Lori Bluemel, Building Fluency and Procedural Understanding with Work Places
ROUNDING UP: SEASON 1 | EPISODE 20
Many elementary educators recognize that timed memorization activities have the potential to seriously derail a child’s identity as a doer of mathematics. But if we want to build fluency, what alternatives are there? Today on the podcast, we talk with Lori Bluemel, a curriculum consultant at The Math Learning Center, about a play-based alternative for building fluency from conceptual understanding.
Mike Wallus: When I meet someone new at a gathering and tell them that I work in math education, one of the most common responses I hear is, “I was never good at math in school.” When I probe a bit further, this belief often originated in the person's experience memorizing basic facts. How can we build students' fluency with facts, encourage flexible thinking, and foster students' confidence? That's the topic we'll explore in this episode of Rounding Up.
Mike: One of the challenges that we face in education can be letting go of a practice—even if the results are questionable—when the alternative is unclear. In elementary math, this challenge often arises around building computational fluency. We know that speed tests, drill and kill, and worksheets—those are all ineffective practices. And even worse, they can impact students' math identity. So today, we're going to spend some time unpacking an alternative, a component of the Bridges in Mathematics curriculum called Work Places. We're doing this not to promote the curriculum, but to articulate an alternative vision for ways that students can develop computational fluency. To do that, we're joined by Lori Bluemel, a curriculum consultant for The Math Learning Center.
Mike: Lori, welcome to the podcast. It's great to have you with us.
Lori: Thank you. It's good to be here.
Mike: Well, let's just start with a basic question: If I'm a listener who's new to the Bridge's curriculum, can you describe what a Work Place is?
Lori: The simple answer would be that it's math activities or games that are directly focusing on the skills or the ideas and concepts that students are working on during Problems & Investigations. The best aspect, or the feature about Work Places, is that teachers have an opportunity to be like a fly on the wall as they're listening in to their students and learning about what strategies they're using and the thinking process that they're going through.
Mike: How do you think practicing using a Work Place differs from the version of practice that children have done in the past? What changes for the child or for the learner?
Lori: Well, I always felt like a piece of paper was pretty static. There wasn't a lot of interaction. You could run through it so quickly and be finished with it without really doing a lot of thinking and processing—and with absolutely no talking. Whereas during Work Places, you're discussing what you're doing. You're talking to your partner. You're listening to your partner. You're hearing about what they're doing and the different methods or strategies that they're using. And [there’s] nothing at all static about it because you're actively working together to work through this game or this activity.
Mike: That is so fascinating. It makes me think of a book that I was reading recently about thinking classrooms, and one of the things that they noted was, there's data that suggests that the more talk that's happening in a classroom, the more learning that's actually happening. It really connects me to what you just said about Work Places.
Lori: Yeah, and I feel like that's the big difference between Work Places and doing a worksheet on your own. You can do it completely isolated without any outside interaction; whereas Work Places, it's very interactive, very collaborative.
Mike: Yeah. So, as a former classroom teacher who used Work Places on a daily basis, how did you set up norms and routines to make them successful for students?
Lori: Well, I actually went through several different methods, or routines, before I landed on one that really worked well for me. One that worked best for me is, at the beginning of the year when we first started doing Work Places, I would take that very first Work Place time, and we would just have a class meeting and talk about what we're doing in Work Places. Why would we even have Work Places? We would create an anchor chart, and we'd have one [column] that would say “Students.” The other side would say “Teachers.” And then we would talk about the expectations. And the students would come up with those. Then we would talk about me as the teacher, what do they think I should be doing? And again, that would come up with all different ideas. And then we always came back to that final thought of,
“We need to be having fun.”
Lori: Math needs to be fun during Work Places. And then we would start in, and students would go to Work Places. They would choose their partner, and then they would get started. And that first few times we did Work Places, I always just kind of watched and listened and walked around. And if I felt like things needed to be slightly different, maybe they weren't talking about math or they weren't really playing the Work Place, then we would call a class meeting. And everyone would freeze, and we'd go to our meeting spot, and we would talk about what I saw. And we would also talk about what was going well and what they personally could do to improve. And then we'd go back to Work Places and try it again. Needless to say, a lot of times those first few times at Work Places they didn't play the games a lot because we were setting up expectations. But in the long run, it made Work Places run very smoothly throughout the rest of the year.
Mike: Yeah. The word that comes to mind as I listen to you talk, Lori, is investment.
Mike: Investing the time to help set the norms, set the routines, give kids a vision of what things look like, and the payoff is productive math talk.
Lori: Exactly. And that was definitely the payoff. They needed reminders on occasion, but for the most part, they really understood what was expected.
Mike: I think it's fascinating that you talked about your role and asked the kids to talk about that. I would love [it] if you could say more about why you asked them to think about your role when it came to Work Places.
