Sara VanDerWerf:
The most common question I use in my classroom is I’ll put something up and say, what do you notice and what do you wonder? They’re safe questions. You can’t get that wrong, but those aren’t the most common questions. The most common question is what else? What else? What else? Develop this neutral voice of… because eventually, as I’m saying, what else? What else? What else in the class, and I’m honoring everything they say and I’m noting it. I’m saying, yes, it’s red. Yes, it’s a curve. Yes, there’s axes. Eventually some student will say, “Hey, there’s a high point.” And I teach a lot of students with low language or whether they’re in poverty or they’re immigrant students. And I will say, because I’m always building language, one of my other passions that I speak about in my state a lot is that intersection of best practices from-

Kyle Pearce:
This week we chat with Sara VanDerWerf, former K through 12 math lead with Minneapolis public schools who taught grade seven through 12. She was the president of the Minnesota Council of Teachers of Mathematics and she’s an independent mathematics consultant.

Jon Orr:
Lean in as we chat with Sara about her journey from being a fast calculator in her own K through 12 learning experience to focusing on making student thinking visible in her classroom. We can’t wait to dive into Sara’s backstory as well as get some great tips and resources for your own teaching practice.

Kyle Pearce:
Get ready because here we go. Welcome to the making math moments that matter podcast. I’m Kyle Pearce from tapintoteenminds.com.

Jon Orr:
And I’m John Orr from mrorr-isageek.com.

Kyle Pearce:
We are two math teachers who together with you the community of educators worldwide who want to build and deliver math lessons that spark engagement.

Jon Orr:
Your learning.

Kyle Pearce:
And ignite teacher action. John, are we ready to get started with a fantastic episode with Sara?

Jon Orr:
Of course. Kyle, of course. We are so pumped to bring you this episode.

Kyle Pearce:
Before we get going, we want to give a quick shout out to [Aya Plum 00:02:05] who left us a five star rating in review on iTunes. Aya says.

Jon Orr:
Appreciate the format. I have been following the ideas and lessons from you both before but really appreciate being able to have your podcasts to listen to on my drive.

Kyle Pearce:
Don’t mind the drive when-

Jon Orr:
I can learn while doing it.

Kyle Pearce:
Thanks. If you’ve been loving the podcast, leave us a review on Apple podcasts just like Aya did by outlining your biggest takeaway. Reviews help more educators hear about the show and in turn we can help make more math moments for students every single day. Before we get to our chat with Sara, we want to chat with you about how to create a culture of engagement and participation in your math class to ensure students are leaning in to learn. That once students are leaning in, how are we going to tackle new mathematical ideas in ways that build necessary conceptual understanding, developed procedural fluency over time.

Kyle Pearce:
Finally, how can we craft our lessons in such a way that every student can access the mathematical content and they don’t just throw their arms up in frustration? We believe that all of the above are important parts of an effective math lesson, but successfully delivering lessons that deliver on all of them is not always an easy task. That’s why we came up with the make math moments, three part framework to deliver math lessons that students won’t only love but will also learn from. You can learn more about why we created a three part framework and what are the necessary pieces that you need to know about so that you could run your classroom lessons without a hitch.

Kyle Pearce:
Head over to makemathmoments.com/framework. That’s makemathmoments.com/framework to learn more. All right, let’s get to our chat with Sara. Hey there, Sara. Welcome to the Making Math Moments That Matter podcast. We’re so excited to have you on the show today. How are things over in Minnesota?

Sara VanDerWerf:
Things are great in Minnesota. We are excited about summer and we have about a month to go in Minnesota until we go back to school. Excited to be here.

Kyle Pearce:
Yeah, we were just talking about this before we hit the record button then. Unlike a lot of the southern States who are gearing up to get back to school or are already back to school, we still have one more month just like you do. We are also pretty excited about that. I don’t know about you, but this last month, August always seems to go way faster than July. What do you think about that? Is that the feeling you get to?

