Rethinking Math for IEPs

Struggling to support your child with disabilities in math? You're not alone! This video features Sarah Noland, special education math specialist at Calvert County Public Schools, and Dr. Rachel Lambert, PhD, and associate professor in special education and mathematics education at UCSB, sharing their expertise. They'll cover practical strategies, helpful resources, and answer your questions about adapting math instruction for diverse learners.

To learn more about math, check out our article: Math Goals in an IEP

Full Transcript

I guess the first question I want to ask is quite a broad one. But what do you think a parent misunderstands about math? Math is a really challenging subject for a lot of people. Parents are not right. Math is challenging because we have this, like, very narrow idea of who can be good at math. It's like you got to be fast and you have to memorize things and you got to be able to basically know it before the teacher even teaches it.

When I ask kids what being good at math is, they say things like that. And adults have the same idea that math is about speed, and it's about memorization. And that's only a very narrow group of the population that can be good at that. And so when we're talking about neurodivergent kids, when we're talking about kids who take a lot more time to learn, kids who have different ways of getting there, then it's even more challenging, especially if the math classes are really narrow and how you can be good at math.

They only have a few ways you can demonstrate understanding, only one way to do it correctly. That's particularly challenging, I think, for students with disabilities. The Gates Foundation just did a survey of parents, and they asked about what's the most important topic in school, and math was the most important topic. And it was the topic that parents said most needed a total change.

They said in the survey that, in general, what they wanted to see from math classrooms as they were more engaging, the kids would be more motivated to do math. The kids would see math as relevant to their lives, and that... so that's what parents are looking for in general. And I don't think parents with disabilities are... parents whose kids have disabilities are any different.

But math is just really challenging because we have certain ways of teaching it that are... sort of don't work for most of the population, in my opinion. Can you tell us a little bit about those standards of practice, and like how that can help a parent understand what their child should be working on? So the standards of mathematical practice, or the teachers call them SMP, is... were designed in a collaboration when they wrote the Common Core State standards between mathematicians and math teachers and math researchers.

And they're basically how you engage in math, not what you're learning, the multiplication, subtraction, but how do you math? How do we math? Like, what is it that when we're mapping and not just like when we're little kids doing math, but when we're like, how do mathematicians engage in mathematics? So the first one is my very favorite, which is to number one, make sense of problems and persevere in solving them.

And that is my number one most important goal for students, because when you present a challenging problem to students, something that's going to... they don't know the answer right away. They need to take a little bit of time to think about it, ask a friend, start visualizing it. Use some manipulatives. This is a basic practice in mathematics. We want to be able to give kids problems that they don't know what to do right away, because that's what math is.

Everybody gets stuck in mathematics, including mathematicians. What do you do when you're stuck? One of the... I did a study on... with and on dyslexic mathematicians, and one of them told me that he thought his dyslexia helped him in math because it taught him how to keep going when he was stuck. Like, he's like, when you're dyslexic and you're dealing with a system that's not designed for you, you know how to keep going.

You know how to work around things. And that's what helped me become a mathematician, he said. Because that's what you need to learn how to do. This problem is challenging. I am going to keep working, and I'm going to find a way through it. So how did those SMPs, the standards of mathematical practice, how does it fit with it?

When we think about the design of how we're writing math goals and objectives, when we start incorporating and thinking about the standards of mathematical practice and how we can connect those to the IEP goals and objectives, we're creating a more inclusive IEP where the student and the teacher kind of see a connection with like, okay, this is how this is what I have to build within the student to build the sense of belonging within that math community.

And I have just found with teacher after teacher, learner after learner in this district, when the IEP includes objectives that are connected to these SMPs, it is more relevant. It creates a more relevant math learning for the student and connected to what's happening in the classroom, versus if we get very focused on these discrete skills.

So what I found is if you have a student in general and they have a skill that is very different than what's happening within the general education curriculum, and it cannot be naturally embedded that it does create this very disconnected feeling with instruction. And then the question comes up of, you know, when am I supposed to provide this instruction when it is so not connected?

And... but that's why if you build in the SMP's depending on the students' needs, if you connect them, it becomes this conversation of like, oh, I can do that. So it's been really interesting. And so it's not every objective that I do that. It depends on the student. Kind of depends on what the goal is. You know, for the student.

But it's been one that we've seen a lot of just promising results, for programming and making programming decisions for students in general. I really like your math criteria, but it still matters. Could you explain that a little? And, maybe, like, give us an example of how you would apply it to a goal? It's a question I get all the time.

And so I'm thinking, well, what do I think about when I'm thinking about if a goal is good, and so I try to make an acronym to help. So the first is that is M-A-T-H. So it's M-A-T-H, five things. The first is that it's measurable. And being measurable is super important because we need, as teachers... And I was a special education teacher for... and inclusion teacher for ten years.

So I was a teacher for a while. And you need ways. It needs to be eight. You need to be able to collect data on whether the student is improving in this area. And it needs to be a way that you can collect data that works for you as a teacher, because teachers are very overburdened, right? So it needs to be measurable and also in a way that kind of works and fits with the way the teacher is working, and the student, it needs to be ambitious.

And ambitious is a word we use in math education. But there's a word called ambitious science, too ambitious science and math instruction, which basically means we're really trying to engage kids in mathematics and science, not just at, sort of lower levels of maybe memorization, but the highest level of engagement. So in science, we're trying to get them to like, do experiments and create experiments.

And in math, we're trying to think about engaging all students in problem solving, thinking visually with mathematics, all of these things. That math is really fun and engaging. We don't want to wait to do that stuff until kids are in college. We want it to be part of kindergarten. So ambitious means that it's towards a really challenging level of mathematics for all kids.

Towards access is the next one, and that's to keep in mind that IEP goals really are not just about learning one content thing, one small, narrow thing. They are supposed to be towards access and participation in general education. So we have to think about whether the goal is going to be useful to help a child participate in general education.

And often, goals in mathematics are like three grade levels behind. And sometimes, like they're not about the math that that child is going to be engaged in the general education. And this is really problematic because... and parents need to understand this. If your goal requires your child to be pulled out to get instruction, you are creating a situation where the child is going to be pulled out to get instruction, because now the teacher is legally required to follow that goal.

So in the example in... I have a book that has a chapter on writing IEP goals. And I think back onto this child that I worked with when I was a classroom teacher, and he was a fifth grader. He came to me with a goal: subtraction. And while I think subtraction is really important, as a fifth grader in my class, which was a full inclusion, no pull out unless I needed to pull him out for IEP goals, I believed I needed to work on fractions with them because it was more important and more likely to engage him in the class.

Like if I'm working on subtraction, the class isn't working on subtraction. I have to find some other way, hand in my calculator. I need to be moving on and making sure that I'm working on the math content that's going to help him engage in the math classroom. So the next one is high leverage. Praxis is the H. And there's two parts here.

And basically, is it worth your time is the question I want them to ask. And that, in general, is kind of like the question I think parents should ask: Is this goal worth my child's time and your time as a teacher? So a high leverage goal means we're picking either if we're going to do a math content standard, we're picking that content area that's super important, super high leverage.

So, fractions, for example, predict achievement in algebra, fractions in terms of understanding equivalent fractions. That becomes important in math all the way through. That's super high leverage. Understanding the number line is a very high leverage because it predicts achievement all the way down the line. And the number line is a model that's used all the way down the line.

Right. So we pick a content standard that really matters, or a standard mathematical practice that we really think will be high leverage. And then the last one is a stakeholder input, meaning that really good IEP goals are not made alone, and they're not made before the meeting. They're made in discussion and collaboration. When we're collaborating with parents, when we're collaborating with general education teachers and special education teachers, and we're really trying to figure out what wasn't the weakest point in the Woodcock-Johnson, and then make a goal line about that.

But like, what is really needed and what do we all want? What does this child want? Hopefully, when a child is in a separate classroom and they... what we know is that they have unambitious goals, right? That very often the goals provided for math, counting over and over, and 1 to 1 correspondence, and... because often the IQ test shows that the child does not understand 1 to 1 correspondence.

Right. And so then they say, okay, if they don't understand that, we have to understand that before we can do any other math. Right. And so that's what they focus on forever and ever. So we... is there a way to use your math acronym to kind of try and get that goal to be a little bit more ambitious?

Doctor Paulo Tan was a colleague of mine, so he's a professor in method and disability studies, and he also is a parent of a child, who had needed... who has significant support needs, who does and has autism. And he himself, even being an expert in these areas, had a lot of challenges in dealing with low expectations and goals for his student.

And he tells a story about in one IEP meeting in fifth grade, where they there is the assessment of the school, showed that the child did not couldn't identify one digit numbers, but he knew that wasn't true because he lives with this child and works on math with the child all the time, but yet faced really resistance in the meeting towards, that that was the goal that was proposed by the school.

And he was like, no, my child already knows how to do this. But what he did to really break the sort of logjam that kind of like a professional logjam that occurred there was he said, what are our goals like in math? What? Like what? Not just this identifying digits. What do I want for my... I'll tell you what I want for my child.

I want my child to engage in mathematics that makes sense to him. That's meaningful to him to learn to do things that are going to be helpful to him in the world. Like, I have these big goals for him and I'm not... These little goals are not going to cut it because this is where I want to go, and that's when the rest of the team was like, Okay, that's where we want to go to.

