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Join us in a Math Mentoring Moment with Katrien Vance where we dive into redefining what success looks like in our math classrooms by planning lessons that elicit questions instead of answering questions that haven’t been asked, promoting mathematical discourse, and helping students build confidence to solve word problems.

Resources

• https://robertkaplinsky.com
• Pentomino Puzzles
• 3-Act Task: Hourglass Multiples
• 3-Act Task: Stacking Paper
• Lesson: The Mullet Ratio
• Christina Tondevold’s Virtual Math Summit
• https://makemathmoments.com/mentor

LEARN MORE about our Online Workshop: Making Math Moments That Matter. https://makemathmoments.com/onlineworkshop

Register for our FREE WEBINAR: 4 Strategies to help students START math problems and STICK with them. https://makemathmoments.com/webinar (Registration closes January 25, 2019 at noon EST)

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Show Transcription:

Kyle: Ok we’re here with Katrien Vance, Katrien can you tell us just a little bit about yourself, just  where you are from, what do you teach, how long you’ve been teaching, just basically about your story?

Katrien: Sure, I am from the middle of Virginia, so near Charlottesville, Virginia but much smaller town. I teach 7th and 8th graders in a little school that goes from nursery school through 8th grade, and it’s such a small school that when they find out you are comfortable doing something, then they have you teach it.

So I started as an English teacher, but I now do English, history, math and music at this school, and I’ve been there for about 25 years now. I’ve been teaching about 32 years.

Kyle and Jon: Awesome, awesome.

Katrien: So currently I teach Algebra One to my 7th and 8th graders but I’ve done everything from 5th grade math through 8th grade math and then pre-algebra and algebra.

Kyle: Oh, beautiful. And what made you want to become a teacher? Was it something that you sort of knew when you were young or was it something maybe a little later? What was inspiring to get you into the field of education?

Katrien: It was pretty much a guarantee because both my parents were teachers. They were English teachers, and I actually grew up on the campus of the school. So I played in classrooms, and I was surrounded by school all the time and loved it. So in college, I student taught in the summers just to make sure that I could actually do this thing that I assumed I was going to do, and I fell in love with it. So it’s been there ever since.

Jon: Awesome, you know it reminds me; my father is a teacher, well a retired teacher now, I remember always thinking that I wasn’t going to be a math teacher, and I ended up going into math for school, doing a degree in math and it sounds like similar to you that I did one co-op job in a summer term where I tutored math at a local college and then that changed for me, I’m like ‘Ok, I think I’m going to switch majors again’ so I was in computer science to start, and I switched to physics. I was all over the place for the first year and a half until I was like ‘Ok, I like this. I think I am going to pursue this route’. And the history is there for sure.

Katrien: Yeah, I don’t really know what anybody else does for a job like I don’t get any other schedule, I lived on an academic schedule my whole life and I always joked that I don’t know what office people do; like how do you know what to do when you walk into the office?

Kyle : Yes, no clue.

Jon: I know.

Kyle: When does the break bell go?

Katrien: (Laughs) Exactly

Jon: It’s interesting, I could just go to the bathroom when I want.

(Laughter)

Kyle: It’s interesting because my wife is also a teacher, you know kind of similar to your parents, we are both parents, we’re teachers and actually my kids go to the same school that my wife teaches at. So she drives them in, and it’s just around the corner. They are there with her before school, and they are there with her after school as doing a prep in there, you know doing their little tinkering around in the classroom and either doing some of their own reading or creating more work for my wife by taking out games and so forth. So I am curious whether they follow in our footsteps similar to your case here.

Katrien: Sure, yeah.

Jon: Well we wouldn’t be doing our jobs if we didn’t ask you this question and I think you answered this question before but can you just answer this one with us now? What is your most memorable math moment? So this could be the math moment that you had in your own schooling or it can even be you as a teacher. When we say math class what pops into your mind? Something that has been sticking with you, it could be a positive moment, it could be even a negative moment. I think you know our moments but let’s hear some of yours.

Katrien: Well, there is one that isn’t quite a moment but it was a whole year of having a high school teacher who spoke super fast. She just drank a tone of coffee and she talked so fast, and I’m writing as fast as I can, and I did in the class but I just remember thinking like ‘I will never teach like that’

Kyle: Well, you won’t drink as much coffee as that teacher.

