November 3 and 4 were intense! Over the course of two days broken up into four half-day sessions, my colleague Regina and I introduced 150(!) K-5 teachers in our district to number talks. Whew! I still get tired thinking about it.
The guy who wrote this doesn’t work in math education so “Number Talks” and “Numbers Talk” are all the same to him. I do wonder what a “Numbers Talk” PD would entail.
We offered two K-2 sessions and two 3-5 sessions. They were all called “Introduction to Number Talks” and that’s exactly what they were. We painted a big picture, got teachers excited and…ran out of time. I’m already formulating a follow up session for this summer that will dive more deeply into planning for number talks and building teacher confidence in the various computation strategies.
This post isn’t about looking ahead, however. Rather I’m going to look back and reflect on what we did accomplish. I’ll start by saying that for the most part the K-2 and 3-5 sessions were identical. There were some key points where we tailored the content to primary or intermediate grades, but the overall flow was the same.
Having led each session twice, I think that was a good call. In the places where it mattered, K-2 or 3-5 teachers experienced content that resonated with them, but as an introductory session, we were able to get more bang for our planning buck by keeping both sessions mostly the same. That said, I’m going to talk about the sessions as though they were all the same session. However, I’ll point out the places where they varied. Let’s get started!
How many dots do *you* see? Take a few moments and think about different ways you could prove your answer before reading on.
What better way to start than by diving in to our first number talk? I gave them the following directions to get them started:
- Think quietly to yourself.
- No pencils or paper.
- Hold up one thumb when you have one way to find the answer. Hold up additional fingers as you find additional ways.
And then I left them to think.
You may be wondering why I started with this number talk rather than something more meaty like 25 × 32 or 198 + 136. And that is a good wondering! First of all, I didn’t want any numbers (symbols). Secondly, I wanted the quantities to be small. Given those constraints, how could anyone NOT figure out the answer?
When introducing number talks, you want to ensure the barrier to entry is low. You want to ensure that every single person can take part and succeed. While the two example problems I shared are cool and rich with possibilities, they can be intimidating to many students (and teachers!), especially when asked to solve them mentally.
The power of number talks is learning to recognize that there are multiple ways to approach problems. If the first problem I give you makes you anxious because you don’t consider yourself good at computation, or if the numbers seem too large and unwieldy to manipulate mentally, then you’re going to tune out quickly. Not exactly the way I want to start a 3 hour PD session, nor the way a teacher wants to start a promising new practice in her classroom.
After a minute or so, I saw everyone holding up multiple fingers. So far, so good! I asked someone what their answer was. The first person I called on in every session told me 10, but I still followed up with, “And does anyone else have a different answer?”
Crickets. (No surprise there.)
“Okay, who wants to defend this answer?” And we were off! Ahead of time I made copies of the image so that I could draw on them as needed as the teachers shared their thinking. Making extra copies like this requires some planning ahead, and I’m not sure it was necessary, but for this introduction, I did like having clean images available to dirty up with each person’s strategy.
By the way, did you actually stop and think about the image when I first shared it? If not, now would be a good time to do that because I’m going to share pictures I took of the board after each number talk. As you look at them, think about how the strategies our teachers shared compare to your own strategies. Then compare and contrast the strategies across the four sessions. It was fascinating to me to see how the same simple number talk played out with four different groups of people. By the way, if you want to know the order the strategies were shared in each session, go from right to left in each picture.
Our first number talk under our belts, Regina and I provided a brief rationale for number talks, including a reminder that fluency is more than speed and getting the correct answer. Procedural fluency is “skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.” (From the Introduction of the Texas Math TEKS) We also talked about our district’s goals for K-12 mathematics, something we connect to every time we’re in front of teachers. We asked the teachers to compare our district’s goals with the goals of number talks. They noticed they fit together nicely!
After trying out a number talk together, I wanted the teachers to get a chance to see number talks in action with students. Sherry Parrish’s Number Talks book is a great resource because it includes a DVD chock full of 19 number talks from grades K, 2, 3, and 5. As much as I would have liked to show them all, there clearly wasn’t enough time. Not to mention, we didn’t want to bore teachers with video clips. We really wanted them to be incorporated intentionally into our sessions.
Chapter 9 includes some advice about providing teachers a schoolwide perspective of number talks. I thought this was crucial to build buy in. I want teachers to understand that number talks aren’t just for one grade level or grade band. They are a practice that can be used across all grade levels, and there is potential for great things to happen if students have the opportunity to do them year after year.
We showed the teachers a series of four number talks, one from each grade level – K, 2, 3, and 5. As they watched each video, their job was to observe how the following areas were exhibited:
- Classroom community
- Teacher’s role
- Student’s role
I grouped the teachers so that during each video they only had to focus on one of the four areas. After the video was over, each group talked and recorded their observations on charts hanging around the room. Then they rotated to the next chart and watched the next video through a new lens.