Sara VanDerWerf:
Yeah, absolutely. Absolutely. In Minnesota we have one of our big math events that happens in the month of August and so in a couple of weeks the Minnesota State Fair will happen, [inaudible 00:04:55] that you use has the largest state fair in the United States and we as a math community but really the amazing Christopher Danielson convincing to state fair several years ago to give us the space where we’ve created a math event that we call Math On-A-Stick. If you’re on social media, be checking us out the next couple of weeks because for 12 days we get to hang out with students and adults are just do and play with math, so [inaudible 00:05:22] we love August.

Kyle Pearce:
I have seen the posts about that in past years and it looks like amazing things happening in Minnesota. Sara, I know we’ve met a few times and we’ve seen you present live. Could you do us a favor and help our listeners understand a little bit about yourself? Where are you originally from, what your role is in education and how did you get there?

Sara VanDerWerf:
I live in Minneapolis and I worked for Minneapolis public schools for 29 years. Technically I still work for them but I’m in the middle of a two year leave of absence with them. I taught middle school, high school mathematics and I was the K-12 math lead for Minneapolis and was out of the classroom for five years, but six years ago I went back to the classroom and love being back in the classroom, but now I’m just living in Minnesota and traveling all over the United States, working with teachers around some of the things that I have been really passionate about in the last several years, but Minneapolis public schools urban education is really where my teaching heart has been.

Jon Orr:
Fantastic. Fantastic. We’ve had this chat in person a few times and we’ve seen you present live and clearly you are definitely eager to share. I’m wondering a little bit more, do you mind diving just a little bit further into how you got into teaching? So what’s your story there? Like what landed you there? We know you’re a passionate educator. You have 29 years of experience with your employer, now you’re doing kind of like we’ll call it almost learning independently with your two year leave of absence so you can go out and about, and I know you were just coming back into town from visiting a school district yesterday. Tell us a little bit more like what got you into this crazy world we call teaching?

Sara VanDerWerf:
Well, I was probably like a lot of math educators. I was really good at math when I was coming up through school and I can reframe that idea of good at math now that I’ve been thinking about that in my life, that really what I was was a really fast calculator and like I was compliant in the classroom and would just be like when we were doing math. Yep, that’s what we’re doing but ultimately I did really well in school and if you’re good at math and you’re good in science, which I was by the metrics of grades, you’re told be a doctor or an engineer and I was like, I don’t want to be a doctor. I pursued computer engineering and I just remember being in college saying, dude this is not what I want to do and at the time I was tutoring my friends and then working with some youth and like I had a couple of people say to me, I think this is so important for our current students.

Sara VanDerWerf:
I had some people say, “You’d be a really great teacher.” And the first 10 times I probably heard that from people, I said, “No, teaching is not for me.” But midway through college I switched out of engineering and into teaching it. I remember that being a really hard decision because there’s still like for in teaching this idea of like Sara you have so much promise, you had these high test scores and these high grades and you could make so much more money. That’s how I perceived that change in decision but I have not looked back. I went into teaching math because it was faster and easier to complete my degree than going into becoming a science teacher and I… student taught and got hired the next day and have been with me [inaudible 00:08:38] public schools literally my whole career and so I was super excited about it but at… like my beginnings of thinking about math, probably go back to my early days with my parents.

Sara VanDerWerf:
My dad was an accountant and… like my parents had us when they were young in their early 20s and they didn’t have a ton of money but my first allowance in the ’70s was 10 cents. That’s the one I can remember and my dad was not like a normal dad. He didn’t like hand me a dime. He actually gave me three different banks and I got that 10 cents given to me in one penny, one penny and eights because one penny went in one of my banks for my savings and another penny was donated and given to the church and then the eight other pennies I could do and I like… I look at that now and think my dad has some kind of beginning understanding of 10 frames and helping us understand 10 damages and all those kinds of things and my mom, she used to stay at home mom and I don’t think she would have defined herself as a mathematician. I know she doesn’t, she used to say, “I don’t know where these kids that I got came from.”

