Chris Colley: 0:12

Welcome back. Another episode of Shift Ed podcast coming to you from Montreal, canada, and I'm reaching down to Michigan, I believe. Kevin Nikoma is coming in to share some math mindset stuff with us. And it's Michigan, right, kevin? It is Absolutely Southwest corner of Michigan. Amazing. And are you still the president of the NCTM?

Kevin Dykema: 0:38

Yeah, so my term actually it was a two-year term ended like the 1st of October, so now I'm technically the past president for a year, so I get the honor of supporting the current president and helping her succeed Amazing.

Chris Colley: 0:54

Amazing, Great stuff, too, coming out of. I mean, there's so many resources out there for math teachers and expertise as well out there for math teachers and expertise as well. It seems to be one of our subjects that gets a lot of attention, a lot of misinterpretations, misunderstandings and struggle as well, and that's kind of what we'll focus on here today is that productive struggle. But before we start, Kevin, were you always into math?

Kevin Dykema: 1:29

Was that your jive at a young age? As you grew up it was. I always felt successful in math and I mean, looking back now I can argue I didn't understand a lot of what I did, but I always did very, very well in mathematics and memorized things. I was a good rule memorizer. I could follow the procedures. It wasn't until I started teaching that I actually had to get to the understanding stage and I think I learned more my first few years of teaching middle school math than I did actually as a K-12 or a college major in mathematics, when you actually have to start to see the why behind things and to start to see connections between different things. And to this day I mean I think every time I work with a group of teachers, work with a group of students, I learn new things or I see things differently because when we allow our, when we allow our learners to share their thinking, good things start happening and they often my students often see things differently than I see the different content areas.

Chris Colley: 2:25

Amazing, amazing, and like, we tend to teach the way we were taught, right, yes, and math is. You know, I remember my math classes in particular, obviously, and how kind of removed the student was from the whole learning process. The student was from the whole learning process and the teachers I see pre-service teachers and first-year teachers coming into the system that that tend to, you know, go to what they know, which is how they were taught. Um, is there a disconnect you find between, like, um, how we're, we're getting teachers ready to teach math? Um, because in elementary school, for example, I mean, it's a lot of non-math experts, right, you're a general in elementary school here in Quebec anyway, and then, as you go into high school, you're expected to be, you know, more of an expert. But, like, is there a disconnect between how we prepare our math teachers to the reality of it?

Kevin Dykema: 3:25

Yeah, I'm not sure if there's necessarily a disconnect. I think a lot of our colleges of education are doing a great job of saying this is what it could look like, but then they get into a school system where it doesn't look like what they're doing. That you know, in education world we're slow to change, especially in the math world. And you know, when I think about the secondary folks, for many of us we were great rule memorizers and school worked for us. Having the teacher just say here is the steps, here's step one, here's step two, here's step three, memorize it and you'll be good. That worked for us and we became math teachers. And because it worked for us, we think it should work for everybody, and I'm overgeneralizing here. But for Autism, we think it should work for everybody and the reality is it does not work for everybody.

Kevin Dykema: 4:12

Having math be taught very, very procedurally has not worked for decades and decades and decades for all. It works for some and if we're truly interested in meeting the needs of all of our learners, we need to look at doing things differently and change is hard. So I think they're in many colleges of education. They're being taught what they should be doing, but then they get into the school setting and the school setting looks the same as it did 30 years ago, 40 years ago, 50 years ago, oftentimes in math. That doesn't mean we haven't made some improvements in math, but there's a lot of room to grow and I love how you noted. I mean I don't love how you noted, but I appreciate how you noted. You know, in math it hasn't been very student-centered in the past. It's been very much teacher-driven. And when we think about productive struggle.

Chris Colley: 5:03

we need to get our students engaged in that learning. That's required in order to make sense of the mathematics. Absolutely, and Kevin, what is mathematics Like? I saw one of your presentations where you led with that question Like what is it Like?

Kevin Dykema: 5:19

could you expand on, like what that term is? Yeah, and I think that's a. I think it's a fundamental question and I think the way that you answer that question of what is mathematics affects how you think that math should be taught, how math should be learned, or even why we have to learn math. I think for so many of our students. I'll go from the student perspective first. I think many of our students see math as I just need to learn this formula, I need to learn this equation, I need to follow this procedure and poof, I'll get a correct answer.

Kevin Dykema: 5:42

Getting correct answers is very, very important, but I think when you talk with a lot of mathematicians, when you talk a lot of mathematics educators, words that come to their mind instantly.

