Practical Access Podcast

S12 E3: Building from Strengths: Teaching Mathematics to Students with Disabilities.

• Season 12 • Episode 3

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In this episode of Practical Access, hosts Lisa Dieker and Rebecca Hines welcome Dr. Karen Karp, a professor emerita in mathematics education at the University of Louisville and recently a professor at Johns Hopkins University. Her scholarship lies at the intersection of mathematics education and special education. She is the author or co-author of numerous book chapters, articles, and books, including the U.S. Department of Education Institute of Science’s What Works Clearinghouse Practice Guide on Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, and other titles such as Strengths-based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K-6, The Math Pact: Achieving Instructional Coherence within and Across Grades, and Elementary and Middle School Mathematics: Teaching Developmentally which has been translated into seven languages. She also was on the authoring team of the NCTM- CEC Joint Position Statement. 

Dr. Karp is a former member of the board of directors of the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators. In 2020, she was selected for the NCTM Lifetime Achievement Award for Distinguished Service to Mathematics Education. She also is a member of the U.S. National Commission on Mathematics Instruction. This summer she represented the United States as the Chair of the Topic Study Group on Teaching Mathematics to Students with Special Needs at the International Congress on Mathematical Education in Australia. She holds teaching/administrative certifications in elementary education, secondary mathematics, K-12 special education, and K-12 educational administration.

Karp's scholarship stands out for its direct and visible impact on practicing mathematics teachers. Her work goes beyond theory, with her ideas being actively implemented in classrooms, shaping how mathematics is taught. In this podcast, Dr. Karp offers invaluable advice for general education teachers working with students with disabilities in math. She emphasizes the importance of early collaboration between general-ed and special-ed teachers, advocating for a proactive, rather than reactive, approach to math interventions.

Throughout the conversation, Karp discusses strategies like using multiple representations in math instruction, focusing on the strengths of students rather than their perceived weaknesses, and ensuring that Individualized Education Programs (IEPs) are written with concepts and skills. She shares practical methods to engage and empower students to succeed in math, using examples such as the "Whole School Agreement" and success stories from students she's worked with.

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).

Karp’s bio and publications: https://www.mathbykarp.com/publications 

Unknown:

Music.

Lisa Dieker:

Welcome to Practical Access. I'm Lisa Dieker.

Rebecca Hines:

And I'm Rebecca Hines and Lisa, keeping with our theme this season, I know you have someone that you're excited

Lisa Dieker:

Yeah, so I'm actually giddy. That's a great to present. word for today. I'm so happy we were able to get Karen Karp with us, who's a professor in math education, who really does in our work, have the intersection of special education and mathematics. So Becky, we don't have enough friends in that area, so we're super happy to have Karen on the call with us today. So thanks for joining us, Karen.

Karen Karp:

Thank you so much for inviting me. I'm really looking forward to our conversation.

Lisa Dieker:

Well, I'm gonna start with the first question, and I would just love for you, imagine I am a brand new teacher, and I have a student in front of me that has a disability in mathematics, and I'm a little intimidated. I'm a general-ed teacher, I don't know where to start. What would be your beginning advice for me to think about or to do? Or, you know, you, you are the expert here. What? What? What should I be thinking about as that new novice, first-year teacher working with kids with disabilities?

Karen Karp:

