It's More Than Numbers with Sarah Powell | Season 8 Episode 3

When most people think about math, they picture numbers and equations. Today’s guest, Dr. Sarah Powell, explains that math is more than just numbers – it’s vocabulary, language comprehension, cognition and executive functioning on top of understanding number sense! Throughout the episode, Sarah digs into the language of math, gives tips on how to teach math vocabulary and discusses why supporting all of the underlying skills builds stronger learners now and in the long run.

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. She is a former kindergarten teacher who became interested in school-based research. Her research, teaching and service focus on mathematics, particularly for students who experience mathematics differently. Powell is currently principal investigator on a number of grants and research projects looking into word-problem solving and working collaboratively with elementary and middle school teachers who provide mathematics instruction to students with mathematics difficulty.

Transcript

Stephanie Landis:

Hello and welcome. Today our guest is Dr. Sarah Powell and she is at the University of Texas in Austin with a specialty focus on math. So welcome. I'm so excited to have you here.

Sarah Powell:

Yeah, thanks so much, Stephanie. I'm really excited to be here as well.

Stephanie Landis:

I told you before we started recording, but I never thought I'd get to the point as somebody who loved words and did not like math growing up, that now as adult math is one of my soapboxes as a speech language pathologist. That's great. I like

Sarah Powell:

To hear that

Stephanie Landis:

Now people can hear about it from an expert instead of just me.

Sarah Powell:

Oh, I think you probably have enough expertise to speak about mathematics really well, so give yourself some credit there.

Stephanie Landis:

Well, thank you. I spent so much time supporting students in the classroom and over the years I found myself just being drawn more in and in during the math times. And at first I was really pushing against pushing in during math and now I'm like, let me in, bring me into a math class. I cannot help you multiply, but I can help you with the other things.

Sarah Powell:

Yeah, well, why were you pushing against math at that time?

Stephanie Landis:

Mostly because I am bad at two things, spelling and math. And now I find myself at the parish school when I started in the early childhood classrooms and I got to do all the fun word languagey, like play things that I love. And then as I started moving up into elementary, then I had to start teaching them with reading about spelling more and more. And then I started coming into math and I was like, oh my gosh, now I have to do all those things that are really hard for me,

Sarah Powell:

But it's okay because bottling things that are hard for you. Probably one of the first things people talk about in math is not telling young students that you're bad at math.

Stephanie Landis:

I don't tell them that I'm bad at math. I tell them that I love words more and I tell them that I am not good at spelling yet.

Sarah Powell:

Well, and that we are all working toward becoming better spells, becoming better readers and becoming better mathematicians. And even if things are hard, it doesn't mean that you don't like it, but it just means that you're going to work on it and we can work on it together.

Stephanie Landis:

Love that. You're pushing the growth mindset too. Well, now that we heard how I stumbled into being a proponent for math, how

Sarah Powell:

Did

Stephanie Landis:

You tell us about your journey into researching and helping teachers in schools become interventions and do interventions with math focus? Focus on math?

Sarah Powell:

Yeah. Well, maybe a little bit like yourself. When I was in middle school, I would say I was not a strong math student and really did not understand math, and my parents were quite worried about it to be honest with you. And then I went to ninth grade and had just a really wonderful algebra teacher named Mrs. King who explained things in math, I think for the first time where I started to really understand that. And I realize now she was teaching very explicitly and modeling every step, and that worked really well for me. And so I liked math, but I'm not, I wasn't a math major in college or anything like that. But then I ended up doing a master's degree at Vanderbilt University in Nashville, Tennessee. And there was a job over in the Department of Special Education, and I'll describe it as a job because I did not know what I was getting myself into at that point where they needed a research assistant to go out and collect data in schools on a kindergarten and first grade project.

And I had done all my student teaching in college in kindergarten and first grade classrooms, and I love the littles. And so I went and got that job and it just happened to be on a math project. It could have probably also been on a reading project, and we could have been talking about reading today, Stephanie. So I was in schools working on this project that was led by a professor named Lynn Fuchs who did a lot of work in the math intervention space. And I just really liked it and it really clicked for me. And also having that experience myself of having struggled with math and math didn't make sense for me always in my life, but realizing through the power of research, we can make math more accessible for students. One little job led to basically my now entire career. And math does make sense for me and I really like it, and I think we can really help students see, there's a lot of beauty in math and there's a lot of very cool connections in math, but math is not just math.

And I wondered if you were going to get to this when I asked you a little bit earlier, what do you not like about math? Because math has a ton of literacy within it. And in fact, so much of mathematics is actually related to your language and literacy. There's a whole lot of cognition that is really important for math. And so the old days of just thinking math is how do you add, subtract, multiply, and divide? That's not really the case anymore. And so it doesn't surprise me that you might have a lot of students who experience difficulty with reading or experience difficulty with language, who also experienced difficulty with mathematics just because those language and literacy skills are really, really integral for success with math.

Stephanie Landis:

And that's exactly what my soapbox this past few years have been is that math is no longer just math. It's now a reading comprehension and language and cognition, and especially when they start throwing in word problems. And I think that's what's pulled me into math now is helping teach it is that I'm like, oh, from the language perspective, I can help support this for sure,

Sarah Powell:

And you need to support that, right? Because starting typically in grade three and in public school spaces, but I would say that this is the case in most spaces in the United States, really, students show off what they know about math, not through solving true math problems. It is through word problem solving and word problem. And solving involves this whole understanding of being able to read these problems and understand the vocabulary and the problems. To be able to answer the word problem question, you have to have strong cognition, especially related to working memory and processing speed to be able to work through the problem in a really smart way. And then you also have to have that math knowledge. But students show off what they know about math through problem solving. And so if we aren't supporting students in all of the aspects of problem solving, which I would say the big three buckets there are math and reading and cognition, then we're really not going to allow students to show off all this cool stuff that they know about math if they aren't able to be problem solvers in math.

Stephanie Landis:

Yeah, we keep talking about math as a language. What do you mean when you talk about math as a language?

Sarah Powell:

Yeah, that's a great question. So math has an overlapping language with general English, but it also has somewhat of a separate language. So there's a symbolic language of math. So as we think about the plus sign, what does that mean? Or the equal sign, that's my favorite math symbol. The inequality symbols, the dollar sign, the cent sign, the fraction bar. That is the symbolic language. We also have the symbolic language of the numerals. What is a two, what is nine? And then those we can be used to show numbers. So what is 1 3 113? What does that mean? What is three fraction bar four? What does three-fourths mean? So there's a whole symbolic language that's attached with mathematics. There's also a whole world of mathematics vocabulary that students have to understand. So in three-fourths we have a numerator and a denominator. If I'm talking about $1 and 23 cents, what does sense mean?

And if you're telling me to look at the plus sign and the plus sign means to add or put things together for a total or a sum add, put together total sum or all math vocabulary terms that are really, really integral to understanding what the students have to do in mathematics. So we've got the symbolic language, we've got the language of math, but then when it comes to word problem solving, students have to understand general English. So even if I'm just asking how many animals does Stephanie have at her house, I have to understand what is animals? What is a house? Who's Stephanie? Can I read that name and understand that that's a person's name? And then to think about, well many, what is that actually asking me about this prompt? So all of those things really contribute to, I would say often a lot of word problem difficulty because there's so much that students have to do. So while there is this separate aspect of the language of math, it's really integrated with just what we would consider our general English language and how we interpret that language.

Stephanie Landis:

And my son was bringing home word problems now would just be one at the end of it. But even starting in first grade, it's starting so young

Sarah Powell:

And on top of those, well, you bring up the one at the end of it is such a classic word problem thing. Many times students have an activity page or a worksheet, whatever you want to call it, and it has the math at the top, and then there's a word problem at the bottom. And actually a few years ago, one of my friends was telling me that her son's homework came home and the teacher had said, oh, you don't have to do the word problem at the bottom. And she was like, oh no, you do. And he was like, no, mom, don't make me do that. She's like, no, you really have to get a lot of practice with word problem solving, which we'll probably end up talking about today. But everything that students do in their entire lives is really learned through practice. And that's really, really important in mathematics. You are not going to be successful with mathematics if you aren't regularly practicing math. And if you aren't regularly, and I would say every day learning how to set up and solve word problems, even at kindergarten, first, second grade before word problems really seem like the thing that students have to learn how to do, then students are not going to be as successful with word problem solving just because they haven't had enough practice with those problems.

Stephanie Landis:

And that was the same thing. My son also wanted to skip that, skip it, and it's usually they were more frustrating, especially since for some of these kids you were talking about with the cognition, some of these were already two step word problems and just the executive functioning skills that went into going through that. And you were mentioning the language of reading the word problems. One of the areas that my students struggle with most is that the inferencing of what are they saying? What are they not saying? And then sometimes I swear some of these word problems, like throw in extra things just to trick you.

Sarah Powell:

Oh yeah. And

Stephanie Landis:

I'm like, but that isn't relevant. And they're like, well, everything in this problem is important. And I'm like, actually, they kind of tried to trick you. This doesn't mean anything.

Sarah Powell:

Yeah. So you bring up two things that I think about immediately. First is irrelevant information. So a lot of word problems do have irrelevant information in them. We see that more as students progress through the grade levels. So it's not often if you are 5, 6, 7 years old that you're seeing a lot of word problems that have irrelevant information like, oh, I need to know about the cows and the horses, but I don't need to know about the chickens. And so one of the things that I see that we do often in math, and this is not always intentional, but we condition students to think about math in only one way, and that'll get to my second point in a minute or so. But if the first 100 word problems that students ever solved, whether that was an orally presented word problem presented by the teacher or a problem that they read aloud as a class, they never included irrelevant information.

We've conditioned students to think that every time all of this information is important, and we haven't set students up to think, oh, today, do you only need to focus on the cows and the horses and you don't need to focus on the chickens. So that's one thing, irrelevant information. A second thing is that there's this big issue with word problem solving related to keywords tying them to operations. And this starts very early with students as well. We kind of condition them to use keywords even if we're not explicitly doing it, that it's implicitly there. And then by the time students get to second or third grade, that keyword strategy has fallen apart and is not helpful anymore. And by what I mean with that keyword strategy is that there are certain words or terms in a word problem that mean a specific thing. Some of the very common keywords that people will talk about are altogether and total.

So oh, anytime you see altogether in a word problem, that means you add that is not correct. Right? Your listeners should not ever say that and do not think that. But in the first maybe 10 word problems that students saw with the word altogether, sure they did add. And so we've conditioned them say, oh, you saw this term and you added, Hey, look at that connection there. Even if we didn't connect those dots for the students, they're starting to connect those dots themselves. But many times the word altogether does not mean that they're going to add. We see altogether in problems where students may end up subtracting or multiplying or dividing. And so there's no time where a single word or term means a specific operation, but many times in the earlier grades, students start to make that connections, or they may see a keyword poster hanging in a classroom.

That's a big no-no, we shouldn't have those up there because by third grade or fourth grade, the people who write a lot of these word problems know that that keyword strategy is out there. And they will intentionally include word problems where the keyword doesn't work, or they'll intentionally include word problems where there is irrelevant information. And so we really need to make sure that our word problem instruction is better than the status quo so that students don't fall into those pitfalls of using all the information on the word problem only thinking about the word problem by its operation, or taking this keyword and tying it to a specific operation.

Stephanie Landis:

See, this is why math stresses me out. It's like playing chess. We are just talking about work problems right now. Exactly. We just got to outsmart the question and this we do. And then it gets so tricky for the students that I'm working with because the majority of them have language difficulties, if not just math dyscalculia, but most of them have underlying language difficulties. And so we're trying to explicitly teach them these definitions, and then it turns out like, oh, but in this instance it means

Sarah Powell:

You can

Stephanie Landis:

Different in this. And then they're getting frustrated because they're

Sarah Powell:

Like,

Stephanie Landis:

I finally learned what some means

Sarah Powell:

We're all together means different. But just because you see means something different doesn't mean you're going to add. Right. Well, and some is such a great word to even think about because we have, I'm thinking right now of SUM, right? That's what happens when we add numbers together. But there's SOME, I would like you to grab some crackers. And so you go in and you say some, and some students are thinking about addition. Other students are just thinking like, oh, I just got to grab some. Or how does that relate to some thing, right? So there's so many ways that we can interpret this single word that have some math meanings, multiple math meanings sometimes. Sometimes there you go. Or the many times it has meanings in math and outside of math. And that can be really confusing for students that, as you were talking about, learners with language difficulty, reading difficulty, and then also learners who are multilingual learners. Just think about the complexity that we are throwing at those students in terms of mathematics language.

Stephanie Landis:

Indeed, you brought up a great point. There's the double meaning words and homophones some and

Sarah Powell:

Some

Stephanie Landis:

You said base earlier

Sarah Powell:

Base

Stephanie Landis:

Can mean a lot of different things.

Sarah Powell:

Yeah, there's some real good one. Base is a great one, right? Are we talking about a base in its exponent or the base to a three dimensional figure? So there's two. There's actually probably multiple meanings in mathematics, more than two. But then if you say base and we're talking base in it's exponent, kids could be thinking about baseball or a military bass or then we have homophones, like a bass guitar or a bass drum. And so you can say one word. And for some of these math terms, I bet you could come up with 10 different meanings, some of which are math related, some of which are not. And so if you think you've got 10 students in your intervention group, they might be thinking about 10 different things based on that singular word. So

Stephanie Landis:

How do you advise people to go about explicitly teaching the language of math?

Sarah Powell:

That's a wonderful question, Stephanie. So first is through what you said in your prompt is being really explicit with our math. I'll say mathematics vocabulary instruction. Two big ideas that I would consider first are that students need to use the formal math terms. So there's a lot of opportunities where students use more informal math language, and they should replace that with opportunities to use more formal math language. And I say they should replace that, but teachers need to be really mindful of providing these opportunities for students and caregivers as well. So if I am thinking about a fraction, we should not be talking about a top number and a bottom number that is informal language. It's actually not really correct language. Instead, we should be talking about enumerator and a denominator. Okay, yeah. When we talk about adding numbers together, instead of always asking about an answer that's very informal, instead, let's talk about that sum right, give students the opportunity to hear that word, SUM and what that means.

And that's what happens when we add numbers together. So exposing students and giving students a lot of practice to that formal language of math, that's going to be first and foremost. Then second, making sure that students have a precise definition of those terms. So it's not enough that students can know the word numerator, and by know it, they have to be able to read it, they have to be able to hear it and understand what it means. They have to be able to write it and they should be able to say it. So when I think about students with language difficulty, whether that's receptive language or expressive language, whether students have reading difficulty, whether that's more based on word reading or reading comprehension. I mean, there's so many things that can cause difficulty in a student's world. We have to make sure that they not only know that formal term, but then have a definition of that term.

Because students will, they could tell you, oh, I know the term numerator and denominator, but the next question is, well, what do those terms mean? So I would like you to be able to tell me that the denominator means that you've got this whole divided into equal parts and that the numerator is naming parts of that fraction. And so it's like formal language first and then the precise definition that goes along with that. And so those would be the two things that I would focus on first and being very explicit and intentional with instruction related to that formal language and those precise definitions. So explicit instruction, a lot of modeling and practice is going to be important. And then a lot of different types of practice activities. So you can practice math language in a lot of fun and exciting ways, but students have to know those terms first so that they can engage in that meaningful practice.

Stephanie Landis:

I mean, you can turn a math thing like I've done in the classroom strictly into vocabulary lessons

Sarah Powell:

And

Stephanie Landis:

Just playing vocabulary games with it without even ever touching actual number problems or using number sense

Sarah Powell:

Because that language of math is really integral to everything that students are going to do in the math classroom. I also would say thinking about vocabulary is that taking opportunities to pre-teach vocabulary. So if we do have a unit coming up about fractions, what are the five or 10 or 15 terms that might be important in that unit? Even if I'm working with very young students, five, six, and seven years old, I'm going to talk about, we are going to add, let's say that together. I've got the plus sign, I have the equal sign. I would probably introduce them to the terms, those are the numbers you had together and some, so those are five vocabulary terms that I should pre-teach before I even start to get into edition or teach alongside as I'm introducing edition. But then you also have to think about going back and reteaching terms and not making assumptions that just because this is a term that students probably learned in kindergarten doesn't mean that every third grader knows that term and either knows the formal term or has a precise definition of that term. So we often want to think about assessing both formally and informally students' math vocabulary knowledge so that you understand when it's time to pre-teach or reteach math vocabulary just so that students have access to the mathematics that they're learning.

Stephanie Landis:

That's a great idea because there have been so many years where I've asked kids a vocabulary thing and they're like, never heard of it. And I was like, I taught it to you last year.

Sarah Powell:

I talked to you last year. We talked about this, and I know on the word wall in your classroom the year before that. So I mean so many math terms students learn when they're 2, 3, 4 years old. There's just, in fact, the earliest learning that students do in mathematics is through language. If you, oh, he has more goldfish crackers than I do, well, more is a mathematical term that's describing that one of these students has more and one has less. There's a lot of early spatial language that students, you're next to me or you're behind me. Those are things that students are learning 2, 3, 4 years old, and then that transitions into more formal math that students start, we'll say usually in kindergarten, but all of its language driven, and everything that students hear in the classroom or see in the classroom is accompanied by language. And so how are they hearing that language? How are they expressing that language? And it may not always be from an adult or from a peer, it could be from a video. If I'm watching a video that's with a song about math, it's still all language. And so the more that we can focus on that language of math, understand which terms students know and which terms students need work on, then that can really inform our instruction in a meaningful way.

Stephanie Landis:

One of the things that we focus heavily on at Perish to help our students across every single subject is making things very multisensory.

Sarah Powell:

Yeah.

Stephanie Landis:

Do you have tips for making math multisensory?

Sarah Powell:

Yeah, so we're talking about the language of math, and I feel like a nice natural connection there is thinking about different representations that students can use in mathematics. So in math, we'll use the word representations and often it's called multiple representations to emphasize that students really should be working with math in a variety of ways. And typically that falls into three categories, the concrete. So those are hands-on tools that students can touch and move to look and see and demonstrate different math and procedures. Those can be math manipulatives that are typically found in a lot of math classrooms, so you can buy those and use those, but tools can be paperclips and pencils and candies, and really anything that you can put your hands on can often be used to describe something in math. The second area when we talk about multiple representations is this pictorial images of mathematics.

So these are two dimensional images that students can look at and they can still help them understand math. So any drawings that students do, a number line, a graphic organizer, all tally marks, all of those are drawn, but they can all help students represent mathematics in another way. There's also this entire world of virtual manipulatives that I typically put in that pictorial camp. You could say it's another category of representation there, but those are if students are playing on an iPad or a tablet and they're moving unifix cubes or snap cubes around or working with base 10 blocks, that's a pictorial image of math that students could benefit from using because it could help deepen their understanding of math. And then we use the concrete and the pictorial so that students understand mathematics in the abstract. That goes back to what we initially started talking about today, Stephanie, that's math with the numbers and symbols and words. And so if I'm thinking about 34, I can represent that as three tens and four ones. I could use base 10 blocks. Those are rods and units that show actually tens and ones. So I could show three tens and four ones. I could draw three tens in four ones, and then ultimately I connect that to three four, which represents three tens and four ones or the number 34.

Stephanie Landis:

I think I was also reading somewhere where you were talking about using hand movements.

Sarah Powell:

Yeah, that's another I would put that in the kind of concrete area, but I agree. Yeah, so gestures are really important in mathematics. We use a lot of gestures in our word problem work to help students connect the word problem to the concept or the schema of the word problem. And so we can put our hands together to show a word problem where we're putting together things for a total, we can hold one hand out and increase it or raise it up or lower it to show a word problem where you have an increase or decrease. But there's also a lot of more informal gestures that students use in mathematics. So I've done some work around the equal sign and talking about the equal sign is balance, and although you can see it, no one who's listening to this podcast can, I am holding my two hands out and I'm showing a balance, which I'm kind of wiggling them back and forth to show a balance between one side of the equation and the other side of the equation.

There's also a lot of finger gestures that students use not only in counting 1, 2, 3, 4, 5, but I can also do, if I'm adding four plus three, I can put four on my fist and then count on three four by holding up 1, 2, 3 more fingers to think of the, what did I say? Four plus three? Yeah, four plus three or seven. So there's a lot of concrete tools that you actually carry with you that you can use in addition to all of the things that you can buy at a teacher store, buy online, or just fine at your desk or craft area. And

Stephanie Landis:

I find that so helpful because typically what I see is when students have to make that jump from the really concrete learning into the abstract that it becomes so difficult.

Sarah Powell:

It does become difficult, and there's a lot of reasons why that could become difficult for students. But one of the things we really want to think about is how do we scaffold that pathway from using these concrete tools and these pictorial drawings to tying that to the abstract? And one of the things that I'm always talking with teachers about is that this isn't a sequence. We don't start with concrete and then move only to the pictorial and then move to the abstract and we're done. That's not exactly how this works. It's more of a framework. So even if I'm working with five-year-olds and I'm talking about, we'll just say the number four, and maybe I have four counting bears out there, and we're touching and counting those four bears, I would then always say, how many bears do we have? We have four. I would be writing the abstract form of four there.

So writing the numeral four and then saying, okay, how many bears do we count? Four? Pointing to the abstract, pointing to the concrete, and then maybe even asking students to draw four circles to show four. So there you could have the forebears, which would be concrete four circles, which would be the pictorial, and then you could have the number four and you could even write FOUR to tie that into the word form of four. So when it comes to representation of number, we want to always have the number, the word form, and some type of quantity representation. So being able to connect all of those with the concrete pictorial abstract is a really meaningful way for students to see those connections so that we're not holding off to the end to get to the abstract. But I would say that the abstract should always be present as we pull in these different representations to help students understand what the math means

Stephanie Landis:

That really makes sense to try and expose them to it so that they can start building on that early on.

Sarah Powell:

Yeah, exactly. And you don't always have to call attention to it, it can just be there. But often I see that the abstract is your launching point into using the representations instead of the thing that we're working to get to the end.

Stephanie Landis:

And sometimes kids really surprise us and they pick up on the stuff earlier than we would think.

Sarah Powell:

Yeah, a lot of exposure can do a lot of students a lot of good.

Stephanie Landis:

And when working through these things, again, the cognitive part of it, you've been mentioning talking through things, it seems like those word problems are there not just to be like gotchas from my angle. I'm like, oh, they're just reading comprehension. Gotcha problems. They do feel

Sarah Powell:

Like that often. Yes.

Stephanie Landis:

But I can see as the adult having helped my two children through learning math from home is that it did make them stop and have to rationalize the problem instead of just go through and memorize the multiplication facts and memorize the multiplication they had to rationalize, well then they're what that knowledge

Sarah Powell:

Both are important. It is really important that students have that fact knowledge, and typically we expect that they have that knowledge eventually with automaticity. But then it is when students do math in the real world, they don't typically run into five times four written out and it's abstract form. It's more saying, okay, you have to buy five. What would we buy? I'm trying to think, what would we buy four of maybe like five packs of light bulbs and there's four light bulbs in each pack. Then how many light bulbs will you have purchased? So you use that five times four knowledge to solve that problem, but you have to be savvy enough to understand, okay, five packs, that means I have five different groups and I have the same number within each group. So that's five groups of four, five times four. And then with that fact knowledge, five times four equals 20, then you can easily solve that problem.

But think about all of the things that have to happen before you get to five times four. There's that reading, there's the interpretation of the vocabulary and the understanding of the problem. And then there's also that persistence not being turned off by this word problem and immediately writing. A lot of kids do for us. They write IDK, I don't know, and they just go to the next problem. So there's a lot of persistence there. You also have to keep information on your working memory. Oh, I'm working with these five packs of four light bulbs and negotiate with that. So that's where that math bucket, that reading bucket and that cognitive bucket all come together to combine to either make word problem solving really complex for students or to support students as they set up and solve those word problems

Stephanie Landis:

For teachers who are looking to help support their students more explicitly and intentionally through word problems. What is your advice or how do you usually have teachers? I think I'm getting at how do you help teachers? Yeah,

Sarah Powell:

What should they

Stephanie Landis:

Do?

Sarah Powell:

Yeah, good question, Stephanie. So the two things that we see time and time again, many, many programs and many research studies have emphasized are basically two evidence-based practices that have emerged from word problem solving and they end up being used in tandem. But the first one is to have some type of attack strategy for just helping you attack a word problem. I call these attack strategies. Other people call them cognitive or sometimes metacognitive strategies. But the idea is that students see a word problem and they should immediately think, oh, I do this, and the thing that they should do first is read it. So that's a good first thing for any attack strategy. And then they should make some type of plan they should solve and they should go back and check their work. There's a lot of different attack strategies out there, but a really common one is UPS check where students U understand the problem, P, make a plan S solve the problem and check, go back and check their work.

And they should do that every single time they see a word problem, whether they're six years old or 16 years old, whether the problem is working with simple numbers like two and three or whether we're working with fractions or negative integer. So having that attack strategy is really, really important. And adults don't always think about this because if you give an adult a word problem, 95% of the time, the adult will read the word problem. If you give a second grader a word problem, I would say 95% of the time they're probably not going to read a problem. They're just going to look at their numbers or guess they just start doing stuff. And attack strategy helps organize your process through the word problem.

So that's what we want to get in place first. Then the second thing that's really important is that students understand what's going on in these word problems. And so this is a little bit more complicated than the attack strategy, but it gets into a conversation about what we call the word problem schemas, or some people call these structures or concepts or problem types. The idea is that when in word problems, there's not a lot of different word problems actually. And in fact, across grades K through five, there's typically five schemas or five structures that students see regularly. And so if we can teach students to read the word problem, try to get an understanding of it, and then ask them what's going on in this story, is this a story where we're putting things together for a total? Is this a story where we're comparing amounts?

Is this a story where we have this set that increases or decreases? Those? Right? There are the first three schema, total difference change, and in grades K two, almost all word problems fall into those three categories. And so the idea is that if students can say, this is a problem where I have these parts put together for a total, it does not matter if the numbers are different. It doesn't matter if they're working with cupcakes one day and dolphins the next day and money the day after that. The idea is that this is a problem where parts are put together for a total and you know how to solve a problem like that. And so it just makes word problem solving more accessible, and it really helps students see the connections from the cupcakes problem to the dolphins problem to the dollars problem. And so what you do is you take that attack strategy, that process for working through a word problem, and then you combine that with a focus on what is actually going on in this story, that schema knowledge or the conceptual underpinning of the word problem. And then that can really help students with their approach to setting up and solving word problems.

Stephanie Landis:

I like that.

Sarah Powell:

And I make it sound simple. It's a little more complex than that, and it's develop Easy peasy. Yeah, easy peasy. No, we got it. By Friday. Everybody will be great at word problems. Start with the attack strategy,

Stephanie Landis:

Check it off the box.

Sarah Powell:

Yeah, yeah, exactly.

