Episode #432: Helping Teachers Move Beyond the Algorithm in Math Instruction: Resistance to Teaching Multiple Strategies in Math

Dec 9, 2025 | Podcast | 0 comments

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Are your teachers reluctant to move beyond the standard algorithm—even when it clearly isn’t working for their students?

In this episode, we explore a real-world example of a school trying to shift toward computational fluency—but getting stuck. The teachers agree that students need more accurate and efficient methods, but many still believe offering multiple strategies only adds confusion. Instead of pushing a solution, the school’s principal is taking a different approach: creating space for math epiphanies, building content knowledge, and shifting belief through structured staff learning.

If you’re a school leader or coach supporting math fluency in your school or district, this episode unpacks what it really takes to create shared commitment—not through mandates, but through deep learning.

Listeners Will:

  • Learn how one school is building teacher buy-in for strategy-based fluency
  • Understand why resistance to multiple strategies often stems from gaps in math content knowledge
  • See how protected staff time is being used to shift beliefs and build instructional confidence
  • Discover practical moves (like ICQ protocols and fluency-focused video routines) that create space for reflection and dialogue
  • Reflect on the dual role school leaders must play—as both facilitators and math thinkers

If your school or district is working toward stronger fluency and deeper math learning, press play to explore what it really takes to lead that shift.

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FULL TRANSCRIPT

Yvette Lehman: We’re going to talk about a common frustration today that I’m sure you have experienced, John. know I have. My favorite one, honestly, is I taught grade six here in Ontario. And of course we get to the end of the year and we have EQAO. So that’s our standardized province-wide assessment. And I did grade six, eight years. So it’s like every year I was, this is what we do. And I really loved when we would get to that assessment and then kids would come up to me and say, like, you never taught us this.

Jon Orr: Mm-hmm. Always high school. is common in high school. I didn’t learn that last year, sir. We didn’t, we didn’t do solving equations last year. Like, of course you didn’t. Yeah.

Yvette Lehman: I’ve never seen this before. Yeah. right? I know and like it breaks your heart a little you know because blood sweat and tears went into teaching that concept and now it’s as if it never happened. I remember famously I had one of my students say that I had never used the word data before. Never. Like he was like you have never said data. I don’t know what that word means. I’ve never even heard it.

Jon Orr: Never. It’s a strand. It’s a whole strand. We did it least like a sixth of the year.

Yvette Lehman: I just, it was great. So this is the challenge that we’re gonna tackle today, which is one that many educators face, which is this idea of retention. know, like how come it feels like we’re constantly starting over and reteaching and it’s almost like every year is a blank slate. And what are we gonna do about it? What is the solution? You know, and we always ask the question, if the results we’re getting are not the results that we want.

Jon Orr: you Yeah. Yeah.

Yvette Lehman: What has to change?

Jon Orr: And in this case, think, because we’re going to dive into a specific example from a team we’re supporting, and they are taking a path that, very similar path, the way myself, Kyle, took in our work that we were doing to address this issue. I think what I love about what the work they’re doing is, and again, we’ll look at the specifics, but really they’re giving permission when people didn’t think that they had permission to do. or take an approach or take an idea and then try to come up with a sort of like implement that idea that’s not exactly the way it’s been done before. And then therefore, but then give everyone that permission. They’re like, this is how we can do this. And it actually there’s research behind why this is important. So let’s unpack it and then let’s not be cryptic anymore.

Yvette Lehman: Yeah, so this is a school here in Ontario that we support. And this was their dilemma, right? The dilemma was retention. Why do we get to the end of a summative assessment and students don’t remember even being taught these concepts? And so this was their solution. So they determined that they would dedicate some time. They had a professional development day in August. And they dedicated that entire day for grade level teams or division teams to identify based on they in addition to ⁓ like EQAO or standardized assessment, they have a benchmark assessment at each grade level as well. So they use that that data to identify high leverage key concepts that they’re like, you know what, we know that this concept is only taught maybe once or twice throughout the year. It shows up in unit four and again in unit seven. But we just recognize that students need more exposure, more opportunity to interact with it, more, you know, a distributed practice of this particular concept. And so

Jon Orr: Yeah, it’s related to maybe something important next year as well, that kind of thing.

Yvette Lehman: Yeah, so based on their data, based on their understanding of, you know, the curriculum at their grade level, each team identified, you know, about six to eight of these really key concepts. Okay. And so then their next phase was once they’d identified the key concepts, they mapped them out in their current pacing guides and they were like, well, when did these show up? And then they looked for opportunities or ways to introduce them earlier and create more opportunities for students to interact with them. So it’s like, let’s say for example, know, operating with fractions doesn’t show up until May. It’s like, well, that’s too late. Like we can’t only see operating with fractions in May. Where are the opportunities to introduce it sooner, to spiral it into our curriculum, even just to create through our centers, more opportunities for students to interact with this concept, because we know that three weeks in May is not going to lead to mastery.