Sara VanDerWerf:
I tell people that my mom’s job growing up was saving money. She was an amazing couponer and triple coupons and had thought through things but I remember being shopping sales at a store and something would say it’s 30% off and I’d say to my mom, how much is this going to cost me? And she’d go, well it’s 19.99, that’s around 20 bucks and it’s 30% off and if you take 70% and take the seven, you multiply the seven times the 20, it’s going to be $14 and she was… just had developed all these ways and she would say this stuff out and they were just making their thinking visible and then in school I was good. In the fourth grade they had this thing called charting your own course and that could go at our own speed in math, and by October me and another student had run out of math to do for the year and then they just had nothing for us.

Sara VanDerWerf:
I remember thinking in fourth grade there’s got to be something more than this because it was just [inaudible 00:10:40] to do a bunch of tasks and then middle school, I had the same teacher for a couple of years and he would tell us what to do for 10 minutes and he would… in class then make us be silent while we worked on whatever we were doing and I was a compliant kid and I was fast. I get my math done right away but he would watch and put our names on the board if we talked at all.

Sara VanDerWerf:
I was fine but I just remember looking around the room watching these kids struggling and just not knowing what to do, and so they would misbehave and get their names on the board and we would get as a punishment this thing called numbers where you’d have to write out the numbers. One. One, two. One, two, three. One, two, three, four. One, two, three, four, five all the way up to 70 and like what a waste of time but like I would… it was like my first little business because I was done with math and I had nothing else to do and I couldn’t tutor my friends.

Sara VanDerWerf:
Just remember thinking I could help these people out. Like I actually would sit and do numbers even though I never got in trouble and I would sell them to my friends. I remember thinking at the time like, there’s got to be a better way of thinking about this. Even though I was being successful in this system, I was doing that but probably my most pivotal moment came when I went to teaching.

Kyle Pearce:
You’ve got some wonderful experiences that I think shape… we all have wonderful experiences that shaped the math educators we become and you’ve got some foundation there for sure and I think we can relate. We’ve talked about this on our podcast before that we were similar. We got into teaching because we were good calculators. I really like the phrase that it’s like you were really fast calculator and I was always a good memorizer. I could follow the instructions very well and we come to realize that it’s not always perfect for our students and what we want our students to do, but we ask everybody on the podcast, what their most memorable math moment has been but I think you’ve given us a few, like you’ve talked about your dad and your mom and how they shaped some of your skills and you talked about school there too but is there anything else you want to add to memorable math moments from your schooling in particular?

Sara VanDerWerf:
Yeah, I think the only thing I want to add is just when I first became a teacher. The thing that’s probably shaped me more of my career was when I came into teaching in the early ’90s. It was the era of the NSF grants in the states around all kinds of new curriculum that had been written and the district I was in highlighted a curriculum that was completely radical at the time. When I entered teaching, I was told you will teach IMP, interactive mathematics program in its pilot form and it was one of the first really radical problem based curricula and anybody that taught that curriculum way back in the days, and I use that curriculum for my first 13 years. It’s like we have a little sorority of sorts and when we run into each other, like I had an interview for a job a year and a half ago and I happened to mention that I entered teaching using IMP, and at the end of the interview, the people interviewing me said, “Oh, we knew we wanted to hire you as soon as you said IMP.”

Sara VanDerWerf:
It just really brainwashed me in terms of changing what I thought about being an educator and I really remember the third year of the curriculum, there was a series of lessons and activities that developed the idea of the beginnings to understandings of a derivative and I remember thinking out loud in my head that, “Oh my God, a derivative is a rate of change. Just like the slope of a line is a rate of a change.” How come nobody ever told me that a derivative [inaudible 00:14:14] is a rate of change and I think so many of us educators who had been fast calculators, it wasn’t until we started [inaudible 00:14:21] that either A, some things we finally were like, oh my God, these things are connected and interrelated.

