Show #113 Solving for Why- Math is for ALL learners

Tanscript 

Lori Boll:

Hi everyone,  On today’s episode, I’m joined by Dr. John Tapper, founder and CEO of All Learners Network, longtime educator, researcher, and author of the award-winning book Solving for Why. With more than two decades of experience as a classroom teacher and math interventionist, John is a passionate advocate for equitable, accessible math instruction for all learners.

In our conversation, we talk about what truly inclusive, strong Tier 1 math instruction looks like, why productive struggle matters, and how understanding student thinking is far more powerful than simply checking for right answers. John also shares real classroom stories, insights into supporting neurodivergent learners in general education settings, and how AI can be used thoughtfully to support teachers without replacing human connection.

Well, hello John and welcome. Welcome to the podcast.

John Tapper: So glad to be here.

Lori Boll : Super happy to have you here and share all of your math inspiration with us. So to start things off, how did you come to focus so intensely on making math accessible to all learners?

John Tapper: So I started my career in an elementary classroom. I was an elementary school teacher for about 20 years and during that time about a third of the students, I worked in a public school and about a third of our students were on IEPs and it was a multi age classroom. So we had children from 6 to 10 years old learning together. So I got this approach by necessity that I had to be able to accommodate everyone who was there, whether they were younger or older, whatever their grade level. Didn’t really matter because we’re all together.

And then when I went to do my doctoral work in New York City, I spent time in a Lower East Side school as a math interventionist. And I found that working with children who are having difficulty with math was really interesting and fun.

But also I started finding that problems with math were way overblown. That was where I first really began believing that everybody can do math. And then over the years I’ve worked with a variety of students. I’ve worked as a math interventionist in the K2 school and I’ve done consulting work with a group called the I Team here in Vermont that supports children with really complex needs.

Those children, for example, who are deafblind or who have low recorded IQs and are autistic, who have multiple challenges that they’re dealing with. Most of their math was repetitive and not really focused on learning as much as memorizing and almost always focused on time and money out of a belief that was really practical. So the incredible educators at the I Team came to All Learners Network and said, can you help us with this?

And so I had the chance to do clinical interviews with a couple of dozen students and work on ways to make math accessible to them. And at that point I can honestly say that everybody can do math.

An extreme example was a child we consulted on who could only move her eyes. And we worked with her on eye gaze technology.

The difference, and maybe we’ll talk about this later, is that I really feel that research suggests that students benefit when they struggle a little with math and come to their own conclusions, that making it easier and giving them tips or tricks actually doesn’t do much for them mathematically. And it takes away the opportunity for them to struggle, which is really important if you’re going to learn mathematics.

Lori Boll (she/her): That productive struggle.

John Tapper: That productive struggle.

Lori Boll: That’s right. So much of what you said is so inspirational and important. Going back to your first teaching where you said that you worked to ensure that every student in your classroom who came in your classroom door was learning math.

I think that’s where so much of our education system right now, often people say, oh, that student’s on an IEP, so that student needs to do math with the learning support teacher, or that’s not my student. So tell me a little bit about that, about how you made that decision, that these were all your students.

John Tapper: Right. There’s a persistent belief somehow that math is different from other subjects and that math is hard and only some people can do it. And it’s a very self serving belief for mathematicians. But honestly, there isn’t anything particularly more difficult about math than any other subject.

There is in the way that math is taught. It definitely privileges certain kinds of kids. So the standard operating procedure for teaching math is, let me show you how to do it and then you do it a few times and then you’ll know what I know. And so there’s very much a sense of think what I think and think the way I think.

And unfortunately what seems to be true is that this works for a small number of children who look like the teacher because they have the same cultural and perhaps racial experience that the teacher has. And so think like me resonates with a few of them. It doesn’t even resonate with all of them.

In the United States, only 25% of the high school kids are math proficient, but a good deal of RTI research says it should be 95%. So the gap is in the teaching.

