Danielle Robinson and Dr. Melissa Hedges, The Promise of Counting Collections

Mike Wallus, Vice President for Educator Support


Earlier this season, we released an episode focused on the complex and interconnected set of concepts that students engage with when they learn to count. In this follow-up episode, we’re going to examine a powerful routine called counting collections. We’ll be talking with Danielle Robinson and Dr. Melissa Hedges from Milwaukee Public Schools about counting collections and the impact this routine can have on students.  

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Choral Counting & Counting Collections: Transforming the PreK- 5 Math Classroom

Learning and Teaching with Learning Trajectories

Taking Action: Implementing Effective Mathematics Teaching Practices in K-Grade 5

Principles to Actions: Ensuring Mathematical Success for All

Catalyzing Change in Early Childhood and Elementary Mathematics


Mike Wallus: Earlier this season, we released an episode focused on the complex and interconnected set of concepts that students engage with as they learn to count. In this follow-up episode, we're going to examine a powerful routine called “counting collections.” We'll be talking with Danielle Robinson and Dr. Melissa Hedges from the Milwaukee Public Schools about counting collections and the impact that this routine can have on student thinking. 

Well, welcome to the podcast, Danielle and Melissa. I can't tell you how excited I am to talk with y'all about the practice of counting collections. 

Melissa Hedges: Thanks for having us. 

Danielle Robinson: Yes, we're so excited to be here.

Mike: I want to start this conversation by acknowledging that the two of you are actually part of a larger team of educators who really took this work on counting collections. You introduced it in the Milwaukee Public Schools. And, Melissa, I think I'll start with you. Can you take a moment to recognize the collaborators who have been a part of this work?

Melissa: Absolutely. In addition to Danielle and myself, we are fortunate to work with three other colleagues: Lakesha King, Krista Beal, and Claire Madden. All three are early childhood coaches that actively support this work as well.

Mike: So, Danielle, I wonder for some folks if we can help them see this practice more clearly. Can you spend time unpacking: What does counting collections look like in a classroom? If I walked in, what are some of the things that I might see?

Danielle: Yeah. I think what's really amazing about counting collections is there might be some different ways that you might see counting collections happening in the classroom. When you walk into a classroom, you might see some students all over. Maybe they're sitting at tables, maybe they're on the carpet. And what they're doing is they're actually counting a baggie of objects. And really their job is to answer this question, this very simple but complicated question of, “How many?” And they get to decide how they want to count. Not only do they get to pick what they want to count, but they also get to pick their strategy of how they actually want to count that collection. 

They can use different tools. They might be using bowls or plates. They might be using 10-frames. They might be using number paths. You might see kiddos who are counting by 1s. You might see kids who are making different groupings. At times, you might also see kiddos [who] are in stations, and you might see a small group where a teacher is doing counting collections with a few kiddos. You might see them working with partners. And I think the beautiful piece of this and the unique part of counting collections within Milwaukee Public Schools is that we've been able to actually pair the counting trajectory from Doug Clements and Julie Sarama with counting collections, where teachers are able to do an interview with their students, really see where they're at in their counting so that the kids are counting a just-right collection for them—something that's not too easy, something that's not too hard, but something that is available for them to really push them in their understanding of counting. So, you're going to see kids counting different sizes. And we always tell the teachers it's a really beautiful moment when you're looking across the classroom and as a teacher, you can actually step back and know that every one of your kids [is] getting what they need in that moment. Because I think oftentimes, we really don't ever get to feel like that, where we feel like, “Wow, all my kids are getting what they need right now, and I know that I am providing the scaffolds that they need.”

Mike: So I want to ask you a few follow-ups, if I might, Danielle.

Danielle: Yeah, of course.

Mike: There's a bit of language that you used initially, where — I'm paraphrasing, and tell me where I get this wrong. You use the language “simple yet complicated,” I think. Am I hearing that right?

Danielle: I did. I did, yeah.

Mike: Tell me about that.

Danielle: I think it's so interesting because a lot of times when we introduce this idea of counting collections with our teachers, they're like, “Wait a minute. So I'm supposed to give this baggie of a bunch of things to my students, and they just get to go decide how they want to count it?” And we're like, “Yeah, that is absolutely what we're asking you to do.” 

And they feel nervous because [of] this idea of the kids, they're answering “how many?”, but then there's all these beautiful pieces [that are] a part of it. Maybe kids are counting by 1s. Maybe they're deciding that they want to make groups. Maybe they're working with a partner. Maybe they're using tools. It's kind of opened up this really big, amazing idea of the simple question of “how many?”, but there's just so many things that can happen with it.

