), it appears much more related to our current unit of study. We looked at the comparison of the difference and removal ideas about subtraction (although I noticed that because of the types of problems I’ve given students from Kent Haine’s balloon and sandbags game, most of them are using only the removal strategy – I just thought of how I need to tweak it to encourage them to use the distance idea: “How far did the balloon move if it started at # and wound up at #?” I think I’d love to try that in a number talk on Thursday (after our quiz tomorrow on subtracting with negatives, but before we move into multiplying with negatives!). We also did a few problems from Pam Harris’ integer strings, and I’d like to incorporate more of those, because that’s where I saw some real sense-making beginning to happen, as they began to use the previous number statement to reason about the sign of the new one or to think about whether the balloon went up or down relative to the first number (i.e. doing 3 – 8 and then doing -3 – 8). During this third week, we did a number talk three of the five days of school.

This week, we’ve done NO number talks so far. I felt a bit rushed in trying to get my kids ready for their quizzes and keeping to a department timeline of when we should be moving into the next topic, so I decided to skip them (not a decision I’m necessarily proud of or happy about, but there it is). I know I don’t have time tomorrow to do it, but I want to be sure to try to do some on Thursday and Friday.

Anyway, I’m feeling a bit lost with my number talks right now. In 6th grade, I think I just need to get in the habit of making three days of the week “number talk day” and NO MATTER WHAT, we end with number talks that day, using the last ten to fifteen minutes (OR we begin with them??). In 7th grade, I want to think about fractions, decimals, and percents – I’ve noticed that MOST of the students are pretty comfortable with the basics, so I don’t think I need to go back to basics, but I don’t know that they have familiarity with any types of representations of their thinking – I think most of it has just been mental math done quickly and without analysis/thinking about how they know.

I find it a bit scary: researching a new teaching technique, reading all about it, planning for it, and then when you try it out, it doesn’t go exactly the way you wanted it to, and you’re not sure how to modify or fix it. My colleagues at my current school are NOT using number talks: at least not formally. Two of my colleagues don’t use them at all, but one of my colleagues instinctively builds them in as issues arise in class. For example, the other day, she told me her class was discussing the probability of getting 00 in roulette (based on a student question), and they were looking at the fraction 1/38 and considering how to turn it into a percent. She led them through a set of problems that she came up with on the spot to help them see how if they knew 1/4, they could easily figure out 1/40 or if they knew 1/3, they could easily figure out 1/30. I think that type of problem (relationships between fractions) might be a good place to begin with my seventh graders.

I feel like I’m not ready to completely give up on number talks for a few reasons, even though I feel like I’m having a rocky start to them:

  1. I think that the number sense and flexibility my students will gain from being exposed to different strategies and discussing them will be infinitely valuable to them.
  2. I think that different students may participate in number talks than in the “rest” of class, and I want to keep this activity that allows different groups of students to share out.
  3. I think that these strings can highlight strategies that the students may never have thought of before and I want to give them as many tools as possible to create versatile problem solvers.
  4. I think that the number strings will help them become fluent in the language of math calculations, if we do them enough times.

Anyway, I’m hoping to begin a conversation with other people who are trying or who have tried number strings/number talks, because I’d like advice or feedback about where to go next or how to troubleshoot the problems I feel like I’m running into so far.

As an aside: I’ve taken a bunch of pictures of my board after doing my number talks, and if I can figure out how to sync my photos on my phone with my blog, I will! Maybe this weekend….


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