TIMESTAMPS
[00:00:04] Introduction
[00:04:03] Remarkable math gains in a struggling school
[00:07:05] What they learned in teacher education about math instruction
[00:14:49] A school facing years of poor math outcomes
[00:17:54] When classroom reality didn’t match what was being taught
[00:23:43] Illustrative Math and issues with problem-based instruction
[00:33:50] A close look at an Illustrative Math lesson
[00:43:14] Recognizing the teaching approach didn’t work
[00:46:35] How they transformed their math instruction
[00:54:28] What explicit instruction looks like in the classroom
[00:58:52] Creating more opportunities for students to respond
[01:01:54] How administrators responded to the results
[01:06:11] Evidence-informed teaching has a huge impact
[01:11:38] Advice for teachers
[01:15:03] When a teacher’s work feels hopeless

[00:00:04] Anna Stokke: Welcome to Chalk & Talk, a podcast about education and math. I’m Anna Stokke, a math professor and your host. Welcome back to another episode of Chalk & Talk.

Today’s episode is a little different. My guests are two elementary school teachers from California who are appearing anonymously so that they can speak candidly about their experiences. So, this episode is audio only and we won’t be using their real names.

Both teachers earned master’s degrees in education and now teach in a school where math achievement has been persistently low. Like many teachers, they were expected to use a particular program with their students. In this case, it was Illustrative Math, which is quite popular in the United States.

But as they watched many of their students’ struggle, they knew something wasn’t right. Rather than accepting those results, they took it upon themselves to learn about effective practices. They started listening to podcasts, reading the research, learning a bit about cognitive science and evidence-informed instructional practice, and rethinking everything that they had been taught about how children learn math.

And the results were extraordinary. Their students began the year performing below the national average in math. By the end of the year, both classes had climbed to well above the national average, despite teaching in a school where overall achievement remained very low.

I found this conversation incredibly inspiring. It’s the story of two teachers who refused to settle for poor outcomes. They were willing to challenge what they’d been taught, and they showed just how much difference great teaching can make.

And my hope is that other teachers, school leaders, and policymakers will be inspired by their example. One more thing, Max and Todd are genuinely interested in hearing what you think about this conversation and to answer any questions you might have. So, I’ve put a link in the show notes where you can submit your comments or questions. If we get enough of them, we’ll address them in a follow-up episode.

I also have a couple of big announcements. The next episode is going to follow a different timeline because it’s going to be live. On September 29th at 11:00 am Central, I’ll be hosting a special Chalk & Talk live stream on YouTube, where Montserrat Gomendio and I, will be unpacking the newly released PISA 2025 results and what they tell us about education systems around the world. I’m really excited because you’ll be able to join us live and ask questions during the live stream. To join us, subscribe to the Chalk & Talk YouTube channel, click on the live tab, find the September 29th live stream and click notify me. I’ll also put a direct link to the live stream in the show notes. And if you can’t join us live, don’t worry, we’ll release the recorded version on all the usual podcast platforms later that week.

Also, Chalk& Talk has a brand-new website at chalkandtalkpodcast.com. You’ll find every episode there and it’s now much easier to find the show notes, episode transcripts and resources mentioned on the podcast. Again, that’s chalkandtalkpodcast.com. Please check it out. Now, here’s my conversation with Max and Todd.

My guests today are two teachers who are appearing anonymously. They work in a school in California, and they’d like to be able to speak freely without unintentionally embarrassing colleagues or school administration.

So, we’ve agreed to protect their identities, which is why this episode will be audio only. Todd is a third-grade teacher, and he has been teaching for seven years. He received an MA in Education from Stanford and spent two years as an English teacher in Taiwan on a Fulbright scholarship before teaching in the U.S. Welcome to the podcast, Todd.

[00:04:26] Todd: Thank you so much. It’s great to be here.

[00:04:28] Anna Stokke:
And Max is a fifth-grade teacher, and he’s been teaching for six years. He also received an MA in Education from Stanford. So welcome to the podcast, Max.

[00:04:40] Max: Thank you, Anna. It’s a privilege to be here with you.

[00:04:43] Anna Stokke: Thank you. So earlier this year, you reached out to me.

And during that conversation, I heard something that I hear from teachers all over the world. So, you were taught certain approaches for teaching math in teacher training. And you entered the classroom, you were given a curriculum that was supposed to help students succeed in math.

And by curriculum, we mean what we’d call in Canada a math program, but in the U.S., you call it a curriculum. Yet neither of these things seem to work for your students. And the data from your district certainly reflects this.

The school has a substantial math achievement problem. Statewide assessment data from your school show that overall, more than 60 percent of students are not proficient in math and almost 40 percent are testing at below basic, so well below grade level expectations. More than 80 percent of English learners are not proficient in math.

That’s huge. And 50 percent of English learners are testing below basic. And over 70 percent of socioeconomically disadvantaged students are not proficient in math.

And 44 percent of that group are testing below basic. So, it’s fairly serious. But you found practical ways to work around the unhelpful curriculum you’re supposed to and to move away from the bad advice that you were given in teacher prep for teaching math in order to help your students succeed.

So let me tell the listeners something about the results for your classes. And this is based on NWEA math testing, which tells us how students are performing compared to students across the United States. Todd’s students’ median math achievement grew from the 39th percentile in the fall, that’s in September 2025, to the 71st percentile in the spring in May 2026, so over the school year.

And Max’s students’ median math achievement grew from the 36th percentile in fall to the 72nd percentile in spring. So, your students started below average nationally and they ended well above average nationally. That’s what that’s telling us.

So, you’re producing unusually large gains despite the school context. And I thought our listeners could learn a lot from your experience and what you’ve done to turn things around for your students. So, I’m really, really excited that you agreed to come on and share your story.

So, let’s start at the beginning. So, Todd, let’s start with you and let’s go back to when you were training to become a teacher. What were you taught in your teacher education program about how students learn math and what did good math instruction look like according to your education professors?

[00:07:45] Todd:
Sure. So, at Stanford, we would talk a lot about what is commonly called a low floor, high ceiling task. And the idea is that these tasks are supposed to be the center of your math lesson. And there’s sort of an acknowledgement there that it’s a low floor, high ceiling task because you’re going to have students of various levels.

And you want to make sure that students have access points into the math or into whatever it is that they’re working on that day, despite the level of achievement that they have. The best types of math tasks are those that have multiple access points. They have multiple ways of getting the correct answer.

And the very best ones don’t even have a single correct answer. And that this was pitched to us as being a solution to this equity problem that you alluded to in the introduction, where we have students who are really struggling in our math classes and how can we teach the whole class? And so, the solution was these types of math tasks. In addition to that, we were really taught to prioritize leading mathematical discussions with students.

I don’t know if you’ve read the NCTM has this, I don’t know if it’s a paper or a book, but it’s the five practices of leading mathematical discussions. So, the NCTM has these five practices for leading mathematical discussions. And what we would do is we would practice giving students math tasks, and then you would take a look at their work.

You would sequence it in some way that would make sense to move the discussion along. And then you’re expected to lead a discussion with students at the end of the task. Sometimes this is called a synthesis.

And what that does is that the idea is that students who were working at the lower level, students who are working at a higher level, they all have something to learn from each other in that context. Some of the things that we didn’t learn or some of the frustrations that would come up from my fellow teacher candidates who were in this program with me was we would ask a lot about what this looks like practically in a classroom. We didn’t have a lot of opportunities to actually practice these things in class.

