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How to help students see tools and math manipulatives as gateways to understanding rather than crutches?

If you’ve ever struggled with how to effectively use tools and math manipulatives in the classroom—or if you’ve worried about students “playing” instead of learning—this episode dives into strategies to transform those worries into math wins. Listen in as we speak with Bethany Lockhart Johnson, an elementary school educator, author, and cohost of Amplify’s podcast Math Teacher Lounge so you can: 

• Learn how to use tools and math manipulatives to create equitable access to mathematics and foster deep conceptual understanding.

• Discover practical ways to integrate tools and math manipulatives into your teaching without losing focus on learning objectives.

• Gain actionable tips to build a community of math educators who support and inspire your journey.

Listen now to discover how to transform tools and math manipulatives into powerful allies for student learning and strengthen your math classroom “tree”.

Resources:

• Register for the Make Math Moments Virtual Summit
• Make Math Moments Problem Based Lessons & Units

Attention District Math Leaders:

Follow Bethany Lockhart Johnson on X → @lockhartedu 

See her session in the 2024 Make Math Moments Virtuals Summit – Join the Make Math Moments Academy

Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/ 

Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com 

Looking to supplement your curriculum with problem based lessons and units? Make Math Moments Problem Based Lessons & Units

FULL TRANSCRIPT

Jon Orr: Hey there. Bethany. Welcome to the making, Martha one what’s it Matter? Podcast. We are pumped. We’re pumped to chat. It’s been a long time coming, and, we’re we’re excited. You’re. You know, your session for the McMath Moments Virtual Summit is coming up where we want to talk all things that we want to talk fluency. We want to talk math anxiety.

We got we got a list. You know, we got a list. Let’s get into it. But, you know, how are things going? Well, where abouts are you coming from today? You know, fill our listener in on on, you know, all things Bethany right now.

Bethany Lockhart: Well, thank you for having me. I’m delighted to. To join you is very a alliterative math space. You know, I, I can get with that, I appreciate it. Yeah, I’m, I’m in Southern California, and it has been, like, 102 degrees. And now it’s day. It was like, cold and foggy. And my toddler is like, what is happening? You know. Oh what it you know. So I’m very excited I said put on your jacket. You know, it’s very it’s a very like a farm on October. So. Right. You know the pumpkins are out but the sweat is also out.

So it’s, you know.

Right. Yeah. I’m doing great. I have a three and a half year old, and so it’s difficult to, have any conversation that doesn’t involve him. So. Right. He’ll come up again because he’s pretty, you know, toddler. Are you parents?

Yvette Lehman: Yes we are. Yes.

Jon Orr: I have three daughters.

Bethany Lockhart: They’re three.

Jon Orr: They’re all teenagers now. So, we’re we’re in the teenage world, you know, they’re all in high school and does all the high school drama happening. You know, it’s it’s. But you’re right. Every conversation is is about them.

Bethany Lockhart: My best friend my best friend has a teenager. And I was asking her something about this was last year. I got to ask him something about potty training. And she she’s like, what? She said, you know, when the last time was that I thought about potty training. You know, it’s it’s a whole different world.

Jon Orr: Different world. You’re it’s like what we were talking about before the hit record. It’s like your brain just dumps stuff that you don’t think about anymore and you don’t want to think about because it’s like, can you even talk to talk to me about, like what I did and what we did? It’s like I have like, this is this is we’re getting completely sidetracked here. That would not work. But I love it. I love. But but I.

Bethany Lockhart: Saying in the mouth. Right.

Jon Orr: Exactly, exactly. But what I, I’m convinced that like in our the human experience completely like your brain is, is wired to forget all of that stuff that you went through, all the hard stuff that you went through. Because now when you’re older, you’re like, yeah, kids are like, every, every waking moment is amazing with my child. And it’s like, and then you tell your, you know, your as a gran, you’re getting ready.

You’re telling your own kids that. So they’re like, they keep the species going because otherwise otherwise you would we would all be done.

Bethany Lockhart: I know it’s.

Jon Orr: Such a pessimistic view. All I have.

Bethany Lockhart: Is like, my brain will like, forget that until it’s like 2:00 am and I’m trying to fall asleep. And then you remember, like, every negative thing, you know. So anyway. And it’s like that’s a different that worries.