So when the teacher says do it like me, students who don’t have the same experience as the teacher, who aren’t white middle class folks, often have difficulty. So you have to flip the script.

And for me, this came back to some work I did with Marilyn Burns in the early 90s. But the notion that the learner really has to build their understanding of math. And this is terrifying to lots of teachers, especially elementary school teachers, because we really feel like we have control over what kids are learning. But in fact they still have to come and do the learning.

High school teachers know this because they have kids check out of their classes all the time. But when you change the approach to teaching, when instead of saying, do what I do, you say, well, here’s a problem. What sense can we all make of this? Now the work becomes the work of the learner.

And particularly in high school classes where we’ve worked, it’s transformative. From kids looking bored and sitting and doodling in notebooks, to kids up and around the room and writing on whiteboards and having conversations about math with each other.

The sheer number of minutes of math that kids are actually doing when we change the pedagogy, whatever their learning status, is much more impressive when the kids are doing the learning. And it’s the same with students who have learning differences. They need a chance to do learning for themselves.

And when they’re older, they’re so used to being spoon fed that there’s always a little bit of a transition. You know, how would I know how to do this? Well, let’s think about what you know and let’s talk to other people. Let’s work in a group.

I worked in a high school in Illinois. I was guest teaching and the teachers were not really buying into what I was selling, unfortunately. So I don’t like to demo teach because you watching me ski is not necessarily going to help you learn how to ski. But these teachers were not buying it at all.

So I offered to guest teach. They said, what do you want to guest teach? I said, you pick the class. And so of course they picked a pre algebra class, lowest performing. Half the class was on IEPs and they were really ready to watch me crash and burn.

But I had a really interesting problem and we talked about it and then they all went to the whiteboards to work on it. And every kid was engaged.

In fact, the classroom teacher said to me, even the kids who were not actually at the whiteboard talking about the math with their partners were at least watching what was going on, which was more than was happening in class.

And the most gratifying thing was that at the end of class, several kids, two groups of kids, went to the teacher and said, are you going to be erasing our work? And when she said yes, they said, could we please take a picture of it so we can finish this problem. And the principal said, I’ve never even heard of that. They were engaged enough to want to do it.

So whenever we work in classrooms where kids who were pulled out are brought back in and we give them an opportunity to be part of the larger group through a variety of techniques, it’s always good for everybody. It’s really good for the kids who are being pulled out. But it’s also good for the kids who are in the classroom.

Having a diverse classroom is not a bad thing. When I was an elementary school teacher, we had a student who was eight years old who had a medical accident and couldn’t speak. Things on his IEP were like swallowing on his own. And he had a nurse, a full time nurse, and he was mainstreamed into my classroom.

And I have to admit that when they told me he was coming, I said, well, what am I supposed to do with him?

Lori Boll: Right. I’m not trained in this.

John Tapper: Yeah. It was an amazing year. He would indicate his happiness to be around peers in a variety of different ways. But I think really important was the kids had this great experience of taking care of and being a part of a community that included someone with these sorts of disabilities.

When we were doing sustained silent reading, the kids figured out that since he couldn’t really read on his own, two of them every day would volunteer to be his readers. And one would hold the book up in front of him and the other one would track the text with her finger and whisper into his ear.

And there was like a waiting list for kids to be able to do this. And there was one particular day where they were reading and he started following the text on his own. And it was like this ripple through the classroom. Everybody stopped what they were doing to watch and share in this accomplishment, that he was actually participating by reading on his own. It was very powerful.

Lori Boll: I love stories like that. Let’s talk about neurodivergent students. What do you think the biggest challenges you see when teaching neurodivergent students in general education classrooms…

John Tapper: There are two issues that we try to address with the structure of our lessons. One is: how do I effectively create access for the student when we’re doing whole class learning, new learning?

If a student is only doing remediated learning, then they’re sentenced to always behind. So there has to be some time when they’re with their peers learning grade level content. And that’s a big stretch for some students.

Over and over again, we see that there are ways to get that done.

