Episode 191: Math Teaching Strategies: Highlights from the 2025 Virtual Math Summit Live Sessions

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National Council of Teachers of Mathematics

Welcome fellow Recovering Traditionalists to Episode 191: Math Teaching Strategies: Highlights from the 2025 Virtual Math Summit Live Sessions

The day I’m releasing this episode is March 2nd and tomorrow is the last day to watch the replays from the 2025 Virtual Math Summit for free.  If you’ve already registered, but you are thinking you’d like more time to watch the sessions, go to VirtualMathSummit.com/upgrade to see your options for extended access.  If you haven’t joined us yet you can still register at VirtualMathSummit.com but you’ve only got today & tomorrow to watch sessions.

This year we did 6 live sessions during the summit so I didn’t have clips from those presenters to share with you.  Now that those sessions have happened, I can share a clip from each of them.  

Peter Liljedahl & Maegan Giroux did our opening keynote about Building Thinking Classrooms and they shared some of the tasks from their recently released book, Mathematics Tasks for the Thinking Classroom.  Here’s one of my favorite parts of their session:

{Maegan} And there’s also the Non Example. And this one is really, really, great because I think that sometimes we want to give people a way to solve the problem, but the best way is to tell them how to NOT solve the problem.  So the classic example is… 

{Peter} Tax Collector [a BTC task]. Tax collector, right like if you start with 12 it goes badly very quickly. But that’s okay. That’s where they want to start, that’s where we’re going to start. Because this helps them understand what the task is about without telling them how to do the task. 

{Maegan} Exactly. And that is the same with the Carnival Conundrum [a BTC task].  We have Thane losing, right? He loses and then you know how not to solve the task. But also, surprisingly, you do know how to solve it from there without us telling you.  

{Peter} And this is one of the things we actually found in our research, too, is that teachers’ examples are too good. And when teacher’s examples are too good, the kids just copy it. We need to create, as often as we can, non-examples. Bad examples, be worse at your examples.

{Maegan} Be really, really bad at your examples. 

Now this is my favorite thing because I see teachers do this and myself do this all the time, is we like to tell kids things “just in case.” And it’s like right before you are about to send them off, you will have this like an itching to tell them everything they need to know about task 25. And then you go [scared face] and then you say like this “let me tell you something,” “let me tell you something,” and you need to like tell them everything right before they go. DON’T

{Peter}  And it’s Juli Dixon is the one who coined these terms of “just-in-case” versus “just-in-time.” And what we tend to do as teachers is we want to you know “just-in-case” you’re going to see one with negative numbers let me do that one for you, and “just-in-case” you see one with a fraction let me show you one of those, and “just-in-case” and “just-in-case” and “just-in-case” and now we are 17 and a half minutes into the lesson and the kids haven’t even gotten out to play yet, right?  We have to stop doing the “just-in-case” and we have to lean more into the “just-in-time” which we will talk more about in a little bit. 

{Maegan} Exactly, so let them go, give them just enough to do the first task. 

{Peter} Yeah.  

{Maegan} That’s all they need.  We can figure out the rest later.

Pam Harris also has a new book coming out in just about a week about avoiding the trap of the algorithms.  She is always a favorite at the summit and she didn’t disappoint this year:

Sweet so I can use what I know to solve problems. Hey don’t tell Christina but I came a little unprepared for today’s presentation so I don’t actually have… Will you notice with me that if you look at what we’ve done so far I kind of gave you a “helper”. Look at my shared screen, I gave you a “helper” to do that problem and I gave you a “helper” to do that problem and I gave you a “helper” that you could use to do that problem and I gave you a “helper” that you could choose to use to do that problem and I gave you a “helper” you could choose to use to do that problem.

What if, what if for the next problem I don’t give you a “helper”? What if I came unprepared? If you guys will help me create the helper next time I do this presentation I’ll be totally… I’ll look totally slick. So what if I were to give you a problem like I don’t know something like 500 or excuse me 5,468 + 2,997. I’m going to move that just a little bit to give us some space. What if… Whoa what if… what… what is the problem that goes right here? What would the “helper” problem be? Don’t look in the chat if you’re still thinking. Think. Everybody think.

If we were in a class right now I would be having everybody pause, give me a private signal. I’d give everybody a chance to think. What could be a problem, if you were going to follow the pattern that we’ve been using? What could be a problem you could use to help you solve this one? A lot of people are putting in the chat, could you think about 5,468 + 3,000? Y’all what is 5…Now to make this one 5,468 plus whoa that huge jump of 3,000. A lot of you are saying that’s 8,468.

So if that’s 8,468, what would be adding just a little bit less? In fact, how much less? Just 3 less. If we just backed up that 3, would that jump then instead be 2,997? Cool and you guys are saying that that is landing on 8,46o…. What’s three less? Five! Is it? Anybody want to check that? Right now, do you get a desire to like line those numbers up and check it? I’m okay if you do that. I might suggest to you, that you could just put it in a calculator.  Like if you’re going to do something sort of mindless that you’re just kind of mimicking and you’re doing the thing, you could do something equally mindless by typing in a calculator…if you feel the desire to check.