Katrien: (Laughs) No, I won’t even do that. And then another was in calculus class: my teacher, he made up a place, he would say ‘In calculus land, a conical reservoir is draining at the rate of…’ and I’ll always remember that. I can’t do differential equations but I remember the conical reservoir was draining at a particular rate.

Kyle: Awesome, well we’re wondering while we’re on the phone here, as teachers ourselves and I’ve recently come out of the classroom doing a consulting role but we’ve all experienced challenges and and struggles throughout our careers and we are wondering is there anything on your mind lately that we might be able to kind of work through together while we have you here on the line?

Katrien: Actually, what I would love to tell you guys is about successes if I can.

Kyle: Sure, that sounds great.

Katrien: I just had a colleague over the holiday break ask me for some help and I was so excited to talk to somebody about this because I’ve completely changed my approach to teaching math this year, and it comes out of your workshop, originally out of your workshop. What I thought I was going to do was to be able to create big problems, like big lesson plans that would have these long, engaging, interesting problems, and what it actually is; it’s not that at all. It’s realizing that it’s an entirely different approach to everyday in the class like there doesn’t have to be a special problem that I’m looking up and using but it’s that for example; if I want to teach inequalities, the approach is; I have to start with a situation, not with vocabulary, not with any kind of definitions or we might think we have to start and pre-teach and do building blocks but I just say to the kids ‘There’s this construction elevator, and it can only hold 440 pounds, and I’ve got these bricks and they are 42 pounds. What’s the most bricks I can put on this elevator? Go!’ and the kids are like ‘What? What do you mean you have a construction elevator?’ But they just go from there and I don’t tell them anything, and that’s brand new. It’s a little bit scary but there’s always some moment where a kid goes ‘We could just…’ and then they unlock the whole thing for themselves in this incredible magical way and then all I do is tell them what the name is for what they just did or what the symbol is that they use to write that down but they already knew how to do it or they talked their way through it. So it doesn’t feel hard or foreign, it feels like ‘That was my language, that was me, that’s my method’. And so we just finished right before the break ‘Absolute value inequalities’ which have always been a nightmare like ‘Why do you flip the inequality sign and how come there are two equations?’, and I’ve never done felt like I’ve done a good job. It was the easiest time I’d ever had teaching it because it flowed out of ‘All right, so you want to be a featherweight boxer, you have to weight within 4 pound of 126 pounds. What do you have to weight?’ and they all knew how to do the math, so the math wasn’t hard. They knew obviously that’s a 122-230 pounds. I said ‘Ok, let’s figure out how you would write that down’ and it was engaging and interesting and not scary and not foreign at all to them. So when my colleague asked, she was under this name ‘Miss Impression’ that I was like you have to find these elaborate problems and sort of stage them and have it be.. I don’t know a lot of work… And also you have to find the right, exactly the right problem for the lesson that you’re trying to teach. So I would have to search the internet for it ‘Absolute value inequality problem’ that someone had made up for me and I said ‘No, you just have to start with the situation’. Then let the kids figure it out and tell them what they have just done and then give it the right language so that they will know it again when they see it. The most exciting part of all of this is that when we go to do; I don’t use the textbook anymore ‘a’ which is very exciting but what I will use it for us to check like to take a quiz or to look at the unit test, the questions that are easiest for the kids are the word problems.

Kyle: When does that ever happen, right?

Katrien: The terrifying word problems; they are like ‘Oh, we know how to do this’. Because that’s where started, that’s not where we ended it’s where we started. So it’s been incredibly exciting, yeah.

Kyle: That’s amazing. If I had to, could I maybe say back to you what I think I heard and you tell me whether I heard it correctly. At the beginning you had mentioned starting with a situation, some sort of context or story line that would sort of spark that curiosity, and then allowing students to kinda tinker with and I am assuming that that story, although you haven’t necessarily had to go to internet to find Robert Kaplinsky’s task on this idea but you’ve come up with at least an idea based on the learning that you are hoping to pull out of that particular lesson and then consolidating that learning at the end and that’s where you sort of introduced the more formal language or maybe even some of the more formal notation, and some of really the part where you get to do the teaching.