Mike: There's two words that kept just flashing in front of my eyes as I was listening to you talk. And the words were “access” and “differentiation.” And I think you didn't explicitly say those things, but they really jump out for me in the structure of the task and the way that a teacher could take it up. Can you talk about the way that you think this both creates access and also the places where you see there's possibility for differentiation?

Danielle: For sure. I'm thinking about a couple classrooms that I was in this week and thinking about once we've done the counting trajectory interview with our kiddos, you might have little ones who are still really working with counting to 10. So they have collections that they can choose that are just at that amount of about 10. We might have some kiddos who are really working kind of in that range of 20 to 40. And so we have collections that children can choose from there. And we have collections all the way up to about 180 in some cases. So we kind of have this really nice, natural scaffold within there where children are told, “Hey, you can go get this just-right color for you.” We have red collections, blue collections, green, and yellow. Within that, also, the children get to decide how they want to count.

So if they are still really working on that verbal count sequence, then we allow them to choose to count by 1s. We have tools for them, like number paths, to help do that. Maybe we've got our kiddos who are starting to really think about this idea of unitizing and making groups of 10s. So then what they might do is they might take a 10-frame and they might fill their 10-frame and then actually pour that 10-frame into a bowl, so they know that that bowl now is a collection of 10. And so it's this really nice idea of helping them really start to unitize and to make different groupings. And I think the other beautiful piece too is that you can also partner. Students can work together and actually talk about counting together. And we found that that really supports them too of just that collaboration piece too.

Mike: So you kind of started poking around the question that I was going to ask Melissa. 

Danielle and Melissa: [laugh]

Mike: You said the word “unitizing,” which is the other thing that was really jumping out because I taught kindergarten and first grade for about eight years. And in my head, immediately all of the different trajectories that kids are on when it comes to counting, unitizing, combining — those things start to pop out. 

But, Melissa, I think what you would say is there is a lot of mathematics that we can build for kids beyond, say, K–2, and I'm wondering if you could talk a little bit about that.

Melissa: Absolutely. So before I jump to our older kids, I'm just going to step back for a moment with our kindergarten, first- and second graders, and even our younger ones. So the mathematics that we know that they need to be able to count collections, that idea of cardinality, one-to-one correspondence, organization — Danielle did a beautiful job explaining how the kids are going to grab a bag, figure out how to count, it's up to them — as well as this idea of producing a set, thinking about how many, being able to name how many. 

The reason why I wanted to go back and touch on those is that we know that as children get older and they move into third, fourth, and fifth grade, those are understandings that they must carry with them. And sometimes those ideas aren't addressed well in our instructional materials. So the idea of asking a first- and second grader to learn how to construct a unit of 10 and know that 10 ones is 1 ten is key because when we look at where place value tends to fall apart in our upper grades. My experience has been, it's fifth grade, where all of a sudden we're dealing with big numbers, we're moving into decimals, we're thinking about different sized units, we've got fractions. There's all kinds of things happening. 

So the idea of counting collections in the early elementary grades helps build kids' number sense, provides them with that confidence of magnitude of number. And then as they move into those either larger collections or different ways to count, we can make beautiful connections to larger place values — so hundreds, thousands, ten thousands. Sometimes those collections will get big. All those early number relationships also build. So those early number relationships, part-whole reasoning that numbers are composed and decomposed of parts. And then we've just seen lots of really, really fun work about additive and multiplicative thinking. 

So in a third-, fourth-, fifth grade classroom, what I used to do is dump a cup full of lima beans in the middle of the table and say, “How many are there?” And there's a bunch there. So they can count by 1s. It's going to take a long time. And then once they start to figure out, “Oh wait, I can group these.” “Well, how many groups of 5 do you have?” And how we can extend to that from that additive thinking of 5 plus 5 plus 5 plus 5 to then thinking about and extending it to multiplicative thinking. So I think the extensions are numerous.

Mike: There's a lot there that you said, and I think I want to ask a couple follow-ups. First thing that comes to mind is, we've been interviewing a guest for a different podcast, and this idea that unitizing is kind of a central theme that runs really all the way through elementary mathematics and certainly beyond that. 

But I really am struck by the way that this idea of unitizing and not only being able to unitize, but I think you can physically touch the units, and you can physically reunitize when you pour those things into the cup. And it's giving kids a bit more space with the physical materials themselves before you step into something that might be more abstract. I'm wondering if that's something that you see as valuable for kids and maybe how you see that play out?

