On this episode, Joel and Misty get a little off topic while discussing World Plant Milk Day, indulging in their stream of consciousness thoughts around plant milks, dairy products, and allergens.
Then they have part 1 of an invigorating discussion about fostering and supporting positive struggle for students with disabilities with their guest, Dr. Malia Hite, a seasoned mathematics educator with over 20 years of expertise in working with students with disabilities.
The More Math for More People Podcast is produced by CPM Educational Program.
Learn more at CPM.org
Twitter: @cpmmath
Facebook: CPMEducationalProgram
Email: cpmpodcast@cpm.org
On this episode, Joel and Misty get a little off topic while discussing World Plant Milk Day, indulging in their stream of consciousness thoughts around plant milks, dairy products, and allergens.
Then they have part 1 of an invigorating discussion about fostering and supporting positive struggle for students with disabilities with their guest, Dr. Malia Hite, a seasoned mathematics educator with over 20 years of expertise in working with students with disabilities.
The More Math for More People Podcast is produced by CPM Educational Program.
Learn more at CPM.org
Twitter: @cpmmath
Facebook: CPMEducationalProgram
Email: cpmpodcast@cpm.org
Hello, hello, it's August 22nd 2023, and this is episode 9 of our third season of More Math for More People.
Speaker 2:Cheers.
Speaker 3:Hello, there, I'm. Joel.
Speaker 1:And I'm Misty.
Speaker 3:And you're listening to the More Math for More People podcast, an outreach of CPM educational program.
Speaker 1:We have a lot of conversations about math and math education on this podcast. We're passionate about continually improving the way math is taught and we hope that you learn something in every episode that helps you become better at what you do.
Speaker 3:And we hope that you have some fun and laugh as well. That always makes things a little more interesting.
Speaker 1:Yep, we're pretty passionate about having fun Joel.
Speaker 3:So please have a listen and we think it'll be well worth it. Boom.
Speaker 1:Okay, so we're here again with another national day of and. I am wondering what day it is, Joel.
Speaker 3:Today is World Plant Milk Day.
Speaker 1:World Plant Milk Day. Like are you planting milk to grow a milk tree? I do not understand.
Speaker 3:I don't know if you know that, as our listeners know, I was a pasteurizer at a dairy for some of my life and if you take milk and you bury it in the ground, more milk will grow.
Speaker 1:I'm kidding, I'm kidding, Okay because we don't want to get sued for people planting milk and then having things go awry.
Speaker 3:He would start stinking very soon. No, it's plant milk, like almond milk, and those types of milks.
Speaker 1:Yes, I always think of those as alternative milks, but ones that are made from plants instead of cows, that's right. Okay, cool. So it's World Plant Milk Day. Yes, World Plant Milk Day, Okay all right, well, can you tell us about it?
Speaker 3:I can tell you that the sales of non-dairy alternatives for milk $2.95 billion just in 2020.
Speaker 1:I wonder how that compares to dairy milk. You might have that number available, but I don't.
Speaker 3:but I bet that would be a good comparison. I want to know if it's more or less. I imagine Right, right yeah.
Speaker 1:Like what portion or percentage or something Absolutely. I have many questions, I have many wonderings.
Speaker 3:We're going to have to start googling. I think let's see 65% of young children who do not meet the required daily dairy intake. Okay, why does that mean? I don't know, I mean it 65% is the percentage of young children who do not meet the required daily dairy intake. That means they should drink plant milk, I don't know. Or are they not getting their dairy Because they're drinking plant milk? I don't know. Can they meet it by drinking plant milk? I don't know what that?
Speaker 1:means yeah. Also to say it's a required dairy daily intake I always have. I always have some dispute with that because no one has to eat dairy.
Speaker 3:Right.
Speaker 1:We're a strange being in that, as adults, we still.
Speaker 3:We still drink the milk.
Speaker 1:Drink milk. No other mammals do that.
Speaker 3:Not to be confused with drinking the Kool-Aid.
Speaker 1:Yes, no other mammals do that either.
Speaker 3:Here's another fun fact 40% is the percentage of children allergic to cow's milk who are also allergic to soy milk 40%.
Speaker 1:That's the overlap of the Venn diagrams.
Speaker 3:Of children.
Speaker 1:Interesting. Yeah, that's interesting. I know that there's all these things around when and how you introduce children to allergens. One of my good friends just had a baby a year ago. They're at that place of they start giving her peanuts and they start giving her soy. They do it in this very precise, measured and specific way to help deal with allergens, which is really interesting because, like when you and I grew up, we just ate people our parents just gave us stuff and Like nobody knew all these.