Sara VanDerWerf:
And, or like I remember thinking about learning about partial products and being like, I had figured that out in my head as a method for multiplying. I just didn’t have a name for it and I remember thinking what if all my friends way back in school had been taught some of these things and not just taught like, made meaning for themselves out of these things so they owned that information. I feel really lucky in how I entered education.

Sara VanDerWerf:
That NSF grant also came with just tons of professional development. I had two weeks a year, I had a mentor. I did co-teaching and I had that for the first five years of my career, and so like I look today at so many teachers who just… the huge classrooms and lack of funding around supporting teachers in like… because that journey to go from just teaching tricks and skills and I teach, we do together and you do and flipping that into a problem based way of making meaning and reasoning for students is a hard change for so many students and I just feel really lucky that I entered education in a way that I just thought, “Oh, this is normal.” Even though that’s not what my K-12 experience had been. So, yeah that’s what I bring to the table.

Kyle Pearce:
Well, that’s fantastic and I know John and I are shaking our heads with these, oh my gosh moments where you know, why didn’t somebody tell us and some that we’ve mentioned before. I know John’s brought it up a few times the idea of the Pythagorean theorem, like why A squared plus B squared equals C squared. It’s because the squares actually add to the… like that idea mind blowing. Something else even just for me, when I was exploring moving from secondary down to elementary and really trying to get a handle on why do students get hung up early on and so I explored multiplication first and even just looking at a raise and realizing like, “Oh yeah square numbers. It’s because you can make a square out of them.” And that extends all the way into secondary when we start looking at completing the square and I go, “Oh that’s because you’re making a square.”

Kyle Pearce:
Like these are things that seem so obvious and whether teachers just assumed it was so obvious so they didn’t show it. I think it really highlighted for me as a teacher like wow, I’ve got to be way more explicit and I have to make sure that I’m helping uncover some of these ideas that maybe I’d never uncovered myself, or at least I wasn’t able to see some of those connections even if maybe the teacher had intended for me to see them, I didn’t and if I managed to get through it, I was much like you Sara, where I was a pretty good calculator. You just give me a bunch of stuff and I’ll do it, but I didn’t really know what I was doing and if we want this to be an equitable experience for all students in our classrooms, we’ve got to do better and it sounds like you’re on that journey. You are well on that journey anyway.

Sara VanDerWerf:
Yeah. I would hope I am… Ultimately, what I know… one of the reasons, and based on where I’m currently, where the stuff that I’ve been reading as an educator and the stuff I’ve been thinking about and learning about, I believe my teachers probably settled a lot of things out loud. I just didn’t take them in. I didn’t own that understanding back in those days. I think it’s because I was told all these things and I just didn’t own it and so I had not created that meaning for myself in my brain and how my brain processed all that stuff. I had not done that, and so as I look at where I want to be working with students and how I want to be thinking with also adult learners, I’m really passionate about them having a chance to make meaning out of things.

Sara VanDerWerf:
One of the things I say a lot when I am working with teachers is the lens that I bring into how I work with students and planning my own lessons. It’s a little catch phrase [inaudible 00:18:16] I’ve kind of picked up on in my work, but I’m always trying to get students to see it before I show them what’s going on. How can I create the experiences so they can see the mathematics I want them to say and that they will say it before I ever tell them.

Sara VanDerWerf:
I know there’s a lot of people out there doing that, but that drives me as a educator, right there. Is how do I create those experiences so that students are making meaning of this and I’m not just spoonfeeding them something they’ll forget as soon as they’re done with my assessment, because a lot of teachers… like I would get in my early days like, well they’re doing really well on the assessments in my classroom, but the assessments in my classroom. I mean I was just teaching to them, so of course they were doing well temporarily and then I’d wonder why a month or two later they hadn’t owned and kept this information in their head. That’s what drives me right now as I think about what I do in my classroom.