Here are the sets of posters and some action shots from each session. I enjoyed listening in on their conversations and hearing how they were picking up on so many important features of number talks from watching the videos.
Session 1 (K-2):
Session 2 (3-5):
Session 3 (3-5):
Session 4 (K-2):
I heard a lot of good questions as they talked in groups. For example, many teachers observed that the classes in the videos seemed small, more like 15 students in a class rather than our usual 22-25. That made them a little skeptical about what number talks look like with larger groups of students. However, I also heard a lot of excited comments about what they were seeing, especially as they saw number talks moving up through the grades.
After the final video, I had each group stay at their final poster. Now their role shifted to analyzing all of the comments made through that one lens so they could share out to the whole group key similarities and differences. Their observations were on point. Listening to them share out each session showed me how powerful this activity had been.
We ended this activity by having a look through one final lens – the process standards. Each table group had 2-3 process standards, and they were tasked with identifying which of those process standards they observed in the four number talks.
The teachers were already so excited to see all the great thinking and talking in the videos. When we talked and realized that pretty much all of these process standards appear in number talks in some form or fashion, that pretty much sealed the deal. “So you’re telling me that in 10-15 minutes my students can develop understanding of content while simultaneously incorporating 3, 4, 5, maybe even all 7 process standards? Count me in!”
That is what we call a great bang for your teaching buck.
Everything after this point was gravy, and boy did I take full advantage of it! Talking about the key components of number talks allowed me to sneakily embed some general teaching practices I feel passionately about.
Talking about component 1 allowed me to make my first plug of the session for Intentional Talk by Elham Kazemi and Allison Hintz. As the teachers watched the four videos, one of the recurring comments in each session was how obvious it was that the students felt safe taking intellectual risks in those classrooms. To me this is one of the most critical components of math instruction in general, not just number talks. We read and discussed a short excerpt about establishing norms from chapter 2 of Intentional Talk. My secret hope is that any work teachers do to establish and/or reinforce norms during number talks will inevitably bleed into other areas of math as well.
Even though this component is about the discussions, I used it as a chance to reinforce the full routine:
- Tell the students to solve the problem mentally, holding up a finger to show they have an answer.
- Wait time is crucial. Wait until most of the students have an answer.
- If you find that no one is answering, the problem may be too difficult. You are allowed to adjust! “I’m not seeing many thumbs on this one. Let’s pause on this one. I want to try a different problem first…”
- Ask students to volunteer answers. Accept all answers – whether they are correct or incorrect – and do your best to keep a good poker face while writing them all on the board for students to consider.
- Ask, “Who wants to defend one of these answers?”
- Students share their strategies and justifications with their peers. This is powerful because it allows you to share authority with your students in determining whether an answer is correct.
- Allow yourself and students to make mistakes. Use them as opportunities to learn.
This is where I got to make my second plug for Intentional Talk. While watching the four videos earlier, teachers were amazed at all of the mathematical ideas the students were sharing. We talked about how this is a learned skill for most students, which means they need our support in learning what and how to share. That’s where talk moves come in! We read another excerpt from chapter 2 of Intentional Talk, and then we watched a short video to see talk moves in action.
I actually embedded talk moves throughout our PD sessions. I printed each one out on a piece of paper and posted them front and center so teachers would see them for the full 3 hours.
I told the teachers if they wanted to start using talk moves, they should post them in their classrooms. There are a lot of talk moves, and it can seem intimidating to start using them. Putting them up on the wall gives teachers a visual reminder to look at any time they want.
Having them posted is also a great way to get students to start using them. I shared one strategy I’ve seen where a teacher focuses on using one talk move throughout a lesson to help students learn and practice that particular talk move. (Check out this video, specifically around 1:13 to see an example.) Over time the students will have the opportunity to practice each talk move individually, and then they can start to use them as needed during number talks.
Or who knows? Maybe they’ll start being used in other areas of math or other parts of the school day?
My secret hope.
Next we talked about the role of mental math. We looked at this from two angles – efficiency and place value / quantity. This is one time where I provided different examples in the K-2 and 3-5 sessions. Well, I provided different examples when discussing efficiency, but I opted to keep the same example when discussing place value / quantity because I thought it would resonate with both groups.
Here’s what K-2 talked about for efficiency. The goal here was to illustrate that while the standard algorithm leads to the correct answer – that is never in question – it is much more cumbersome for this problem than a strategy such as using landmark numbers.
In the 3-5 session, we looked at the following multiplication example. Again, the standard algorithm will work – that is never in question – but other strategies will also lead to the correct answer and they may do so more efficiently.
