Practical Access Podcast

S12 E1: Adapting Curriculum Tasks and Materials in Mathematics to Specific Learning Goals

Season 12 Episode 1

In today's episode, Drs. Lisa Dieker and Rebecca Hines have a conversation with Sarah Powell. Sarah Powell is a Professor in the College of Education at the University of Texas at Austin and Associate Director of the Meadows Center for Preventing Educational Risk. Her research, teaching, and service focus on mathematics, particularly for students who experience mathematics differently.

Powell discussed practical tips for teaching mathematics to students with disabilities. She emphasized the importance of understanding students' foundational math skills and using research-validated practices like vocabulary development and mathematical representations. Powell highlighted the need for extensive practice, suggesting that students who struggle with math may require 10 to 30 times more practice opportunities than typical students. She also mentioned the potential of AI in enhancing math education but stressed the importance of conceptual understanding. Powell concluded by reassuring new teachers that anyone can be an effective math teacher with the right knowledge and strategies.

We love to hear from our listeners! If you have any questions, feel free to reach out. We look forward to receiving your questions on our Twitter (@Accesspractical) or Instagram (@Practical_Access).

Powell’s bio: https://education.utexas.edu/faculty/sarah_powell/ 

Here's a free word-problem intervention developed by Powell and colleagues: https://www.piratemathequationquest.com/

Here is a website with many great free and downloadable math resources: https://mathspiral.com/ 

Powell’s Recent Publications:

Rojo, M., Gersib, J. A., Powell, S. R., Shen, Z., King, S. G., Akther, S. S., Arsenault, T. L., Bos, S. E., Lariviere, D. O. & Lin, X. (2024). A meta-analysis of mathematics interventions: Examining the impacts of intervention characteristics. Educational Psychology Review, 36(9). doi:10.1007/s10648-023-09843-0.

Powell, S. R., Moore, C. E., Vander Tuin, M., Fall, A.-M. & Roberts, G. (2024). Investigation of the initial feasibility of extended mathematics read-alouds used by kindergarten teachers. Frontiers in Education, 9(1379491). doi:10.3389/feduc.2024.1379491.

Lin, X. & Powell, S. R. (2024). Development of a fraction vocabulary measure. Assessment for Effective Intervention, 49(3), 138–147. doi:10.1177/15345084231202407.

Lariviere, D. O., Powell, S. R. & Akther, S. R. (2024). A synthesis of pre-algebraic reasoning interventions for students with mathematics difficulty in grade 6 through 8. Learning Disabilities Research and Practice, 39(1), 4–17. doi:10.1177/09388982231222179. 

Lisa Dieker:

Music. Welcome to Practical Access. I'm Lisa Dicker

Rebecca Hines:

And I'm Rebecca Hines and Lisa, I know how excited you are about today's guest because we both know what a problem today's topic can be for teachers today, so why don't you introduce who everyone has a chance to listen to?

Lisa Dieker:

Yeah. So we're really excited to have with us, both a friend and a colleague, Sarah Powell, who is at the University of Texas at Austin in the College of Ed where she holds the Audrey Rogers Meyer Centennial professorship in education. And I'm giddy because she loves mathematics and kids with disabilities. So welcome Sarah, and we're excited you're here.

Sarah Powell:

Thank you so much, Lisa. And thank you, Becky. I'm very excited to be here as well.

Lisa Dieker:

Well, so you know from the title of our podcast, it's focused on practical tips for teachers, parents, anybody else that might want to listen. And so we're excited to have you kind of share some of that wisdom. And so I'm going to start with a really, I think, a fairly simple question. But when you think about teachers working with kids with disabilities, what would be the first thing you'd want them to think about when a kid is struggling in mathematics?

Sarah Powell:

Oh, well, that's a loaded question, but I'll try to provide a somewhat simple answer to me, when I work with teachers, the first thing that's really important is knowing where students are in mathematics. Mathematics is cumulative, so easier math skills are really important for later math skills and so for all of the students in your classroom, or maybe it's all the students who are in your small group, or even if you're working with students individually, really understanding where they are in mathematics, what they understand, and then where their opportunities for growth are. That's going to be really, really important for designing effective math instruction for those students. So I would say that's a good starting point. And then the second big thing would be to have a toolbox that's full of some of what we would consider the research validated practices in terms of mathematics instruction, and we can probably talk about those throughout this podcast, but understanding what are some of the go to strategies that can go alongside any curriculum that will will be very important for helping improve students math outcomes.