Like, well, let's all go there together. So my first thing, and this is, you know, from his work, Doctor Tan, is that it's about creating a collective vision of where we want that child to go. And I think this is particularly important for students with significant support needs, because the whole team has to say, we want... we have a vision of where we're going to go here.

And mathematics is not just this small memorization thing. Math is a part of this vision. We want kids to be able to go to the store. We want kids to be able to fill out time cards. We want kids to be able to think about mathematics and hopefully understand statistics that are presented to them, like making a bigger vision of what math is and what math can be, is a part of getting goals that are higher, that are towards access, that are high-leverage goals.

So one thing parents can advocate for is, is everybody in? This will be included in professional development, in math, everyone together, special educators, and along with general ed educators, so that we can use their expertise together. So this is something I advocate for. We have a class at my university at UC Santa Barbara that's math methods for special educators.

It's their own class where we focus on mathematical development so they can understand how kids learn how to count. And all the way up to say, algebra and beyond. So that's one important thing is to understand the content. And you can also... because if the math teacher, if the special education teacher changes the way they teach math, then the goals will also change.

So they can... either one can be leverage. Let's change these IEP goals to make them more meaningful, more high-leverage. But let's also change the math instruction. So it's more focused on what students know, more focus on problem solving. The two will influence each other. Sometimes the schools don't want them to have calculus. Sometimes it's the parents that don't want them to.

What do you need to know about adding a calculus? If you have a calculator, where do you start with that? And is there anything to look out for? One of the things that is a learning curve for many of our teachers is to say, starting and really end of second grade before they get into third grade, we need to be stating, do they need the criteria for that?

And can they get that accommodation? And we have teams that are reluctant to consider that because we want to delay the use of a calculator, to give them continued time just on that normal sort of progression of building fluency with single digits. I totally get that. However, for some of our students with disabilities, I would say that what we need to be considering more is those tools.

Because the tools are what are essentially reducing that barrier, right? That we are leveling the playing field for the student to engage in grade-level math with the tools I would... I'm okay with it, and I'll talk with my teams about not giving them the calculator in third grade. Just make sure they have the tools. Make sure they have the number right.

Make sure they have the fraction bars. Make sure they have connect counters. Make sure they have the hundreds chart. The addition chart. Let them have those things. Put them in the box. Write them in box that that's what is allowable because that's what they use in instruction. And make a statement that says, the calculator is not currently being used through third grade.

I think that's appropriate again, depending on the needs of the student. So most of the kids, though, I would say starting at the end of fourth grade, is when the calculator becomes pivotal because again, it's about leveling the playing field. And if we get into fourth grade and we're looking at standards that they have to multiply multi-digit numbers, they have to divide, they have to multiply decimals, you know, things like that.

If their access and their tool to meet that standard is going to be the use of a calculator, I think that's okay. Do I want them to understand it? Absolutely. Do I, as a teacher, as an educator, need to be strategic with how I'm building in the use of a calculator? Absolutely. Do I want to build in routines like you're going to solve this?

First, I'm going to ask you a bunch of questions. Then I'm going to give you the calculator and have you check your work. But it's important for some of our students that they start working with the calculator in fourth grade because it gets them proficient with it, and they continue to use that calculator in middle school if they go to middle school, if a student goes all the way through elementary school, never saw a calculator, and then they go to middle school and they get a counselor, they're not going to know what to do with them.

And then that's when we really see a lot of impact with calculation. And it's because some of our students are still working on addition, say, a kid with an intellectual disability, and they're still working on basic, basic adding and subtracting. But there may be a middle or high school. And how can you write a goal that then could be used in a general education classroom?

Has that kind of work for many parents, that's impossible to imagine. So we have a child who really needs to work on it, like basic number sense. They're in a middle school classroom. We want to increase inclusion, but also meet their specific needs. Right. So this is a giant problem. So, a couple of things that can, I think, depending on the kid, I would recommend different things.

So one way to work around this problem is to write a goal focused on the standards of mathematical practice. So a goal that's more about that child's engagement in the classroom, their participation in the classroom, and what they're doing, the how of how they're engaging their talk, their problem solving, that collaboration, then the content that could be the strategy that a parent wants to go with.

I want everyone to focus on how my child engages in math class. But you could also have that and content goals. But sometimes you might need more than one content goal where things strategically about which you want it to be. So you could. If you want the teacher to focus on the number sense that the child still needs to develop, then I would advocate for a number sense goal, but maybe also advocate for a goal that's connected to the mathematics of the classroom.

This is pretty tricky, but there are ways to connect grade-level mathematics to the mathematics a child is learning. So, for example, if you think about algebra, algebra has a ton of different goals in seventh grade. But one of the main ideas about algebra is equivalence. So the idea that, you know, a plus b equals C, right? It's that it's a bunch of equations.

And if you don't understand that these two sides are equivalent, you can't do any of the algebra. That's a core idea. But that idea also can be used, with kids who are working on earlier grade level things, they might not be working quite on a variable, but one thing we do with kids is we'll say things like, eight plus seven equals blank plus one.

This was a... so kids, and actually, the older they get, this is like all kinds of kids will write 15 in there because they think the answer comes after the equal sign. They think the equal sign means the answer comes next. Not that these two things are equivalent. So we do a lot of work with even. It's very simple addition, subtraction, multiplication.

But it's about understanding that those two little lines, they mean that these two things are the same. So you can do work on basic number sense that is connected to the most important ideas in algebra. What I would say are the core ideas of algebra, which is... one of them is equivalence. But like I'm saying, you can design instruction that begins.

It's about number sense, but it's also about this core idea of equivalence. So this is about IEP goals. But this is also about inclusion in mathematics. It requires a lot of understanding of mathematics to do this work because you need to be able to say okay, algebra. What is the core idea here? I want this child to come out with.

They're not going to understand everything about algebra in the seventh-grade class, but what is core and important, and it might be equivalence. It might be matching graphs with equations. It might... It's you have to pick something that really matters. That's ambitious. That's the high leverage. Right. But that requires mathematical understanding. And so sometimes that can be pretty tricky for parents.

And it can be tricky for teachers, which is why I continue to advocate for more professional development for special educators. In a lot of people, the first thing they want to do is go to skip counting, and that is as challenging as any counting. Right now, we're going to learn another way of counting. Whereas using a multiplication table ties into a visual area method.

Right. And so other ways that you can push towards using those kinds of strategies in multiplication and division, often people are like, well, you can't start that until you've mastered the others. In third grade, you start multiplication. You also start early fractions. And kids are often so happy in math in third grade, because it's like we put those big numbers in those procedures to the side, and now we're doing multiplication.

And so fresh and so new, and can be in... multiplication can be so visual for kids. There's an intervention sort of routine with multiplication that I've used for kids who need more help with it. And it is, I'll say, go, make me... I give them lots of blocks, make me two towers of three blocks, two towers of three blocks, and they make it.

How many blocks? Six. Then we do: make me four towers of three blocks. And then those blocks become arrays. They become columns. They support skip counting. But then, if a kid needs to count by ones, they can count by ones. But if they can start to skip count, it supports the development of skip counting, like what's called an array, which is like a box, but it has to have all the little boxes filled in for kids when they start, or has to be made out of blocks.

Or we take pictures of like, things in the world. Like when I worked in New York City, we used to go on little field trips and take pictures of skyscrapers and then count the windows. That was... it was... for some reason we found some multiplication. So what I'm saying is that multiplication is easier for a lot of kids than subtraction.

So that's why we don't hold kids back, because they are. I've seen a lot of kids who can do higher mathematics but can't count accurately. So as parents, we need to understand math is not a ladder where they have to understand every single thing before they move on. It is not. A better metaphor is that math is a house, and some walls are load-bearing and some walls are not, certain things like number sense.

Understanding how digits work place value in a meaningful way that really matters because kids can't know how numbers are bigger or smaller without that. That's a load-bearing wall. But we have to figure out what really matters and what we can put to the side and just keep, because we're going to keep building this house. Now, my metaphor, we're building giant... many layers and stuff.

That's... but so let's talk about the idea of functional math, because that comes up quite a lot. Like people say, we want this to be functional math, or we want to... we should have at it. I focus just on functional skills. And the question is, is it all math functional? Yes. Yes, it is all functional.

And what is functional? Is it that we are still teaching counting coins, or is it that we're teaching, do I have enough money, and I have a bank card. So I think when I think about functional math, my brain defaults to that. Thinking of, like, I have to teach them counting coins.

I have to teach them, you know, time to the hour, like, because how do I function in life? But again, it goes back to, in order to function, if I think about really, truly what is functional math, it is functioning within our world, which is math. I talk to kids all the time. They're like, I hate math.

I said, sorry, kids, life is math. Math is life. You can't get away from it no matter what you do, so you might as well make sense of it. So I think that's my big thing, like what? What is functional? And maybe it's individual. Like for a student, what is functional for that student? Is it for that student that it's supervising?

I think that's functional. If a student isn't supervising for three, I'd say, okay, we've got to get them supervising the three at least, because I want them to be able to know that instantly. So I feel like you said, I think it is all functional. And if we just... if we kind of stop saying functional and just say what?

What are the math skills that the student needs to develop so that they can be a stronger member of the community, or they can be independent? What are the skills that the student needs, that will lead to independence?