Katrien: Yeah, right. So what was intimidating was thinking that I have to either find or make up something like a Robert Kaplinsky task for every single day like every lesson needed that. It turns out it doesn’t have to be that exciting. I literally walked in the classroom, I knew what I wanted to do like rate time distance problems. I walked in the classroom and I said ‘Imagine Elissa gets up, she runs out the door. How fast does she run?’ and the kids go ‘15 miles an hour’ and I was like ‘Ok, she is super fast.’ ‘So she runs out the door’, an hour later, because we are so focused on that we don’t even pay attention. ‘An hour later, Adam notice that she is gone, he gets on his bicycle, he races after her. How fast does he go?’ ‘50 miles an hour’ ‘Ok, great’ and I am just writing this on the board. ‘When will Adam catch Elissa?’ They are totally hooked, they wanted to know and so you know instantly a kid goes ‘Well, in an hour Elissa went 15 miles’, I said ‘How did you know that?’. And so then we could talk about ‘What operation did you just  do? How did you know the multiplying, what two things did you multiply?’. They had all of the tools, and they really wanted to know when will Adam catch Elissa.

Kyle: That’s exciting to hear, I am wondering; do you notice a difference in the mathematical discourse? Like when we think about the student voice and has there been any sort of changes since you sort of maybe…like what I am hearing is maybe a less scripted approach; while I am sure in your mind everything is scripted, you know what it is, you want to do that day, but maybe to the students their perception is; it’s not open the book to page whatever and do the first thing or here’s the definitions; we are going to need to re-learn or learn before we actually do something interesting. Have you noticed on that student voice side, that empowerment side of things?

Katrien: Yes, well here’s the exciting thing is that; you know in every class there are the kids who are good at math and then there the kids who are going to let the kids who are good math do all the talking and lead us through. Suddenly, there’s no distinction, everybody has a voice in this because we are all sort of just playing. And so we were using; I think you guys showed me the pentomino exercise on desmos. So we were playing with that and they were discovering that if they moved that pentomino, the sum went up by five, and they have figured that out. I asked some question a very tentative young girl said ‘Well, couldn’t we just divide by 5?’ and I literally had to stop traffic and say ‘What did you just say?’ and make her say it again. That unlocked the whole key to how do we turn this blob of five blocks into something that we could turn into, you know an expression, an algebraic expression, and then an equation, and then learn how to solve that equation. It was exactly what I think you guys said, then they wanted know how to solve the equation. There was a reason to want to solve it instead of just now you are going to learn how to solve equations. But each time there has been a moment it has come from an unexpected source. It would be a kid just offering ‘What if we divide?’ or ‘Elissa will go 15 miles’ or whatever it is, and it isn’t just the kids who are good at math who are offering those ideas, everybody gets to just try out ideas and I saw this quickly. Just the confidence I guess, and the surprise. A girl said to me ‘I really love it that you gave us problems and you don’t tell us how to do them’ and I said ‘You really love that?’. I was so surprised, and she said ‘Yeah, I really love it’ and it gave her the confidence because she knew that she didn’t know how to do it and that gave her the freedom to play. Just today I handed them a sheet and said ‘I haven’t taught you how to do this, take it home and just mock around with it for a little while.’, and I said ‘So, when you can’t do number one; are you going to give up?’ and they said ‘No’, and I said ‘Why not?’, and they said ‘Because we know we don’t know how to do it?’. So there is just this free pass to, I know I am not supposed to know how, so that gives me licence to figure out  for myself instead feel bad when I don’t know how to do it’

Kyle: What if I actually did get it then it’s like ‘Wow, look at that! I just did something pretty cool without having been told, and now there’s no fear of me doing it wrong the way I was told because I haven’t been told yet’. So it just gives them a little bit of that you know kind of dip their toes in a little bit and seeing not be so fearful.

Katrien: Yes

Jon: And we have experience similar things when we’ve made that switch that it’s such a wonderful thing that you can switch learning instead of being on the front and talking; just asking them to come up with it first, and just knowing where to look for and listening to what the students say. You know what, it changes the culture of your room, and did you notice that too? Has it changed your room culture? What did your room like before you made these changes? You said radically changed how you taught math. Can you maybe give us a snapshot of what your class looked like before you made some these changes? Because I think, some teachers out there are thinking or maybe wondering what that looked like, and also comparing to what they are hearing from you right now.