Speaker 1:they didn't know all this stuff in the same way, and so it's really interesting how, now there's all, you really what the pay attention and do things then, yeah, so and so yeah, yeah, for sure, I have a friend with kids the same way and every night they have a little, just a little cup of yeah, like she eats a little almonds every day or something.
Speaker 1:Yes, I wonder, I I wonder if that I Just have all these thoughts of like how it helps people be less allergic, because I feel like there was this really intense influx of allergies around, or at least knowing around, allergies around peanuts and very things like when. I was a kid, no one ever said, oh, have a peanut allergy. And then when I was in school, like we had to be really be conscientious of kids at peanut allergies.
Speaker 3:That's right, even just like on your skin, oh yeah.
Speaker 1:Yeah, so I'm hoping that these kinds of things actually help with for sure.
Speaker 3:That's not really about plant milk, I mean, it's true. Well, do you know some activities that you could do on world plant thing?
Speaker 1:other than drink plant milk. This seems like the most.
Speaker 3:Well, that's actually one of them, but yeah, number one but you, it says, you could head to the market and buy multiple flavors to see which one you prefer.
Speaker 1:If you're allergic to any of them, that's right or you'll find out.
Speaker 3:Maybe it's okay. You could the other ways to apply the plant milk theory to other dairy.
Speaker 1:So if you incorporate Plant milk into other products like cheese or things like that and and you just go buy it, go to store and buy ones that were made from plant milk use.
Speaker 3:I think you would go to the store and do that unless you are a cheese maker, which I am not, oh you can make cheese at your house.
Speaker 1:Yeah, yeah, I understand. I've done that.
Speaker 3:We're, but they can get up some vegan cheese.
Speaker 1:I've made yogurt out of coconut alternative. Oh, there you go before in a yogurt maker, I See. So so applying the what can I do with dairy question to plant milk. Yes, I would suggest it might be hard to make butter. I.
Speaker 3:Believe you. I don't know, they don't have the cream to make the butter from. I don't know.
Speaker 1:I mean, I don't know how you make butter, and if you don't have, that's another Google search, and the third. We're creating more questions than answers to that the third activity that you can do.
Speaker 3:This is my favorite one. Okay, you can go for a walk. What Just it says take some time To celebrate your own health to celebrate plant milk day, go for a walk.
Speaker 1:Okay, that one seems the least relevant and but also the most relevant.
Speaker 3:Yes, at the side, take a breath of fresh air.
Speaker 1:Great yeah, think about plant milk.
Speaker 3:Excellent or or not. That's right.
Speaker 1:Just appreciate you. Well, that's great. I there's.
Speaker 3:There's so many options and Many questions if you can't help it, not celebrate, that's right.
Speaker 1:And they're wondering how we could talk about plant milk for this long. So I hear you go, people.
Speaker 3:We did a good job.
Speaker 1:Thank you, and off we go.
Speaker 3:Okay, today we're here with dr Malia height, who is the executive licensing coordinator for the state of Utah, and and she has been a mathematics educator for over 20 years in four different states, with a focus on On students with disabilities. So welcome Malia.
Speaker 2:Well, thanks so much for having me. I'm pleased to be here.
Speaker 3:Tell us a little bit about. We want to focus today on students with disabilities and your work around that, especially in a mathematics classroom. Can you tell us a little bit about how you got involved or how that started for you?
Speaker 2:Yeah. So I started my career as a high school math teacher and found that I really enjoyed working with students who struggled learning mathematics just in general, and so that led me into the world of students with disabilities just by nature, because they are the ones who struggle with mathematics, and so I was really lucky in that. A couple of my early teaching jobs I had special educators around me that helped me to understand disabilities and helped me to know how to help them to understand mathematics. I'm a general educator. My teaching license is in general education, but I've, through the years, have really gone head first into the world of students with disabilities to learn more about how do the disabilities impact student learning and how can I, as an educator, overcome and accommodate those learning disabilities so that they can access their general education mathematics, because that really is what we want right, and I want all of my students to understand math at deep levels, and I think it's possible. We just have to know how to get them to that higher level.
Speaker 1:So Joel and I both watched a recording of a talk that you gave for NCTM a couple years ago, and one of the things that I really liked in that talk was how you talked about what productive struggle is and how to help students with disabilities get to that place of productive struggle that isn't now unproductive, and I shut down right. Can you talk a little bit about that?
Speaker 2:Yeah, I think that productive struggle is something that in general, math educators they know when they're feeling it as a learner, as an experiencer of mathematics, but it's hard to know when their students are feeling that productive struggle.
Speaker 2:I think we, as math educators, were of a generation that when we were in high school or middle school learning math, it was like, oh, you've got the right answer correct, or you completed your multiplication table in under two minutes, so you're ready to go. And so we didn't really experience productive struggle as learners in the K-12 setting. And so I think that's one of the disconnects is that we don't know what it feels like as a student, and so we don't know what it looks like for our students, just as part of our past experience. And so productive struggle is really I like to put it into the same area as the zone of proximal development, the ZPD, which is led by Gatsby, very old psychoanalyst in the learning field, and it is this sweet spot between the level of competence of a student and the challenge that they're experiencing, and so it's finding the place where the challenge is equal to their level of competence. And there's another he's another psychologist called Chimansaga Got it.
Speaker 3:That's a good one yeah.
Speaker 2:Chimansaga, and he has more recent research. That's very similar to the zone of proximal development that's called flow, where a task is challenging but it is of same or equal value to your level of competence. That just stretches you just a little. And it's the flow, or the ZPD is where we're stretching our challenge just a tiny bit more than we can do with ease and that's where productive struggle lives is where the learner is stretching and they're learning as they engage with things that maybe they know how to do 90% of, but it's that 10% push that gets them into the ZPD or into that area of productive struggle.
Speaker 3:And what are some ways, I guess, to get into that space right, like it's got to be a teacher? Maybe every day changes, I'm just curious.
Speaker 2:Yeah. So I think that a lot of how you create moments of productive struggle in the classroom is really understanding where your students are as far as their mathematical understanding and then giving them things that are not. I think of it as if you give them something that they can do and get an answer and be done, then that's not going to foster conditions that productive struggle will live in. Conditions of productive struggle live in areas where there are multiple opportunities to engage, so they're task based, typically mathematical experiences where there's a low floor and a high ceiling, low threshold that anybody can enter into and engage in the task and can push it or take it as far as the learner is able to. So when I think of conditions that cause productive struggle to exist in a classroom, it's something where there's multiple opportunities to engage, there's multiple pathways to get to a solution, there's a requirement to justify how you got to your solution. It isn't just like, oh, the answer is 12, and now I'm done.
Speaker 2:The answer is, I think, 12 because and here's my mathematical reasoning to support where that answer comes from and so when you start to look at productive struggle in the classroom, it's not giving them 30 problems and having them do the same kind of 30 problems with different numbers.
Speaker 2:That's not an environment where productive struggle lives, because either a student knows how to do it and will just do it, or a student maybe needs a couple of supports and then can do it, and then they do it, or a student looks at it, can't even fathom how to engage and opts out, and those really are the only three options. If you have an activity or a learning experience that doesn't capitalize on productive struggle in the classroom, but when you have something in the classroom that does capitalize on productive struggle, then you're going to be able to have some sort of an activity where the students maybe need a tiny bit of support or a scaffold to get in to the task, and then they keep going and they can engage in the mathematics and discuss with their peers and collaborate in ways that will help them to understand more mathematics, rather than just regurgitating the same process and procedure that they were taught on the board 10 minutes ago.
Speaker 1:So if I can paraphrase what I think I'm hearing you say, is that, in order to have productive struggle, the math task itself is critical. Yes, you can have a math task that allows for productive struggle and maybe still need to support it to get kids into that, but you can't have productive struggle without a math task that builds, that allows that situation to develop. Is that?
Speaker 2:Yeah, I believe that that's true. I think that if you're in a one-on-one tutoring situation you can, as a tutor, you can foster productive struggle, even if you're in a do these 30 problems worksheet kind of situation. But in a classroom setting, the mathematical task is really the hallmark and critical piece to make sure that the productive struggle can exist in the classroom.
Speaker 1:So, assuming I have a task that is set this way, are there particular, particular, different struggles or particular kinds of struggles that students with disabilities learning disabilities might have that I need to be aware of as a teacher, and how can I, how can I, anticipate those or interact with those in a meaningful way?
Speaker 2:Yeah.
Speaker 2:So whenever I see students who are struggling to engage in a mathematical task, what it looks like from the outside is either the student is not engaging or they don't know what to do next.
Speaker 2:They'll ask that question I don't know what to do next, or which isn't a question, right? They say I don't know what to do, yeah. Or or they are copying the work of a neighbor, but they're not really engaging in the mathematics, and so it looks like they're opting out. And so what it looks like from a teacher perspective can be oh, this kid just doesn't want to be here and they don't care, and they're having attitude and they are drawing horrible things all over their paper instead of doing the math, and so that's what it looks like. But what's really happening behind the scenes most often is that there's some sort of a learning disability or lack of a background knowledge that is impeding their access to the task. So when we're looking at specifically students with disabilities, oftentimes there really are three the big three that learning disabilities impact almost always. In the Venn diagram of learning disabilities, the little middle piece that is covered almost always is executive function poor working memory and processing speed, and executive function is impulse control and planning and prioritization and thinking about what goes first and then what comes second and what goes third, and time management and organization is all the executive functioning area. And even if a student doesn't have a disability, that is specifically executive functioning disorder. Maybe they have a math learning disability but that impacts their function or their executive function, or they have a reading specific learning disability and reading and that also impacts their executive functioning, and so that's one of the big three. One of the other is working memory, poor working memory, and so it's holding on to multiple things in your brain at one time, and that's you can see how that's related to executive functioning where it's. I got to do this first, then second, then third. Well, if I had poor working memory and I know what I have to do, first, I can't remember what. Second and third, because that part of my working memory can't hold on to that many pieces, and so those, you can see how those two are related. And then the third is because it's taking so much mental energy to try and keep track of what I'm supposed to hold in my working memory and I'm supposed to keep track of. How am I supposed to? What am I supposed to do in this order. How am I going to organize my thoughts? How am I going to organize my work?
Speaker 2:That third thing that happens is that the processing speeds slows down. So then we have lots of things that are impacted by an aid disability, which maybe has nothing to do with executive functioning or working memory or processing speed, but those three things show up. And so if somebody gets to a place a student gets to a place where they don't know what to do next, or they can't remember what you just told them to do, because their working memory is poor, or you said it at an average speed, and the students who have an average processing speed are on board, they know what to do, but if they are still like, well, she said something, but I can't figure out what it means, because they have poor processing speed, then they don't know what to do. They have no access to even the directions of how they're supposed to engage in the task, and so then that's what it looks like they are not doing anything.
Speaker 2:They say I don't know what to do or how do I start, because they are trying to grapple with all of these things together, and so I think those are the three biggest ones that we see because they're present in all kinds of learning disabilities. We of course have, like specific math learning disabilities or reading disabilities that will impact specific things. But I think if a teacher wants to try and help their students with learning disabilities and wants to get the most bang for their buck and pull the biggest lever, if you can attend to assisting them with their executive functioning, their working memory and their processing speed, accounting for those things, then it's going to leverage what the student can do and help them to engage in productive, struggling, meaningful ways.
Speaker 2:Well, that sounds great you just have to deal with those three things.
Speaker 1:The next question is then how do I address those three?
Speaker 3:things.
Speaker 1:Which is I get a huge question.
Speaker 2:And this is again something where each student with a disability is unique, and we, just like all students, have things that they like or don't like, or things that they are more interested in or are more challenging to engage in. That's true for learning disabilities. So there isn't like a magic wand that will do all of them, but there are some bigger levers that we can pull that can help scaffold and get students into meaningful mathematical experiences. There are a couple of things that I think are really helpful. One is having appropriate tools to help students, and a lot of times when we say, okay, we're going to give you a tool, it means I'm going to give you this calculator and now, you're good, you should be fine now, right? Oh, you have a math learning disability. Let me just hand you this calculator and everything's going to be great.
Speaker 2:The challenge is that that might be the appropriate tool, that, because of the executive functioning and because of the poor working memory and because of the slow processing speed, they don't know how to use it and they don't know how to apply it or when to use it, and so we have to explicitly teach how to use the tool of the calculator, and this is true for any kind of scaffold or any kind of thing we do to support students with disabilities is that we have to explicitly teach how to use whatever the tool is or the thing we're doing to help them, and then we have to reference it, often because they are not going to remember it, because that's executive functioning. They're not going to remember oh, I don't know how to do this. Oh wait, there's an anchor chart on the wall. I know that if I look at it it will help me to know what to do next. They don't have that skill. That is one of the synopsis in their brains that doesn't fire accurately, and so we have to train them and reference whatever the tool is. Often so using appropriate tools like a calculator or software Desmos is great, all of those kinds of things to alleviate the computation, but I think a bigger lever than that is to help them understand conceptually what's happening mathematically.