Jon Orr: Well, hey, these are the moments that, that we remember and or we don’t remember. So now let’s, let’s.

Is that. Yeah. The moments that matter and remember. But, let’s spin it. Let’s let’s ask you a moment about math. Like when we say math class, what would be your math moment? Like what comes to mind that sticks with you all these years about math and math class?

Bethany Lockhart: I, I feel like it’s an unfortunately, the moment that comes out first is a negative one. Yeah. It was kind of, I let’s Genesis, shall we say, of my math anxiety when a teacher told me this was in high school, told me that I don’t belong here, and he said, you don’t belong here.

And, you know, I think that that’s crazy. To his credit, I don’t really want to give him any credit, but to his credit, I think legitimately, like I wasn’t ready for that math course. So. But what my brain talking about brains, the way I processed it was I do not belong in mathematics in the world of math. Math isn’t for me.

I’m not a math person. So I really extrapolated. Right. And and, it I took it on as part of my identity. I was like, right, right. I don’t belong here. And so I think that moment has really shaped the way that I think about mathematics. I think about what math gets to be and who math gets to be for.

And I think that really influences my teaching and so in some ways, I’m grateful for it. After a lot of processing and, some, some therapy, I, you know, I, I mean, for reals, like, you know, and reclaiming mathematics, I reclaimed that as a grown woman, after I’d already gotten my college degree when I didn’t technically need to be.

As before, I was teaching in the classroom, and I. I genuinely reclaimed mathematics. I said, oh, and I discovered a whole new relationship with math. But that moment has been kind of the you know, I don’t know that the moment that I measured so many moments of math against.

Yvette Lehman: And I certainly don’t wish your experience on anybody, Bethany, but I certainly have a similar one like that was exactly my experience as a secondary student, where by grade ten, it was basically you were just not a math person. Like, and that’s it for you. You know, you have to find a different path. This is not for you.

But I will say that that is kind of our superpower as teachers, because we refuse to let that be the experience that our students have. And so that means that we are going to position ourselves to create an accessible and empowering experience for our students. And I think had we not had that ourselves, had math come really easily for us, I don’t know that we would be as passionate about ensuring equitable access to higher mathematics for all students.

So as much as that was a negative experience, I do truly I feel that for myself as well. It’s what has, given me so much inspiration in doing this work. And I know that that’s the same for you. And it actually it lends so well to your topic for this summit about the power of tools and just how unutilized they are and how they’re such a, a great way to create access and to create, you know, conceptual understanding for students in a way that’s such a powerful, you know, barrier Breaker.

So can you talk to us a little bit about why tool talks, why you’re, you know, advocating for the use of tools in classrooms?

Bethany Lockhart: Yeah, I, you know, I think that, I want to say too, that touching on your point, there is a way to as somebody especially in early childhood, Ed, I feel like because I’m in the K through two land primarily, primarily kindergarten and then for early childhood ed and then, you know, the math that I kind of love working with kids the most often is our early math mathematicians up through our three, two, etc., but I, I think two part of my role is not not only to help make the classroom, like, help, cultivate a space where our students can feel like math is is foreign about them, but also the parents as

well. And I feel like I part of my job as a kindergarten teacher has so often been to make space for parents to experience math in a new way, because so many of the parents that or caregivers that come into the classroom were that, that I have conversations with, whether it’s in a conference or back to school night or whatever, or at the gate in the morning, you know, has has really reflected a sense of trauma about their own school experience.

And many parents or caregivers also kind of reflect back this fear of mathematics or this idea that math isn’t for them. And I’ve had parents tell me, oh, yeah, I wasn’t a math person either, or oh no, no, no. Like or when we’ve had like, talk to your parents about math like I don’t use that I, you know and it’s, it’s coming from a real place that they that the parents or caregivers truly believe that.

Right. But the way that they’re talking about mathematics is impacting the way our students are kindergartners or are thinking about math. Right. And at that young age, it’s it’s so it’s so amazing to see how quickly and how early math anxiety presents. Right. I definitely don’t blame parents and caregivers as like the only way that that happens. But it’s a big it’s a big, opportunity for healing and repair around their own math experience as well.