But how many of you, take a deep breath…How many of you are really clear in this minute that because you know what 5,468 and 3,000 is, that it’s got to just be 3 less? And you’re actually like, “I don’t really need to check that, like it’s got to be… it’s got to be just three less than that, it’s got to be 8,465.” That’s kind of interesting that when you reason through using relationships you’re pretty darn confident in that answer.

Shannon Olson was a woman after my own heart.  Her session was about effectively using and connecting math representations and using them as tools to observe and assess student thinking, identify misconceptions, and guide instruction.  Listen in to a part of her session:

“Now we are going to unpack how we define different types of representations now that we’ve engaged in a task to actually work with those representations. All right and this visual comes from NCTM, it’s also been published in so many books about discourse and representations and effective teaching practices. But it talks about we have these five types of representations and that we can connect between all of the different ways and continue to make sense of math through these representations. I like to use more like student-friendly words. I know that when I first heard of these representations, I was all on board about Physical, Visual, and Symbolic. I feel like so often we hear things like ‘Concrete, Representational, Abstract’ and we’re just really comfortable with knowing we use objects, pictures, and equations. And it took me a little bit to understand what do they mean by Verbal, what do they mean by Contextual? 

And so I have started to think of Contextual, actually, as the one that leads our work. I used to think of Contextual as this thing we add on a context. And now I’ve started to that actually, Context is what helps us build objects and create drawings and equations. And not that we always have to start with context, but I really think of Contextual Representations as just the stories we tell. Whether that be a word problem or a math task or just any context of something that we’re working with. Physical is objects and that can be commercial manipulatives or just real life physical objects that we work with. Visuals – any type of drawing or diagram or picture that we use to represent our thinking in math. Symbolic is anything with numbers and equations. So it can be literally just writing the number 5, the number 12, or it can be writing 5 + 7 or it can be having a multiplication equation with parentheses and all kinds of other things we could work through. Verbal is really just using our words to describe our thinking and it can be when we provide sentence frames to students or just saying “this is how I see the dots on the page.”

One of my favorite tools for elementary kids to use are ten frames. Kim Rimbey’s session showed us how this tool can be used throughout the grades.  Here’s a great part of her session:

Oh yes, the counting collections idea. I just saw someone ask about this. I totally connect this with counting collections. This is one way kids can represent their thinking when they’re working with their counting collections, right? So here’s what you should have. Some… uh… Leora, is that how you say your name? She wants to see decimals. Hold on, we’re heading there.

So here we go, 635 million, when we touch that comma we’re going to say million, 92 thousand,843. Again, I can’t say it enough, you have to make sure that the kids understand that nesting nature of place value. Over here in the millions period, these dots have a magnitude. Each one has a magnitude of 1 million, each line is a group of 10 million, each circle is a group of 100 million. The only thing we’re counting, the whole time, are just the little orange tiles, right? It’s how many of these are grouped and nested and nested and nested and nested.

So the yellow lids, they’re just covers. The blue lids are just covers, covering with a white piece of paper, it’s just a cover. We’re talking about how many are grouped together. That is something that has eluded most of our conversations. We know that intuitively, but the way we talk about this with students matters. And it’s really hard to have a tool that really helps us have that conversation unless we’ve explicitly thought it through. So that’s why I have you participating today, is I want you to just be really thinking this through. How are you going to explain this to your 5-year-olds? How are you going to explain this to your fifth graders? And everything in between?

So a couple of notes as we’re looking at this before we shift into decimals is that, first off, I’m hoping that you’re seeing what I mean by what happens in the ones place happens in every place, right? We have this structure, and I’m using the 10 frame structure in every place for the kids to see that in every place, although the magnitude is changing, the structure has a common theme. And now we’ve just added another another corollary or a corollary to this: what happens in the units period with ones, tens, and hundreds is replicated in every period, right? So the millions period still has a ones, tens, and hundreds, but the magnitude has changed. So that’s where I’m going with this. So you guys have been doing such a great job of participating in the chat box as we go. I just want to give everyone a chance to reflect. So far, what are you noticing about the patterns as we go from small numbers to large numbers?

Latrenda Knighten is the President of the National Council of Teachers of Mathematics and I’ve been a member of NCTM since I became a teacher back in 2000. Well, actually I think I became a member during the spring of my first year of teaching so it was technically 2001. I highly recommend educators join this organization.  I’ll link up NCTM in the show notes.  But let me get back on topic, here’s a clip from Latrenda’s session about using instructional routines to build students’ understanding of math content and language:

So let’s go back to the activity that we did from Is 2 a Lot? This is one where I chose to incorporate children’s literature. One thing that we don’t need to, that we should make sure we don’t discount is those opportunities to bring multiple resources in to support our students with their mathematical learning. We know that using children’s literature is a non-threatening strategy. A lot of children will gravitate to using literature. Even like some of the books I have pictured here are books for older students, they’re chapter books, but they’re talking about mathematics, they’re exploring those concepts, and so it’s a great way for some students who need just the extra little push to feel more comfortable to talk about their thoughts, their ideas, or their feelings in mathematics is to use those as a context.