And so, we wouldn’t practice teaching. And that was something that was very challenging because we weren’t actually practicing. For example, a math task has a launch.

How would you launch this task with a student, even if we’re going to assume that this is what you should do with students? And we would talk about it theoretically, but we wouldn’t actually put it into practice. And we wouldn’t learn about the sequence of content from K through six. What does a third grader learn in third grade? What does a fifth grader learn in fifth grade? That is a frustration that would come up a lot because we didn’t really know what the content of math would look like in the classroom with students and how to really carry this out with our students on a day-to-day basis.

[00:11:02] Anna Stokke:
Okay, got it. So, this was kind of like a theory that was presented to you and sounds good, right?

Let’s come back to that low floor, high ceiling idea later in the discussion, and we’ll talk about like how that actually looked in the classroom. But it sounds like during teacher education, you were learning this in your classes, but you didn’t really see this done in practice, or you hadn’t really applied this in practice maybe until you got into a school. Is that right?

[00:11:37] Todd:
Yeah, that’s exactly right. And really these things feed into each other, right? So, if you’re going to have a mathematical discussion where you are going to have a lot of examples of different student work and different student thinking, then you’re going to have to need a task where that type of thinking can occur. And basically the worst type of task that you could give to students would be called a closed task. And a closed task is a type of math task or question where there is only one right answer or one solution path, which is why, for example, the standard algorithm is so frowned upon, because there’s only one right answer, right? And there’s only really one procedure that you’re supposed to follow to get that answer.

And if you do that, then what is the discussion, the argument goes, what is the discussion that you’re going to be able to have with students about their learning?

[00:12:34] Anna Stokke:
So, we got some background information about your teacher education program, which was at Stanford.

Well, very respected institution, but I suspect the same thing is probably happening in education classrooms across North America. Let’s get some background information about the school you teach in. And Max, maybe you can tell us about this.

So, for example, how large is it? What grades does it serve? What kind of community does it serve?

[00:13:04] Max: Yeah, our school is a TK through fifth grade school. TK precedes kindergarten. And it’s about 450 students.

And about 40% of our school students are considered English learners. And 50% of them are considered socioeconomically disadvantaged. Although it’s probably higher, because in California, the way we determine the percentage of socioeconomically disadvantaged students is by the amount of students that qualify for free and reduced lunch.

And school lunch is now universal in California. So, families don’t necessarily need to submit that form. And so, we kind of get a lower read than it probably actually is.

So, it’s probably in between 50 to 75% of our school are considered socioeconomically disadvantaged students. About 70% of our school is Latino. 15% are Asian.

10% are white. And our district overall is pretty polarized in terms of economic status. We have very wealthy areas and on the other end, very poor areas.

And there’s about 10 schools in our district.

[00:14:16] Anna Stokke:
Okay, so it sounds like your school is serving a lot of children for whom what happens at school and what they learn in school and how well they do in school is really going to impact their life chances. Would you say that?

[00:14:34] Max:
Yeah, these students are, we would call them instructurally sensitive students.

They are relying on us to do the right thing at school. Their families are relying on us to educate and support their student. And we make a huge difference in their life.

As opposed to some other students from other schools in our district where I said they’re very wealthy. Those students have access to enormous wealth of resources. Their parents might just teach them virtually everything they need to know at home.

They go to tutoring after school. They have all sorts of enrichment. They have a very, very enriched childhood.

And those students are less sensitive to how well their teacher is going to teach them and how well their school is going to teach them and educate them. So, when I come to school, I understand and I reflect on this is, you know, I need to get this right. For the students, because they’re not going to get it somewhere else.

[00:15:29] Anna Stokke: Yeah. And it sounds like things maybe aren’t going that well generally in the school. So, we talked about the math scores in your school at the beginning.

And just going back to that again, more than 60% of students are showing that they’re not efficient in math. This is showing up on the state exams. Almost 40% are well below grade level expectations.

It sounds even worse once you start talking about English learners. So more than 80% of English learners not proficient in math, right? 50% testing below basic. A lot of people would consider that unacceptable.

So, we’ll talk a little more about that. But I’m wondering, how long have the scores looked that way in your school?

[00:16:23] Max:
So, if we look at CASP data, CASP is California Standardized Testing. We can look back 10 years on CASP.

And over the 10 years, math failure among English learners and socioeconomically disadvantaged students is actually trending upward. The more students are failing at math. Our math achievement for the entire district over those 10 years is essentially flat.

And for our school, failure is trending upward. And so, when we look at data as a school, we usually look at a very small picture. We just look from three months ago to now.

And even though we brought up these concerns of like, we need to look farther back to see if we’re not just vacillating up and down. We need to actually see how are we doing in the long term. And in the long term, we’re essentially doing worse than what we were in the past.

And there’s a little bit of a blip when you look over the course of the pandemic. Obviously, the scores went way down and then they kind of come back up a bit. But if we look back 10 years, we didn’t go anywhere since 2015.

[00:17:29] Anna Stokke:
Okay. And so, we’ll get into that a little more about why that might be happening. And I think you have shown that this isn’t like a life sentence.

Like if someone comes from a background where they don’t have all the opportunities, they’re socioeconomically disadvantaged, this isn’t a life sentence. It’s not predetermined that they’re going to do poorly in school. That’s not it.

That there are ways to improve. So, we’re going to talk about that.

[00:18:02] Todd: Yeah. I mean, just to give Stanford a little bit of credit, something that we did talk about a lot is that all students are capable of doing math and that all students can reach the highest levels of math proficiency. And that it does, when you accept that to be true, then looking at this data, you look at it through a completely different lens. Like you said, it’s completely unacceptable and it shifts the burden of responsibility away from the students to the adults who are in charge of caring for them.

[00:18:34] Anna Stokke:
Okay. So, Stanford got that right.

But let’s talk about the things they told you about teaching. So, Todd, what were some of the biggest challenges in math you noticed when you started teaching? And did you apply those methods, like the low floor, high ceiling, and did it work?

[00:18:52] Todd:
And maybe Max can talk about this as well, because he was at the school a year before me, but when I got there, this might be a little bit shocking, but there was no curriculum.

And I don’t know how it is in other countries. I hear that really you don’t design the curriculum yourself, but at least in the U.S. context, you have a boxed curriculum that comes from a publisher with a teacher edition, a manual that has all of the lessons in it for the entire year. And that did not exist at my school, in my classroom.

I did not have a teacher manual. I had no materials, no student workbooks, no manipulatives for students. There was basically nothing, except for our common core state standards, which outline what a student in a certain grade is supposed to have mastered by the end of the year.

But that doesn’t even give you a progression. You know, where do you start if you have the end goal from the standards? And so, yes, I mean, I was lucky enough to be working in a grade level team who had come up with some sort of system and progression that they were working with. And so, I followed along with what they were doing.

And I definitely was doing the low floor, high ceiling tasks. A lot of times my criticism of what my grade level was doing was the tasks aren’t open enough. We need better tasks.

And trying to do this lesson structure that I actually learned at Stanford, which was you start with a number talk, and then you do like a launch. So, you launch the task, and then students will have time to explore and come up with their own strategies and work together. And then at the end, you have a discussion.

And so that was kind of what my math block looked like.

[00:20:35] Anna Stokke: And did it work when you did these things? Were the students learning math? Were they getting better? What was happening?

[00:20:42] Todd: Here’s the thing that’s really tricky, and I would say pernicious about some of these ideas, is that it does seem like for some students it works. I had about 50% of my students, I would give them the end of unit assessment.