Jon Orr: Yeah. Exactly.

Yvette Lehman: So the one thing that they looked at was revising their pacing guides to integrate more frequent opportunities for students to interact with these six to eight key concepts. And then another commitment that they made as a school team was that they were going to create more opportunities for mixed practice and mixed assessment.

Jon Orr: Hmm. Yeah. And that makes sense. Like the research there is like mixed space practice versus mass practices. You know, you know, an important idea that is not new, you know, it’s not new. It’s it’s I think many educators are still trying to figure out or have been trying to figure out like, how do we do this and without chunking? How do we do this within units? How do I how do I mix in, know, doing a little now a little later, a little a little near the end and and and and not get myself overwhelmed with trying to map that out when typically our curriculums, our resources, our core resources don’t do it that way. They’re usually siloed and maybe there’s some strategic choices around the introduction of it and then they spaced out, know, maybe there’s a trickle. But, you know, it’s an important idea because there is a lot of research that says space practice is way more important than doing that math practice.

Yvette Lehman: think one thing that was important for this team to recognize is also that they don’t have all the answers yet. Even the six to eight high leverage concepts that they identified, are there some that they missed that are more critical? Is there one that it’s like, actually, this one’s actually not as high priority as we thought? Are the opportunities that they’re creating enough to actually shift the retention for students? Are they gonna get pushback from parents?

Jon Orr: right.

Yvette Lehman: who are saying, well, now there’s a unit test at the end of the unit, but it’s not only on decimals. There’s other concepts that come from prior units and maybe that’s just unfamiliar for families. And so I think the big idea here with this work is that the work is not like, this is a plan that is constantly evolving and changing in response to evidence of student thinking and evidence of student achievement and impact on the learning. So.

Jon Orr: Great.

Yvette Lehman: you know, next year when they come back together in August and they look now at their benchmark data and they look at their standardized test data and they ask themselves, you know, did we see gains in those key areas that we identified and did it translate to summative assessments at the end of the year? They may need to come back and revisit again.

Jon Orr: Right. Right. they, the really great part here is right. It’s like, this is some of the things that we help our teams with is identifying like, what are the measures that you’re really looking for to indicate whether the work you did had impact and, are you actively looking for that throughout the year? So while you’re saying that they could be looking at that data at the end of the year, but what are they doing during the year to make pivots along the way or, or small, small adjustments along the way so that it’s more of an iterative approach. through the year to make sure that by the end of the year, they actually hit some of those goals. And then they can start reflecting on like what we’re gonna make, keep that iterative process going from into the next year. what, like share a little bit of like, what are some of the moves, the cyst, like this school, because they’re doing this as a school and the leadership is on board. there’s key moves happening here throughout the year with the team and the school team. to make this actually a reality.

Yvette Lehman: Yeah, it’s interesting. This particular team doesn’t have a lot of time. know, it’s like professional development time is limited. When I asked them, you know, how frequently can you come together now as a grade level team or division team to stop, reflect, ask yourself, you know, what needs to, where do need to pivot? What’s working for us? It was like, once a month, you know, maybe that’s possible. Maybe every other month. And that’s just the reality of many of our systems.

Jon Orr: Everybody’s like that. Mm-hmm. Right.

Yvette Lehman: But I think that one of the questions they have to ask themselves is every time they come together, are they bringing student assessment data to the table? Are they bringing the summative assessments that have opportunities of cumulative review where they’re not only assessing decimals on the decimal unit, but they’re looking at concepts that relate to decimals from previous units. And are they asking themselves, how is retention of the concepts that were taught two weeks ago, three weeks ago? So which questions on the summative assessment is learning that isn’t, you know, from this week, from last week, but from previous units or previous, you know, periods in the year and how are students doing? Because the question that they’re asking themselves, right, is, has retention improved? And if the answer is still no, that, you know, when they look overall at these summative assessments and students are actually struggling still more on concepts that came earlier. How can they adjust? How can they change their approach? Where can they build in more opportunities for mastery of those particular standards or kilm expectations?