Next we talked about place value / quantity. In both sessions, I shared the following problem which was posed to a group of 30 or so teachers in a PD session I attended back in my first or second year of teaching. Out of our entire group, only 2 teachers solved the problem by noticing 100 is 2 away from 98. The rest of us had used the standard algorithm. Until that moment at the age of 25, I had never in my life considered doing anything other than the standard algorithm for every single computation problem I solved. It was a life changing moment.
We wrapped up our discussion by revisiting the definition of procedural fluency and how number talks work to help students develop true procedural fluency.
We finally come to the last number talks component, purposeful computation problems.
Again, this is a time where we varied the examples for the K-2 and 3-5 sessions.
Here’s the K-2 problem string:
And here’s the 3-5 problem string:
The key understanding we wanted to convey here is that a mixture of random problems do not lend themselves to a common strategy. Sure, students will be doing mental computation practice, but the disconnectedness of the problems does not create a common focus for a number talk discussion.
We also emphasized that these problem strings may bait the hook for certain strategies, but there are no guarantees students will bite. There are good chances sure, and even better chances because of our purposeful planning, but never a guarantee. And that’s okay. We just need to be aware of that.
By this point we had spent a lot of time talking so we shifted gears and watched a couple more number talks videos. This time our goal was to look at vertical alignment. In the K-2 session we watched a video from Kinder and 2nd grade. In the 3-5 session we watched a video from 3rd grade and 5th grade.
I knew we weren’t going to have time to dive deeply into all of the various computation strategies students might use. There are lengthy chapters devoted to them in Sherry Parrish’s Number Talks book, and they’re chock full of great information. This is a topic I will likely spend more time on during the session I’d like to plan for next summer. For now, I wanted to at least touch on the idea that math concepts build on each other and how this plays out during number talks.
Now that the teachers had seen 6 number talks, 7 if you include the one we did together at the start of the session, we wanted to stop and talk about the role of models and tools.
It was impressive the variety that we saw – dot images, five and ten frames, rekenreks, hundred chart, number lines, and equations. There are a lot of great ways for students to use tools to think about computation and to show their thinking.
Because the videos from grades 3 and 5 had mostly shown symbolic representations, we did watch an extra video in the 3-5 session that showed how a 5th grade teacher used a number talk to help her students tackle misunderstandings about representing division using arrays.
By this point in each session we were very much behind schedule. We had wanted to give teachers the chance to practice recording student thinking like they’ll have to do when their students share their strategies in a number talk. Unfortunately, we could tell there just wasn’t going to be enough time. In the first two sessions, I was annoyed that we didn’t get to it, but by the end, I think it worked out fine that it got cut. I don’t want to rush that activity, so it tells me that it is appropriate to wait and spend the right amount of time doing it in our summer session.
Even though we had to skip the activity, we did briefly talk about anticipating student thinking.
Nearing the end of our session, we wanted to close with some tangible steps for getting started implementing number talks once the teachers left and went back to their campuses.
We let them know where they can find pre-planned number talk strings in Sherry Parrish’s book. We showed them a document located in our curriculum guides where we collect various resources about number talks. It includes links to videos, articles, planning templates, etc. We closed by sharing final tips and advice for getting started.
And then we were done.
After the session was over, I sent out a link to a short survey to collect feedback from participants. We heard back from 20 folks. In case you’re considering leading a number talks PD, I thought I’d share their feedback so you can see what they liked and what they suggest we change for future sessions. Why not learn from my experiences?
1. What worked well in the Number Talks PD session?
- Loved the videos – being able to see a number talk in action. I liked that we began the PD with a number talk.
- There was lots of great information presented. It was nice to see number talks for various grade levels and to talk with teachers from other campuses.
- Watching the videos and moving through the charts to debrief. Tying the number talk work to the Process Standards.
- I liked reflecting on the video clips and observing them from 4 different perspectives. It really made me notice what was going on.
- The clips and talking about each element of Number Talks reinforced what I am currently doing and answered some questions I had about certain parts.
- You explained everything in great detail. I love the rotation on different lenses. The discussion was amazing and watching the videos from different grade levels really demonstrated the building blocks from K-5 and beyond.
- Such a great PD! Loved all the videos and examples.
- Videos and discussions with table groups were very helpful. I can’t wait to start using it.
- Knowledgable instructor, great examples, great discussions facilitated nicely. Tied directly to NCTM standards, ARRC, TEKS, etc. Clearly showed vertical alignment and expectations.
- Liked the jigsaw talk about the videos and examples.
- Brian demonstrating a Number Talk. Sharing after the videos really helped us to put ourselves in the shoes of the teacher, student and classroom community. I liked doing each one individually so that we could focus on that area. It was also great to see the vertical alignment of Number Talks.
- Videos were helpful; lots of dialogue/discussion among the group
- I loved it all! I would like to do almost the exact same training for the staff at my school.
- I knew the theory behind number talks and how they can helps students improve their numbers sense/computational fluency, but I like how this was practical for getting it started in the classroom.