They would do great. You know, the beautiful reasoning, their work was neat. And it looks like for those students, it is working.

And then I would have other students who were obviously just really struggling. I mean, you couldn’t even make sense of what they were attempting. They’re in essence trying to mimic each other and not doing a very good job of that.

And on the whole, I would say it was a mixed bag. And that’s what sometimes comes up with these ideas, is that you tend to focus on the students who it is working for. And you’re saying, oh, well, these students are getting it.

So, there’s something going on with these other students who aren’t getting it. I need to do it more. It’s just not enough for them.

And I would say for my, what Max called instructionally sensitive students, it was not very effective for them.

[00:21:41] Anna Stokke: Okay. And, you know, Amanda Vander Hayden has this phrase for students that they seem to do well kind of in any situation.

They’re teacher-proof. So, there will be a bit of that always going on. And there’s always, you know, the thing with the parents at home helping out.

Why did you start changing though? Why did you think that you needed to change things?

[00:22:05] Todd: I wasn’t happy with how students were doing.

I think 50% is pretty low. If you believe what I had been taught, that all students are capable, then why aren’t all of my students doing well, right? You had Dr. Kimberly Nix- Berens on your podcast, and she talks about listening to the student. The student is always right.

And so, I’m sitting here thinking, well, there’s something going on with my instruction where this isn’t working for them. And I remember thinking also, if you just think about the history of mathematics education, I mean, this is a subject that we have been teaching students in forever. There must be someone or some method or some research, right, that is going to show me some more effective way.

Because what I’m doing right now, I’m making up my own scope and sequence for teaching multiplication, for teaching division. This is something students are learning all over the world. Why do I have to create this on my own? That kind of led to my search for answers because I knew I couldn’t be the only person who was experiencing this.

[00:23:10] Anna Stokke: Yeah, you make a good point. I’ve often thought about that myself. It’s not like anything is new here.

Math is a subject that’s been taught since schools existed, right? So how could there not be a whole bunch of programs out there that work really well? It makes absolutely no sense. And why do people keep creating programs that seem not to work? Normally, we get better at things. In medicine, we get better at things.

You know, fewer people get sick over time. People live longer because we progress. But in education, it seems to kind of be like we go back and forth between these pendulum swings, which this has never made any sense to me.

But speaking of math programs, let’s talk about the math program that you were using in your school or that you are using in your school. And maybe Max can say something about that. So, what curriculum or math program, as we call it in Canada, were you given to use? And what was the philosophy behind it?

[00:24:23] Max: So about three years ago, our district adopted Illustrative Math, and it considers itself a problem-based curriculum.

And what that means is that you essentially present a problem to students. And through that problem, they’re going to then figure out all the mathematical ideas that they need to learn in this grade level. Illustrative claims to flip the I do, we do, you do, as this was mentioned in a recent interview with their new CEO, which gives you an idea of what is this curriculum about.

If you flip the I do, we do, you do, that means you’re starting with you’re going to do it. And then we’re going to end where I show you the correct way to attack a problem or something like that, which essentially is offering students problems that they have neither the skills nor knowledge to actually solve. And what I’ve realized over time is that really the only students that are getting there are the students that have already learned this, like at home, or their parents have showed them how to do it, or they learned it at tutoring or something.

While everybody else, like I mentioned earlier, the instructionally sensitive students essentially walk away confused, or they’ve not learned what you intended them to learn. And that’s commonly portrayed as being like, that’s productive struggle. Oh, they’re just struggling through it, but they’re actually making sense of it.

But there’s really no evidence that they’re making sense of it because they started, they’re doing poorly, and then they end the unit doing poorly, and they end the year doing poorly. So, when does this actually pay off? Few more things about, I have a couple of quotes from their website. One quote is, “meaningful math experiences do not have to look like silent seat work or a perfectly polished solution pathway on a whiteboard.

In fact, at IM, we hope they often don’t.” Which I understand that math class isn’t just about sitting down quietly and working completely in silence for an entire hour, or that it’s in fifth grade, the whole purpose of fifth grade math isn’t to just have a perfect looking work on a whiteboard. But I also don’t understand what would be wrong with making sure students really know how to work through a problem.

Especially when fifth grade is, at least in my district, is the last grade of elementary school, and these students are going to go to middle school, and they’re going to start learning pre-algebra and algebra, and then go to high school and learn algebra two and geometry and all these things. And they’re really going to need to know how to organize their thinking in a way that they’re going to be able to go back and use to structure the way that they attack a problem

So, this whole idea of IM is that students are just going to come and have a very thoughtful, meaningful experience doing math, and they’re going to develop their math identity. And these are terms that are thrown around constantly.

They sound very attractive, because you’re like, oh, you know, why wouldn’t you want a student to have a positive math identity? Of course, I want a student to feel confident that they can do math. But that seems to be, these flowery terms seem to be the only thing that this curriculum really uses, right? That’s how they kind of form a facade to hide that the students are not really becoming proficient, or that students that are struggling are not becoming proficient or acquiring the skills they need to acquire, because, oh, well, they’re just exploring. They’re just developing their math identity.

We don’t want them to be at a desk, right? We want them to be doing all these other things. But is that effective? Well, no, it’s not effective. At least in our context here, I’ve not seen any proof that this is going to raise student achievement.

Our achievement is flat, if not getting worse over time. That’s our current experience using illustrative math. And it’s a very popular program right now.

Another large school district in the area recently adopted it. They adopted it at New York City public schools on the East Coast. And so, there’s a lot of, and I think they’re getting a lot of pushback, but it’s very popular in the United States at the moment.

[00:28:06] Anna Stokke: It’s hugely popular. I know this. I don’t even live in the United States, but I have teachers writing me all the time about Illustrative Math and asking me to review it and things like that because they think it doesn’t work.

I just want to follow up on a couple of things that you mentioned there. So, the first one is it sounds like they disparage students sitting and working independently on math. That quote that you gave, that’s essentially what it’s saying, right? I mean, that’s a tale as old as time.

In 1989, NCTM standards, they were disparaging pencil and paper math. This is the same idea. And I just want to say that if students don’t have a lot of that sort of thing, or if they don’t have much time to sit down and actually think about things and work through things independently, they will never get enough practice to become good at math.

I would encourage anyone listening to ignore that advice from illustrative math. And then the second thing I heard you talking about was this idea of productive struggle. And it’s interesting the way you explained the reasoning behind it.

And the students are struggling, they’re still struggling. And it’s like, what’s going on? This doesn’t seem to be working. And the answer back to that seems to be, well, you have to wait it out.

This is going to pay off. That’s how I was hearing it. Does that sort of sound right to you?

[00:29:38] Max: Yeah, it’s like it’s going to pay off eventually.

And the thing is, is the perspective I have right now is when I was hired, I taught second grade for three years, and then I moved up to fifth grade. What I can say in second grade is that you’re often you got told they’re going to get this next year. We’re going to continue working with addition in third grade.

But when I taught, now I’m teaching fifth grade. Do you know the students that are struggling in second grade? I actually had some of the same students again, because I moved ahead of them in terms of the grades. And the students that were struggling were still struggling when they got to fifth grade.

And the students that didn’t know how to add in second grade, they still didn’t know how to add in fifth grade. So, these problems do not just magically work themselves out. You know, we are responsible for making sure that the student that enters my doorway knows and learns what they need to learn from me, the teacher that is being paid to ensure that they are being educated and supported.

[00:30:29] Anna Stokke: Yeah. And thank you for saying that. I completely agree.

And I mean, this idea, it’s very damaging because it seems to just it keeps getting pushed along that eventually they’re going to get it. Eventually this is all going to pay off. And then it literally never does.

And then the other thing I wanted to back up on is this idea of math identity.

I mean, that is a phrase that I would like to throw in the trash because it doesn’t really mean anything. It’s something that people use to just say, look, you know, the reason that students are struggling in math is because they feel like they’re bad at math. Look, they feel like they are bad at math because they are.

That’s what’s actually going on here. And we need them to get better at math. And the way to get better at math is to teach it well and to get lots of practice.

So, whatever a math identity might be, the students are not going to have it by just telling them they have it or having talks about everybody can do math. You actually have to get them to do the math. You have to get them good at it because once they’re good at it, then they feel good at math.

[00:31:45] Todd: I just wanted to say that, especially at an elementary level, it is very difficult to put yourself as an adult into the shoes of a student who is experiencing this lesson. And when we talk about, for example, multiple strategies and you’re doing two-digit addition in second grade, as an adult, I can come up with a ton of strategies for two-digit addition.

When you’re talking about multiplication, there’s this famous example, it comes up all the time, right? What is nine times eight? That’s a math fact a lot of people get wrong. And you can come up, me as an adult, wow, you could think of it as ten times eight minus eight. You can think of it as nine times five plus nine times three.

But for a student, that is just extremely overwhelming. And they’re not going to get there on their own. And so, I think that there’s something that comes up with adults, teachers, especially me, when I was a teacher candidate, I did not have a great experience with math when I was in high school, elementary school through high school, through even into college.

And it was something, a subject that I struggled with. And then I see someone presenting this different way of teaching math to me of, you know, we can explore these problems together and we can think about solving these problems with these beautiful representations. And for me, as someone who is fluent in addition facts and multiplication facts, these make sense, right? The area model of multiplication, I see it and I’m like, wow, that makes a lot of sense to me.

I’ve never seen this before, but I got it. But that’s not the experience for students who are not fluent in their math facts, who are not fluent in their operations. And so, we have this response as adults when we see this, it’s like, oh, wow, that sounds like a great idea.

And I wish I were taught math this way. Really, you don’t, because if you were taught math this way, I would not be as proficient as I am at math today as an adult.

[00:33:40] Anna Stokke: I 100% agree with that.

And I think a lot of this is about the adults, the adults seeing something and it’s the curse of expertise, right? So, the adults seeing something and thinking, oh, my gosh, that’s so cool. I wish I’d been shown that as a student and falling into that trap. And it’s really easy to convince people, particularly if they feel like they could have been better at math.

It’s really easy to convince them that this is in fact the answer. When in fact, usually when people fall behind in math, it’s actually because of a gap in their learning process, because gaps compound really quickly in math.

So, Todd, maybe you can walk us through a concrete lesson, an Illustrative Math lesson perhaps, and what it looked like in practice.

[00:34:30] Todd: Sure. So, I’ve selected a lesson here. I would say it’s pretty typical.

It’s not a one that’s especially egregious. The first thing you need to know about illustrative math is that every lesson from at least third grade through high school has the same lesson structure. They all start with a warm-up, two activities, a synthesis, and a cool-down.

Every day for every grade level. There are also centers that for the upper grades are kind of like an optional add-on. And for lower grades, the centers, which are kind of like math games, are kind of, there’s space that’s hollowed out for it within the week.

But at least when we’re thinking about third grade, that’s just what it is. Warm-up, activities, synthesis, cool-down. For this lesson that I picked, it’s about solving time problems.

So, elapsed time questions. Something else to note is that in third grade, there are only three time lessons for the entire year. One lesson is about identifying time or reading clocks to the nearest minute.

And then the other two lessons about solving elapsed time questions. So, there’s only three that they get and then they move on. And the assumption is they’ll get it again in fourth grade.

So, when we’re looking at this lesson, it starts with a choral count, which is the warm-up. And so, you’re going to count with students by intervals of 15. You start from, let’s say, 12 o’clock and then you go to 3 o’clock.

And you’re going to count all together and write down the times on the board as you count. So, you’re at 12 o’clock, 12.15, 12.30, 12.45, 1 o’clock, 1.15. And at the end, you have some discussion with students. You say, what patterns do you notice? What do you notice? What do you wonder? You talk about that and that lasts about 10 minutes.

And after that, you have the first activity. The first activity here, it’s saying that Kieran arrived at the bus stop at 3.27 PM. He waited for 24 minutes for his bus to arrive.

What time did his bus arrive? And the expectation is students go off and they try it on their own. And they try to figure out. I think what this lesson is trying to get students to do is to attach addition strategies to solving time problems.

But that’s not called out explicitly, right? And it’s actually mentioned. It’s kind of a bonus if they start to do this. You can talk about it in your discussion.

But just let students do whatever they want with this question. And then there’s a second question that’s very similar. Elena arrived at the bus stop at 3.45 PM.

There’s 3.45. It’s a callback to the warm-up where you counted by intervals of 15. Elena arrived at the bus stop at 3.45 PM. She also waited 24 minutes for her bus to arrive.

What time did the bus arrive? The issue here is that we’re working in not a base 10 system anymore. We’re working in base 12 and base 60, right? And so, there’s all these challenges that are going to arise when students are trying to add minutes to time. And you’re not calling that out explicitly.

That was something you would do at the synthesis. Oh, what happened when you tried to add 24 minutes to 3.45? Do you get 3.69? Is that a time? No. So then, oh, I had to regroup.

That’s kind of the discussion that they want you to have, right? That’s the first activity. And then you go into the second activity, which is another question. And this one is about trying to calculate the amount of time that has elapsed instead of calculating like the end time.

So, it says at 6.32 PM, Elena got on a bus to go home. She got off the bus at 7.10 PM. How long was her bus ride? And this is a completely different process now.

Now we’re talking about calculating elapsed time instead of adding on minutes or hours. At this point, students are typically very confused because they’ve not been given any instruction in how to do this. The students who are most successful are the ones, oh, okay, I can just put this on a number line, an open number line, right? And I can add up my minutes and great.

But then you’ll have students who are trying to do some version of the standard algorithm with time. You’ll have students who are just trying to count on their fingers. There’s just a whole bunch of things that come out of this.

And then you do some synthesis. You come back together. You talk about it.

And then at the end, you have a cool down, which is kind of like an exit ticket, typically a printed piece of paper that you would give to students with a similar question that they solve on their own.

[00:38:51] Anna Stokke: Okay. So just to clarify, so are you not encouraged to teach them how to solve problems like that before giving them these exercises or?

[00:39:02] Todd: No, I mean, even I’m reading the lesson right now and I’m looking at where the second activity and the instructions to the teacher say that students are not required to solve the problem, but students may choose to do so as they think about ways to reason abstractly about the solution.

So even the success criteria here are very vague. What would it actually look like for a student to be successful with this? If they don’t need to solve the problem, then what are we doing? You just want them to talk with a partner about their solution or what they would do. And another point that I brought up a little bit earlier is that there is a very efficient way of teaching students how to solve these problems with an open number line.

And you just put the time on a number line and then you can see very clearly, oh, do I have the start time? Do I have the end time? Am I trying to find the amount of time that’s elapsed? And nowhere in that for the teacher is that even brought up because that would be something helpful for me as a teacher to know. Students might have different strategies of how they’re going to approach this problem, but here is where we want to nudge their thinking along to get them to, we want to be relating this to addition and subtraction. That’s nowhere there.

[00:40:11] Anna Stokke: Okay. So, the idea is that the students are just supposed to sort of generate some ideas, but we don’t really care so much if they actually get the right answer. And there’s not even a bunch of practice problems for them to do with support from a teacher or anything like that.

[00:40:29] Todd: No, there’s three questions, the whole lesson.

[00:40:32] Max: Yeah, I had a similar experience in fifth grade, and I’ll be brief with it is that the first lesson for decimal addition, there is one problem and it says the students can attempt this problem with whatever strategy they’d like. And keep in mind, this is the first time they’re being asked to add decimals to the hundredths place.

And so, there’s one problem. And then the rest of the lesson, they’re supposed to play a game and that’s it. And the problem with that is that the students don’t know how to do this correctly.

And then the game is not helping them because if the game involves adding decimal. So, I mean, if you don’t know how to do that correctly, if you don’t say the place value, the magnitude of the numbers that you’re trying to add, what happens is that the students don’t actually get anything out of this game or even worse, they start to practice doing something incorrectly and then they acquire a mistake. And I always thought that lesson was particularly poor because, I mean, how are you supposed to ensure that the student learned the skill that you’re trying to teach them with one problem? And then a game where everyone is playing the game with a partner and the teacher can’t really, you have to walk around and look at each person trying to play and it’s very unclear if they understand.

And so, it’s just highly ineffective at making sure that the student learned what you wanted them to learn, which is how to add decimals.

[00:41:52] Anna Stokke: Okay. So, it sounds to me like two things are going on.

So, the first thing is there’s not a good explicit lesson that a teacher would be supposed to give. There’s nothing there that tells the teacher how to teach or what they’re supposed to teach. It sounds like it’s meant to be a group project.

Students just kind of brainstorm, but the students don’t, of course, have the background knowledge to be able to do that. So really what’s happening is this factivity that should be applied later in the instructional hierarchy, as we’d like to say it. So, after students have maybe become fluent, they have better ideas about some of these concepts and they’ve done a bunch of practice and received good instruction, then we might want to do tasks like this.

But it sounds like these are kind of the only tasks that you’re doing for one thing. And the second thing is they’re just not effective. Does that sound right?

[00:42:48] Max: Yeah. I have no problem with students playing some sort of a math game. That’s great. You want to reinforce a concept that they’ve learned with a math game that students enjoy it.

I don’t want to sound like I’m anti-fun, but if we’re in the acquisition phase, the students are just learning this for the first time, it’s probably not time for a game yet because, well, they’re not going to play the game accurately and it’s not reinforcing what you want it to reinforce because, well, like I said, they didn’t learn it yet and you need to teach them how to do it. And one problem is not enough to do it. I’ve never learned something from doing once before and I don’t think the students clearly are not learning from that either.

[00:43:24] Anna Stokke: Okay. So, you’ve got the math scores in the school are quite poor. You’ve been taught these things in ed school, which don’t sound like they were really helping.

And then you’ve got this curriculum that doesn’t seem to help either. So, you figured out something wasn’t right. And when you realize that, what did you do? Did you talk to your colleagues? Did you talk to administration? And what sort of response did you get?

[00:43:54] Max: I feel like we knew these things were wrong very quickly because the students were not making progress.

So, we gave it a genuine try. We’re being told this is going to be effective. Okay, I’ll do it.

If you’re telling me this is going to work, I’m going to do whatever it takes for the class to learn. However, the students did not make progress with this. I wouldn’t even call it a strategy.

It’s just like this philosophy of how they’re going to acquire math skills and become fluent and able to apply them. And that especially, like I mentioned earlier, was clear to me when I moved to fifth grade and I saw that students had enormous gaps in learning from years that we already had adopted Illustrative Math. So, you’re telling me they’re supposed to have learned how to add and subtract in second and third grade.

And by the time they got to fifth grade, they still had not acquired those skills. And in fact, a lot of the challenges I had this year were because students were not able to do prior things that they were supposed to have learned in the past. They had never learned, right? So even the lack of addition fluency, not being able to add and subtract accurately caused us a lot of problems this year in fifth grade.

So, the students, and you can see, we can see using NWEA, the assessment data we talked about earlier, we can see their progress over time. And you see a lot of kids just flatline or they start to get worse. They start to score worse because the expectation is much higher in fifth grade and that where they’re supposed to be at in middle school is going to become much higher as well.

[00:45:22] Todd: I was just going to say that I was part of the pilot committee that piloted this curriculum and another curriculum that we were looking at. And it wasn’t just like me and Max who had issues with this. I mean, teachers would just look at it and they would read a lesson like the one that I described to you.

And something seems off here. Where’s all the practice? Why are we introducing three different problem types in one lesson? And then moving on, there was a lot of consternation from teachers in the district and pushback there still is from teachers. And we brought these up with the district administration who was leading the pilot.

We brought it up with our own site administration. And the response is, or was, continues to be that this is a new way of teaching math. And so, we’re going to feel a little bit uncomfortable because it’s different.

And it is not different. This is what I was taught at Stanford. This aligns to Stanford’s teaching philosophy, which I’m sure is used by other teacher ed programs.

I mean, this is not a new way of teaching math. But if you just as a teacher, just like the normal everyday teacher doesn’t necessarily know that or has the knowledge to push back against that. But what they do say is there’s something that feels strange here.

[00:46:43] Anna Stokke: Okay. So other people notice this and what you got back was maybe gaslighting. I’d call that gaslighting where it’s, well, you know, I think maybe the problems with you, you’re maybe often you’ll hear you’re not using the program properly.

Like we’ve just started. It’s new. Of course, it’s going to make you uncomfortable, right? This is a new way of teaching math.

So, are you required to use that curriculum, that illustrative math?

[00:47:15] Todd: Yes, we are. And basically this is how districts work, at least in the United States, that we have board approved curriculum and the board members are elected officials. And so, we are required to have the curriculum in our classroom to use it as it represents the will of the community through the actions of the district.

[00:47:38] Anna Stokke: Okay. But you have found ways to work around it though, correct?

[00:47:45] Todd: Yes. So maybe if I would go back and amend my answer.

Yes. We are told that we have to use it. I do not use it.

I did not use it basically the entire school year this year. I used Jump Math, which I heard about on your podcast with John Mighton to great effect. But we have to change our messaging a little bit.

I’m not going out and skipping down the hall and saying that I’m using Jump Math. I’m saying, oh, I have this other program that I’m using that’s supplementing, right, the Illustrative Math, or I’m still following the sequence, or I still do warmup. I’m doing the warmup and I’m doing activities and I’m doing a cool down, but I’m not using their materials.

I’m using materials from Jump Math, mostly, and some other things that I’ve got together. But if someone walks into my classroom, I can justify, sure, I’m following the philosophy of the program. The students have the workbooks and all of these other things that we can check the box because I find that that’s really what administrators are worried about, that someone is going to come down to them and say, your teachers aren’t using the materials.

And so, then they have to make sure that the teachers are using materials so that doesn’t reflect poorly on them. So, this is kind of like a team effort. The administrator wants to look good for their people at the district office.

So, I’ll play the game a little bit here and we’re able to make it work.

[00:48:59] Anna Stokke: Okay. Interesting.

So, you mentioned that you’re using Jump Math. Max, maybe you can also say a bit about what you’ve changed in your teaching and how you did this within the constraints of what the school expected.

[00:49:12] Max: Yeah. I mean, when we adopted the program, they were extremely strict about everyone doing it exactly the way it said. And if you said, even if by the end of the unit, hey, half the class failed the assessment, we should probably review or reteach. And they would tell you, no, you’re just going to continue.

They’ve lightened that hold on us a bit this year. And I have just changed the curriculum. I’ve skipped things I think are ineffective.

I create additional practice. Sometimes we just break out the whiteboards and I’m just going to teach you the concept explicitly. And I use like Mr. Barton’s math from Craig Barton to generate lots of practice or space the practice out or interleave lots of different concepts we’ve learned in the past.

I was able to get away with that because our administrators are, they tend to be busy with lots of administrative bloat assignments that they can’t really pay close attention to me or a lot of other teachers. And so, you can, when it comes down to just doing the right thing, all right, we’re just going to do it. And, you know, we have the workbook right here in case you walk in, look, it’s right there.

I’m just reviewing how to do this. You can kind of dance around it a bit. And there’s really no reason to put a microscope on me either because Todd and I have the best results in the school.

So, they just let me and let us do our thing. But they won’t necessarily endorse what we’re doing.

[00:50:30] Todd: I would say that I was using Gem Math or Max is saying he uses Craig Barton’s materials. It’s more than the materials. It is an understanding of how a student progresses from being a novice to an expert.

And I think really the most impactful resources that I use are the ideas of people much smarter than me who have figured these things out, who talk about the instructional hierarchy. I’ve learned from them. I’ve learned from the work of John Sweller, cognitive load theory, desirable difficulties, and what Max was saying with spaced practice and interleaved practice and retrieval practice and all of these things.

And so, once you have an understanding of that, the phases of the instructional hierarchy, I think probably most important, but then you can build in all of these other effective practices that come from behavioral science, that come from cognitive science, that they all have something valuable to say here. And you can use these to shape your math lesson. And that’s really what we’ve done.

[00:51:34] Max: Yeah, I think Todd said it perfectly. Essentially understanding the biggest thing that has been helpful for me is understanding the instructional hierarchy, because then I can take Illustrative and I can take the lessons in there that are fine and I can sift out all the stuff that’s not going to work.

Just understanding where my class is, if we’re in the acquisition phase, probably not going to start playing a game, right? Or we’re not going to just do one practice problem. And then I was able to construct how is it going to work from there? So, we did use some of the curriculum, but mostly I either changed it, shifted things around, shifted the order of the units, because in fifth grade Illustrative, you do fraction multiplication before you even do whole number multiplication. And that was very difficult because they were not able to multiply the whole numbers.

So, let’s just focus on that first and just kind of like a logical progression, or we’re not going to wait till the end of the year to talk about place value. So those shifts, understanding the instructional hierarchy was pretty much the most impactful thing to help me design effective instruction.

[00:52:33] Anna Stokke: And I’ll just do a very quick recap on what the instructional hierarchy says, just in case anyone’s listening for the first time. And we’ll also link to another podcast episode in the show notes that would help you learn more about it.

But essentially what it says is that when anyone is learning something new, so for example, a student learning math, they go through four stages. The first is the acquisition stage where the student is, we just want them to be accurate. So, we’re giving them all sorts of guidance, explicit instruction, lots of feedback, worked examples, things like that, because we just want to get them to the point where they’re accurate.

After that, we want them to be able to do the skill more effortlessly and quickly without having to think too hard about it. And that’s the fluency stage. There they need lots and lots and lots of practice and feedback and the kind of practice that sometimes you sit down at a desk and do.

So, there we go. And then the last two stages are the generalization and adaptation stage. So, you may have a student who’s fluent and accurate, so they can perform the skill accurately and effortlessly, but they’re unable to apply it in a new context.

We see that all the time too. And that’s because you need to teach them how to do it and use it in different contexts, right? So that’s where you bring in things like interleaving. And then the adaptation stage is really the problem solving stage where we think outside the box and we can apply that skill in an entirely new setting.

And what it sounded to me like Illustrative Math was doing is it was giving adaptation stage problems to novice learners. And that’s why it won’t work. You have to move up that hierarchy.

We’re not wanting to ignore that top part of the hierarchy, but we’ve got to do this in the right order.

[00:54:29] Todd: I have no problem with students discovering things, right? Or students working on difficult problems that they’ve never worked on before, collaborating together to try to solve problems. I mean, that’s what I want my students to be doing. That’s the end goal.

But we, exactly as you said, with Illustrative Math, we’re mixing up the order here. And that this just isn’t how a novice learner goes from being a novice to an expert or a relative expert.

[00:54:57] Anna Stokke: So, give me some idea of what it looks like in your classroom. One of you or both of you can speak on that now that you’ve started applying some of these techniques.

[00:55:08] Max: We had some consultants from who were like licensed to teach us about Illustrative common.

One thing they came and told us was don’t review, right? You just need to go right into the grade level math. And I just want to say that because one thing I always start with now is review the prerequisites where we’re starting a new learning episode for some sort of a new concept. And one thing I’d recommend to anyone listening is Brendan Lee’s Essential Guide to Explicit Instruction in Mathematics, because that really lays it out.

I use that all the time and it’s really made it very easy for me to understand where students are in the instructional hierarchy and what to do next. Like it’s step-by-step. So pretty much if we were doing a new, let’s say in fifth grade students are supposed to be able to add and subtract fractions with unlike denominators.

So, I would start by reviewing the prerequisites, which is, well, add and subtract fractions with common denominators. Then I would give a precise explanation of the new concept and we try a very atomized example together. Maybe when I say atomized, I mean the most simple thing first.

And the most simple thing first in this example would be just recognizing if the fractions are ready to be added. And so, we would do that several times together. I would give students the opportunity to respond, call on students.

For example, just show them an example and ask a student, are these fractions ready to be added? The answer would be yes if they have a common denominator or no if they don’t have a common denominator. And then expect the students to be able to respond as in they’re not ready to be added because they do not have the same denominator. And we would practice that corally and try to maximize the amount of opportunities that a student has to respond.

So, and those tend to be like coral responses. So, responding all together, practicing with like a partner or using mini whiteboards so that I can quickly identify any students that need me to immediately support them. Then we’ll try like a worked example.

I’ll work through an example. I’ll explain it step by step. When students seem to be ready to try it themselves, then we’ll try the guided practice.

So, we’ll do a problem 100% together. Then maybe once we have a high success rate there, then we’ll do it 75% together, then 25% independently. So that last, for example, you’re going to finish the last step on your own.

And that’s where I’m going to circulate. I’m going to check and make sure that everybody is where they need to be before we move on. And that’s drawing on this from Doug Lemov’s Teach Like a Champion.

He calls this active observation where you’re just going around and you’re making sure you meet and observe as many students as possible and provide as much feedback as possible. And when we do this guidance fading, you know, where it’s like 75% together, 25% and independent, it lets the teacher, myself in this instance, understand exactly where the students are having issues or they’re going to have a problem. And then we can pause there and we can target that to make sure that everyone gets that before we move on.

And we’ll do half together, half independent. And then eventually you fade it out where the student is going to be able to do it on their own. And once you have a high success rate there, at least 80%, if not 90%, or frankly target the whole class, we’re going to go in for 100% success rate.

Then you’re ready to add complexity to the problem. If we were just doing where one fraction needs to be changed, we want to just change. If we’re adding a third and a sixth together, we just need to change the third into two sixths.