Melissa: Yes, it's a great question. I will always say when we take a look at our standard base ten blocks, “The person [who] really understands the construction of those base ten blocks is likely the person [who] invented them.” They know that one little cube means 1, and that all of a sudden these 10 cubes are fused together and we hold it up and we say, “Everybody, this is 10 ones. Repeat, 1 ten.” What we find is that until kids have multiple experiences and opportunities over time to construct units beyond 1, they really won't do it with deep understanding. And again, that's where we see it fall apart when they're in the fourth and fifth grade. And they're struggling just to kind of understand quantity and magnitude. So the idea and the intentionality behind counting collections and the idea of unitizing is to give kids those opportunities that — to be quite honest, and no disrespect to the hardworking curriculum writers out there — it is a tricky, tricky, tricky idea to develop in children through paper and pencil and workbook pages.

I think we have found over time that it's the importance of going, grabbing, counting, figuring it out. So if my collection is bears, does that collection of 10 bears look the same as 10 little sharks look the same as 10 spiders? So what is this idea of 10? And that they do it over and over and over and over again. And once they crack the code—that's the way I look at it—once our first- and second graders crack the code of counting collections, they're like, “Oh, this is not hard at all.” And then they start to play with larger units. So then they'll go, “Oh, wait, I can combine two groups of 10. I just found out that's 20. Can I make more 20s?” So, then we're thinking about counting not just by 1s, not just by 10s, but by larger units. And I think that we've seen that pay off in so many tremendous ways. And certainly on the affective side, when kids understand what's happening, there's just this sense of joy and excitement and interest in the work that they do, and I actually think they see themselves learning.

Mike: Danielle, do you want to jump in here?

Danielle: I think to echo that, I just recently was speaking with some teachers. And the principal was finally able to come and actually see counting collections happening. And what was so amazing is these were K–5 kiddos, five-year-olds, who were teaching the principal about what they were doing. This was that example where we want people to come in, and the idea is, what are you learning? How do you know you've learned it, thinking about that work of Hattie? And these five-year-olds were telling him exactly what they were learning and how they were learning it and talking about their strategies. And I just felt so proud of the K–5 teacher who shared that with me because her principal was blown away and was seeing just the beauty that comes from this routine.

Mike: We did an episode earlier this year on place value, and the speaker did a really nice job of unpacking the ideas around it. I think what strikes me, and at this point I might be sounding a bit like a broken record, is the extent to which this practice makes place value feel real. These abstract ideas around reunitizing. And I think, Melissa, I'm going back to something you said earlier where you're like, “The ability to do this in an abstract space where you potentially are relying on paper and pencil or even drawing, that's challenging.” Whereas this puts it in kids' hands, and you physically reunitize something, which is such a massive deal, this idea that 1 ten and 10 ones have the same value even though we're looking at them differently, simultaneously. That's such a big deal for kids, and it just really stands out for me as I hear you all talk.

Melissa: I had the pleasure of working with a group of first grade teachers the other day, and we were looking at student work for a simple task that the kids were asked to do. I think it was 24 plus 7, and so it was just a very quick PLC: “Look at this work. Let's think about what they're doing.” And many of the children had drawn what the teachers referred to as sticks and circles or sticks and dots. And I said, “Well, what do those sticks and dots mean?” Right? Well, of course the stick is the ten and the dot is the one. And I said, “There's lots of this happening,” I said, “Let's pause for a minute and think, ‘To what degree do you think your children understand that that line means 10 and that dot means 1? And that there’s some kind of a connection, meaningful connection for them just in that drawing.’” It got kind of quiet, and they're like, “Well, yep, you're right. You're right. They probably don't understand what that is.” And then one of the teachers very beautifully said, “This is where I see counting collections helping.” It was fantastic.

Mike: Danielle, I want to shift and ask you a little bit about representation. Just talk a bit about the role of representing the collection once the counting process and that work has happened. What do you all ask kids to do in terms of representation and can you talk a little bit about the value of that?

Danielle: Right, absolutely. I think one thing that as we continue to go through in thinking about this routine and the importance of really helping our students make sense and count meaningfully. I think we will always go back to our math teaching framework that's been laid out for us through Taking Action, Principles to Action, Catalyzing Change. And really thinking about the power of using multiple representations. And how, just like you said, we want our students to be able to be physically unitizing, so we have that aspect of working with our actual collections. 