Kevin Dykema: 5:51

When we talk about what is mathematics, it's problem solving, critical thinking, reasoning and sense making, explaining the real world around them. So there's this disconnect between what we think mathematics should be and what many of our students see mathematics as, and that's on us as a mathematics education community to change that and to really help our students begin to see that math is understandable. It's not all these random sets of procedures and we know they're not random sets of procedures, but for many students, they're viewing them as just random sets of procedures that they have to follow. We need to teach math in such a way that it makes it coherent for our students and so that it builds from grade to grade to grade and they see, oh, what I'm learning in grade seven is really taking some of that work that I did in grade three and just generalizing a little bit more. And then, oh, when I go to grade 10, I'm going to take that same learning and just extend it a little bit more.

Chris Colley: 6:52

And we don't have as much of that as we could if we're truly interested in meeting the needs of all of our kids. Totally, totally, yeah, super interesting. And I mean your book Productive Math Struggle. You mentioned worthy of struggle, right, that students have to go through this and as teachers, I mean we're very compassionate and empathetic towards our students. Sometimes it makes us uncomfortable when we see them struggling, right. How do we change that mindset that we need to let them struggle and that they're worthy of the struggle? I love that term.

Kevin Dykema: 7:25

Yeah, and I think we know it's got to make sure that we're defining struggle carefully, right, whereas I'm certainly not advocating, for you know, when I walk into class and all the kids are in tears or all the kids that put their heads down, I'm not like, oh, this class is rocking it, it's that productive struggle, it's got to lead somewhere. And is rocking it. It's that productive struggle, it's got to lead somewhere. And I think about you know learning in general, if I go out of the math classroom for a little bit, when you think about you know learning a new instrument, there's a lot of struggle involved with that. But yet we value that struggle and we recognize it's okay that you don't have it perfect right off the bat. It's okay that you're exploring, that, you're messing around, trying to figure things out, sort of grappling with how to hold the instrument, how to blow with a horn, whatever the case may be.

Kevin Dykema: 8:05

But then in math it comes sort of to a grinding halt and too often we just teach math as this, procedure to procedure after procedure, and our students don't see math then as something that they need to be studying because realistically they say I have a calculator, I'm at all times with my cell phone.

Kevin Dykema: 8:22

So I think when I think about you know, mathematics seems to be worthy of a struggle and it's that all students should be doing that we need to help our students recognize that math is understandable. There's a reason for that. It makes sense, and let's teach math as sense-making. Let's get our students actively engaged wrestling, struggling, grappling whatever word you want to use at that point in time to have them begin to make some of that sense. I often think, you know, in a typical traditional classroom and it's for decades and decades and decades the teacher is the one that's doing all of the intellectual work maybe not all doing the vast majority of the intellectual work in a math classroom and the kids are sort of along for a free ride. We need to get our kids doing that deep thinking that's required to be able to make sense and the teachers are providing that support along the way and helping to ensure that every student is being successful.

Chris Colley: 9:18

Right, I love your examples too, that it is a skill that you, you develop. You know, I mean similar to creativity, example, right, like some teachers, you know, or some people, I should say, oh, I'm not creative, right, but again, it's this muscle that you work on, right, and grow and develop. Um, oftentimes, though, I've noticed that, the relevancy, right. So you mentioned, like learning an instrument, I see the value because I'm motivated in it's relevant to me, right, I'm interested in how do you turn that in a math class to make it relevant? Um, and I I remember you had mentioned that math is all around us and, again, that disconnect between students seeing it relevant in their world. You know, when they walk outside of the school, that they start to notice these patterns or things that are similar. Or can you expand on that a little bit?

Kevin Dykema: 10:13

Absolutely, and I think some of it's. You know it comes back to the how are we thinking about math and what are we? What are we looking at with math? And, if we're being honest, much of the math that we do in the K-12 setting is not the math that they see in the world around them. You know I pick on high school sometimes that you know you factor trinomials in high school but you're not factoring trinomials outside of the walls of your school for most adults. I mean there may be some that are doing that for their career.

Kevin Dykema: 10:42

So we have to quit trying to find every single topic that we may teach in math and say, oh, it definitely applies to the real world in this way. But we need to help our students recognize that math was developed for a reason, somebody at some point in time, and math is still being developed. I want students to walk away thinking, oh, it's just all this past stuff that we're just redoing. But then somebody had a real life problem that they needed to solve, and because they needed to be able to have some way to describe a curve, different mathematics was generated. Because they needed a different way to describe the way a leaf may grow on a tree and we get new math that is created at that point in time.

Kevin Dykema: 11:24

So we need to help our students see we need to do a better job of helping our students see the connections between developing math and that math has been used to solve real-world problems. We can look at some real-world situations and use some mathematics, use some data, use some statistics to help analyze some of those different situations that are going on in the world around them and helping them just begin to see there's a lot of math in there. People are using some of that logical thinking, that critical thinking. They're using data to make decisions and when we look at you know, especially the last 10 years, the amount of data that's being collected and the amount of data that's being used to make decisions has rapidly increased and we owe it to our students to have them develop a good understanding of that world around them and how we can maybe describe it mathematically.

Chris Colley: 12:14

Right, right, totally cool. And I mean I love these ideas too, that that when we are teaching math and that students are going through that process of figuring it out, that they bring certain luggage with them the kids and you talk about it in your book this, this kind of math trauma of sorts, where they don't feel like they belong yes, In math you know like they belong, in math you know like they. Just there's this wall and it's really hard to break down. But I love in your book you talk about the belongingness in that struggle. Can you expand on that a bit? Because I find it so fascinating that this sense that if I don't feel like I'm, I have a purpose within this class that's talking math, that I, you know, I'm excluded from it, which again perpetuates this math trauma that our young kids go through.

Kevin Dykema: 13:09

Very much so and you know, sometimes I like to frame it around this idea of a mathematical identity United States and Canada and I can't speak for all of Canada and all of the United States, but as I work with educators, primarily in the United States and some in Canada, you know I hear that frequently, that you know, in society it's generally it's very cool to say I'm not good at math, right yeah. But you don't hear that same adult say I'm not good at reading. They may say they don't enjoy reading. So as a society we've sort of made it cool to say I'm not good at math, so it's okay to feel like you don't belong in there because nobody does good at math unless you know.

Kevin Dykema: 13:47

We think of who is a math person For many of us. We grew up in a time you know where it was. Those that were pocket protectors were those that did math or those that had suspenders or it was sort of the geeky type of stuff. So we have to break down some of those walls and we need to help our students recognize that we're all capable of learning math and we need to share stories of people who are doing math. When you ask a typical K-12 student describe a mathematician. A mathematician it's an old person, often somebody who's dead, somebody who's Caucasian most of the time male, frizzy hair.

Kevin Dykema: 14:26

As a math education community, we need to be sharing stories of other mathematicians. We need to be finding mathematicians who are still developing math. We need to find those mathematicians who are young, so that students see themselves as capable of learning math. They're recognizing oh, it's not just Pythagoras, it's not just Euclid, it's not just Archimedes, it's not just Gauss, it's not just those that we think of from centuries and centuries ago as mathematicians. People are still doing mathematics and it's not just dead white males that did mathematics that they see themselves. And when they see themselves reflected in people who are doing math currently, they're going to begin to get a sense of belonging. And I also think that when we focus on really getting to math by understanding, rather than just math by memorizing, students start to feel like they belong in there. Then because they recognize oh, I am capable of understanding this. Math is an understandable subject and there's so much work that we can do to help increase mathematical opportunities for all of our students.

Chris Colley: 15:37

Absolutely Well said, well said. Could you elaborate a bit? Students, absolutely Well said, well said. Could you elaborate a bit? In the book it talks about the six-point action plan for fostering this kind of perseverance and I'd even extend that in developing that community, that math community within your class where everyone feels that they can contribute to the thinking that's going on. Can you talk a bit about those six points and how that leads to?

Kevin Dykema: 16:03

Yeah, yeah. So you know, when John Susie and I wrote the book, we said you know we need to come up with sort of an action plan for teachers, because it's not just going to happen instantly that all of a sudden the kids are going to be like oh.

Kevin Dykema: 16:16

I'm so excited to have to think deeply about math and to do that. It's not like a light switch that you can go and flick on. So what are some of those intentional steps that we can do? So the first thing we said you know we need to work on valuing this notion of really wrestling, grappling, making sense of the math max, both from the educator perspective as well as helping our students see there's value in not just being told what to do and just memorizing. There's value in having to work hard at developing a good sense of understanding. So that first action step is value. That second action step is to foster positive mathematical identity. We talked about that with the belonging. If they don't feel like they belong in the world of mathematics, they're not going to feel capable of doing that. So we need to foster that positive mathematical identity and help all students recognize they are capable of learning mathematics. The third action, then we need to build a classroom community that's supportive of really wrestling. And what does it look like? What are the norms? What does it look like when you're, when you sort of get stuck? How might we get unstuck, for lack of a better word? What are some things that we can do at that point in time. That fourth action, then, is to plan our lessons for it. What can we do? Where can we really provoke that deep thinking? What are some strategic changes and some questions that we may have asked in the past? How can we change, then, a problem that we may have done to make it a little bit deeper thinking at that point in time? And then, as part of that planning, then it's also anticipating what are the students going to do? How are they going to do it correctly? What are some of those correct strategies they may do, as well as what are some of those misconceptions or partial conceptions that they may bring? And then how am I going to respond to that? What am I going to ask? So it's not just me rescuing their thinking or rescuing their answers. I'm rescuing their thinking and really helping them go from there.

Kevin Dykema: 18:00

That fifth step, then, is to support the productive struggle. What am I going to do when the kid hits that point where they say they're stuck, and I think so much of that's because of the planning? If I've planned well, I'm going to be able to support better at that point in time, and when we support, we have a rich history in mathematics of when a teacher helps a kid, we grab their writing utensil and we do all the writing for them. That's not what we're talking about here with supporting the struggle. It's really getting to that student's thinking, helping them explain what are they currently thinking and then providing some prompts to help them make sense.

Kevin Dykema: 18:34

And then that final action, that final step, is to reflect back on that productive struggle. We need our students to see hey, three days ago I might have thought this was the most impossible thing in the world, but because I didn't give up, because I kept trying to make sense of it, now I've made sense of it. I'm like, oh, it's not so bad, and when we do a little bit of that, reflecting back on it, then we can celebrate it with the students, which then just helps to build that positive mathematical identity. So we look at those six actions the valuing, the fostering, the building, the planning, the supporting and the reflecting as a way to really engage all of our students in this notion of making math understandable and doing math by understanding rather than math by memorizing.

Chris Colley: 19:21

Yeah, totally.

Kevin Dykema: 19:23

And like walk us through a period Like how would you see a successful thinking mathematically classroom, like how would it start and then what would the teacher get the students doing, and could you kind of walk us through what that would look and feel like yeah, and you know, and depending on the content, the concept you're learning, it's going to look a little bit different and you know what it looks like in the first grade class is going to look different than in the grade 11 class or a grade 8 class. But overall, you know, the kids are going to be working on, on a good rich task, a good rich problem, something that's going to going to spark some thinking at that point in in time. I'd often like to, you know, start out with that problem that so often, you know, for many of us, we did all the. Some people call them the naked number problems, where there's no context. And then question number 38 was a real life application and sometimes, let's be honest, the real life application and sometimes, let's be honest, the real life applications that we use aren't real, real life. But starting out with a contextual problem, helping them understand why we even care about this, get the students actually engaged, get them sharing their thinking in small groups, and then, as we're trying to wrap it up, that's maybe when we get a little bit more of that procedural fluency, when we get some more of that procedural stuff, I think, historically, one of the flips that I like to think about.

Kevin Dykema: 20:47

Historically in math, we've told our kids here's the procedure to follow, here's the steps you need to do.

Kevin Dykema: 20:52

Now you think, when I'm thinking about productive struggle and I'm thinking about what a good math classroom should look like, could look like, let's get our kids thinking right off the bat. We can provide more of that step-by-step at the end as a way to wrap up, as a way to formalize their thinking, as a way to make sure that, yes, we are good to go on from there. But a good classroom, the kids are doing the work, the kids are thinking, the kids are not just sitting there listening to the teacher do all of the thinking, all of the talking all class long. And it's hard. It's hard to shift that because you know, we talked about it earlier For so many of us as educators.

Kevin Dykema: 21:34

We grew up in a time where the teacher did all the work in the math classroom and we just had to sort of follow along and hope that we could mimic the teacher's steps. We need to be changing that. We need to be getting our students to do that rich, deep thinking. Help the students see the connections between different things, help the students make sense of the mathematics and then we can provide some of that structure towards the end of a typical math class.

Chris Colley: 22:00

Then yeah, for sure, I love that idea too. It's a small tweak, but just throwing the question at the start or the problem at the start and allowing the students to kind of like struggle with it a bit and then if there's any misunderstandings, you can clean those up at the end, yes, um yeah, and we have to recognize not not all kids are gonna do the problem the same way and that's okay.

Kevin Dykema: 22:23

And if I'm being honest, sometimes my students see problems a whole lot neater than I do, that my brain, because I'm driven just so focused on math, math, math, math, math. I jump straight all the time to let's write an equation for it. Most students do not jump straight to let's write an equation for it. Most students wrestle through and actually think with that. With that One of the things I often like to do when I'm leading some professional development either, with sharing a math night for parents, working with teachers, working with administrators, working with students, I may say how would you do 245 plus 98? And for most people they say, oh, if I'm going to do 245 plus 98, I'm going to think of it as 245 plus 100 and subtract 2. Or some other strategy that they may have.

Kevin Dykema: 23:07

There's lots of different strategies Like all right, this is what we need to be making our math classes like. We need our kids to be doing that thinking. We shouldn't just say, oh, back in 19-whatever, here is the one and only one way that we could do the 245 plus 98. Let's get our kids thinking, sharing their reasoning, and that means we need to have that comfort of recognizing it's okay if they don't do it the exact same way that I may have done and it's okay if they have a way that I'm like, oh, I'm not positive that it works for us to say, all right, hey, let's try it with a different set of numbers and to see if it works.

Kevin Dykema: 23:41

And it's a shift for the kids and it's a shift for the teachers. But it's so powerful for our students and it helps our students to see that math is capable of being understood and math is useful. It's not just the subject that people did decades, centuries ago and that we're just redoing, relearning everything that they did, however, many years ago, and there's really no value in it. We had to have our students see the uses of that, see when they would use the mathematics in a variety of different settings For sure, you know.

Chris Colley: 24:15

It's interesting that you're saying that too, because I'm thinking about when I'm working with kids in coding. You know, either doing a scratch project or like programming in Arduino or something like that thought process is very similar to what you were mentioning there, and I wanted to ask you that crossroads, because coding definitely seems to be something that is becoming more and more relevant. It's going to affect way more people's lives. Where does coding and math meet?

Kevin Dykema: 24:46

Yeah, that's a great question. That's one of those things that I think about and I talk with other people and you know I don't think as a collective education community we've come to any resolution yet about how to intersect those. Everybody's saying, yeah, there's a lot of overlap in there, but to figure out, how do we fully integrate that into there? And you know we have a finite set of minutes that we have our students in there. But to figure out how do we fully integrate that into there? And you know we have a finite set of minutes that we have our students in school. So anytime we try to add something in, theoretically, something needs to go out and we need to figure out what is it that needs to go out.

Kevin Dykema: 25:22

I often like to, instead of thinking you know, what are we eliminating? What are we de-emphasizing? What are we going to emphasize? What are we going to to de-emphasize a little bit, and and sometimes when we start thinking about, oh, I can de-emphasize this after a period of time, we're like all right, why am I even doing this anymore? But sometimes it feels harsh just to say, oh, I've loved doing x for however many years, I can no longer do it. Let's just sort of gradually do a little bit of phasing out, and you know some of it's. We've got to recognize what are the skill sets that our students are going to need to have in order to be productive citizens in the world. And you know, coding is definitely one of those that they need to be able to have a better understanding of what it is and the more and more technology driven that we become, we need students who have an appreciation and have some skill set in that world of coding.

Chris Colley: 26:16

Right, right. Well, this has been a really fascinating conversation, kevin. I really appreciate you carving a bit of time to share your thoughts with us and I'm really excited that you're going to be supporting, um, our math consultants and teachers and, um, I think that these kinds of conversations are super rich and just kind of reflecting on our practice a bit, um and, and realizing that it's not a you know, like we have to change everything. We can make small adjustments that allow more thinking into the classroom and giving it a bit more back to the student, which I really appreciate. Those thoughts and your book is just, really just a great plethora of ideas and starters. I wanted to talk a little bit about rich tasks, but I mean, your book touches on those a lot. But maybe my final question to you as we close here is what makes a good rich task in your opinion?

Kevin Dykema: 27:15

Yeah, I think a good, rich task is something that has an interesting context and I acknowledge an interesting context for student one is not an interesting context for a student two, so you're not going to have a task that every single kid is going to be like oh, I love the context of this.

Kevin Dykema: 27:30

But it has to be in some sort of a relative interesting context. It has to have a variety of different strategies that students may use for it. Some may make a table of values, some may jump to an equation, some may make a graph, some may reason through it. There has to be some way for all the students to be able to at least get started on the problem. They may not all have the ability initially to find a solution in a relatively quick amount of time, but whether they all can get started at that point in time it has to be aligned to the content. We can't just pull out these things and say, oh, this is kind of a fun thing to do. It has to actually promote that good, solid thinking that's necessary in order for them to learn that content. But it's really you know the multiple strategies something that's contextual, based, so that they see that math is useful, math is relevant to my life as a whatever grade student I am at that point in time.

Chris Colley: 28:28

Amazing. Well, these have been some math nuggets for sure Again. Well, I mean just that rich task. I mean I'm just it's starting in the reflective process, which is amazing, so amazing kind of thoughts that you've thrown out. And again, thanks so much and I wish you all the best, have a great holiday season with your loved ones and again looking forward to seeing your influence in our system throughout this year.

Kevin Dykema: 28:57

Well, thanks for having me on to talk math education Awesome.

Chris Colley: 29:01

Thanks, so much, thank you.