Jon Orr: Totally. Completely agree. Do you do you get a sense that and this this is I think what I’m trying to maybe convey here to you is, is related to tools and manipulatives and, and conceptual understanding is do you think even at the early elementary level, there’s, there’s still a rush to get to the abstract, to get to the, you know, let’s let’s make sure that we’re, we’re basic math facts, even that, that such an early level to to and you will always hear it is as though let’s prepare them for the next grade level.

So you feel like that’s related to like why parents are, you know, still, you know, still speaking this way because they learn it. Like one of the things I I’ve always heard from parents is that, you know, they hated math, but they still want it taught the way that they learned it. And it’s it’s really probably because they want to be able to be in a position to help their student or their child when it’s time.

But do you feel like there’s there’s this pressure at, say, the early grades to, you know, get to the abstract before they really have this understanding of, of their of their conceptual understanding of the concepts.

Bethany Lockhart: Well, I yeah, I definitely I think that the reason I get so, you know, jazzed to talk about tools and I know it’s a virtual conference. So it’s, it’s a little different. You know, I don’t have the, the tour in front of you, the physical tools in front of you to like solving problems with this and without.

But I think one of the things I like to remind educators is, well, one like, what is that rush for? Right? To the to the abstract. And really, I think unlocked so much of my love of teaching math once I started saying cognitively guided instruction, really focusing on how students make sense of concepts and how they come to understand an idea and how they can picture and, and, visualize and I think that there’s when I see, teachers and educators not wanting to use tools so often, it’s about them.

It’s about the things that are they’re worried are going to stand in their way, like, oh, the kids are just going to play with the tools, or they’re going to throw them, they’re going to break them. They’re you know, they don’t need them. And there is so much power in the concrete before the representational, before the abstract, and seeing in that concrete space.

And even once you get to the abstract, dipping back into the concrete, modeling things with tools, there is so much power in that. And I the standards for mathematical practice are meant to go, you know, K through five and that we’re California. So we’re coming courses, state school, Common Core standards state and the standards for mathematical practice are designed to go through K through 12 and so, Math practice five is all about using and selecting tools strategically.

Right. And so the idea is we use tools. We use tools all through our, our educational career. We use tools as adults all the time. And to in any way stigmatize the use of tools or to make them inaccessible, or to make it a failing that you would utilize tools is such a missed opportunity for students to dive in and and make meaning of the mathematics.

Yvette Lehman: So this makes me think of John. We actually had a mentoring moment, podcast episode not long ago with a kindergarten teacher, a super dedicated educator who was struggling because she said, you know, I’m doing number talks and number talks and kind of more the traditional sense of the number talk, where it was very much, you know, a provocation on the board.

And students were responding to it. And she had some concerns just about engagement or about, you know, the level of complexity that she could really get to with the kindergarten standards. And I wish I had had this conversation with you before that call, because it sounds to me like maybe a solution is a tool talk where we’re still engaging in rich number concepts, exploring operators, exploring big ideas, but where students actually have a tool in their hand to be modeling.

So can you tell us a little bit more? Because I think you hit on the point that sometimes we are afraid of it becoming play or not intentional or or it being, you know, distracting. So how do we leverage the tool talk structure to ensure that, you know, we’re maximizing our time with students? We’re getting to the learning objective, but in a really meaningful, concrete way, building conceptual understanding.

Bethany Lockhart: Well, I, I you something you said, you said, you know, we get worried about the play, right. But the play should be there, right. We want the play there. And our students learn through play, especially our younger students. And when I think about a tool talk, I mean, in my class we would do tool talks on day one and that was we talked about a pencil and what and what you thinking of the pencil as a tool?

We talk about our hands and our fingers being tools. And I’ve had, parents and educators saying, you know, they won’t stop using their fingers and it’s whoa, whoa, that’s fantastic. Look at this tool. Look at this amazing tool. Right. And in kindergarten, where our big focus is five and the power of five. Hello. I mean, yes, we’re you know, we it it just is so powerful.

And I really think that the power of Tool Time, there’s been there’s so many amazing educators thinking about tools. But I what I get excited most about is really giving our students the opportunity to be curious about tools. And, you know, we set up the format day one where we’re sitting together and we introduce it and we talk about it, and everybody then gets one and we talk about where have you used it, where have you seen it?