Katrien: Sure, I teach at a very small, very informal school. It’s the kind of school where the kids call me by my first name, so there is already a lot of informality, a lot of give and take, a community of learners in the classroom but I still would have, in the past, scripted everything out. So if I thought I was going to teach word problems, or distance-speed-time problems, and I did this actually; I typed out like 6 pages of ‘Here’s the thing I need to say, here are the examples, here’s the step by step of what you would do to solve this problem, and it was almost like right before I went in the classroom. I looked at it and I went ‘Wait, stop! What are you doing? You know not to do this just go in and…’ and that’s when I said ‘Elissa just ran out the door, Adam is going to chase her.’ So well it looked like to me, very carefully paving the way so that there was nothing that could trip the kids up. ‘So let me make sure I define this term for you, let me make sure what it looks like when it’s written this way. Let me make sure I show you what to do when it’s written this way, let me make sure I show you…’ you know every possibility that you can never feel lost. I really thought that was my job.

Kyle: Is it fair to say that; you know I am picturing myself teaching for the majority of my career and thinking, like I am going to plan this lesson so well that I am not going get one question from the students. (laughter) And now when you think of it the way you are describing now, it is almost like, how can I plan this lesson, to elicit, as many possible questions as I can, to get as many kids get talking as I possibly can, and to really not only engage them and pull them in but also to really allow them to lead some of that learning in that direction like you are saying because if the kids are asking me these questions then let’s spend time on those questions because now they are the ones asking them, it’s not me asking the kids to answer questions. It’s them asking the questions and now they are actually asking me for me help and support. It’s kinda counter to the way, I would have done things more traditionally where I would give answers to questions that they never had yet.

Katrien: Right, a good day was me teaching something, and then saying ‘Does that make sense?’ and them nodding. They are never going to be the one to go ‘Could you say it one more time or I don’t understand’. Whereas in this case, there is nothing to make sense because I haven’t taught them anything. What I’ve done for example; I also teach them history and we just finished a game in history class that had points in it, and so for percent change, I got to talk about the difference between the points they started with and the points they ended with, and I said ‘How could you compare these?’ Of course you could talk about the number of points and the way it increased but what might be a better way so that we could compare all of the teams fairly and they got the percentage, they’ve never heard of percentage change. I said ‘How would you do that? What numbers do you need?’. They instantly knew; they knew the difference, and then they knew to compare that to the original number. They derived the formula perfectly on their own and then I just wrote it on the board. And the homework was ‘Make up some questions, you have all this data from the game. Ask questions and solve those questions and then bring them in and that’s what we in class and I answered their questions about the data from the game. Teaching them percentage change and all the different kinds of percentage problems you could think of but generally they are all from something they were really curious about. Because it was their own class data.

Jon: Very cool. You mentioned when you were talking about the way you used to teach compared to now, I am wondering what was the the tipping point that made you like ‘I need to make this change’ or what’s the story there for us to understand.  

Katrien: Well, over the summer, I did the virtual math summit and watched a lot of math. I think I watched almost every single one because I was trying to take notes for my colleagues as well. The theme over and over was this idea of ‘Strip away all the pre-teaching’. So there were examples of just terrible math problems from textbooks. There was one guy that showed ‘Eight kids go out to play, how many mittens will they need’ so this was for much younger kids, right? but then the textbook walked the children through like ‘Assume each child has 2 hands, assume …’ it was amazing how much…

Kyle: Got to be politically correct. (Laughter)

Katrien: So that theme that resonated with me; just take away all of that stuff that they are telling them to and let the kids figure out ‘How would I solve this’. We have always been at the school, we’ve always been really honouring different methods, different ways of arriving at an answer. But I had never this explicitly thought about ‘Just ask the question without all of the lead up to it’. So I knew I wanted to do that but I didn’t totally trust that it would work and I heard when my colleague asked me over the holiday at lunch, I heard that same doubt in her voice of ‘Yeah, but how do you know they are going to get there?’. So for me the tipping point was that moment when using those pentominoes when one of my really shy students said ‘Let’s divide by 5’ and I was like ‘Oh my gosh’. They will do it, you just have to give them the space and you have to just be quiet long enough and not feel like ‘Are you getting it yet?’. Just let them mess around and eventually somebody is going to come up with something and at each time if you trust the process, in my experience, they have gotten there. We’ve taught each other exactly what my goal was that I would have taught them before.