And then we don’t need to change the sixth. Once the students have mastered that in terms of the atomization aspect, we can add two fractions that where both of the denominators need to change. And once you have achieved like high success rate through that, then students are ready to work on independent practice and building fluency with these skills.

And so, I’d recommend don’t rush the fluency, make sure students are super accurate. And then from there, you can interleave this practice throughout the year or interleave these with other concepts they’ve learned in the past. You can space practice

And every morning I have the students come in and they have eight problems to do. I’m just using Mr. Barton’s super eights, which just generates eight problems. And I just pick things that I know we need.

We’ve either worked on in the past or massing practice for something that we are like currently working on. But that’s kind of what it looks like in my classroom and had like very high success rate using things that, I mean, it’s not that complicated. It’s that it’s like pretty straightforward.

I’m just going to ensure that they all understand the problems.

[00:59:32] Anna Stokke: Was there anything you wanted to add to Max’s description, Todd?

[00:59:36] Todd: I would say it looks very similar for me. I think one of the best things you can focus on as a teacher is to ensure that students have just a ton of opportunities for response throughout the lesson. That’s something I am always thinking about is how am I going to make sure that students are either just saying it out loud corally or writing it on a whiteboard? There has to be some accountability so I can check, right? But you really want to build in those practice opportunities throughout the lesson.

That’s what keeps students engaged as well. And it keeps them motivated because all of a sudden they have gone from getting three questions wrong over the course of an hour math lesson to now they’ve gotten 30 questions correct. Just rapid fire, right? They feel successful and confident and happy.

And you as a teacher, you’re motivating them. You’re saying, oh my gosh, you just got that question, right? Here, I’m going to give you something a little bit harder. I bet you can’t do this one, right? And you give them something else and they go, wow, you guys are so smart, right? You’re just constantly praising them and celebrating their growth.

And it’s really fun. And for students, it’s a very fast paced, rigorous, interactive environment. And you hear people talk about it in a way that’s like drill and kill where you get this image of students who are just at a desk, just doing like all these problems.

And, you know, sure, there’s a place for that when you’re building fluency. But when you’re really in the front of the classroom with students, there is a back and forth here that is really interactive and fun. And I guess the final thing I would say is that when you’re modeling for students and then you’re expecting them to do what you’re modeling, it makes the feedback process so much easier because you don’t have 24 students trying to do this in seven different ways.

You have 24 students trying to do this in the same way that you just showed them. And so, you can anticipate much more easily the types of mistakes that students are going to make. You can rehearse how you’re going to respond to those mistakes.

And it just makes the whole process of teaching easier on the teacher, I would say.

[01:01:51] Max: And I want to add to what Todd just said.

I think there’s sometimes a straw man argument against explicit instruction that it’s like cold and it’s very silent and it’s like the Illustrative Math example. You know, we don’t want them to be in a room that’s just completely silent, but it’s actually really not. It’s fast paced.

It’s the room, the energy in the room is really good. I’m coming around. I’m checking each student.

There’s a lot of fist bumps, right? There’s people supporting each other if they need to. Sometimes you tell a partner that if they got it down, hey, check your partner really quick, give them some support. So, it’s a really like electrified room.

It’s fast paced, like I said, and it’s enjoyable. And the students feel most importantly, their self-esteem is being raised because they’re for the first time for some of them feeling successful in math.

[01:02:34] Anna Stokke: So, it sounds like you’re happier as teachers because your students are succeeding and things are going well in the classroom. The students are happier because they’re succeeding and you’re getting better results, a lot better results than other classes in the school. So that leads me to the question, administrators know this, right? I mean, they can see what your results are like.

They can see your data. What are they doing? I mean, do they want to know what you’re doing and have you maybe speak to other teachers about doing that as well?

[01:03:12] Max: Yeah, they did notice. Administrators, there was more of an emphasis placed on like administrators and teachers looking at student data this year, which is absurd in a way that this wasn’t always the case, especially when we were collecting this data.

But the interest was very superficial. It was treated like it was good luck. We just had a lucky year or that it’s not replicable.

So that, for example, I shared actually the Guide to Explicit Math Instruction from Brennan Lee with our principal and because she was like, so what are you doing? Just kind of like a bit of curiosity. I said, this pretty much tells you exactly. I could try to explain it to you, but this pretty much tells you exactly what it is that I’m doing.

And I don’t know if she read it, but we never talked about it again. And there was frankly no interest in making this something that we’re going to discuss as a school staff. We’ve had this discussion many times of what is effective and is not effective.

And the district even came out with a training that said, you can just do, I do, we do, you do in any order you feel like. You can start with the you do. And Todd and I pushed back hard on that.

We’re like this, the order does matter. The order you do something matters. I mean, how are you going to start with the you do? And we were pretty much told, no, it doesn’t matter.

You can just, it’s nonlinear. They kind of have these packaged phrases. And we asked, what is the evidence you have to show that that’s effective? And they could never responded to it.

And they never provided the evidence, even though we have a mountain of evidence that shows Anita Archer’s work and explicit instruction. I mean, it’s just to answer your question, did the administrators notice? Yes. Did they care? Not really.

[01:04:46] Todd: I would say that they see all instructional strategies as being equal almost. It’s like, okay, well, you’re getting these results with explicit instruction, but we’re doing problem-based learning and problem-based learning is also effective. And if we can figure out the right way to do it, when we bring them up with these things up with administrators, they’re saying the response is, oh, that’s nice.

Good for you. Happy for your students. But there’s no ownership of maybe this is something that we should be moving towards because they have faith in what their methods are.

And I don’t use the word faith lightly. It does feel like almost an orthodoxy, right? We’d asked for some evidence about what do you mean you can do gradual release of responsibility in any order, even starting with the you do and then moving to we do and then I do.

And they gave us a paper that was basically an opinion piece. Someone who was thinking about this abstractly and how they hold these things equally because we could provide something like why minimally guided instruction doesn’t work by John Sweller and Paul Kirschner and they would hold both of these at the same level of evidence.

[01:06:10] Anna Stokke: And they’re not. And this is something I talk a lot about when I give presentations, I try to mention this that the thing with education is there’s lots of different types of research that’s done in that field. And some of it I personally wouldn’t call research, but let’s say we call all of it research and it gets published in various places and some research is generalizable, meaning that the study has been set up well, there is some good statistics going on in the background and tells us that we could probably generalize it to And some research is not generalizable.

So, a philosophy piece is not like it’s when someone’s just writing their opinion and they’re thinking about it, even if it seems really smart, that is not generalizable. We have to be careful about that sort of thing in education

[01:07:01] Todd: I’d say too that these techniques that Max and I and everyone on your podcast talks about, these are things that you could implement in your classroom tomorrow and see immediate results with students. If you start teaching your students this way, at the end of the lesson, you will have much more students proficient in what you were teaching them than they were at the beginning of the lesson. And it’s not like the two of us here are, we don’t have PhDs in this.

We’re not researchers, right? But we were able to read what’s out there and kind of understand it and think, okay, let me try to apply this to my context. And you get immediate results. And then of course, from there, there’s the fine tuning that happens, right? This problem-based learning, discovery-based learning, inquiry learning, whatever you want to call it.

If you were to do that in your classroom tomorrow, you would get confusion. And that there’s no amount of fine tuning that you can do to this to make it work for novice students. And so, I would say even just that is enough evidence, at least for me.