And then how do we help our students understand that “You have counted your collection. Now what I want you to do is, I want you to actually visually represent this. I want you to draw how you counted.”? And so what we talk about with the kids is, “Hey, how you have counted, if you have counted by 1s, I should be able to see that on your paper. I should be able to look at your paper, not see your collection and know exactly how you counted. If you counted by 10s, I should be able to see, ‘Oh my gosh, look, that's their bowl. I see their bowls, I see their plates, I see their 10s inside of there.’” And to really help them make those connections moving back and forth between those representations. And I think that's also that piece too for them that then they can really hang their hat on: “This is how I counted. I can draw a picture of this. I can talk about my strategy. I can share with my friends in my classroom.” And then that's how we like to close with our counting collections routine is really going through and picking a piece of student work and really highlighting a student's particular strategy. Or even just highlighting several and being like, “Look at all this work they did today. Look at all of this mathematical thinking.” 

So I think it's a really important and powerful piece, especially with our first- and second graders too.; we really bring in this idea of equations too. So this idea of, “If I've counted 73, and I've got my 7 groups of 10, I should have 10 plus 10 plus 10, right, all the way to 70. And then adding my 3.” So I think it's just a continuous idea of having our kids really developing that strong understanding of meaningful counting, diving into place value.

Mike: I'm really struck by the way that you described the protocol where you said you're asking kids to really clearly make sure that what they're doing aligns with their drawing. The other piece about that is it feels like, one, that sets kids up to be able to share their thinking in a way where they've got a scaffold that they've created for themself. 

The other thing that it really makes me think about is how, if I'm a teacher and I'm looking at student work, I can really use that to position that student's idea as valuable or position that student's thinking as something that's important for other people to notice or attend to. So you could use this to really raise a student's idea’s status or raise the student’s status as well. Does that actually play out in a reality?

Danielle: It does actually. So a couple of times what I will do is I will go into a classroom. And oftentimes it can be kind of apparent … which students may just not have the strongest mathematical identity or may not feel that they have a lot of math agency in the space. And so, one thing that I will really intentionally do and work with the teacher to do is, “You know what? We are going to share that little one's work today. We're going to share that work because this is an opportunity to really position that child as a mathematician and to position that child as someone who has something to offer. And the fact that they were able to do this really hard work.” So, that is something that is very near and dear to us to really help our teachers think of these different ways to ensure that this is a routine that is for all of our children, for each and every child that is in that space. So that is absolutely something that we find power in and seek to help our teachers find as well.

Mike: Well, I would love for each of you to just weigh in on this next question. What has really come to mind is how different this experience of mathematics is from what a lot of adults — and, unfortunately, what a lot of kids — might experience in elementary school. I'm wondering if both of you would talk a bit about what does this look like in classrooms? How does this impact the lived experience of kids and their math identities? Can you just talk a little bit about that?

Melissa: I can start. This is Melissa. So we have four beliefs on our little math team that we anchor our work around every single day. And we believe that mathematics should be humanizing, healing, liberating, and joyful. And so we talk a lot about when you walk into a classroom, how do you know that mathematics instruction is humanizing, which means our children are placed at the center of this work? It's liberating. They see themselves in it. They're able to do it. It's healing. Healing for the teacher as well as for the student. And healing in that the student sees themselves as capable and able to do this; and then joyful, that it's just fun and interesting and engaging. 

I think, over time, what we've seen is it helps us see those four beliefs come to life in every single classroom that's doing it. When that activity is underway and children are engaged and interested, there's a beautiful hum that settles over the room. And sometimes you have to remind the teacher, “Step back; take a look at what is happening.” Those guys are all engaged. They're all interested. They're all doing work that matters to them because it's their work, it's their creation. It's not a workbook page, it's not a fill-in-the-blank. It's not a, “Do what I do.” It’s, “You know what? We have faith in you. We believe that you can do this.” And they show us time and time again that they can. 

Danielle: I'll continue to echo that. Where for Milwaukee Public Schools and in the work that we are seeking to do is really creating these really transformative math spaces for, in particular, our Black and brown children. And really just making sure that they are seeing themselves as mathematicians, that they see themselves within this work, and that they are able to share their thinking and have their brilliance on display. And also to work through the mathematical processes too right? This routine allows you to make mistakes and try a new strategy. 

I had this one little guy a couple months ago. He was working in a pretty large collection, and I walked by him and he was making groups of 2, and I was like, “Oh, what are you working on?” And he's like, “I'm making groups of 2.” And I thought to myself, I was like, “Oh boy, that's going to take him a long time,” because they had a really big collection. And I kind of came back around, and he had changed it and was making groups of 10. So it really creates a space where they start to calibrate and they are able to engage in that agency for themselves. 

I think the last piece I'd like to add is to really come to it from the teacher side as well, is that what Melissa spoke about was those four beliefs. And I think what we've also found is that counting collections has been really healing for our teachers too. We've had teachers who have actually told us that, “This helped me stay in teaching. I found a passion for mathematics again that I thought I'd lost.” And I think that's another piece that really keeps us going is seeing not only is this transformative for our kids, because they deserve the best, but it's also been really transformative for our teachers as well to see that they can teach math in a different way.