So one challenge is: how do I make a lesson? Let’s say we have a student who’s adding and subtracting numbers within 100, and they’re in a fifth grade class that’s doing work with fractions. How do we create an environment where that student can have access to some of that content and can work with peers?

And then the second is within the context of a daily lesson: how do we help the student do some just right learning?

So we have these periods in our lesson: main lesson, which is the inclusion piece where everybody’s together. Then we have menu where everybody’s still together, but they’re working on just right stuff.

Another story. There was a teacher in Maine who came to one of our workshops and she had three autistic students in her class that were pulled out for the entire math class. And so she got really excited when she heard about our stuff.

And so she and the special educators designed individual menus for these three students. So the class as a whole had a kind of menu with some individual variations, but these kids had their own menus. And the whole point was that they could be in the room with their peers.

I came to visit her class three months later, and they were there for everything. The launch, the main lesson, they had their own menu. They were a working part of that class.

And the teacher said honestly that once she got over having them there and started thinking about accommodating them in the classroom, the whole thing kind of unfolded.

And she also said that it made her think differently about all the students in her class because she asked the same questions. Not every kid is on board right after this exploration or lesson. So how can I help students who are at various levels who need challenge, for example, or who need to circle back to some content?

It helped her to think about them as a group, but also about their individual needs.

Lori Boll: Perfect example of universal design for learning, right?

John Tapper: Yes. A lot has been written about this. Actually, a woman who works at All Learners Network, Ashley Marlo, just wrote a book on universal design for learning with mathematics.

Lori Boll (she/her): Okay.

John Tapper: We explore those pieces.

Lori Boll: Yeah, I’ll try to check it out. It’s on Amazon.

John Tapper: I believe so. Yeah.

Lori Boll: Okay, I’ll try to add that to the show notes.

John Tapper: Great.

Lori Boll: Well, speaking of books, you have a book entitled Solving for Why. That’s right?

John Tapper: That’s a clever title.

Lori Boll: I love it. And so it centers on understanding the why behind math struggles. So why is identifying root causes so critical before moving to intervention or remediation?

John Tapper: So let me give an analogy. Imagine that you were going to a therapist and the therapist had a curriculum for everybody. And so they just did their curriculum for you. So there would be some people who would benefit from the curriculum you created. Here’s the curriculum for 40 year olds who are married and…

But of course, to be effective, a therapist has to understand the person they’re working with. And teaching is a stronger example of this than therapy is, because it’s an everyday proposition.

So you can’t effectively teach your students if you don’t understand how they’re thinking. Primarily you need to understand: what would a child be thinking if they came to X and Y conclusions?

Unfortunately, a whole lot of math curriculum and instruction is focused on: is the answer right or not?

But the rightness or wrongness of the answer is like an artifact. It has some utility. But a kid can get the right answer for all the wrong reasons and they can get the wrong answer and still really understand what they’re doing.

So the rightness or wrongness, a test where you just look at is the answer right tells you very little.

When we have teachers give a task and collect student work, we have the teachers do sorts of the work. And when we first started doing this more than 10 years ago, teachers would always sort the work by got it, almost got it, out in left field. But that has no usefulness for what you’re going to do next.

So very quickly we changed to: what are the strategies or misconceptions that are evident in the work?

And when we’re training our AI to do work sorts, it does the same thing. It looks for what are the strategies that students are using, the models they’re using, or the misconceptions that they have. And that gives us information about how to choose what’s next for each student.

Lori Boll So many schools really rely heavily on the intervention piece that you just mentioned, but I’d really like to talk about tier one instruction. What, from your perspective, does really strong tier one math instruction look like to actually prevent students from struggling in the first place?

John Tapper: Yeah. So first of all, it means tier one instruction needs to have what I used to call with my undergrads, Tapper’s golden rules. One, the learner does the work. And two, what the students have to say to each other is usually more important than what you have to say to them.

So tier one instruction needs to focus on the students making meaning from the math they’re doing, personal meaning, which means you have to resist the temptation to tell them what they should be thinking.