Jon: I find it also amazing when I decided that I was going to do that too like I was just going to just let them show me what they knew first, and I can step in if I needed to. What’s the harm if we pre-present that problem to them and you say ‘Go’ and they start to come up with strategies and they are working it. You know they get stuck or they are not sure what to do next or they are at a point where they need some gaps filled in. Then you can step in and show them some of them stuff. There’s definitely something to be said for letting kids show us what they know at first and I never did that for so many years. I assumed they knew nothing. Peter Liljedahl has a great quote and he says ‘We’re always planning our lessons assuming kids couldn’t think or they wouldn’t think’ And all my lessons were planned that way. I mapped everything else and there was no success, sounds like you were too. When I decided to let them show me some stuff, they know so much stuff, they know a lot. I would never give them credit for it in the beginning.

Kyle: And something very interesting too, and you know kind of very closely tied to this idea is something that I know I did when I was in the classroom and I felt this very same way but when I go whether it’s working in my own district or working with teachers in other districts, when I challenge them to do a problem in their classroom, you know ‘Here’s the topic that we are going to focus on for this workshop and I challenge them to go back and take that task or something like it, they can modify it however they choose to go back into the classroom and do it, and the number one thing I’ll hear from many teachers and again I see myself saying the same thing, back only a handful of years ago is like ‘I haven’t done that yet’ or ‘We did that a long time or we’ve already done that unit.’ What I am trying to, or hoping that; overtime we’ll all see is that it’s ok if they have never done it before because the reality is that they probably have, right? If it’s an idea that’s not brand new to the curriculum that specific year, the reality is they have probably done it at some point and if they can even get started with it then what does that say about the way we teach in general anyway if students aren’t able to sort of grasp or retain that new information so for me it’s just like we should really be pushing this idea of using tasks as a way for students to learn and be introduced to new ideas not as a way to sort of consolidate the learning later after writing all of the steps and procedures for them. It’s like ‘Let them have at it’ like you said just mock around and you know sometimes we are going to hit a rot and hey that’s fine, you know we’ll figure it out at that point or maybe students come out and it’s like ‘Well look at all this knowledge that they brought with them’. I never used to respect when students came into the classroom. I just assumed that they were blanks with no information in there and I barely knew their name. Although sometimes they don’t write their names on the top of any work which is a whole other story. You know I am wondering, I am very curious about how’s your colleague progressing like? Have you felt there’s any successes there? And maybe your colleague  might be at a very different place than you are based on you having the experiences in the Virtual Math Summit with Christina Tondevold in the summer and all those fabulous presenters. Is your colleague sort of like sticking with it or you are there kind of coaching along the side, they are trying to sort of root him or her on as they go along?

Katrien: It’s a great question. I need to do more of the rooting her along. I know she did the timers tasks ‘When will these timers all run out at the same time’ and I actually don’t know how it went. I know she was doing it and she was in the middle of it. I needed to check back in and see, because there is a level of just trusting, trusting like you said; honouring what the kids do know, trusting that. Even if they don’t do the lesson the way you thought they were going to do the lesson, there is going to be something that’s learned from it. For example I did you stacking paper lesson, right, and I was thinking ratios and proportions and they weren’t. They didn’t go there at all, they went to multiply and I was like ‘Ok, you can multiply it!’ but how great!

Jon: And that’s allowed, yeah.

Katrien: So in the real world no one is going to say you are only allowed to solve this problem this particular way, have it be about problem solving in that moment.

Jon: What I love about that is, when the students do solve it in a different way than you anticipated. Within each other there are multiple solutions hanging out there is if your lesson goal, and this is the way I like to use these tasks is I’ll have that lesson or learning goal in my mind of where we want to go, for me I think I used that same lesson of Kyle’s to solve proportions and I know that I wanted to tackle solving proportions that day but when they solved it with multiplying and doing some unit rates, I love that we can tie say the solving proportion solution, even though no one in the room did it that way, we can go ‘Ok, let’s look at it in this light, like we have been working on solving proportions in the past, let’s solve a proportion this way and this now can be the teachable moment and what I love about showing them that solution is; they get to see all the numbers. The same numbers that they had popping up in that same solution I am showing and they are now making connections to the proportion work we did a couple days before or a week before and also the unit rates work like they did all in the same problem. They get to make those connections, they are doing it on their own but then you get to make them like explicit you know like ‘Look at how similar these solutions are, there is nothing wrong with Judith. It’s awesome, somebody else might have done it differently and they are very similar you know.