Well, you said general-education teacher, and that's, you know, an important start, because they are the ones who are delivering the math content on one level. But I'd ask that new teacher to partner pretty quickly with a special-education teacher in their building, and start to develop a partnership with them, because I really believe that that is the best approach. I'm afraid in some cases, that a student with disabilities is in kind of a limbo space. If we're not careful, that the gen-ed teacher might say, well, I don't know that much about special ed, so I'm not sure that this child is fully mine. And then the special-ed teacher will say, Well, I'm not sure about the math part, so I'm not sure. I think it's the other person's to do and and no one does. And so what we need to do is start a partnership right away, because it's everybody all in, everyone's in. And so that, I think, you know, is critical. But the main thing is, is to keep trying different things and be very proactive. The one thing I'm working on right now is math interventions is proactive. It was the original intent of response to intervention, and it was preventative and after the medical model. But in fact, that's not how it's played out. It's very reactive, and we wait for a child who's struggling in math as the one you describe, before we act and do anything. Well, we're saying to have little collaborations between the special-ed teacher and the gen-ed teacher, where they work two weeks in advance of new content together and they prep each other as they're priming for what interventions will take place. And the interventions are not pre-teaching the lesson you have no goal or no interest in that. They are building in everything that goes into the lesson to come. So for example, for something like perimeter, you know, what we want to do is have those kids measure just a lot of length and just practice with a ruler and constantly be measuring. And we want them also to see that if we add another line to the line they have, they can measure this length and that length. We're not going to do the parameter thing. We're just prepping them. And then the gen ed teacher, and that's our new teacher on board. The special-ed teacher will say, these are the things that I've done with the children in the interventions. Start your first lesson with these. And so we're going to use those as a way to have these kids shine, that these kids are going to do things they just did a few days ago in their intervention class that I've already reviewed, and now the new teacher gets to call on those children first. And so we're trying to make it that the children really, really are feeling that the lesson is theirs and not flying over their head at fast speed. And so that new teacher has to learn this new model, proactive intervention. So that's one of the things that I suggest.

Rebecca Hines:

Yeah, I love, I love to hear the word collaboration. Lisa, I harp on collaboration all the time. So your your basic tip is, let's make sure that we're collaborating to ensure success. And for this young teacher, when they go to a special educator and say, I'm having trouble with X, Y or Z, I generally would advise them go with. You know, go with the sample of work, and don't say I'm having a problem with this kid. I'm having a problem with the way with this solution. So do you have ideas? But what do you think is a good, a good entry into that conversation? Karen, how do they how do they go and elicit this help, what they might not even know the special educators in the school?

Karen Karp:

I love your idea of bringing a piece of students' work, because one of the things I always say to all teachers is we're not about fixing children, we're about fixing structures, and so that's why I'm focusing on the structure of the collaboration, because we're not about at all thinking that the child is it some way. You know, the change, it's not that it's changing everything around the child and and I think that that's, that's quite the important piece, and I may be missing what you're asking.

Rebecca Hines:

Yeah, let me. Let me. Let me. I'll ask that a little more specifically, as a faculty member in special ed, we talk to special-ed teachers about collaboration. I don't know that all of the gen-ed faculty when they're preparing teachers, I don't know if they similarly present our special educators as also experts. They're just experts in something different. So as a faculty member who might work with, you know, math education majors, what would you tell them when it comes like, literally like, if you were preparing teachers, how would you tell them to approach a special educator, you know, with, with the problem?

Karen Karp:

Total partner I mean, I really think it's got to be that way. We each have, you know, a collection of information, and we just have to find ways to share it well. And I think that the preparation of both kinds of teachers, the gen-ed teacher and the teacher who's gone through special education is quite different. And so they are definitely differently prepared. And yeah, we can say what's a good thing to do there, or what's not, but the reality is, is that together, they have to make this work. And you know, with many children, it's not only students with disabilities. It takes two people to think about the situation.

Rebecca Hines:

Right.

Karen Karp:

And it could be two gen-ed teachers. It could be, I need two more special-ed teachers if they're available in the building, and even sometimes paraprofessionals and teaching assistants who are working closely with that particular child, they need to be in on the conversation too.

Rebecca Hines:

Oh, good. I think, I think we have a good, a good article to write there.

Karen Karp:

We have something called, we have something called the Whole School Agreement where we work to get everybody on board across the entire school so that math is taught well, and that, you know, special-education teachers, paraprofessionals, teacher, long-term subs all go to the same math PD as the gen-ed teachers.

Rebecca Hines:

Love it. I love that.

Karen Karp:

Totally aware of what's going on. They're not used as subs during a PD event at a school. They are in, they're in it.

Lisa Dieker:

I there's so many things you've said. I like, I like the Whole School Agreement. I like everybody's in I even like your really strong, proactive focus on the strengths of the kid, not the failure of the kid in math. And I, I think that's so much what the field needs to hear. So I know we agree on this, but I would love to hear your thoughts and help for any teacher, teacher, coach, about that kid who we know needs to be in with their peers having discourse, but really struggles in being in with their peers and having discourse. What are some things that you found helpful? Especially in the area of math, where, you know, some kids have math anxiety, which we know that literature is high there.What are some things you've seen teachers do, or you would suggest to teachers for that kid who we want them to be sitting next to their peers and having that rich mathematical discourse, but they might struggle with that?

Karen Karp:

Again, you know, again, I, you know, I think some of this proactive work will support, you know, all children, but there are complex situations, and we have to think about those as well. The main thing is, is to use multiple representations for all groups. And I didn't mention this before, but this is a great resource for brand new teachers as well as veteran teachers, but I was involved with a wonderful bunch of other co-authors on the IES practice guide for assistance, assisting students struggling in math that just came out about three years ago. And in it, we make six important recommendations that it's mainly for the elementary school, but it really travels all the way up, and we made six important recommendations that teachers should consider that's based on evidence-based research, and one of the ones that I think is most important, and if I go to a school I talk about, and when I talk about any child in general, multiple representations. Now special ed uses well may still call this CRA math educators call it CSA, because the R that is used for representations, they're all representations. Concrete is a representation, abstract is a representation. So that R doesn't really stand for what it really is, which is semi-concrete, like a drawing or a sketch or sometimes even a chart, depends. And I and we in math education like to overlap those so that you're seeing concrete. And if I need to, for this particular student, write the equation that goes with it, first time I will do that, then I might have a collection of cards that have different equations on it, and say, which one do you pick that goes with this model that we just made? Then I get them to write it. So, you know, there's lots of progressions that we can to support that child in, in moving towards more, more of an independent ability to handle some of those questions, but there are very, very important models that help children think and do math and take action and make it less anxiety producing, where we're not demanding memory, where we're not demanding time, where we're giving the time to think, and we're giving the supports that are needed with even acting out problems, taking the time to just stop and act it out. A lot of kids need that role-playing. Others just sometimes will say, imagine this situation in your head like a story, and that that's helpful too. So there's lots of things we can do to try to bring them into the action part of this. So it's not just rote memorization, and to be frank, things that 10 years from now will be completely done by AI or my watch.

Rebecca Hines:

And do you? Do you? Do you think, Karen, that that on those occasions when we when we have students who are who individually, are struggling and but we suspect that you know intellectually, they're capable of understanding the the concept, the broad concepts, but they're just lacking some of the skills, and there may not even be time for them to get all they had caught up in all of those skills. So how do we, how do we as instructional coaches, you know, what? What can we do? Or what ideas do you have, whether it's me or I'm bringing a para in to to provide support or even a volunteer to help with the coaching piece to get them caught up on the sideline, just a little bit?

Karen Karp:

Well, one of the things that I think, and this is tangential to your actual question, but I think would be useful in that, is that the IEPs have to be written to be more conceptual. A lot of the times I'm seeing IEPs written, and the IEP is strictly about skills, and it talks about an assessment where we're getting more digits correct than we did yesterday or whenever it was done. And I really asked teachers all over the country, what do you do with that information about the digits? How does it inform your instruction? And none of them can really answer me. It's not that. It's not doing the trick. So I say write them more conceptually, talk about talk about place value, knowledge and things like that, that we can really bring the students in on with these materials that we're talking about. And those provide the total foundation for the other components, but it isn't putting kids in a tight kind of situation of constantly be doing algorithms and procedures and to be frank, those are very elegant ways of doing math, but they can they. They are not some of the most joyous things in math. Sometimes, that I'd like them to experience some of the joy and beauty of the subject, too. And they sometimes don't even have an IEP on geometry, which can be for some children, the place where they can really, really shine. And I'd like to see more of that. And I also learned, you know, of course, that you can't write the same IEP every year. Yet we see this multiplication facts thing travel along, and the Supreme Court came out against that same IEP can't be written two years in a row or even again. So we need to delve into some. Of the other things that may, in fact, be a doorway for children who do have tremendous strengths. I never go in thinking that they can't do it. I always go in thinking they can, and I just have to find a way.