Rebecca Hines:

Yes, that's a great point about the cumulative nature of math. So I'm going to ask you to kind of tie that into the tools question. So a teacher gives this pre-assessment to determine exactly where a child is, as we know kids who struggle in math because it's cumulative, they get farther and farther and farther behind. So when it comes to those tools, what is your first tool that you would use as a teacher when you realize

Sarah Powell:

Yeah. someone has reached his or her threshold in any given moment, and while everyone else is moving on? Oh, that's a really good question Becky. So, I'm not going to give you one. I think I'll give you two. So when I work with teachers, often there are two research validated practices. One is emphasizing math vocabulary, and the second is using mathematical representations. And I would describe those, I can probably think of a better way to describe them, but I would usually describe them as lower hanging fruit, like these are things that you can start doing with your students next week that typically are going to be important for improving math outcomes for students. So first vocabulary, it might be interesting to be tuning into a podcast talking about mathematics, and the first thing we talk about is vocabulary, but math is an entire. How do I want to say it? Like math is an entirely different academic language than students are usually used to and so we have to make sure that students understand that academic language in math, so that they can be what I would consider a full participant in the math classroom. So, if I have a student who is struggling with mathematics, one of the first questions I might ask is, well, why are they struggling? Is the language of mathematics a barrier for these students? And so it could be that as a teacher or as a caregiver who's working with my own child, maybe I need to address this idea that there are hundreds of math vocabulary terms at every grade level that a student has to know in order to be able to talk about math, to write about math, to read within mathematics and to answer, for the most part, most mathematics questions. So I'd say vocabulary is one of the first tools that I would want teachers to pull out of their toolbox and start to build math vocabulary with students. Then the second one, which is often talked about in mathematics is this use of representations. Um, some people call this the concrete representational abstract. I typically prefer the concrete pictorial abstract, but the idea is that you are using a lot of different representations to really get at what the mathematics means. And so those representations could be hands on tools. Those could be store bought manipulatives, but they could also be paper clips and candies and pens and pencils, they can just be things that are laying around the house. You can use those as math manipulatives, but with those math manipulatives, students can touch and move those things to see different concepts and procedures in math. The representations also include a lot of drawings that students might be doing or that teachers might be doing. Those drawings could also include graphic organizers. That's another visual that students might need to understand math concepts and procedures. And then, if one of the things that came from Covid was a good thing, we have now an entire world of mostly free virtual manipulatives that we can access on the phone or maybe on a tablet or even on a computer. And students can use, there's dozens of them, probably almost 100 at this point, different types of free virtual manipulatives to also understand math concepts and procedures. And I say these representations are important, because if students are struggling with math, there's probably some gaps in what students understand in terms of math concepts or procedures, whether that's with addition and subtraction, geometry, fractions, algebra, you name it. And many times, students don't have a good idea of what the math means, because they haven't seen the math beyond just numbers and symbols and so bringing in those representations, it's something you could start to do next week, and that could hopefully start to help students improve their understanding of that math content.

Lisa Dieker:

Yeah, and so I love that that you went to vocabulary, because I think, I think much like you and have had the privilege of co-teaching with some really great math professors and teachers really learning from them and with them, and yet, you know, I know you have a an article coming out, it looks like in teaching exception children on intensifying the vocabulary for kids, what do we do? Because I know you believe in dialog and discourse as part of mathematical instruction. What do we do with those kids who struggle with using that language and adapting those tasks? What have you seen teachers doing for those kids who you know can't recall that right word, or really struggle with that type of language, or struggle with communication? What are some tips you might have for teachers in that regard to adapt what they're doing?

Sarah Powell:

Yeah, that's a really good question, Lisa, and there are probably many directions we could go with this in our intervention efforts, we just practice, I'll say, the heck out of math vocabulary. We're practicing it every day. But not only are the tutors using that vocabulary, but it's really important that students are using that vocabulary, because we have been in some situations where we see that the teacher in the classroom is doing a real nice job with math vocabulary and using the terms with precision, but then students don't always have an opportunity to interact with those terms. So, this is where asking students a lot of questions, so those checks for understanding are important anyway, but getting students talking about math, whether that's answering a question, maybe that's doing a turn and talk to a partner, but if you are doing any small group discussions or partner discussions, giving students specific terms that they could use in their explanations. So, we do a lot of work in word problem solving, and one of the things might be, I'd like you to turn and talk to your partner and talk about why this is a change problem, and use the word increase or decrease in your explanation, right? So right there we're starting to give students some of the terms that might be important to use. And then we've also done this within mathematical writing. We've been asking students to use math writing to explain what they know about word problem solving and some other math content. And we have a word bank. These are some of the 12 terms that you might choose to use in your mathematical writing. And so giving students the opportunity to use those terms. So I think just starting out in terms of putting some parameters on the terms that students could use, and then hopefully they'll be able to go beyond that once they have the foundation down.