And it goes up on a chart. We put a picture of the pencil on there. Yeah. And we, we do talk about boundaries too right. I, we can do some pretty cool things with pencils right. But I also you’re not to we don’t want you to run with it. We’re not you know, you’re not poking someone with it.

Like, I don’t think that even through people, you’re going to make place swords with it, right? Like there’s ways that you are giving boundaries and parameters while also like having students be curious about what can this tool do, right. And run on that, that poster that we’re going to keep adding to all year long. Every time we introduce a new tool, it goes up there.

And so when the students are, are are having the opportunity to do some problem solving, one of my first questions would always be what? What tools do you think you want to use and having them selected. Now when I’m teaching about a tool, like when I’m introduced a tool, I may encourage, you know, we’ll do activities like let’s say with a two sided counter, two color counter.

And I want them to explore that tool in like a problem solving environment. But when they’re trying to, like, solve problems to solve, maybe a story problem, I’m not going to tell them, but you have to use, like, using a two color counter. You have to solve it this way because I want them to look at the tools that are available to them and really use them to make sense.

And I also, I, I encourage them, I is there another tool you could show that same idea with. But I’m not pushing them like, oh, but nope. This is a problem where you have to use colors because there are five, you know, puppies on the playground. And so you have to have all the five counters know that there’s countless ways to solve, the problems, and the students need to utilize the tools in ways that, that mean something to them.

And I have that tool, students who choose a tool that I would never think to use. And sometimes that tool is helpful. Sometimes they’re able to use that in a productive way to help them, like make sense of the problem. And sometimes like that didn’t help me. Right. And that’s okay. That’s okay. That’s part of the journey and part of the conversation.

Jon Orr: Yeah. And I think what your your highlighting and making sure everyone you know here listening also understands is that is that you’re using the tool as a as it’s intended to make sense of the mathematics or help make sense of that or make sense of the mathematics and not the opposite. Right. Like sometimes it’s like we, we force the tool because it’s like we got to use this tool.

But really what happens is when you use a tool and this is true with models as well in class, as you say, move to the you move to the visual. Come. You know, version is that is that we get hung up as teachers to like say this is the model, this is the tool you want to use and then it be now it really becomes teaching the student how to use that tool without any sense attached to it.

And it’s no different than, say, than just going straight to the abstract and teaching them an algorithm. Because. Because they’re seeing this tool as like this thing that actually a black box. But I don’t really know why I’m using it or, or how it’s useful to me. But I’m now I know how to use it because I’ve, I’ve, you know, memorized it or I’ve, I’ve been shown how to use it, but I don’t actually know how it makes sense to be like, it’s so important that we treat those tools as, as useful for sense making or help to make sense of your sense, what? You’re trying to make sense of the mathematics and not the opposite. Not just, Hey, let’s just use this tool.

Yeah. What would you if we if we think about some other, some big, you know, big moments that you’re going to give in our session, in this session at the summit, what would you say is a another, another big kind of nugget that, people are going to get when they attend ten?

Bethany Lockhart: So what? I definitely hope that folks feel like, they have some of their concerns addressed. Right. I want to whether you are really excited to use tools in your classroom or whether you’re looking for new ways to use tools in your classroom, I want to also like, acknowledge that it is not completely smooth and seamless. Right. Students are going to build with the excuse, right?

They are going to treat them as Legos, right? Like, yeah. And it’s a conversation. It’s a continual conversation. Right. And it’s not it. I, I know that a lot of teachers have, this concern about the mess or about, like we said, with play. And I want to be able to have conversations about that. And what are we worried about?

Right. What are we worried about when we’re keeping those tools? And the ones that I most frequently hear is the play. It’s the mouse and it’s the, the becoming dependent on them. Those are the things that I most frequently hear, as you can make dependent on the tools. Those are the things that I most frequently hear as concerns or worries. When we when I talk to educators about using tools in their classroom.

Yvette Lehman: If you could, I like this. You know, your magic wand and you could see these tools have been, you know, being used routinely in every kindergarten. Like, what are your go to? It’s like, if you could say like, it would be great if I saw, you know, this being used consistently because, you know, from your experience, it’s versatile.