Kyle Pearce:
We’ve even quoted you saying that phrase a few times here in the podcast and I think you sum up a way of teaching that I think we’re all trying to strive for very well. When you say, see it before I show them and they’ll say it before I tell them. I think that’s great. I’m wondering, because this is something that I always wonder about. Is about the… our process from starting where we started to moving towards where we are now. I think that’s a huge part of actually being a teacher and when you say, see it before I show them and say it before I tell them, I’m wondering what did your first year look like or first few years look like, and were you doing it then or what are some of the big moments that made you start switching to this mantra?

Sara VanDerWerf:
It’s a little bit hard to remember back to my first couple of years, but because I had a really rich curriculum that actually honored the idea that kids made meaning out of this problem based curriculum that I was using, I really was radically transformed in my head about how kids might learn math and what had worked for me as a K-12 student worked for me as a new educator in my early 20s. I was a rule follower and so they told me, this is how you got to teach problem based learning and so even though it was foreign to me, I was like, all right, I’m going to trust these people who are providing me professional development and I’m going to do this and I saw students start to make meaning at this. That sat in the early days. I remember… I mean, this is like I went to college as a typewriter and these are the early days.

Sara VanDerWerf:
I remember making a bulletin board out of tinfoil to explain the foil method for how to multiply binomials, like making it pretty and making out of tinfoil, how clever and putting all kinds of energy into that because even though we had rich curricula in our district, it was amazing how many of us educators could take parts of it and bring it always back to what we were comfortable with, how we had learned math and we had racked all these tricks and all these different things but I kept getting the same results that I talk about it being the lucky one third.

Sara VanDerWerf:
This lucky one third of us who like… we just get it the way we’ve been teaching math in America for all these years. I’d see the same five or six hands up when I was going back to these things that… like I occasionally would want to revert, but ultimately I was really lucky in that I started to also see a lot of success, or again, like kids would just have these aha moments, these light bulb moments and would understand things that I was sometimes shocked.

Sara VanDerWerf:
Like I think a lot of us teachers come into it and think if I just come up with the best explanation, they’ll all get it. I just got to explain it better the next year and when I started to divorce myself from that and trust that students could make meaning if I relied on some really good resources, like I started to see things go. As the years went on, I became more and more skilled at developing these little micro moments myself. I was really passionate in the early days and I don’t really know where this came from, but I knew that students did not know what math was, and so 20 some years ago, I really always started my school years talking to students about reframing for them in the first week of school, what is mathematics? Because I think a lot of people define being good at math to be the fastest one to get the answer and when they know they can’t win that race, they disengage in math and become very compliant.

Sara VanDerWerf:
They’re not engaged, they’re just compliant and I started talking to my students all the time that math is a study of patterns and that’s the definition that we would use patterns and relationships and I would jokingly say if you see me in this class not… in a class period us not having to describe and notice and generalize patterns and relationships, then you need to contact the principal and tell them to fire me because I’m not doing my job as your math teacher to create you as mathematicians, because mathematicians, we notice and we describe and we generalize and that became a mantra and a poster that we had up in my classroom and it became how I framed what I did in my classroom that students deserve if they were committed to become mathematicians and nowadays I say, “I’m not turning you into Siri.”

Sara VanDerWerf:
Siri can do all the math I did in school and can be a calculator. I want you to be a mathematician and therefore every day in this class we’re going to notice and describe and work on becoming better at generalizing our thinking, and then I tell students that they are mathematicians because from birth research says that we have the ability to notice patterns. Just like a baby… When babies eat lemons, they all make the same face. No one taught them that face. It’s just something innate within them. That’s what research says is true about us in our ability to notice patterns and somehow in school, some of us believe because we’re not honored for the noticings that we have and that those things are not seen as the beginnings of mathematical meaning and that we’re not honored that that’s how we make meaning out of math.