Kyle: What hit home for me was back about, it would been a handful of years now when Jon and I first co-presented. It was probably one of our first times presenting and in the middle, we had obviously talked about the presentation we had done and all these things and we used the stacking paper problem as one of the exemplars but we weren’t going to actually consolidate the task, it was just a quick sort of snippet about curiosity and so forth. I went on to say what I used that task for, the learning goal that I used that task for, just the look in Jon’s face, I still remember he looked over at me ‘That’s what you used that task for? I used it for a direct variation, linear relationship you know  why equals mx type thing and Jon sort of looking at me like I got two heads and he is like ‘Oh I used it for solving proportions’. At the time we were confused but then later we sort of came back together and realized ‘Oh my god, that’s exactly what we want to happen in our classroom.’ We want to elicit students that are leveraging other ideas and making connections to different parts of the curriculum, so it’s like ‘Oh, you are doing that for algebra, I am doing this for proportional relationship, and somebody else is doing some type of division over here.’ There’s all these different strategies that give us not only an opportunity to make connections but then also to allow kids to actually kind of recall some of the other content that we did in the past that maybe we haven’t seen in a while and now it’s brought back to the front or the forefront, and you know students get to go like ‘Oh, yeah. I must be able to do it that way if it’s really just the same as doing it that way. For me that was a big ‘Aha!’ moment when that happened and we were just sort of shocked that we have been using this task independently in our classrooms. Well I won’t say completely separate because obviously they are very closely connected but very different parts of our course.

Katrien: Yeah, and I am sure this has happened in your classroom where while you are working on proportions say, the kids would know to solve something as a proportion but once you go to another chapter and there’s a problem that comes up, they think that they have to do it in a different way because you are not in the proportion chapter anymore.

Kyle: Right, format the brain.

Katrien: Here’s a problem; you pick the way you want to solve it, you figure out what’s the best strategy that works for you that’s most comfortable for you or most efficient for you. I think that’s a much more important thing to teach kids; how to solve a proportion or how to do a linear relationship.

Jon: Right, it’s a conversation I’ve had with many teachers in the past about. The example I always bring up is, ‘Is it more important to factor or knowing when to factor, when you want to factor right? Everyone wants to say or everyone does say knowing when to factor is more important which I totally agree with but we spent so much time on hammering ‘Factor, factor, factor’ which we definitely need to do. It’s just a skill that I value more highly than the other.

Katrien: Yeah. So the other thing I want you guys to know is the way that this has spread into other aspects of my teaching because I do get to teach history, English and music. And so in my humanities course for example right now, my team teacher and I are doing a couple of days about the 80s because we can so… (laughter)

Jon: Love it.

Katrien: So I said ‘Just show a clip, just show a clip of breakfast club or war games or something like that’

Jon: Perfect (laughter)

Katrien: Yeah. And then ask the kids ‘What do you notice and what do you wonder?’ and the other teacher was like ‘What?’ because she hasn’t done any of this and I said ‘No setup, don’t tell them anything, just show it and then ask and have them notice ‘Oh my gosh, the phone has a cord’ or you know ‘What’s all the different things about technology? What’s that thing he’s sticking into the computer?’ There’s so much that let us then talk about the things we wanted to talk about in terms of the themes of technology or the cold war or whatever but we got the kids to ask the questions first so it’s been really fun to bring that into other aspects of teaching as well.

Kyle: That’s awesome. I thought when you said 80s, I thought you were going to pull out mallet ratio problems. If you’ve never seen that problem you definitely want to check out the show notes. I will edit it in and I just made a note in our doc here; Mat Vaudrey and John Stevens – Classroom Chef – they do a really funny rendition of that one and I know that task has been such a wonderful hit for so many teachers including myself. One last thing we wanted to ask you about; it sounds like you’ve had like huge wins over the past little while and we so appreciate you sharing with us some of the effect that doing the online workshop with Jon and I this past fall has had. We are wondering are there any little challenges that you are still kind of working on or maybe even just thinking of your next step, like what’s your next move in terms of your own professional learning journey. You have been at this thing like same school for 25 years, teach for 32. I am so impressed that going for over 30 years and you are still clearly a lifelong learner so there’s probably something going on there that you have as something that you want to kind of put a thumb on and see how you might be able to influence it in your classroom.