There are many benefits from using children’s literature, but there’s so many opportunities for us to provide our students with problem posing content, problem posing concepts and opportunities by using literature. We are so fortunate right now that there’s so many wonderful literature books that authentically incorporate mathematics that they’re just so many to choose from. Sometimes I feel as if I’m going broke because every time I see a new book release I’m thinking how can I use this and I feel as if I have to have it. I have to have this book because I may be invited to go to someone’s classroom to use this. So take advantage of those things. You know, encourage the librarians on your campuses to make sure they’re purchasing those books.

One of the things I love about using the literature is because remember it doesn’t have to be fictional, so you really have an opportunity to bring in historical cultural context as well as practical applications of mathematics. So it really helps enrich that experience for all students and enhance that learning environment. But one of the best ways I found for teachers to incorporate discourse in the classroom on a regular basis is through the use of routines, and so Adding It Up reminds us that the point of classroom discourse is to develop student understanding of those mathematical ideas. And so these are opportunities for us to emphasize a model, reasoning and problem solving, but at the same time we can enhance our students’ disposition towards mathematics.

That means if I’m having an opportunity to talk about what I’m doing, I’m having an opportunity to listen to my peers and learn other ways of doing this in mathematics, I am growing my repertoire of this concept or these, this content. But also students are feeling more comfortable with mathematics because they are getting to talk about it, they’re getting to reason, they’re getting to problem solve, they have the opportunities to ask those questions. So in order for this to be meaningful and productive, we have to plan for it. It’s not just going to happen. Now students are going to have those discussions, productive or unproductive, but as adults who are in control of the room, we need to plan those opportunities so that we provide students with the necessary tools and resources to have those productive discussions.

Our final LIVE session was from Ann Elise Record.  I love using word problems to connect math concepts to a context for students and I love using visuals in math.  Ann Elise combined both of these in her session:

Now we get a whole flood of the answers happening in the chat bar. I’m seeing both blue and green, seeing both blue and green. Now I’ll tell you both are not correct. Only one of them matches the way this story is written. And what I’m going to ask you to do is is reread the top first sentence: “There are two more ducks than frogs.” So what does there have to be more of? 

Two more ducks than frogs, right? That means there has to be ducks. Ducks is the higher one, so it can’t be that frogs are seven of them.

So why is this, right? So this one on the right hand side, this story structure: “There are two more ducks than frogs.” So I know, and these numbers are tiny—this is what I’m saying, give yourself grace, this is zero judgment, right?—that these are tiny little numbers, but this is the power of this work and the research. 

So there are, uh, the relationship is there is two more ducks than frogs, and there’s more ducks, and we know there are five ducks. So this having the five ducks, the relationship is there must be three frogs. The relationship is that two more, that additive comparison. But I made this a tougher problem type because I used the word “more” but the smaller amount was the unknown.

So that, this is what I’m talking about, this is the power of this, and this is how the structure, the visualization of this will help you build your confidence. And then we can facilitate that confidence with our students. And the more we do this at the K-2 level with the problem types involving adding and subtracting, the more we can continue it all the way through their journey as we add on multistep, the numbers get larger, we get decimals and fractions, we’re adding and subtracting, and we also add on multiplication and division.

So why is it then that so many people, teachers that I meet and the students, is the choice of that blue side? What is the gut reaction of “it must be the blue one”? Because we’ve learned that key words, right? The word “more” means add. So I pluck the numbers—Graham Fletcher calls them pluckers—the kids pluck the five and the seven[2], they add the five and the seven[2]. Five and two make a seven, that must be it, the answer is right there, I must be right! Right? But that is not the case. This is why we can’t be doing keywords. You cannot be using things like cubes or any other ways you have for problem solving that involve underlining a key word that would somehow tell us what operation we want the students to use. That is not a part of this journey. It’s about finding out the structure, and once I understand the structure, I can choose the way I’m going to calculate my answer for you. We’ll get into that uh for sure.

So again, if you’d like to watch these sessions you have only until tomorrow, March 3rd.  If you want longer than that to watch them, you can become a member of the Build Math Minds PD site because our members have access to not only this year’s sessions, but all 9 years of Virtual Math Summits, for as long as they are members.  You can join at BuildMathMinds.com/bmm 

Until next week, my fellow Recovering Traditionalists, keep letting your students explore math, keep questioning, and most importantly, keep Building Math Minds.

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