And secondly, there needs to be a whole lot of time when students are talking to each other.

I got to go once a week to a high school class locally where the teacher had agreed to teach this class. It was something like math 2, part 2, but essentially it was a class full of IEP kids that the school had given up on, and he had decided that they were going to learn about linear functions, they were going to really understand about linear functions.

And so he was dedicated to not telling them how linear functions work, having them drive that.

Now, there are high school teachers who are listening to this who I know are saying, yeah, good luck with that. But I want to emphasize that the school had basically given up on these kids. So he was free to focus entirely for almost a semester on just linear functions.

He would give them series of numbers: 2 and 4 and 6 and 8 and blank. And he would have them work at whiteboards in groups of three and try to figure out what went in the blank and how to predict what would happen in the future.

All of them were on IEPs with communication components, and all had written into their IEPs that if they got really tense, they could leave, take a moment and come back. So when I started going in September, it was like a revolving door. They were in and out and in and out.

And he would do this thing where they would do their work, and then he would have them walk around and look at each other’s work, gallery walk. And then they would stand in a circle. And they had to comment on each other’s work, what it showed them, what they thought was going on.

And this guy has no ability to be uncomfortable. We would stand there. The first time, it was over a minute. No one is saying anything. And he is communicating absolutely, I am not going to say anything. You have to say it.

I was so uncomfortable. I kept wanting to jump in.

But fast forward three months. Those sessions were really rich. Kids would have questions for each other. If a kid tried something in the problem they were working on the board and it didn’t work, it was not the end. They would try something else. Kids would talk about their successes and failures.

He started this thing for them to take notes because he didn’t want them to take notes that he was giving them. So the notes said, future message to myself, about things that kids wanted to understand.

And they built up notebooks with all these thoughts about how the line is a model for the function. They called the equation the formula for the longest time. They called the slope the number you multiply by. They called the y intercept the place where you start, because they developed all of these ideas.

And I interviewed the kids both individually and in focus groups throughout the year. And not everybody loved this style. There were definitely some kids who were like, I just want the teacher to tell me what to do. This is hard work.

But kids who you could not have imagined doing math were doing algebra, math with deep understanding.

There were four kids in that class out of 16 who actually turned out to be good mathematicians on anybody’s level. They had just been taught so poorly that they never had a chance to really develop their thinking. They took concepts in class and brought them way farther.

So to me, there was no tier 2. This was tier 1 instruction that emphasized the students had to do the work and there had to be lots of time for them to talk to each other about what they were finding out. That’s how you get the most students to access the math content.

Lori Boll: Yeah, that’s great. Well, John, you’ve really mentioned how you’ve gone into classrooms and worked with teachers. I’m curious what your organization does besides that, because I know you do a lot. So please share.

John Tapper: So we publish a lot of stuff. We publish blogs and articles. We’ve had articles in Ed Weekly and a variety of other kinds of journals. So we’re advocates for good math instruction.

We work with districts. Our favorite kinds of places are places that have really low math achievement. Usually they’re high poverty areas. And we work with teachers to improve math instruction.

And since math is so important to success academically, it changes outcomes. We’ve worked in a large school district out west, a poor performing school district. And over the course of three years, their measurable improvement is kind of amazing. High effect sizes, significant gains.

So we think about transforming, getting into a district or a school, transforming the math instruction over the course of a couple, three years and then leaving. But we want to put in place structures for constant improvement. Math committees, training of administrators so they know what to look for. What does good math instruction look like? Because really ineffective math instruction can look good to the uninitiated.

If the teacher’s using manipulatives and kind and encouraging, but only teaching some of the kids in her class and telling them what to do and how to do it, it looks great, but it’s not going to be effective. So we help administrators understand what to look for.

We also have developed over the course of a year and a half this kind of amazing AI tool. We don’t believe that AI is a good tool for students. In fact, one of my fears is that high poverty schools are going to end up with AIs while richer schools are going to end up with teachers. So our AI is an AI math coach.