Lori: I wanted them to realize that I was there to help them. But at the same time, I was there to help their peers as well. So, if I was working with a small group, I wanted them to understand that they might need to go to another resource to help them answer a question. They needed to make sure that I was giving my attention to the, the small group or the individual that I was working with at that time. So, by talking about what was expected from me, my hope was that they would understand that there were times when they might have to wait a minute, or they might go to another resource to find an answer to their question, or to help them with the situation that they were in. And that seemed to be the case. I think I alleviated a lot of those interruptions just by talking about expectations.
Mike: So, I want to return to something that you said earlier, Lori, ’cause I think it's really important. I can imagine that there might be some folks who are listening who are wondering, “What exactly is the teacher doing while students are engaged in Work Places?”
Mike: And I wanted to give you an opportunity to really help us understand how you thought about what your main focus was during that time. So, children are out, they're engaged with the Work Places. How do you think about what you want to do with that time?
Lori: OK. So, I often look at the needs of my students and, and think about “What have I seen during Problems & Investigations? What have I seen during Work Places previously? And where do I focus my time?” And then I kind of gravitate towards those students that I want to listen in on. So, I want to, again, be like that fly on the wall and just listen to them, maybe ask a few questions, some clarifying questions about what they're doing, get an idea of what strategies or the thinking that they're going through as they're processing the problem. And then from there, I can start focusing on small groups, maybe adjust the Work Place so that they can develop that skill at a deeper level. It helps me during that time to really facilitate my students’ practice; help students make the most of their practice time so that as they're going through the Work Place, it's not just a set of rules and procedures that they're following—that they're really thinking about what they're doing and being strategic with those skills as well. So that's my opportunity to really help and focus in on my small groups and provide the support that students need. Or maybe I want them to advance their skills, go a little bit deeper so that they are working at a little bit different level.
Mike: You know, I'm really interested in this idea that Work Places present an opportunity to listen to students’ thinking in real time. I'm wondering if you can talk about an experience where you were able to tuck in with a small group and listen to their thinking and use what you learned to inform your teaching.
Lori: ( chuckles ) One experience kind of stands out to me more than others just because it helped me understand that I need to not assume that my students are thinking about, or thinking in a specific way. So, there was one student, they were playing the Work Place game in grade 3, Loops & Groups, and she had spun a six and rolled, I think, a six as well. So, her problem was to solve six times six. And this student had actually been in front of the class just a few days before, and several times actually when I had worked with her, had solved a problem similar to this by thinking of it as three times six and three times six, which is a great strategy. But what I really wanted this student to develop was some flexibility.
Lori: So, I asked her to explain her thinking, and I fully expected her to solve it: “Oh, yeah. I thought of it as three times six and three times six. And when I add those two together, I get 36.” And she totally shocked me. ( laughs ) She said, “Oh, I, I thought of it as five times six, and I know what five times six is. That's 30. And if I just add one more set of six, I get 36. So, she had already developed another strategy, which was not what I was expecting. With that, her partner was a little bit confused and said, “I don't understand how you could do that.” So, I asked this little girl if she could use tile, maybe, to explain her thinking to her friends. So, we got out the tile. She set it up and she explained this thinking to her partner. And her partner was still a little bit unsure, not really sure she could use that with her own thinking. But what it did was, in the future, just days later, that partner started trying that particular strategy. So, it taught me several things. First of all, don't assume. You don't always know what students are thinking. And also, students are their peers’ best teachers. It really encouraged her partner to try that method just a few days later.
Mike: We kind of zoomed really in on a pair of children and, and kind of the impact. The other thing that it makes me think is, by doing the fly on the wall, you as a teacher get a better sense of, kind of, the themes around thinking that are happening across the classroom.
Lori: Yeah. You definitely do get that, that perspective. And I think the questioning that you use also will help draw that out. Asking students to explain their thinking: “How did you solve the problem? How could you check your work? Is there a different strategy that you could use that would help you make sure that the answer you came up with, the first strategy you used, was correct?” Those kinds of questions always seem to really help students kind of pull out that thinking and be able to explain what they were doing.
Mike: Lori, thank you so much for joining us today. It has really been a pleasure to have you on the podcast and to be able to talk about this.
Lori: You bet. Thank you for having me. It was fun.
Mike: I want to thank all of you who've listened in during the first season of Rounding Up. We're going on a short break this summer, but we'll be back for Season 2 in September. Before we go, we're wondering what topics you'd like us to explore, what guests you'd like to hear from, and what questions you'd like us to take up in Season 2. This week's episode includes a link you can use to share your ideas with us. Let us know what you're thinking about, and we'll use your ideas to inform the topics we consider in Season 2. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability.