Kyle Pearce: How to Make Math Visual

Kyle Pearce talks about how to make math visual for students. Discussing current theories supporting effective math teaching, Kyle helps us understand how to improve math understanding with kids who struggle.

Free Digital Citizenship Webinar: Thursday, May 10 at 5pm ET, join me for the 9 Key P’s of Digital Citizenship sponsored by NetRef AND get a free pilot of NetRef’s internet management and monitoring solution. Sign up at

Listen Now


Enhanced Transcript

How to Make Math Visual

Link to show:
Date: May 3, 2018

Vicki: Today we’re talking with Kyle Pearce K-12 math consultant in Greater Essex County, Ontario.

So Kyle, today we are talking about making math visual. Why do we want to make math visual?

Kyle: Well, hi Vicki. Thanks for having me.

Making math visual is something that’s near and dear to my heart. For years I was trying to teach students in high school and I found that often students were struggling, like in many classrooms.

Why do we want to make math visual?

When I started making math more visual, I was able to access all the learners in my classroom. That sort of sprouted into some of these new ideas, such as

Vicki: So give me an example of how you’ve made math visual.

How do we make math visual?

Kyle: Well, what I’ve actually tried to do now is I actually try to start from a concrete stage, where we try to look at the math in the real world.

We think about younger grades in mathematics, we do a great job with this, right? We count objects around the home. We then use linking cubes and square tiles, and we do all kinds of fabulous things with manipulatives.

But then as we get a little older, things become a little more difficult. I believe it really stems from our ability to actually understand the conceptual understanding behind the mathematics.

Most of us were taught procedurally in nature, and thus we tend to do the same thing. so when we think about things like multiplying fractions, we’re more likely to teach students a bunch of steps and procedures, rather than actually allowing them to see the mathematics that we’re actually engaging in, which will make that procedure a whole lot easier, later on when they’re ready.

Vicki: Now, what you’re doing is actually based in research. Tell us about that research.

Tell us about the research around this idea

Kyle: Yeah. There’s quite a bit of research about the importance of concrete manipulatives as well as visuals.

One such theory is called concreteness fading. In this research, they suggest three stages. Although I would argue that within each stage, there are more subtle stages as well.

Generally, we want to start with a concrete stage where we’re actually looking at physical manipulatives. So for example, if I’m counting donuts in a box, it’s great to have a context. It’s great to actually have the donuts.

Over time, what will happen is students will become comfortable with that concept, and they’ll stop needing the actual concrete manipulative. They’ll start moving to the more — what we call “visual” stage. They can actually make a drawing or some sort of diagrammatic representation of this visual.

Over time, we tend to use symbols, like numbers and operations, in order to represent these visuals. But the problem is that many of us tend to start with the symbols and try to unpack them for students, rather than starting with concrete and working toward those symbols.

So that’s really the push from this research and what I’m trying to do with my website and in my classroom.

Vicki: OK, so the problem is with high school. So we’re moving into algebra, and we know how important algebra is.

How can teachers get started, in addition to going to your website?

How do teachers make things more concrete or more visual? I mean, they start off at your site, but are there things they can do in the classroom?

Kyle: Absolutely. You know, I can get into the higher grades. If you’re in grade 11 or grade 12, things do get more abstract. There the visual might be something like graphing. It’s great to be able see it happening in the real world, aside from the graph as well, or at the same time.

But when we think about middle school and heading into subject areas or courses like Algebra 1 in the US, we can be doing things like solving equations by actually showing students how equations work, whether that be with a balance model. We can do this with all kinds of different manipulatives on the web. SolveMe Mobiles, for example, is a great tool online that really makes solving equations visual and very intuitive.

So there are all kinds of tools that are out there. It’s just unfortunate that not all of us are aware of them yet, anyway.

We’re hoping to try to share some of that through this show, here today.

Vicki: So Kyle, what do you think is… if you’re working with a math teacher, and they’re struggling to really help their kids understand math, but you know you can kind of tell that the teacher is struggling, too.

Where do they start, if they’re kind of a struggling math teacher working with struggling kids to kind of move in this direction?

Where does a math teacher who is struggling with a concept even begin?

Kyle: Yeah. I think that we really have to focus on understanding our curriculum, and that doesn’t… That’s not just knowing the curriculum we need to teach, but also understanding where it comes from.

So if I’m teaching a grade 9 class, for example, and I’m trying to teach a concept, and I’m not really certain why that concept works. I’ve really got to start doing some research online. Luckily for us, you know, Vimeo and YouTube and Google just in general, we can be going and learning about some of these concepts, and really trying to think of them from a conceptual standpoint.

So if my lesson sort of sounds like steps and procedures, “Follow this, and do this, and then do that and then that,” that might suggest that maybe I’m not that comfortable with the conceptual underpinnings of that concept. That means that I’ve got a little bit of homework to do first, before I can then help my students.

Vicki: But math teachers are so busy. Or they might think, “Well, I’ve always taught it this way. Kids just aren’t paying attention like they used to.”

What do you say to that?

It’s not me, it’s the kids.

Kyle: Absolutely. I felt that way. I was there.

I taught the majority of my career from a procedural standpoint.

Again, we’re not teaching that procedures are not important, because they definitely are.

But the reality is that if students aren’t understanding the concept, that they’re not understanding how it works, if it’s just memorization of steps and procedures, or they’re just trying to mimic what the teacher’s doing?

You can imagine that as they go through school, eventually they’re going to lose their interest in mathematics. The engagement’s going to go down.

And that’s typically what we see, as students struggle, they sort of think, “Math must not be for me.”

But if I’m teaching it where only students who are really good memorizers and are able to regurgitate content can do mathematics, then we’re really not being equitable to all the students in our classroom.

So we really want to access that concrete and that visual as a way to lower the floor on problems, and really help students understand the mathematics so that they can work toward some of the procedural fluency that we’re hoping they will achieve by the end of our course.

Vicki: Kyle, if you could travel back in time and talk to Kyle, first year math teacher about this, what would you say?

What would you say today to a younger you?

Kyle: Oh! I would say, “You think you know so much, Kyle, and you know so little. Every single day, I realize that, you know, I really didn’t know a whole lot. I like to say now that I have a university math degree in procedural fluency, but about a grade 7 or 8 level in conceptual understanding.

So I am still learning as well. And I’m hoping that with all the teachers online and with our teachers and colleagues at schools that we work with, we can all support each other to better understand the math in service of our students in our classroom.

Vicki: Wow. And how many years have you been teaching, Kyle?

Kyle: This is my twelfth year, and second year in the K-12 math consultant role. So I’ve learned a ton, getting to spend all kinds of time in elementary as well as secondary. I just can’t wait to continue to learn.

Vicki: Do you think students are different now than when you started?

Are students today different than students of years gone by?

Kyle: You know what? I think we’re all the same. I mean, the world around us has changed quite a bit. But you know what? Nowadays we do such a great job at making sure that students come to school. We’re seeing a lot of different students that we might not have seen twenty or thirty years ago. A lot of students might just drop out if they felt that school wasn’t for them, so right now, we’re keeping lots of students in the seats, all the way through high school to get a diploma.

I think we’ve just got to do some digging in order to make sure that we can help all students succeed because I truly believe that everyone is a mathematician.

Vicki: So Kyle, give us a 30-second pep talk for math teachers to reach every child in those seats.

Why should math teachers try to reach every kid in every seat?

Kyle: I want to say that if I’m not understanding where that math comes from or where it develops — if I don’t understand how math develops over time, that’s from K-12.

I like to think that if I’m a high school teacher, I can’t just focus on the secondary curriculum. I need to understand how students learn math in grade 1, how they learn it in grade 2, all the way up to grades 9, 10, 11 and 12 in order to have success in order to have potentially reach all of those students in my classroom.

Vicki: Wow, that sounds overwhelming, Kyle! Is it possible?

Kyle: I think it definitely is. And I think as we continue to do this learning together through things like the internet, when you can go on Twitter and see people posting animations of math concepts. Little 20-second video clips. I can learn so much in such a short period of time.

If I’m looking for that learning, I can find it. You’ve got so many people willing to lend you a hand, so just make sure that you’re not scared to ask for that help. Someone will come to help you out for sure.

Vicki: Well, as we finish up, what are the hashtags where you’re finding these?

Where do we go to find help?

Kyle: I love looking at the Math Twitter Blogosphere. That’s #mtbos.

Now a lot of people are using #iteachmath as well. I like to do a lot of my posting of visuals on as well as the Twitter handle @mathisvisual.

Vicki: So, we have all of these resources. We also have that Kyle has created for all of you math teachers to be more remarkable and to make math more concrete and more understandable for all of our students.

Thank you, Kyle!

Kyle: Thank you so much, Vicki! I hope everyone has a great night!

Contact us about the show:

Transcribed by Kymberli Mulford

Bio as submitted

Kyle is the K-12 Mathematics Consultant with the Greater Essex County District School Board, where his passion for mathematics fuels him to uncover creative ways to spark curiosity and fuel sense making through the inquiry process using tasks that are contextual, visual and concrete. He shares his most recent noticings, wonderings, and reflections in mathematics pedagogy and effective uses of technology on and


Twitter: @MathletePearce

Disclosure of Material Connection: This is a “sponsored podcast episode.” The company who sponsored it compensated me via cash payment, gift, or something else of value to include a reference to their product. Regardless, I only recommend products or services I believe will be good for my readers and are from companies I can recommend. I am disclosing this in accordance with the Federal Trade Commission’s 16 CFR, Part 255: “Guides Concerning the Use of Endorsements and Testimonials in Advertising.” This company has no impact on the editorial content of the show.

Never miss an episode

Get the 10-minute Teacher Show delivered to your inbox.

Powered by ConvertKit
Picture of Vicki Davis

Vicki Davis

Vicki Davis is a full-time classroom teacher and IT Director in Georgia, USA. She is Mom of three, wife of one, and loves talking about the wise, transformational use of technology for teaching and doing good in the world. She hosts the 10 Minute Teacher Podcast which interviews teachers around the world about remarkable classroom practices to inspire and help teachers. Vicki focuses on what unites us -- a quest for truly remarkable life-changing teaching and learning. The goal of her work is to provide actionable, encouraging, relevant ideas for teachers that are grounded in the truth and shared with love. Vicki has been teaching since 2002 and blogging since 2005. Vicki has spoken around the world to inspire and help teachers reach their students. She is passionate about helping every child find purpose, passion, and meaning in life with a lifelong commitment to the joy and responsibility of learning. If you talk to Vicki for very long, she will encourage you to "Relate to Educate" or "innovate like a turtle" or to be "a remarkable teacher." She loves to talk to teachers who love their students and are trying to do their best. Twitter is her favorite place to share and she loves to make homemade sourdough bread and cinnamon rolls and enjoys running half marathons with her sisters. You can usually find her laughing with her students or digging into a book.

All Posts »

Leave a Reply


This site uses Akismet to reduce spam. Learn how your comment data is processed.

The Cool Cat Teacher Blog
Vicki Davis writes The Cool Cat Teacher Blog for classroom teachers everywhere