Mike: Absolutely, and I think you really got to this next transition point that I had in mind when I was thinking about this podcast, which is: Listening to the two of you, it's clear that this is an experience that can be transformative mathematically and in terms of what a [child’s] or even a teacher's lived experience with mathematics is. Can you talk a little bit about what might be some very first steps that educators might take to get started with this?

Danielle: Absolutely. I think one thing, as Melissa and I were kind of thinking about this, is someone who is like, “Oh my gosh, I really want to try this.” I think the first piece is to really take stock of your kiddos. If you're interested in diving into the research of Clements and Sarama and working with the counting trajectory, we would love for you to google that and go to learningtrajectories.org

But I think the other piece is to even just do a short little interview with your kids. Ask each of your little ones, “Count as high as you can for me,” and jot down what you're noticing. Give them a collection of 10 of something. It could be counters, it could be pennies. See how they count that group of 10. Are they able to have that one-to-one [correspondence]? Do they have that verbal count sequence? Do they have that cardinality? Can they tell you that there is 10 if you ask them again, “How many”?

If they can do that, then go ahead and give them 31. Give them 31 of something. Have them count, and kind of just see the range of kiddos that you have and really see, “Where is that little challenge I might want to give them?” I think another really nice piece is once you dive into this work, you are never going to look at the dollar section [differently]. You are always just — start gathering things like pattern blocks. I started with noodles. That is how I started counting collections in my classroom. I used a bunch of erasers that I left over from my prize box. I use noodles, I use beads, bobby pins, rocks, twigs. I mean, start kind of just collecting. It doesn't have to be something that you spend your money on. This can be something that you already use, things that you have. I think that's one way that you can kind of get started. 

Then also, procedures, procedures, procedures, like go slow to go fast. Once you've got your collections, really teach your kids how to respect those collections. Anchor charts are huge. We always say, when I start this with four-year-olds, our first lesson is, “This is how we open the bag today. This is how we take our collections out.” So, we always recommend, “Go slow to go fast,” really help the kids understand how to take care of the collections, and then they'll fly from there.

Mike: So, Melissa, I think this is part two of that question, which is: When you think about the kinds of things that helped you start this work and sustain this work in the Milwaukee Public Schools, do you have any recommendations that you think might help other folks?

Melissa: Yeah. My first entry point into learning about counting collections other than through an incredibly valued colleague [who] learned about it at a conference, was to venture into the TED-Ed — I think it's T-E-D, the teacher resource site — and that was where I found some initial resources around, “How do we do this?” We were actually getting ready to teach a course that at the time Danielle was going to be a student in, and we knew that we wanted to do this thing called counting collection. So, it's like, “Well, let's get our act together on this.” So we spent a lot of time looking at that. There's some lovely resources in there. 

And since the explosion of the importance of early mathematics has happened in American mathematical culture, which I think is fantastic, wonderful sites have come up. One of our favorites that we were talking about is Dreme. D-R-E-M-E, the Dreme website. Fantastic resources.

The other one Danielle mentioned earlier, it's just learningtrajectories.org. That's the Clements and Sarama research, which, 15 years ago, we were charged as math educators to figure out how to get that into the hands of teachers, and so that's one of the ways that they've done that. 

A couple of books that come to mind is the [Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education]. Fantastic. If you don't have it and you're a preschool teacher and you're interested in math, get it. And then of course, the Choral Counting & Counting Collections book by Franke, Kazemi, and Turrou. Yeah, so I think those are some of the big ones. If you want just kind of snippets of where to go, go to the Dreme, D-R-E-M-E, [website] and you'll get some lovely, lovely hits. There's some very nice videos. Yeah, just watch a kid count. [laughs]

Mike: I think that's a great place to stop. I can't thank you two enough for joining us. It has really been a pleasure talking with both of you.

Danielle: Thank you so much. 

Melissa: Thanks for your interest in our work. We really appreciate it.

Mike: With the close of this episode, we are at the end of Season 2 for Rounding Up, and I want to just thank everyone who's been listening for your support, for the ways that you're taking these ideas up in your own classrooms and schools. We'll be taking the summer off to connect with new speakers, and we'll be back with Season 3 this fall. In the meantime, if you have topics or ideas that you'd like for us to talk about, let us know. You can reach out to us at mikew@mathlearningcenter.org. What are some things you'd like us to talk about in the coming year? Have a great summer. We'll see you all in the fall. 

This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability.