Episode 8 - Through the Math Forest

RAYMOND THOMPSON JR.: So do you want to ask me a question about math?

DIANA MAZZELLA: I did. I have a question for you. 

THOMPSON: OK.

MAZZELLA: What do you remember about math class?

THOMPSON: It's weird, I only actually remember one. And that is my algebra 2 with trigonometry class back at Wakefield High School in Arlington, Virginia. And mostly I remember it because it was kind of torture. [Laughter]. When I was a kid I really wanted to be like science and techie and math and stuff like that. I really wanted to do it but I found that I was not that great at it and the experience of trying to catch up and learn in that very book way that they taught us was very difficult for me because now I know I was a much more visual person, visual learner. So sitting in that class, watching her draw these lines on this transparency was like just torture. I was watching, looking up, looking at my book, reading, trying to understand, she's lecturing and I'm not understanding and then I would go home with my book and try to read about it. I wasn't terrible. I was a solid B-, C student in math so I would pass but I was never going to be an astronaut. 

Did being in those math classes sort of, or experiencing math, influence the career you went into or what you thought you could do when you're older as an adult?

MAZZELLA: Um, I remember thinking that I could do probably anything but like I wouldn't enjoy just doing math like being a mathematician or something. I didn't understand what you could use math for. Like I don't think that was ever clear to me as I was going through these classes. I like statistics and that became useful for my job in journalism. But I don't think I understood that math could help you get to a certain place. I just knew it was something that you had to do.

I’m Diana Mazzella, and this is Sparked, a podcast about the people who are changing Appalachia’s future. I was talking with co-producer Raymond Thompson Jr. about math because we went and did something that most adults don’t do. Because they would rather do anything else. Like bathe a cat or put their hand in the path of oil spitting from a pan or climb a mountain in winter wearing only a tank top and shorts.

We went to a math class. Several math classes, in fact.

The day after Pocahontas County kids made it back to school from a winter break replete with snow days, we trekked into the mountains, through forest and past the rivers to spend a day in math classes talking with teachers and students and watching functions go up on the board. I was nervous because, well math. But today I was also excited going into this math class.

Because Pocahontas County has done something over the last seven years that is unexpected but highly desirable in the United States today. They raised their math scores. The county went from middle of the pack in state eighth grade and 11th grade scores to having the highest percentage of students in West Virginia proficient in math on the Smarter Balanced assessment in 2017.

Pocahontas County eighth graders were seven percentage points ahead of the next proficient district, Monroe County, and they were level with the state that shows the highest math proficiency in the nation: Massachusetts.

So how did they do this? I can tell you how it wasn’t done. It’s not through doing the exact same things as other schools in other places. It’s not through telling teachers what to do. It’s not through doing things faster or finding shortcuts. It’s way more complicated than that.

But I can tell you where it started, with Ms. B-K.

It’s early and Raymond is driving while I’ve got a microphone in Joanna Burt-Kinderman’s face while she eats bites of scone in between explaining her home county.

JOANNA BURT-KINDERMAN: Pocahontas county is one of the most rural counties east of the Mississippi. This is a foresting community and it’s the birthplace of rivers, seven rivers have their headwaters here. There’s no water that flows into this county, everything just flows outwards. So that's a really precious thing as well.

Right now we’re headed to the only high school in the district, it’s right in the center of the county. And we’re going there to join a math class with some sophomores and one of our fabulous math teachers, Laurel Dilley.

MAZZELLA: Burt-Kinderman -- who graduated from West Virginia University with a master’s degree in higher education teaching and learning-- is a math coach. A job I didn’t know existed. It’s certainly an uncommon job, and one that she piloted in Pocahontas County. She was a teacher who had worked in other parts of the world in public and private schools and at the community college level. She moved back home to Pocahontas County with this idea that math education could be different in its five schools.

So she went to the administration and asked if she could try something. It kept paying off, teachers bought into it, students improved and administrators kept supporting it.

When we got to Dilley’s Math 2 class, we saw the chairs in circles, which is becoming more common as American education emphasizes the kind of work you do at work: in teams. And there was a lot of conversation.

BURT-KINDERMAN: Miss Dilley and I are talking in the last couple weeks about what’s going really well for you guys and where we might still have some room to grow. The goal of these is not necessarily to get this problem correct in these first 8 minutes, it’s to figure out in the first eight minutes what you know and where you’re confused. And that’s a pretty important thing to be able to do because once you can say to yourself "Ok this is the thing that I’m not sure of," you’re so much closer to being independent and getting yourself unstuck, which is really different than just being like "I don’t know how to do it," right? And you guys have come really far in that in the last couple years.

MAZZELLA: The students are given a linear function. (You’ll remember in math class graphing lines on x and y axes to express this function.) The students are asked to work the problem and write down specific questions that will help express the roadblock they’re facing in solving this problem and seek targeted help. Burt-Kinderman and Dilley walk around the room noticing which students are pushing forward and which are halted.

Then they do this:

BURT-KINDERMAN: Like are they drawing, are they connecting the dots or are they finding the slopes between points. So I wonder if do you want to divide the room and like at 2-minute increments try to take note of people that are giving up? Because I really want to be strict this year with that feedback to them.

MAZZELLA: Through every lesson we shadow that day, Burt-Kinderman will have a whispered check-in with the teacher to see how the activities she brought are landing. And how the teacher is responding. It’s time to put pencils down. Each student is at some place: confusion, certainty, the right answer, a wrong answer.

Then Burt-Kinderman goes through a scenario with a student, showing how she wants the group to converse about the problem.

BURT-KINDERMAN: Here's my question, this is how I want it to go. And I told them what to say. This is not what they would really say, OK. I'm going to say, OK, my question is I don't remember what a y-intercept is. Could you tell me what a y-intercept is?

STUDENT 1: I think the y-intercept is the tilt of a line.

BURT-KINDERMAN: Thank you.

STUDENT 2: I'm sure that the y-intercept is where the line goes through the y axis.

BURT-KINDERMAN: Thank you.

STUDENT 3: I'm not sure.

BURT-KINDERMAN: Thank you.

STUDENT 4: I'm sure the y-intercept goes through the y axis.

BURT-KINDERMAN: Thank you.

So what did you guys notice about how I did that or what they did or didn't do?

DILLEY: You weren't judgy.

BURT-KINDERMAN: I wasn't judgy. Did you notice anybody say something pretty goofy? Nobody did? Yeah, Amelia said something a little bit goofy. And did anybody argue with her? No, and so this is on purpose. At the end of this task, we're going to let you guys hash it out. But right now I don't want you to have conversation back and forth. I just want you to hear out what each other..

MAZZELLA: They discuss the problem more. Where were they clear on the problem? Where did they get hung up? She has them work each other’s answers.

Then the class is over. And they leave their papers with Ms. Dilley.

DILLEY: Right here, just kidding. On Caleb's desk. Have a great day! [Papers rustling.]

BURT-KINDERMAN: Thank you, guys!

We listen as Dilley and Burt-Kinderman debrief the day’s lesson. Dilley was uncomfortable with how the class ended without a formal closure to the problem.

DILLEY: I feel like I know more what I need to work on but I guess [BK: Define that for me, put that in...] it’s not a typical lesson, right? So normally I would come in and I always try to wrap it up and like "this is what we learned today" and you feel pretty good enough to go and try out your homework on it. That’s not what happened today. So I think they were learning the whole time but it’s definitely like a different space as a teacher for me because it wasn’t a crystal clear like "OK great, there was your lesson and we learned and it now go out the door and finish it up."

MAZZELLA: They’re trying to decide what this lesson was about. Was it about knowing how to complete a linear function or making sure students know how to catch themselves when they fail?

BURT-KINDERMAN: And I feel like if you think about those first eight minutes as fishing, we found two fundamental problems. The first would be just writing the rule for the linear function, and the two things that I noticed that was my job to keep track of, [Dilley: It was insanely frustrating] writing slope reciprocal. OK, that’s a really standard mistake that people make, and it was forgetting the sign. And they all would have caught that. I suppose what happened in my mind there is watching this and thinking "Holy cow, nobody’s catching themselves and so how do we give them the tools to catch themselves." My focus became this is the main problem here not this big wide understanding of functions where you’ve done work and it’s paid off like the kind of conversations they were having are not normal 10th grade conversations. 

MAZZELLA: This back and forth between math coach and teacher is something that Burt-Kinderman learned at the Park City Mathematics Institute. It’s based in Japanese lesson study, a collaboration between teachers to assess student understanding and needs and grow lessons to fit those needs. You can see the time and attention to detail that they spend in educating the students. This model is also good for Dilley, who this spring was named West Virginia High School Math Teacher of the Year.

As a young teacher, Dilley arrived at Pocahontas County High School with confidence. She’d taught high school math for two years and had a bachelor’s and a master’s degree from WVU. Then she overheard the other math teachers, who had already started working with Burt-Kinderman a couple of years before.

DILLEY: My first day we sat down and were going through precalculus level problems together in the library and I was like "Oh my gosh I’ve got to actually work on this. This is kind of hard and the ways they were talking about how to present it to the class and approach, it was mind blowing.

I didn’t know how much I didn’t know until Joanna started helping me out. And in the beginning it can be a little deflating. She didn’t present it like that I would take it like that occasionally because I’m really hard on myself. But when I step back and look at it, oh my gosh I’ve grown so much as a teacher. So much. And I’m continuing to grow. I don’t think that I’m some phenomenal teacher. I got teacher of the year last year. But I still think like there is so much she could teach me. Even just that conversation we just had, I still have questions as a professional like "How do you handle that situation?" and I don’t think that’s something that other teachers get. We find our teaching style right and you get moving and that would have been me if I hadn’t come to Pocahontas County. And I would have been on my roll. You know your curriculum, but your teaching style doesn’t change and the way you present problems doesn’t change unless you have someone pushing you to see things differently.

MAZZELLA: Burt-Kinderman does see things differently. She sees that math can be for students in rural areas and in urban centers, where they may not have the same resources as high-performing schools. Math can also be for students who aren’t great at memorization.

She says this collaborative teaching could be done with any subject. But she chose math for a reason.

BURT-KINDERMAN: I would say first and foremost, it is a gatekeeper. Algebra 2 success itself is a gatekeeper to possibility. And I don’t think all kids need to go to college or that all kids need to be scientists, but I do think all kids deserve that choice. You go talk to your colleagues at WVU and they’ll tell you the biggest thing that holds kids back when they’re at a university from their dreams in science and technology is their math readiness.

Right now in this county, in this state, we have to redefine ourselves and we have to grow a community of young people who are able to look at a landscape and not just see what is and what was but see what’s possible next and then be able to chart a course to get there that includes anticipation of what might be stumbling blocks and includes the flexibility and the ingenuity to figuree out how to get around and through those, and I think math class can be a really wonderful place to grow that habit of mind.

MAZZELLA: Pocahontas County High School students are showing a depth of understanding that surpasses knowing the answer. After Math 2 class, Dilley teaches an AP computer science class, which fills an advanced math slot. The students are still solving math problems but they’re designing algorithms to make it happen. It’s sort of like math class squared.

After Dilley taught her first computer science class, she saw most of the kids go on to major or minor in computer science in college. Clearly, they had a use for advanced math.

Aaron Pritt, one of her current seniors, is the first to advocate for what they’re doing.

AARON PRITT: We’re taking what seems to be like an out of the backwoods school and we’re going to the front of technology with computer science programming, coding, we seem to be continuously moving forward. While some people think, West Virginia not much but then you get this school and you see "Oh they can actually do a real lot with computers."

MAZZELLA: Dilley was proud of how one senior, Hunter Tankersley, used his skills over winter break.

HUNTER TANKERSLEY: So I was at work and I take photos for a dealership in Marlinton and it was cold outside and I didn’t want to go out and take pictures so I designed a program to generate a vehicle description for the vehicles that are on our website.

MAZZELLA: Pritt likens the creativity of making a program like Tankersley’s to making art.

PRITT: It’s like looking at the Mona Lisa, when you look at it you see this big masterpiece but when you break it down into little sections it’s oh he mixed here, he did this here, switched this here and it’s really just a lot easier when you break it down.

MAZZELLA: The class goes through their lesson of making an algorithm in Python programming language to find values that will support a pythagorean triple where a+b+c=1,000. Then they need to find the product of a x b x c. For those like me who couldn’t remember off the top of their heads what this was, a pythagorean triple consists of three positive integers where a squared plus b squared equals c squared.

The students get there in different ways. And they debate how to make their code more efficient. Burt-Kinderman sees how this way of telling math is already in the air around them.

BURT-KINDERMAN: So a lot of what you saw today, it wasn’t necessarily a creative problem but it was an open problem so there wasn't necessarily one way to get into it. And we’re trying to really harness the power of story, which I think is absolutely a central part of being an Appalachian. We tell each other stories. We talk through our issues on phones or front porches or even texting to some degree, that’s the way we come to understand our world. But we’re really putting a lot of juice into how do we get to kids to tell themselves the story of what a linear function is and all its many forms so that’s something they can own and retell which is radically different than how I learned math and I assume you’re also reflecting on this did not look like my high school math class, right?

MAZZELLA: It did not look like any math that I knew. I remember solving a quadratic equation in College Algebra and getting the paper back and finding out that my curved lines weren’t even in the right quadrant or going in the right direction. I mean, what did I know anyway?

I did like the puzzle part of math. The potential to prove yourself. But it didn’t mean anything to me. I used to drive home from community college night classes with my sister and she’d be talking about precalculus and the joy of matrices. It was disgusting to see that much joy about whatever that was. And I was jealous. Why didn’t I like matrices? What was wrong with me?

The stakes right now couldn’t be higher for math education in the United States. The 2015 Program for International Student Assessment showed that the U.S. is nowhere near most of its industrialized peers when it comes to math readiness in 15 year olds. Singapore tops the list at an average score of 564. Followed by other industrialized Asian nations from Hong Kong to Japan to South Korea, the list then goes through Canada and much of Europe, New Zealand and Australia. The U.S. had an average score that year of 470, a few points below Lithuania, Hungary and Slovakia.

The U.S. government’s National Assessment of Educational Progress shows that in 2015, the average across the nation for math proficiency in eighth graders was 32 percent. By state, Massachusetts leads the pack with 51 percent proficiency. West Virginia is toward the bottom with 21 percent proficiency, tied with New Mexico and ahead of the District of Columbia, Louisiana and Alabama.

Everyone in Dilley’s classes may not know these numbers. But they know what people say about them. That’s why the adults in the room are so motivated. They want them to be ready for what happens next. You can hear it in Dilley’s voice, her concern about getting each lesson right. You hear it in the teachers’ conversation about the SAT being just around the corner. The students need to do well on those tests. They need to not leave out steps in solving those functions. No one outside the state is as preoccupied with these students’ success as these teachers are. These are their kids and they’re going to make it so they have as good a chance as anyone.

We’ll be back after the break.

You hear it all the time, worries about the kids today. How are the kids doing in math or science or coding? So we went to find out. Check out the Sparked episode "Girls Can Code" to hear how a group of girls are challenging stereotypes, and go to the episode "Fourth-Grade Scientists" to hear how college students are hooking kids on science. Now let's get back to the episode to find out how the younger kids are doing in math.

There is a time before math becomes an enemy, before we get broken into those who can and those who can’t, or those who won’t. Burt-Kinderman just started in the last year working with elementary classes in the county. And since every elementary school teacher in the county right now teaches math, that’s a big job. Today Brian Smith’s fourth-grade class at Marlinton Elementary School can’t wait to show off their math prowess to Ms. BK.

She brings an activity for them. She has this idea that if she breaks them into groups and they each have a role to explain the problem, to provide an estimate, to restate the problem another way and to create a plan, that they’ll use that method for solving problems on their own.

STUDENT: Farmer Jim keeps 12 hens at every coop. If farmer Jim has 20 coops, how many hens does he have in all? If every hen lays nine eggs on Monday, how many eggs will farmer Jim collect on Monday? Explain your reasoning using words, numbers or pictures.

Mr. Smith, who is also a WVU alumnus, and Ms. BK move around the room working with each group. They notice what’s not quite working. The instructions are a little over the kids’ heads. And a lot of the groups are not completing the problem.

BURT-KINDERMAN: So maybe more streamlined cards themselves. One directive per card. I also noticed this was a multi-step problem and this group nailed the first part and totally ignored the second. 

STUDENT: [Erasing sounds]. There's probably still more stuff that we have to do. 