Speaker 2:So understanding the conceptual underlayer, the foundation of the mathematics, is how students with poor working memory actually can learn math. Oftentimes I know it's the way I was taught mathematics was that these are the steps, this is the process and this is what it looks like. And here's how you know you've got the right answer and I didn't get a lot of the conceptual learning of what the math means in my K-12 experience and our students that have executive functioning and working memory problems. The numbers and symbols and algorithms and steps they get jumbled up. They do this step next because that's what they think they're supposed to do, or those two numbers are together near each other, so I'm going to add them because they're close to each other, even though there's not a mathematical operation saying you should do that. But if they understand mathematically that solving an equation, for example, and they understand that equal means that there's equivalence on two sides of this equation and they can understand conceptually what equivalence means, then they understand that if I add two to one of the quantities, I have to add two to the other side of the equation so that there's equivalence, instead of saying, oh well, I'm going to add two because I subtracted two from this side. That doesn't make sense for students with disabilities. But when you start talking about equivalence and you can make it really concrete and they can put their hands on it literally put their hands on manipulatives or something they can build and see then they can say, oh, that's why I have to add two to both sides, because otherwise my equation is out of balance. When we look at that, it's not just saying, okay, we're going to do the manipulatives and now we're going to do the equation. I think that sometimes we say, oh well, we did it with manipulatives. That should make sense now For students with disabilities specifically, and I think it helps all students.
Speaker 2:But it's a bigger lever for students with disabilities is taking that concrete model and then turning it into a representational or semi-concrete model, so that then they can see how their abstract model, which is the equation, relates to the semi-concrete and relates to the tile or something they put their fingers on, so that they can see why, the why of the mathematics.
Speaker 2:I think if we can teach students with disabilities the why and the conceptual foundations of what they're learning and how it makes sense, that helps them to be able to solve problems and engage in mathematics in mathematically accurate ways, because they understand the language of mathematics. Instead of memorizing the steps of mathematics, a lot of times what I've seen in math educators is they want to make it easier for students with disabilities and so they say oh well, I'm just going to show you exactly. Here are the five steps you do. I'm going to put those five steps on a poster and I'm going to put it on the wall and we're going to look at those steps all the time. They think that that will help them. But the students with disabilities especially impacts their executive functioning disorder. Step one and step two and step three could all be interchangeable and may happen in a different time Because they don't following the recipe is really hard.
Speaker 1:Sometimes the recipe actually does need to be done in a different order or some other thing On top of that. We're telling them do these in this order, but then sometimes they do it in this other order or you do a different thing and that makes it even more complicated.
Speaker 1:Yeah, I liked what you had to say about how you mentioned that a lot of these things like going from the concrete to that, through the representational to the abstract, is something that helps all students. It helps all of our brains because we actually do. That's how we learn. We count on fingers and then we visualize fingers and eventually we stop doing the visualizing but we have the numbers there and that part of our brain still lights up, but it is a bigger lover, in particular for many students. So doing these things is not it's differentiating, but it's not just for those students, it's for all the students and imperative for students with disabilities.
Speaker 2:Yeah, I like that word. Imperative is that providing these kinds of scaffolds and supports for students in your classroom. It will help all students. But for students with disabilities, they will not be able to access their mathematics until they have that scaffold or that accommodation or that support. So it levels the playing field and that everybody now can be on the field where students with disabilities, if they don't have that scaffold or that support or whatever that accommodation is, they can't get in and so it helps everybody play. But it really is imperative and critical for those students with disabilities.
Speaker 3:Absolutely. There's a topic I'd like to talk about, but I don't know. I really know how to ask this question, but what role does assessment have in all of this?
Speaker 2:Cool Assessment is critical Assessment is what Unlock.
Speaker 1:Goodness gracious, that is all we have time for on this podcast. So you'll need to tune in in two weeks for our next episode of the More Math for More People podcast, where we continue our conversation with Malia Haidt and we find out about assessment and more. So come back then, have a great couple weeks. So that's all we have time for on this episode of the More Math for More People podcast.
Speaker 3:For more information and to stay connected, find CPM on Twitter and Facebook. You can find our handles in the podcast description.
Speaker 1:The music for the podcast was created by Julius H and can be found on pixivaycom. Thanks, julius. Join us in two weeks for the next episode of More Math for More People. What day will that be, joel?
Speaker 3:It will be September 5th and it's national be late for something day, so no longer do you have to succumb to the pressure of that busy schedule you have. You have the perfect excuse to be fashionably late for something. It will be fun to hear what we come up with that will be good to be late for. I can think of a good excuse to be late for something is that you are listening to this CPM podcast. That would be a good excuse. Anyway, we will investigate what good things we can be, late for the history of national.
Speaker 3:be late for something day, and don't miss the next episode. It's September 5th where we talk about national. Be late for something day.