I mean, I love reading all the research and all that stuff, but it’s just that this works, right? You do it and it works. And so great. I’m going to keep doing it and I’m going to keep fine tuning it.

Whereas with the Illustrative math approach, right? It’s not working and I bring up, it’s not working and I have these problems with it. And they say, well, just you’re not doing it well enough. Just keep doing it.

Maybe it’s the launch of the activity. They kind of break it apart into all these smaller bits that you have to master in order for this to start working. Whereas, you know, I just started teaching explicitly and first lesson went pretty well.

[01:08:42] Anna Stokke: Yeah. But that they’re saying is luck. You know, the whole message, it’s all sort of consistent.

So, when you use the method you’re supposed to use and it doesn’t work, that’s just bad luck or you’re not implementing it properly. But then when you use something that isn’t what they’re endorsing and you’re getting good results, it gets passed off as good luck, right? So, the message is consistent, but you’re doing the right thing. And what you’re telling people is going to be really inspiring because you can’t necessarily change what other people think.

That can be a hard thing to do, but you can change what you do and you can change the impact that you’re having within your classes. You can present that evidence to other people and hopefully you’ll get some other teachers on board. But what you’re doing is amazing and I’m really inspired to hear about it.

I do have another question about parents. Because the results in your school are so poor, I’m just surprised that the parents aren’t speaking up. And are they not noticing this? Do they think this is normal? What is going on with that?

[01:10:00] Todd: So, our families are from a cultural context, I would say, that is very trusting of the school and to teachers.

So many of our families, they’re immigrant families. They come from Central America, from South America, from Mexico. And there is kind of a trust here, which makes this even more tragic.

I’ve made it to the United States. I am putting my child into school in the United States and they are going to learn what they need to know in order to be successful. And also, what we’ve seen, Max and I are both on an organization at the school, which is called the School Site Council.

And we were basically elected teachers and parents from the community who helped to manage some of the budget of the school. And a lot of parents, which is also tragic to say, blame themselves and they blame their students before they will blame the school and the instructional practices. And so, they will say things like, well, I wasn’t very good at math, right? Or, oh, he’s just never really been good at math.

We just need to practice some more. I need to get him into Kumon, for example. I’ve had a lot of parents ask me about that.

And we see this in reading as well, where parents will say, oh, well, you know, English isn’t my first language. I can’t really help them at home. And so, and they take it on themselves and they will blame themselves for how their students are doing.

And probably the last part is just that they don’t have necessarily as wide of a picture of the data as the teachers do. They don’t necessarily see that breakdown of just how terribly socially, economically disadvantaged students and English learners at our school are doing. They only see their own child or children if they have more than one child in the school.

[01:11:56] Anna Stokke: That is a sad state of affairs. And that trust is maybe being violated a bit. I’m sorry to say but thank you to the two of you for doing something.

Okay. So, going into the last couple of questions here, for a teacher who knows something isn’t working, but feels stuck, what should they do?

[01:12:18] Todd: I would say, first of all, my gut reaction as a teacher initially was to pull small groups and to take students into small groups and say, okay, I’m just going to reteach you the material again, basically. And I think that’s a lot of the reaction that a lot of teachers have, especially in elementary years, maybe not middle school and high school.

And I would caution against doing that. And to really follow what Amanda Vander Hayden talks about, which is to critically evaluate your tier one instruction. When you have so many students who are failing or at risk of math failure, then that really is a tier one issue.

And some of the solutions that we’ve talked about, going back through the instructional hierarchy, looking at that resource from Brendan Lee or the episode that you’ve done, you’ve done more than one episode that talks about it. And also looking at Rosenshine’s principles for effective instruction. I think that there’s a, which you also have an episode about, wonderful, to kind of evaluate your tier one practices there.

Because really what I see when I see a lot of math failure, which was also happening in my class, is what Amanda Vander Hayden says, ABT, right? Ain’t been taught. They just haven’t been taught this material properly. And actually when you do teach students, it’s almost magical.

You start to get this, you know, we talk about MTSS or tiered instruction, tier one, tier two, tier three, and you can very clearly get this striation of students into these different tiers where I felt like at the beginning of my instruction, all my students, 60% of my students need tier two support. Oh my God. No, they just needed better tier one.

And now I have identified two students who really would benefit from more intensive support. And so, I would say focusing on tier one is really, I would say the first step. Yeah.

[01:14:11] Anna Stokke: So, it’s more like it’s an ounce of prevention.

If you get it right the first time, if you do it in the best way possible the first time, you’re going to have fewer problems later on.

Max, what’s your message to a teacher whose results are improving, but the school won’t budge on the curriculum or the approach?

[01:14:34] Max: First thing I’d say is just you continue doing the right thing, bottom line. And to fight this fight to improving student outcomes for everybody, I would find like-minded people because they’re definitely out there because trying to go at this alone can be very isolating and it can be very difficult. And I would identify any potential allies such as school board members, any site leadership, anybody that’s willing to fight with you.

And I just continue having the same conversations over and over again and come with your ducks in a row, come with evidence and stay on message. And I would also try to collaborate with some parents if needed, because for example, this year I’ve had parents that have told me this is my child’s best year. And they were like, we’ll do whatever is needed.

You need us to go to the school board. We’ll go talk to the school board. We’ll talk.

And so. you form a coalition of teachers and community members and parents. You can make a positive effect in your school district, in your school, in your community because you’re just going to be applying lots of pressure from different directions and to get things right.

[01:15:39] Anna Stokke: Well, that’s awesome. And is there anything else you want to add?

[01:15:43] Max: I do want to add one thing and that’s that there was some moments this year and in previous years where I thought this is hopeless. This fight is hopeless because I can do my best. But if I’m working in a system that’s just essentially dooming students’ academic futures, then it feels like it’s meaningless.

And I had to remind myself multiple times this year that it is not meaningless and that there’s 24 souls in my room that are depending on me. And there’s 24 families that are depending on me too. And so, your work does matter.

[01:15:15] Todd: I would say just to listen to your students and teach them and see how they respond and then change in response to that.

And your students, as they say in precision teaching, right, your students are always right. And as long as you believe that every single student in your classroom is capable of doing this, like I said before, we’ve been teaching these things for hundreds of years. I mean, there’s kids all around the world who are learning this.

Why are your kids any different, right? They are absolutely capable of doing what you are asking them to do. And you just listen to and analyze their responses and change your teaching based off of that. And I think if that’s what you do, you can’t go wrong.

[01:17:00] Anna Stokke: So, thank you so much for agreeing to come on and tell everyone about your story.

It’s very inspiring. And I think we’re going to get a lot of feedback on this one. I think it’s really going to help a lot of teachers. So, thank you so much.

[01:17:17] Todd: Thank you.

[01:17:18] Max: Thank you, Anna. It’s been an honor.

[01:17:20] Anna Stokke: Thank you so much for listening. If you enjoy this podcast, please consider showing your support by leaving a five-star rating on Spotify or Apple Podcasts. Don’t forget to subscribe on YouTube and on your favorite podcast app so you never miss an episode.

You can stay connected with me on Instagram, Facebook, TikTok, X, Blue Sky or LinkedIn, all links are in the show notes. And Chalk & talk now has its own website at chalkandtalkpodcast.com. You can find every episode there, along with show notes, transcripts, resource pages, and you can search past episodes by topic or guest. This podcast is funded by a grant from Latrobe University and from the Trottier Family Foundation through a grant to the University of Winnipeg to fund the Chalk and talk podcast.