- Watching the classroom examples was helpful in visualizing and considering how this looks across all grade levels. It also helped in thinking about different ways in which the number talks could be presented.
- Your pacing was excellent. It was great to see the videos at the different levels and with a different lens each time. The Talk Moves was also helpful to guide teachers.
- Frequent movement, lots of discussion, the video slides, important information on the slides – not a lot of words/research/etc., lots of student examples, candy!!!
- The videos helped to see examples of Number Talks, and using different lenses to view them was a great strategy.
2. What could we change to make this PD session more effective?
- It was a well prepared and informative session. I am looking forward to doing number talks better in my classroom this year!
- I think it would be nice to hear more from teachers who are already using it in the district just for some more direct input and ideas. It also would have been nice to be able to practice doing a few.
- From classroom observation – encouraging teachers to understand the power of a number talk vs teaching a trick – especially one that will expire. Maybe a smidge of time to practice the talk moves – a few typed scenarios to read to get used to using the language, hearing it….
- Just mentioning where to find the resources on the ARRC, instead of trying to explain what’s on the links.
- The only thing I would possibly add is time to plan out a number talks for the current skill or every group plan a different one so we can have a bank of talk plans.
- I thought it was great!
- The only thing I could think to add would be to provide a week’s worth of number talks ready to implement in the classroom. (description, any displays or reproducibles already copied or on cardstock, etc) This would be assuming that the teacher needs to start at the beginning of the Number Talks continuum, or appropriate number talks for the current or upcoming math unit.
- I would like a few starter ideas to take with me. Just some basic types of number talks like; dots, equations, and number line ideas.
- This is the best PD I’ve ever been to with RRISD. I’m able to implement it asap.
- I think this PD was perfect!
- I thought it was great! The only thing might be to have grade levels discuss exactly what problems they would do for a number talk.
- It would have been great to get with grade level teams within the PD to think about how these could work into current units. I have not used number talks quite like these before, but would love to start using them. It’s difficult to think of how this will fit in with our current fractions unit – perhaps decomposing fractions in different ways? It may be helpful to offer Number Talk planning sessions for grade levels – what we use and create could also be linked within units on the ARRC.
- Nothing, it was great!
- Print out the presentation slides as a notes handout so we can make notes next to the slides
Thoughts from Brian:
This definitely reinforces why I need a second session. It would be great in the summer if we could do a full day session so the first 3 hours could be an introduction, while the next 3 hours could dive into practice doing a number talk, recording student thinking, talking about computation strategies, and planning first number talks.
I have an idea for an activity where teachers work in trios to take turns leading a number talk. The other two people in the trio will act as students. It’s not the same as a class of 22 students, but at least the teachers would have the chance to practice recording someone else’s strategy who is telling it to them live and in person. They could also practice the talk moves a bit since there are three of them.
Knowing that teachers would want to hear from other teachers in our own district, I recently had everyone in the Math Rocks cohort I’m leading to write a blog post reflection about doing number talks in their classroom. These blog posts are all collected in a document that our teachers can access whenever they want to gain perspective from someone else in the district. If you start with Kari Maurer in the table, she and all of the folks below her are from my district.
3. What support do you need from the Teaching & Learning Department to help you succeed in implementing number talks?
- It seems covered well! Thanks for putting Number Talks in the ARRC!
- I know our coaches are very willing to help with the number talks. I’m excited to implement them in my classroom! Thanks!
- Definitely summer PD Offering help to plan a number talk
- I think just the book to help me have some numbers already to go. Perhaps coaching observations to help me know if I need to add anything or do anything differently.
- Time 🙂 to plan for it
- More PD, seeing Number Talks in action at one of our schools in RR. Or have a veteran Number Talk teacher run a talk with kids who have never been exposed to NT.
- Resources are always great, but there’s already a lot available!
- I won’t know for sure until I’ve had a chance to explore the tools available and look personally at the books referenced. So far I feel confident in my abilities to begin quickly and consistently. Thank you.
- Number talk plans added to the ARRC to correspond with ARRC timeline would be amazing!
- I know the skills covered during a Number Talk can vary, but putting samples in each unit under the Computational Fluency section might be helpful to give teachers ideas.
- Specific number talk examples linked within units on the ARRC.
- I know I can call or e-mail you as needed. Thank you!
- The extra copies of the book on each campus is very helpful! Maybe a training/PD on that other book you discussed – Implementing Strategies that Work (not sure on title)?
Whew! Writing up this blog post was almost as intense as leading the four PD sessions. If you made it this far, I tip my hat to you. I hope hearing about my experiences helps you in some way in your own work. If you have any questions, I’d love to discuss them in the comments.
And now I’m off to continue planning for 12 hours of fractions PD I’m leading this week based on the book Beyond Pizzas and Pies. The fun never ends!