STUDENT 2: Yeah, it says "Farmer Jim keeps 12 hens at every coop. If farmer Jim has 20 coops, how many hens does he have in all? So we found he has 240. But, listen, look. If every hen lays nine eggs on Monday, how many eggs will farmer Jim collect on Monday?

STUDENT: See, that's what I was talking about. There's still more stuff that we didn't do. 

STUDENT 2: So what we have to do is 240 pretty much times 9.

MAZZELLA: With this group project, the teachers are trying to give the students a framework for catching themselves. The kids may not care about that now. But they will when they’re in Dilley’s class some day.

Burt-Kinderman says days like these are her best days, just being in the classroom with teachers and students and seeing them take ownership of learning. Her new work in elementary school tells Burt-Kinderman that the best is yet to come from a project that has already revolutionized math in a forest in West Virginia.

BURT-KINDERMAN: Yeah, we used to take an assessment that a lot of different states in the country took and our eighth-grade scores were right on par with some of the best schools in Massachussetts. That’s not a joke. You know. We don’t know what happens as we send those children through high school. So I don’t think that the cap on that has even been answered yet.

But I do think it’s a valid question whether or not we’re just lucky. Do we have really great educators who just happen to be at one space at one time? And that certainly is part of it, you know? We have the same teachers at the middle and high school now maybe with one exception as we did six years ago and we’re getting drastically different outcomes. But it’s not a quick fix, you know what I mean? I don’t have a brochure and there’s not a certain book. There’s not a technique per se. It’s a paradigm shift.

We’re really investing in how kids see and sometimes really trying to slow down and really understand what they know or don’t know and the ways in which they know it or the reasons why they don’t know it. Which is very very different than let’s find a pack of shortcuts and get kids to replicate that over and over and over again. It’s another way to get a high test score but it’s not what we’re doing here.

STUDENTS: 5, 4, 3, 2, 1.

BRIAN SMITH: Thank you. Unfortunately it is time for us to go to art class. 

STUDENTS:  Noooo! I don't want to go to art class. I want to stay here.

BURT-KINDERMAN: See you guys. Thank you for teaching me a new game. 

STUDENT: You’re welcome. Thanks for coming. That’s the most fun I’ve ever had in math.

BURT-KINDERMAN: I mean, tell me more. 

MAZZELLA: Thank you for listening to Sparked, a podcast of West Virginia University Magazine. This episode was recorded and produced by me, Diana Mazzella and Raymond Thompson Jr.

A big thank you to the teachers, students and administrators at Pocahontas County High School and Marlinton Elementary School. A particular thank you to Joanna Burt-Kinderman, and Laurel Dilley and Brian Smith and their classes.

You can follow Joanna Burt-Kinderman’s work with Pocahontas County schools online at her website problematizingmathteaching.com.

Let us know what you thought of this episode by contacting us through our website, wvumag.wvu.edu. And if you’d like to see the classes we visited in action, you can see photos in the episode notes on our website.

Sparked is a production of West Virginia University, located in Morgantown, West Virginia.

So, what did you think when we went into Laurel Dilley's class?

THOMPSON: Oh, at first I was like sweaty, you know, my armpits were getting sweaty. I was like this is uncomfortable. I see math things on the board. It's like oh, it's coming back, Ms. Trackman's class is coming back to me in a flashback, but very quickly saw that they were working in a very different way. They were coming at it from much of a problem solving way and using sort of these math structures to figure out things that I felt they could probably apply to their real lives. So they're working in a completely different way than I ever learned math.

MAZZELLA: Yeah, it felt like they asked a lot of questions. I feel like so much about math was orders, like "This is a fact and you are going to understand it and you are going to move along and don't be wrong about anything." Where they were more trying to figure out what these students know, where they're getting hung up on problems and how to make math make sense to them not just showing them information and then letting them process it on their own and saying, OK, we're done. I felt a little jealous like, it's great that these kids get to do this but why didn't I get to learn math like this? Why was it so big and scary?

THOMPSON: That is the question that will haunt us until our graves.

MAZZELLA: Probably. They'll start putting little signs on tombstones. Like: Pre-math revolution. Math was hell for them.

THOMPSON: Yeah. It's OK, Diana.