It applies to a lot of situations. It’s going to position students to make sense of a lot of concepts from, you know, the K to two continuum. What would they be like? Which ones do you want people to dust off first from their their closets?

Bethany Lockhart: Oh well, I will say that I think that is one of the keys, right? Is that for many educators, if you look at where are your tools stored right now, they’re probably in a cabinet. And and they probably have this in a lot of them, like come with the curriculum and they’re probably still in a plastic wrap. Right.

So tools are like they need to be out. And whichever tools you choose need to be out and accessible. And I remember going to, a class visiting classroom and the, the that’s one of the things I answer was, oh, where are you tools and the oh, they’re over there. And to get to them like, yes, they’re out.

But it was they were not in sight. They were under like the bottom layer of a cabinet kind of push back. Didn’t have a door on it. So it felt more accessible than being in a locked cabinet. But it definitely wasn’t something that was like the norm that students go over to get tools. And so first I want to say whatever tools you’re using, it should be out accessible.

And the tool use being celebrated. So like that first time someone uses a tool to solve a math problem or to help make sense, it’s a big deal, right? We are celebrating it. We are like, whoa, I’m taking a picture and projecting. And I’m saying, tell us with the students permission to tell us how how did you use this tool, what’s happening here?

And I want that student to be talking about the way they use the tool to make sense. So it’s difficult for me to say I think there needs to be these specific tools. I think I’d rather say what you don’t need to have. Like you, I think you don’t need to have the you know, it’s October. You don’t need to have the Halloween erasers to solve a problem.

That’s about pumpkins, right? You don’t need to have, the bare counters to solve a problem about bears or little people to solve a problem, if you have that. I’m not saying there’s anything wrong with it, but, like, give your students credit that we are. First of all, their imaginations are like way more like chained up than others, right?

And while that might be cute, like, it can also be distracting in that suddenly these pumpkins are like, I’m creating a story about the pumpkins that have nothing to do with the math, right? Right. And so I, I think sometimes there is a drive to get that perfect tool, and sometimes it can be as simple as, okay, well, what do I have available to me?

Okay, I, I have you know, I have unisex cubes or, but I don’t have, you know, the perfect color, unisex cubes or I don’t have. Right. Okay. But do you have unisex cubes or. I have stones, but I don’t have the shiny stones, right? Yeah. That’s okay, it’s okay. And so I really encourage folks to, you know, if you don’t have tools, put out a call to your fellow teachers account that someone has extra sets that either isn’t, you know, using them or they have extras that they’re like, I have so many cubes, I don’t even know what to do with them.

That desk is made of unisex, you know, and they will they will, they will share them with you gladly. And even find a buddy that you can pair with so you guys can explore tool use together, especially if it’s something you’re feeling intimidated by, right? It’s okay to feel nervous, to try something new and it might be a hot mess.

He’s like, oh my gosh, I am still pulling unisex cubes out of my hair, right? Right. You you you you’re like, we’re asking our students to be brave every day. And so I want to encourage educators to be brave and to really take a look at, okay, what are the obstacles that are like real obstacles to my making tools accessible and celebrated in my classroom.

And what are the ones that like, I’m kind of manufacturing because it’s about me, right? Like I love the cute pumpkin erasers. So until I can get to the target, I thought, I can’t do this. I can’t have my kids solve the problem.

I use that money to buy buy some for yourself, you know? So that’s that’s my that’s my answer, not answer to your question.

Jon Orr: No, I love I love the message because I think I think it’s even though it’s say like you said, it’s an answer but not an answer. I think it’s it’s inappropriate and useful and a really important answer to be able to, you know, to, to I know I’ve always said this to about many things. It’s like sometimes you make a, you know, a to do list.

It’s like you’re not to do list. It sometimes. Or more important, and this is the kind of the kind of message you’re sharing here with the audience, Bethany, if they’re like, let’s, let’s now imagine that we’ve, we’ve we all came to the summit, we participated, this you know, your session is over, the weekend is over. And people are, you know, they’re probably exhausted from, you know, spending all weekend in, in sessions throughout that summit. What would you want there? So say big takeaway from your session. Say going into Monday to be yeah.