Rebecca Hines:

That's a great suggestion. Thanks, Sarah. I have a little curveball for

Sarah Powell:

Oh, I like it.

Rebecca Hines:

Lisa and I work often with schools and teachers and districts in the area of inclusion, and math teachers, Lisa that I run across, largely hit a barrier. When, as you mentioned earlier, they understand that a student with a learning disability, for example, has potentially the analytical skills and maybe even the vocabulary skills at some point, let's say somebody has helped remediate that, but they're still performing well below grade level. Do you have a a specific online tool or any kind of online remediation activities that you would recommend for those teachers, really, at any grade level?

Sarah Powell:

Yeah. So, this is a really good question, and I'm probably not going to answer it in the way that you want me to answer it. So, as a researcher, I really try to remain what I consider curriculum agnostic, so I don't typically recommend specific programs. I also don't want anyone to get mad at me for recommending or not recommending. Yes, yeah, but what I will say is, I'll answer this a little more broadly, math learning occurs through practice, and that's actually true for all learning. Like you don't learn things unless you're practicing things. And when we see that students are struggling with math with or without a disability, those students either haven't had enough practice on specific content or haven't had the right practice right and maybe that's the right vocabulary practice, the right practice using representations, the right practice on word problem solving, the right practice on fluency. And so, all practice is going to be helpful for students, whether that's through a technology based program, or whether that's a paper and pencil task, or whether it's more just a dialog between teacher and students, but we have to engage students in practice. And there's usually from the American Institutes for Research. They have some content that probably some of your listeners have heard from the National Center on Intensive Intervention, and there they will talk about that students who have difficulty, particularly difficulty in mathematics, need a lot more practice opportunities than students who don't have difficulty with mathematics. And sometimes the stat that I've seen thrown around out there is 10 to 30 times more practice opportunities. And so, as I've thought about this, and I've talked about this with teachers, that's a tremendous amount of practice that the students who struggle with mathematics the most need and like as I think about the example of pick on you Becky, if you're a strong math student, and maybe we're working on adding fractions with like denominators, if you get that content and 10 problems, great, right? But if I'm struggling with math and I need 10 to 30 times more practice opportunities than you did to learn how to add a fractions with like denominators, I might need 100 practice opportunities where you got the content in 10. And the thing that I always see that just is so overwhelming to me, I think, as a person who works in math, is that students who struggle with math, they typically not only struggle with math, but they also struggle with working memory, they struggle with reading, they struggle with language, and often their processing for working through a mathematics problem is slower than a typical performing student, and so you're just speeding through these problems, and you may solve 10 problems and the time that I solve three, yet I need 100 problems to learn what you did in the same amount of time, and so and so, I think just carving out practice opportunity is key. And as we think about trying to keep students on grade level content for as long as possible, knowing that some of our practice opportunities are going to be on grade level content, but some of them are probably going to have to go back and pick up content from previous grade levels, knowing that key idea that we talked about at the very beginning, how math is cumulative. So I can't just practice fourth grade math. If I'm struggling with math. Often, I have to go back and practice second grade math and third grade math so that then I can be proficient with that fourth grade math. So, carving out the practice time, carving out the way that students practice, whether that's, you know, through a specific program, or just some teacher created materials. I mean, I often say, if you've got a whiteboard and you can write math problems on there, and if you know how to explicitly teach those math problems, that's all you really need. But the practice is key, and carving out those practices practice opportunities is absolutely essential.

Rebecca Hines:

I definitely agree with the practice piece, and it's true, really, of every content area. So, I respect that idea of not I also am not

Sarah Powell:

It is, yeah. in the curriculum business. So, is it fair to say that a good takeaway for teachers might be to look at the resources available in their current curriculum, because often there are online practice materials. Yes.

Rebecca Hines:

Whether textbooks.

Sarah Powell:

Yeah.

Rebecca Hines:

But to identify those self grading that, I think that's why I always lean towards online.

Sarah Powell:

Yeah.

Rebecca Hines:

Or computer based, because you're self grading and the teacher can also

Sarah Powell:

gives you that information very quickly.

Rebecca Hines:

Right, so so you do get that instant feedback. So, we can agree that that maybe the first step is for a teacher to go and identify what in their school's math curriculum, what available tools there are for remediation.

Sarah Powell:

Well, and I often they've got textbooks and a bunch of other materials and probably a lot of apps that the school has invested in that they can use. And as I think about teacher professional learning and a lot of the efforts that we're doing to support teachers, I will say that it's not the materials that matter as much as how you use the materials. And so that comes back kind of full circle to something that I teased at the beginning about research validated practices in mathematics. The What Works Clearing House, about two or three years ago, came out with a really wonderful, easy to read practice guide about how to assist students who struggle in math across grades K through eight, and there they recommend, I'll say six practices. I usually distill it down into five. The first is focus on vocabulary, which we've already talked about. The second is a focus on use of representations. We've also already talked about that. The third is being systematic with your instruction, which often talks about being very explicit with modeling and practice and the support we're providing to students. And then the fourth and fifth practices are fluency and word problem-solving. Now they also list number lines as a sixth research validated practice. I usually put that in that representations category. Not everyone would agree with me on that, but I think five is easier to remember than six. That's why I do that. So, if you are using intervention X or intervention Y or intervention Z, or you are writing problems on a whiteboard, if you are teaching those problems explicitly, if you are bringing in representations, if you're focusing on the language of math, if you're helping students build fluency, that's that ease and accuracy with mathematics, and if you're bringing in a lot of practice on word problem solving, you're hitting upon all of those research validated practices. And that's the sweet spot. That's what we need to do, because intervention X is not doing the work how we interact with that intervention X, that's the most important thing in mathematics.

Lisa Dieker:

I love it, and I agree 1,000% with everything you've said. And I really enjoy that that, you know, narrowing it down to five. And one of the things, a practical thing I have seen, and I think goes with what you're talking about. So I guess I want some affirmation is I know some teachers who, when they assign homework, they actually draw a line and give the kids some kind of site to go practice beyond the traditional program. And yet, I love that. I've seen some really good co-teachers make sure kids have errorless learning, because you don't have a lot of chance to make mistakes, because if you make it wrong 10 times, now we gotta go a million and undo that thinking. So. So, I was curious about about your thoughts about both errorless learning, and really, I think I'd be remiss if I didn't take advantage of your expertise, because I don't know about you, Becky, but every teacher in America, if I say the word kids with disabilities and fractions, there's a groan across the country, so I would love to know your thoughts on on

Sarah Powell:

I thought you're gonna say word problems.

Lisa Dieker:

Yeah. Well actually...

Sarah Powell:

Yeah. probably both emit groans.

Lisa Dieker:

Well remember, we have a really strong background. Our discipline tends to have a strong background in literacy.

Sarah Powell:

Yes.

Lisa Dieker:

We tend to not have a strong of a background in mathematics. And I think, you know, teaching fractions is hard for anybody, but if you're limited in your math knowledge, and you're co-teaching or collaborating, so errorless learning and the role of the co-teacher in somewhere like fractions, can you give us some guidance?

Sarah Powell:

Yeah, so I agree fractions are a stumbling block for a lot of students. And you're you're right a lot many teachers, although I've seen some really excellent teachers who do a lot of really great support in fractions. And it's fractions are so important, because fractions, many people will describe, is kind of the the next step to algebra. So, as I think about that cumulative pathway of mathematics, we can start with early numeracy, and that's counting and early comparison, and students have to have strong skill there in order to be successful with what is often thought about is the operations, particularly around whole numbers. So how do you do early addition, subtraction, multiplication and division? Then, that it opens the door or closes the door to success or challenges with fractions, and then fractions either opens the door or closes the door to algebra. And so really, that's a pathway pretty much across the grades pre K through eight, in terms of what are some of the real essentials in mathematics that are also going to stick with students as they move into adulthood. Um, so fractions are tough because probably most people, including myself as a learner of fractions, did not have all of the exposure to the tools and the strategies that students are expected to know now. And so there are three models of fractions. There's models according to their length, there's fractions according to an area, and there's fractions according to a set. Not every teacher knows that, because in schools, teachers may have only learned fractions according to their area because they just learned a lot about pizzas, pies and cookies and cakes, and so on. Um, and so really trying to, I think being a teacher of mathematics, you have to do two things, you have to not only know how to teach, so we've talked about some of those instructional strategies already, but you also have to know how to do the mathematics. And not every teacher out in every school went through a pre-service teacher preparation program, where they even had dedicated math coursework. Or maybe if they went through an alternative certification program. Maybe they didn't have an entire module on the teaching of mathematics. Maybe they had just one or two sessions on that. And so teachers have to have both of those buckets, that pedagogical knowledge bucket, and that content knowledge bucket very full in order to meet the needs of their students. And so if teachers don't feel that comfortable with fractions, that's okay. There's a lot of free resources out there. My team and I are just one of the teams that do a lot of video work to show how do you use fraction tiles to help students subtract fractions with unlike denominators, and so on. So, there's a lot of really awesome resources out there, but it's just taking advantage of those resources and building your own content knowledge bucket, so that then you can share that information with students and also help students when they do struggle with fractions and say, You know what? Maybe I need to show a different manipulative here, or maybe I need to use a strategy for finding multiples that I hadn't thought about before. So, the content knowledge piece is just as important in teaching of mathematics as the pedagogical knowledge piece.