Jon Orr: Right. Yeah. Yeah. So zoom out for a sec. You’re like thinking about big picture as a district or a system or a school system. Like they’re doing again, I’m to point out two things here that we try to support and help shape, you know, direction of a school improvement or math improvement processing. One is, that they are, they’re asking the right question. Like the fact that they’re asking the question of like, wanna, like, how are we seeing retention shifted? Like that, that right there is saying like, well, we have to, every time we come together, we have to ask ourselves, are we making gains here? How are we making those gains and how do we know? Like they’re doing that well by asking that question instead of saying like, I wanna see my scores go up by 30 % or 10 % or 1 % or 2%. Like, like that’s typically, I think when schools make school improvement goals, they’ll say that. Instead of trying to get more narrow of like, what specifically are we trying to shift here? And let’s focus on that. And then let’s measure that shift or that change. And they’re doing that well. Like they’re, they’re, they’re, they’ve got the right idea around how to design math improvement inside their system. So that, that part, I want to kind of give them a good, good pat on the back for, for, for making sure that they’ve made the shift. Cause that’s the shift, right? Is just to shift goal setting in terms of math improvement towards. the change you’re looking for and making sure you can identify that change and then measure it in the change versus using your standardized test results just to say something specific about overall shift in student achievement. That’s important. That’s important to look at, but it doesn’t tell you whether the shifts you’ve made this year are actually making a difference. So that part, they’re done well. Here’s the other part that I think this team is doing well at is thinking about their flywheel as a whole. So the fact that they’re continually, is an iterative process and they’re committed to the iterative process. throughout the year, we’re consistently bringing artifacts to the table to evaluate, do we need to shift the way that we’re trying to create that change? Yes, no, let’s, yes, okay, yes, let’s figure that out together and then let’s go do that and then iteratively bring that back to the table to continually ask that. You can do that with artifacts, the student artifacts, because that’s the change they’re looking for. But this is a year to year flywheel as well. Most teams, you know, most teams will get to the end of the year and not have that artifact or those artifacts or the evidence to suggest that the work that they were working on this year made, actually made impact. So what happens is year to year, they’re like, well, we did that last year. Let’s pick something else. And then all of a sudden you’re pushing like the immense effort to get your flywheel moving has to start again. You know, like you’re back to the drawing board and trying to create this massive shift in something else, something new, which that’s why you were always feeling like you’re probably banging your head against the wall in terms of math improvement is because you’re constantly starting again. And so this group is going, hey, by the end of the year, we’re going to be like looking at this one piece and then deciding to keep going. know, like this is the work that we’re trying to do year to year to year. your flywheel just gets stronger from year to year because you’re making small increments throughout the year and you’re having the right evidence to suggest that things are working or things are tweaking. And that flywheel is what really causes shifts in math improvement across a system is to create and think by that. So they’re doing that well too, thinking about their flywheel versus isolated initiatives.

Yvette Lehman: My one recommendation is for teachers listening. Like the idea of spiraling, right? It can be interpreted in a variety of ways. But, and sometimes maybe if you’re doing this work alone, you’re like, I’m not really sure where to start or I don’t know what that means for me, but I do know my students need more exposure to some of these key concepts than our current pacing guide or curriculum is allowing. I feel like a call to action to everybody is just to build mixed practice and mixed review and mixed assessment. into your classroom. So right now imagine your unit is on decimals and you’re working on ordering, comparing, adding and subtracting decimals. Okay, what other key concepts that you’ve already taught that are relevant, that are related, could you bring into your practice and bring into your assessment as an opportunity for that cumulative review? And to me, that’s an easy shift. It’s a matter of adding a few items onto your practice and onto your assessment.

Jon Orr: Right. Right. So I guess when you think about two calls, you’re saying call to action is, right there. Now I’m going to give you two takeaways then one in both of being around this. One is if you want to take a deeper dive in spiraling, so you can be putting what you’ve had just recommended into place and you want to learn a little bit about the research behind spiraling. You want to learn about like what this looks like in your classroom or what it could look like in another classroom. Um, there’s a There’s an entire course designed and it’s completely for free for you to go down that rabbit hole. So if you’re a teacher or maybe you’re a leader and you want to explore mixed practice, mixed assessment, spiraling ideas together, then head on over to, I’m going to pick probably is make math moments. Yep. Make math moments.com. was going to say, cause it was originally published on tap into team minds, which is one of our, our precursor websites that make math moments. I guess I could say tap into team minds.com forward slash spiraling. that course will get you everything you need to know about how to get started with spiraling your math ideas in your classroom. So mixed practice, mixed assessment, kind of layering in throughout the year to help address the retention issue that you may be experiencing. The second is if you are looking for something specifically, it might not even be like, hey, we’re not focused on retention right now. We’re focused on something else. But if you need support on how to design math improvement around your main focus, your one thing, but you aren’t sure exactly how to create the alignment. You aren’t sure exactly how to arrange the subsystems of instructional improvement. You aren’t sure exactly what math to focus on to create the gateway for that traction and that buy-in to start, I guess, water falling into more improvement than you’re looking for, or solving, say, what we call the fragility problem in mathematics and thinking about sustainability of your math improvement plan. then we would encourage you reaching out to us and having a quick discussion around what you could be doing to strengthen all four of those pieces up in your math improvement planning, whether you’re at the school or whether you’re a school district, you can do that over at makemathmoments.com, forward slash district. You can talk even with a member of our team about how you can make that happen.

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