Bethany Lockhart: Well, you know, I love a good math conference I love it I love the time to to go to sessions and think about new ideas or think about ideas maybe I’ve explored before, but thinking about them in a new way. So I’m imagining that folks that are attending this summit are like going to be bursting with ideas, right?

They have so many things they want to try and oh my goodness, I don’t know. You know, and I will just speak for myself is that I get a little overzealous. And then the, you know, the notes kind of trickle away and my, my best intentions, you don’t try it right away. So which other sessions you go to?

I would hope that educators would pick an idea to try out right. And or a person that they they went to their session to have a conversation with. Again, and from the tool, the tool session that I’ll be, the conversation that I’ll be leading. I really hope that folks, I mentioned this already, but find a buddy if they haven’t already.

If they haven’t already tried to use or they’re interested in kind of shifting the way they think about tools, find a buddy that you can try it with because it is way more fun to like, deep dive into your classroom closet with somebody. Right? So find somebody that you can say, okay, let’s do it. Let’s take an inventory.

Let’s take an inventory. You go to my classroom, let’s take it all out. Let’s see what we have. And then making a plan. Okay. Fresh eyes on my classroom. How can I put these out so that they’re more accessible? And even if you don’t see anything on day one, even if you just have the tools out, what’s going to happen if your students all of a sudden see these tools out in a way that they want, like, whoa, what’s that?

They’re going to make space for that curiosity. And if you don’t have a person, a coworker who you feel like you can collaborate or try things with, find a virtual one, right? Go on over to, Twitter X, what you know, and, you know, go on to, to interviews, math, math Twitter blogosphere. Right. The hashtag or come back one to the math moments, matter and like making math moments that matter.

I bet you there are other educators that are excited to connect together, right? Or, you know, message me and say, hey, I don’t really have a buddy I can try this with, but I want to try it. Eat right and and I will. I’ll cheer you on, you know? So I think it’s, sometimes trying new ideas can feel overwhelming and scary.

And I think too often as teachers, we can very easily be isolated in, in our own silos, even if you have friends in your school community. And so how can you bravely try to build community around your learning? And so that’s what I would encourage folks to do. Keep it simple. Give yourself the joy and, the eek of making mistakes and, you know, treat yourself like a beginner, too, even if you already feel like you’re using tools in ways that you’re that you see your students using them, see if there’s ways that you can can shift your thinking or partner with somebody that can help you shift your thinking.

Yvette Lehman: So what I heard you say, Bethany, and that kind of closing takeaways that we need to find our people and that person might be in your building, but they might be in the larger math community. And you may I mean, I think about, you know, people that you’ve met through the internet, through conferences who are essentially there to support and inspire you in this journey. And I think that that is a game changer for so many of us.

Bethany Lockhart: And I want to say, like, if you ask someone and they say, I’m not really I don’t want to have time or space, that’s okay. Ask somebody else, you know, somebody out there for one. I’d like one thing I’m saying start small. Do an inventory of the tools that you have and do not. Whatever you do, I’m going to gently, lovingly, loudly encourage you.

Whatever your inventory sure shows, don’t go rush out to go buy more, right? Right. Pause. Pause and just observe. And just, just just see what’s there.

Yvette Lehman: Well, thank you so much, Bethany, for joining us today. We’re very much looking forward to your session at this year’s summit. But for those who may not be able to attend and are just really inspired by your work and want to maybe connect with you like you suggested, how can people find you?

Bethany Lockhart: Well, I technically am still on X, so I’m at LA, call Edu LCC edu and I have not sent out messages in a long time, but I’m I’m I’m reading. I’m reading and learning.

Jon Orr: Because a lot of us are like that. A lot of us are like, I’ve been over there in a bit, but I’m still kind of in there somewhere.

Bethany Lockhart: Yeah, right. So feel free to message me that way. And, happy to happily engage in conversation about about this work.

Jon Orr: Awesome. We’ll, make sure we put that in the show notes and, everyone, make sure if you’ve not yet, say, gone over to the summit, website, to check on registration, get on over to summit. Don’t make math moments.com and get yourself registered. Bethany, thanks so much.

Bethany Lockhart: Thank you for.

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