Stephanie Landis:

No more word problems we're done.

Sarah Powell:

I would love that. Love if it was that easy, Stephanie, but is not. But I would start with the attack strategy and maybe do a few weeks there with that. Just get students used to reading these problems, asking what the problem is about making a plan, solving it, checking their work. And then I would slowly integrate across the year, the focus on the schema, it usually takes a few weeks for students to learn each schema. So you wouldn't ever introduce all five of them at one time or even in one week, but I would probably introduce one of them, do some practice with it now introduce a second, and then go back and forth between the first and second, then introduce a third, and then give practice opportunities for the first, second and third ones. But the cool thing about the schema is that once you learn a schema, you use it for the rest of your life.

This is not a time limited thing, so you might be working with two and three, and then eventually it might be 123 and 315, and then maybe it's two thirds and three-fourths or maybe negative 72 and negative 18. The schema stay the same. And while the math gets more complex, the schema stay the same. So a kindergarten learns about parts put together for a total guess what a seventh grader is solving problems with parts put together for a total. And an adult is also solving problems with parts put together for a total. So there's a lot of staying power with the schemas. And I think that finding things in math that have that staying power that are important not only in school but will also be important for college and career and just general life, those things in mathematics, finding those and capitalizing on those is a really important thing to do for students.

Stephanie Landis:

I like that. I work a lot with executive functioning skills and outside of math, we'll even just talk about cooking or any sort of problem that you might have. And we're always like, when you have to do something, you have to start at the end and then work back.

Sarah Powell:

And

Stephanie Landis:

It's hitting me. The same thing with math. When you get to the word problem, you have start with the end of like, okay, what am I supposed to figure out? And then you can go back and then use that to work for it. And it's like, okay, you got to know where you're going to figure out how to get there.

Sarah Powell:

That's exactly right.

Stephanie Landis:

That is the part that the kids that I work with hate the most is having to start with the end and figure out where they're actually going. You're they just want to jump in and do.

Sarah Powell:

Yeah. And also math is so important for what students are going to do after school, whether math is a thing in high school that either propels students forward to college or holds students back, math is a thing for career that also propels students forward or holds them back. I've moved houses twice in the last year and had a lot of work. People at my house, every single one of them use math. And so even yesterday I had an electrician at my house because I had an issue with the breaker box on my oven, and he was explaining to me, this is a, I'm not going to, oh, I'm not going to get the units of this right and I'm going to sound so bad. But the wire, I don't know, I only had the capacity for I think 30 watts, maybe 30 something. Okay, I'll clarify what units it was.

But he was saying this breaker, I can't put a 40 breaker on this. It's only for 30. So then he's in the oven and it's telling you with the capacity of the oven, and he is literally doing division to figure out your capacity of your oven is 26, so 30 should work, but it's at the upper echelon of that and there's this 80% threshold, and he's running through all of this with me and it's all math. And I've seen tile work done where the workmen or work people are doing fractions an amazing number of fractions and fraction calculations where they're in sixteens and it's just unbelievable. And so probably so many students are like, I'm never going to need math in my career. And I would say, tell me a career where you don't need mathematics, and I'd be really interested to hear more about that. And you need math for your finances and how you just survive on a daily basis. It's all based in mathematics and there's technology's going to make that easier for us in the future, but you still have to understand if you have money in your bank account or how much money you're going to spend at the grocery store. So those things, math is just really, really integral to students. Not only success in school, but success as a person.

Stephanie Landis:

My whole life is figuring out math based off of the clock where I'm like, we have to be here at this time and this kid has to be here, and then time lab takes this long to cook and this long to eat and then not long to get their shoes on. So when do we have to do this? It's all one giant math problem every

Sarah Powell:

Day, even every day.

Stephanie Landis:

I say that I don't like math, I'm not bad at math. I can do math. It's just not my favorite. And then even going to be a speech language pathologist, I went through so many statistics courses and all of my reports rely on me being able to understand statistics and do percentages and all of these sites. And now I do percentages in my head all the time, day long,

Sarah Powell:

And you were like, I'm going to go be in speech and language. I don't need math. We teach

Stephanie Landis:

Kids how to talk and

Sarah Powell:

We're going to play. The joke is on you. Well, but thinking there just of data that you collect on your students and being able to, there's a data literacy component of is this student progressing at the rate that I would expect? That is a math question. And while you might be looking at their letter sounds or their word reading or something else, it's all still math thing. And really having that, I would say that literacy with data, and that is a base in math.

Stephanie Landis:

Math. So when they sit there and they're like, math, math's, never going to do this in life, and you're like, unfortunately you are. So not only do you have to learn math, but then you have to learn all the language involved in math that makes math that much harder.