Lisa Dieker:

Love it.

Rebecca Hines:

Sarah, another curveball. So my final question for you is.

Sarah Powell:

Yeah.

Rebecca Hines:

AI.

Sarah Powell:

Oh yeah.

Rebecca Hines:

how do you? how do you see this, this going in the area of math? Just a

Sarah Powell:

Yeah, that's a good question.

Rebecca Hines:

How's AI going to transform how we teach math? Do you think?

Sarah Powell:

Oh, well, Becky, I don't have a ton of experience in this area, but we're doing a little bit right now. So, we're I'm actually partnered with a company on an Institute of Education Sciences grant, where they are taking some of our word problem stuff that we've done in the past, paper pencil, and they are putting it into a tutoring program that is driven by, I'll say, some extent of artificial intelligence. It's not fully there yet, but it's trying to think about how students set up and solve word problems, and if students struggle with the four struggle with the first part, what are some of the ways the prompts that they can receive or the visuals that they can see to help them understand the first part of the problem? Or maybe they have a hard time with the third part of the problem. And so then it's like, hey, let's look at the math again, or maybe you need to check your numbers, or whatever. So I think there's a real possibility that AI is going to be super helpful in terms of the learning of math. I also think it's going to bring up a lot of conversations about how much math do students have to learn in schools if technology can help them do these calculations and so on. And probably a lot of those conversations are going to end up going over to the idea that students really have to have meaning behind the mathematics, because you may have a calculator with you at all times to help do the computation of the mathematics. And so then trying to balance that, what many people will talk about is this conceptual versus procedural knowledge in mathematics, and where do we spend a lot of our instructional time in schools knowing that students for the next decade or several decades, there's just going to be tools that are emerging every year that are going to help students out with a lot of the learning of mathematics.

Rebecca Hines:

Yeah, I love that explanation.

Lisa Dieker:

Yeah and yeah, when we all figure that out, we won't have to work at all, right, if we can figure out, you know, how to make this easy for everybody. Well, so my last question for you is, really, is there anything that you can think of from the special ed side in the field that we didn't ask you that might make us better at adapting curriculum or meeting student specific learning needs?

Sarah Powell:

Oh, gosh! Wow! Um,

Lisa Dieker:

I know you could probably go on. We could have a two hour podcast with you. But like, what's your one golden nugget that I'm a new teacher. I'm going in to co-teach with you, and I'm scared to death because you're the guru of math, and I've never

Sarah Powell:

Got it.

Lisa Dieker:

where would you tell me to start

Sarah Powell:

Yeah.

Lisa Dieker:

in thinking about working with you?

Sarah Powell:

I would say, maybe my my last words of advice are that even if you as an adult are not confident with mathematics, everyone can be a very strong math teacher, and that's particularly true in the elementary grades, where I think more often elementary some elementary teachers have more of an anxiety about teaching and mathematics than we see in the later grades, because many times later grades math teachers are content area experts. But if you know how to break down something into steps, if you know how to model, if you know how to provide vocabulary instruction, if you know how to engage students in authentic practice opportunities, if you know how to give feedback, all of those things are important for the teaching of math and all those things that I just mentioned, those are things that teachers are doing in reading, and probably they're doing in science and social studies as well. And so I really do think that with a little bit of content knowledge and a little bit of pedagogical knowledge, every person can be an effective math teacher, and that's what students with and without disabilities need. So, I will say those are my parting words, and I just want to thank you for the opportunity to be here today.

Lisa Dieker:

Well, thank you. That was that was some great ending advice, and everybody could be a math teacher, and that's what we want everybody to believe. That's a great golden nugget. Well, thank you. And if anyone has questions, you can send us a Tweet at Access Practical, or you can post questions on our Facebook page. And again, Sarah, we can't thank you enough for all the work you've done in the field and the difference you're making for all kids, but specifically for kids with disabilities. Thanks for joining us.

Sarah Powell:

Thanks, Becky. Thanks, Lisa.

Rebecca Hines:

Thanks, Sarah.