Lisa Dieker:

And so, so my last question, but I went a little bit of commentary with it, so it's funny. I wish my son growing up could have had you as a math teacher, but my husband, I were literally just talking last night about our son works for Trek and has sold lots of bikes. I'm not allowed to say, but he's one of the top 40 salesmen, and yet I laugh that he couldn't do his multiplication facts. Still can't, but he conceptually struggled, right, and he had a calculator. But I do remember in fifth grade, and I think you'll find this funny, we got a letter, and I was like, Josh, I think this is a wrong backpack. And he said, I'm putting your son in gifted math. And it like, yeah, but again, he had this amazing teacher in fifth grade. And she said, look, Lisa, he procedurally is not strong, but conceptually, he gets it. He beyond gets it and and so I think it's a good example for our listeners to realize, realize, you know what Karen's saying, is life changing for kids, because I do think that was a tipping point that allowed him to go to college and do well. And so with that, I just and our listeners to hear because I got the privilege of chatting with you on the phone before the podcast. I really want them to hear your profound wisdom in the IS report from your perspective, and I would love to put that link out on our podcast when we're done. But could you share with me if my son were born today and I was sitting there in third grade and he still trying to do as facts, and I wish I hadn't done flashcards all the way to the gym, because it didn't matter. What would you tell me are six things I should be thinking about for my son today?

Karen Karp:

Okay, and so, well, some of the recommendations I'll give in general, one is systematic instruction. And by that, I don't mean explicit instruction. I mean giving kids the chance to think and do first, and then I'm here to support them but to assume that they have strengths that can play into the information that's about to come their with. And so that, you know, is a very important shift that was very different from the last go around on the IES practice guide that came out in 2009 the multiple representations is all over the place in the practice guide. So I've talked a little bit about that already with CSA. And another thing is the language, the precision of language is particularly important. And this goes to that conversation I had about the Whole School Agreement, where we're all using the same language or not like we're not using borrowing and carrying because they're not conceptually sound. We're using regrouping or trading to replace value purposes. Then kids here it over and over and over and again, which is precisely what you know, students with disabilities need, and multilingual learners and everyone else too. We don't want we want reducing fractions to be said one year and simplifying the next. We want it to be a small stream where everyone knows what's going on and kids aren't saying such things as math is different every year. You know, it's not it's a continuum, and we want them to be on it. Then we separated in these recommendations, one representation out from the others, because the research is so compelling about it, and we want to have all teachers realize K-12, they're responsible for using it officially, and it's the number line. And so we started in kindergarten with number paths, and obviously it moves up to very complicated lines and graphs and other components as they move to middle and high. But that one was pulled out. And then there was another one about solving word problems that that is an important piece of what kids do, and we suggest even using gestures to help them start to see patterns. You know, if I'm dividing and I'm doling out like I'm dealing out cards, that sharing motion is a something that can generalize to other problems, and you feel like you have to share equally, you might be dividing and so and then another one was about fluency activities. It's titled timed activities in the document, but I'm going to be straight with you. I think it should have been called fluency activities, because that's what it's about timed activities are one component of that, but there's lots of other things that help build students' fluency, and so those, those are very important. And, um, you know, you you told the story of your son, which just reminded me of something that I would like to share. I just returned from the National Council of Teachers of Mathematics annual conference, and was fortunate to see one of the teachers I've been working with in Tennessee, there with her, nine of her students with disabilities, presenting with her, and they did an unbelievable job. They have just surprised over and over again, everyone with their strength and interest in math, they call themselves the math scholars, or the FBI, the Fantastically Brilliant Investigators. Depends on what grade they're in, what name they've created for themselves, but the children love math. See themselves as mathematicians, and were a knockout for everyone who was at that conference. So it's wonderful. Lots of strengths, lots of strengths.

Lisa Dieker:

Well, thank you for sharing, and I think that was our last question. We appreciate not only your wisdom, but I love the FBI. I'm sharing that with everybody in America. So if anyone has questions, you can send us a post on our Facebook page at Practical Access, or send us a Tweet at AccessPractical thank you again, Karen, for joining us.

Rebecca Hines:

Thank you Karen.

Karen Karp:

My Pleasure