Sarah Powell:

Yeah, well, it's complex. There's so much in math. A lot of my examples today have been around fractions or addition and subtraction or multiplication division, but math encompasses geometry. So everything that we do with shapes, math encompasses measurement. So anything that we're doing where we're thinking, oh, there's 12 inches in one foot or three feet in one yard, and what's the area of the rug that I need to buy that fits best into this room? Math is also probability and statistics and math is also algebra. So there's a lot of expectations that we have for students in mathematics coming from what they call a lot of different math domains. And really students have to show success across those domains to show success in math.

Stephanie Landis:

And you're right, math is tied with that reading. We spend so much of our day teaching math and reading, but you need those basic things to get through science. Science is math and reading. It really is.

Sarah Powell:

You

Stephanie Landis:

Need to get through it to all of those things. And so having that basic knowledge and understanding and all of science, I mean, science, chemistry, and lab problems are all so much of it. Math word problems,

Sarah Powell:

Just a math word problem. Well, even somebody was telling me, we were talking recently about history and timelines, that's also math related. So yeah, math is everywhere. You cannot avoid it. So we need to do our best to really help students with their math instruction and their math intervention identify students who are struggling with math and provide timely intervention to them. Because at any point when students struggle with math, that can impact later math. In fact, math I always talk about is this entirely cumulative exercise that students learn where everything you learn earlier in math is important for later mathematics. And so if any time when students are struggling with mathematics, we have to make sure that we stop and do something about that at that point to set them on a positive trajectory, knowing that next week's math or next year's math or five years from now, math really depends upon what students are learning in math right now.

Stephanie Landis:

And I love that your approach encompasses than just the numeracy, but it's also the cognitive and the language. Well, they're all meeting them and figuring out exactly where that you can go in and help boost those skills.

Sarah Powell:

Yeah, agreed. Yeah.

Stephanie Landis:

Well, thank you so much. I have one last question, and it can be math related or not at all, but if you had one piece of advice to give to our listeners, which are usually parents, teachers, other industry professionals, you had one piece of advice, what would you give

Sarah Powell:

Just one piece of advice in

Stephanie Landis:

General?

Sarah Powell:

This past weekend, I was talking about this with some teachers, every child really, I'd say craves and benefits from an adult paying attention to them, whether that's sitting there and talking about their day or helping them with their math homework or reading to them. And a lot of students go through their day and they don't get that individualized adult attention. And so the more that we can do that, and for me, I always see that we're doing that through math intervention, but just to be able to sit down and give students the attention of an adult is such an important thing and can really make the difference in the life of a student. So I would say my advice is to pay attention to the young learners around us and give them just even a few minutes a day. And that probably is going to be really important. Not only now, but we may make a long-term impact for those students

Stephanie Landis:

Completely. We always talk about at Paris that you have to start with connection before you can teach them to do anything. You have to connect

Sarah Powell:

With that. If you don't have that connection, it's going to be really hard to make a dent in students' math performance or reading performance. So it all starts there and we all have a little bit of time to give. So I think that's an important thing to do.

Stephanie Landis:

And once kids are connected to you, then they will push through. You were talking about that perseverance. They will push through and they will work, and they will do those hard things. If they have that connection,

Sarah Powell:

Well eventually one day they'll pass it on to others as well, which I think is the beauty there.

Stephanie Landis:

That was fantastic. Thank you.

Sarah Powell:

You're welcome. Thanks Stephanie.

Stephanie Landis:

I so enjoyed chatting with you about my least favorite. No, I'm kidding. My least favorite subject

Sarah Powell:

Now. Your favorite,

Stephanie Landis:

Now your favorite. It's my personal soapbox from my least favorite subject turned into my favorite subject

Sarah Powell:

Of math. There you go. I love it. Well, thank you for the opportunity to talk about math today, and I hope your listeners, if they do want to continue any math conversations, they can reach out to me. I'm pretty easy to find on the

Stephanie Landis:

Internet. Well, we have a few super math nerds at parish school, so I'm sure that they will be looking into it and reaching out. And I'm glad there are many people who

Sarah Powell:

Love created a few more math nerds today.

Stephanie Landis:

I hope so. I like that. I really do.

Sarah Powell:

Yeah,

Stephanie Landis:

Nice. I ended up marrying a math nerd and at least one of my children are math nerds. So great. Love the math nerds in my life.

Sarah Powell:

I love that too. Yeah,

Stephanie Landis:

That's great. Thank you so much. It was such a pleasure.

Sarah Powell:

Awesome. Alright, well enjoy the rest of your day.