Katrien: I think actually, in terms of this, math specifically, it would be spreading this to more of my colleagues and really convincing them that this is the way to go and having the confidence that they start with the situation. They can start by paving that way as smoothly as possible but let there be bumps and things that kids discover and work with along the way. Really all of this came out of trying to figure out how to teach fractions better. That was the germ of it. Just why don’t kids get fractions by the time they get to me. They are still terrified, they will also change a fraction to a decimal. So it’s been a couple of years of me exploring, trying to find that and through that I found these videos and resources and then that has led me to make this shift in general that I think will also have an effect on fractions. So it’s convincing and again as I said we’re a really small school, so some of my teammates convincing them to use the same approach and I don’t think it will be very hard. None of them loves the textbook or is wedded to any particular approach but it’s just trusting and I think to answer your other question in terms of the challenge or what I’m still working on; it would be that my biggest fear or the concern is covering everything and covering everything is in air quotes, right? How do you satisfy the parents that you have covered the algebra one curriculum because I still find myself saying that we’ve covered chapter one, we’ve covered chapter two, we’ve covered chapter three in terms of what the material is that I know we need to do from years of teaching it that way and we’re on chapter four right now and we are not going to get to chapter thirteen which we never do, I don’t know if anybody ever does. How do you give the time for this process, trust the process, let the kids mock through it and cover the curriculum?

Kyle: That’s a big one, big one for sure. What we can definitely do is well for the show notes and we won’t have time to dive too deeply into it in this particular conversation but we’ll add a link to some of our spiralling resources that we put together and that is a big a challenge for many of us, as we try to think differently about how, we are teaching and like if we go back and even just reference how much information students are bringing with them that sometimes we can dive into an idea, and maybe not completely unpack the entire idea, let’s say it’s a unit and we can move on to another and at least allow us to enter into some learning in all of that curriculum. The expectations, I know here in Ontario, often times the units or the chapters that are in our textbooks don’t necessarily match our curriculum as well so that’s another big one that I would recommend for those listening to just make sure that often times we do what the textbook is showing us to do and what we realize way later is that ‘Oh my gosh, there was a lot in there that wasn’t actually wasn’t in my particular standards or my curriculum expectations. So it’s a big one unpacked but we’ll definitely add link to the spiralling resources for those listening and hopefully will be able to touch base with you soon on how you are making up with that process and see if there’s some ideas that you’ve tried in order to kind of kind of maybe opening up your units a little bit so that you can be a little more free flowing and not feel so tight to like ‘Unit 4 has got to be done before I can get on to unit 5, because I know that’s the way I always used to feel and it’s very empowering once you can kind of break free of those silos.

Katrien: Sure

Jon: Well, we want to thank you for being here with us but before we go we would love to hear about your biggest takeaway. Now this could be, since you are a student of our online workshop, it could be your biggest takeaway from the workshop but also could be the takeaway from just this conversation that we’ve had with you. What would you say that would be?

Katrien: Ok, my biggest takeaway is that my job as a teacher is not to make sure that nobody ever makes a mistake or doesn’t know something in the classroom and I used to like I said just try to sort of pave or cushion or pad the walls or do whatever it was so that everybody’s experience was so positive that that would equal being good at math because in class I felt successful and so I guess what I’ve done is redefine success in the classroom. Success now is asking questions and referring with ideas and figuring things out rather than smoothly going through class without stumbling. So that’s been a huge takeaway for me.

Jon: Awesome, that’s a very insightful takeaway I think, very nice to hear for sure.

Kyle: Yeah, that productive struggle I can definitely hear that throughout the conversation and to me it was clear that something that you definitely embraced and I am sure your students are very very thankful for all of the work and as I mentioned, being a veteran teacher and just having that open learning stance I think is the best thing we can possibly do for all of our students because there’s always something for all of us to learn and I want to just thank you for that being so committed, and thank you again for being with us here on The Making Math Moments That Matter Podcast. We are so excited to share it with the world. Would it be ok if we maybe touch base with you in 6 to 9 months, see how things are going, maybe checking on your colleagues, see how she’s doing and be able to kind of come back and share anything that you are working on?

Katrien: Absolutely, that would be wonderful.

Jon: Fantastic. We definitely want to thank you for your time and we hope you have a good rest of your evening.

Katrien: Great! Thanks so much.