And it’s designed to support teachers to make better instructional decisions and works the way we work so teachers can have a conversation with it, where they say, here’s my lesson from virtually any curriculum. How do I make it more accessible to these students in my class? And it will provide resources to do that.

I’d like to have a math menu so I can do just right instruction for the kids in my class. It will provide the math menu: games, reflection, activities, problems, practice for a wide variety of levels.

Essentially, if you tell the AI what levels your kids are working on, or even if you provide the AI with samples of student work, it’ll create the menu for you.

For special educators and for math interventionists, it’s an unbelievable tool because what we see is the preparation for teachers to teach math right now in the US, can’t speak for anywhere else, teachers are not being sent forth with enough preparation, especially special educators.

So our coach will help a teacher make plans. It’ll help write IEPs. A teacher can say, we get love letters about this all the time from people who are using it, I have an 11th grader, he’s still adding and subtracting within 100.

And then the coach, like a good coach, doesn’t just pop off some solutions. It asks more questions to understand that particular student and it saves that information.

So every time you come back and say, okay, well now he’s done this, what can I do next? The coach gives really good information.

We’ve beta tested the coach’s responses with 40 math coaches on our first round of beta testing, and then the second round was 100 special educators to be sure that the information that people were getting was useful and applicable. And it’s a really wonderful tool.

So when districts can’t have us come and work in person, which is economically sometimes the case, the math coach is a way to help support better instruction, particularly for students with learning differences.

Lori Boll: Yeah, yeah. I had the opportunity to play around with it and I was quite impressed with the thoughtfulness of the coach’s questions and how I could put in all the information to help design something that really worked for all kiddos.

John Tapper: So what’s interesting is that the coach’s questions, because we’re a PD organization, we want to improve teacher skill. That’s always our goal.

The questions that the coach is asking are a kind of PD in the sense that they teach you to think about, you know, if you say my student is a second grader who can’t subtract within a thousand, the coach will say, well, is this a place value issue? Do they understand how the number systems work? Are you doing things with regrouping that maybe aren’t working?

There’s a list of things and most teachers don’t think that way about approaching a difficulty. So over time, as you’re used to hearing these questions, it helps the teacher rewire their thinking about what they need to know in order to support the children they teach.

Lori Boll : Yeah, no, it is truly fantastic. Well, you are coming to Dubai.

John Tapper: I am. I’m very excited.

Lori Boll: I’m super excited that you’re coming. Tell us what you’ll be presenting about at the conference.

John Tapper: I’m going to be looking at the ways that student, well, first of all, the session’s called Solving for Why, which is the title.

I’m going to be talking about how student work and student thinking, how you can analyze that in order to figure out what comes next for the student.

So I’m going to try to get teachers engaged in some activities around math for themselves, to thinking about what it looks like when the learner is constructing their own understanding versus when the teacher is giving it to them and what the benefits are, and what that aha moment of understanding, of conceptual understanding actually feels like.

I’m very excited to be doing some international work again. I did a bunch of work for the Open Society Institute in Europe, in Eastern Europe primarily, in the former Soviet republics. And I love that work for a variety of reasons, but I’m always looking for where are there places where access might be problematic for students?

So a difference in culture or a difference in home might have influences that need to be considered. We’ve been doing a lot of work with second language learners lately, multi language learners. So how do we create access for them so that they can be doing the math that everybody’s doing?

So the idea of going to an international event and being able to talk to teachers from other cultures is very exciting to me.

Lori Boll: Yeah, it’s going to be fantastic. And being in Dubai, we have people coming from Europe, Africa, Asia. We even have someone coming all the way from Brazil.

John Tapper: Nice.

Lori Boll: Yeah. Yeah. It’s going to be an incredible conference. So we’re really happy you’re coming.

So I think that’s all we have time for today. But people can see you at our conference, so I’m happy about that. Thank you. John, thank you for your time and for sharing your knowledge with us.

John Tapper: Such a pleasure.