Sara VanDerWerf:
It gets beaten out of us and so somewhere in there I had kind of morphed into how I thought about this but that little message that I do with students at the beginning of year and then just repeat, repeat, repeat throughout the year because I’m catching them noticing, and catching them describing what they notice in the relationships that they see and naming that as being some mathematician started to really impact the students who I now know is their mathematical identity. I didn’t have the words for all this at the time.

Sara VanDerWerf:
When the math forum people Annie Fetter and Max Ray came out 10 years ago, I don’t know when that [inaudible 00:24:54] was that Annie did for five minutes about noticing and wondering about those questions asking what do you notice? What do you wonder? It really resonated with me because that’s what I had been doing for years. It’s like framing lessons because I’d be like asking myself how can I help my students see what I want them to say? I’ve been using that frame question, what do you notice for a long time? Because that’s what mathematicians do. We notice and then we use that to make meaning out of math.

Sara VanDerWerf:
That’s the frame that I slowly developed. I don’t really know exactly where it came from. I can only say I was lucky enough to have a problem based curriculum and so the resources you use matter, but resources don’t solve what we do in the classroom because any teacher can take that and just completely whittle it down to it being a nothing and [inaudible 00:25:42] I luckily my rule following worked for me in the early days to give students the space and believe and trust that they could make it.

Kyle Pearce:
Yeah. Well, something I heard early on in that section was just this idea of divorcing yourself from doing all of the telling and clearly that mantra you have, the see it before I show them and they’ll say it before I ever tell them. Early in our careers, John and I both have said this on the podcast before, like our thought of a good lesson was just as you said, making sure that our lesson was so well prepared so that we could answer any possible question a student might have before they even have it and that we would judge a good lesson when no hands would go up at the end, right, which was hardly ever. Most times if they didn’t raise their hand it was probably because they were disengaged right from the get go anyway. I really love your thinking jive so well.

Kyle Pearce:
Obviously John and I know you well and I’ve seen you present before so we know that our beliefs are very, very similar and like our real focus on the noticing and wondering in our classrooms. Clearly, we just heard that through your conversation and I just love this idea that when you go back to the way we did teach, and this is hopefully for those who are listening, thinking like, wait a second. That’s what I think good teaching is and all my lessons is me trying to essentially answer all the kids’ questions before they have them. Keeping in mind that you have to be good at thinking that through in order to get to the place where you use that same mantra, right, like how am I going to create a scenario for students to see it before you show them and say it before you tell them if we don’t fully understand what’s going on in the scenario.

Kyle Pearce:
I’m wondering like do you have any examples of like an activity or something that comes top of mind that would be a good example for someone at home who’s thinking like, how am I going to go? A lot of people are back to school now and they’re thinking, how am I going to actually try to shift my teaching from me telling to actually creating scenarios where students will actually bump in. This is what John and I say all the time. Bump into the learning that we’ve set out for them that day so it’s not us always just telling, telling, telling. Like, do you have anything that pops into your mind that someone might be able to sort of wrap their head around?

Sara VanDerWerf:
One of my tips I give teachers a lot is just start by taking away some of the details to start with, and so students need a chance to make meaning of the structure of the mathematics and they need an entry point and so for instance, if you’re teaching a unit on quadratic equations, simply putting up a graph of a quadratic curve, a function, and just saying to your students, notice everything that you can notice about it. One that I was using in trainings with teachers yesterday, and this is something I learned from Annie is like the first, Annie Fetter is… the first four or five things that students will notice are seemingly like not that interesting. Like the picture I was using yesterday, the graph of the curve was red and so students will often say, I noticed that it’s red and they need to get those noticings out so they can start to notice the nuance of those things.

Sara VanDerWerf:
I might want my students to write an equation of that, but to write an equation of that curve, they have to notice all kinds of things and if I keep saying, the most common question I use in my classroom is I’ll put something up and say, what do you notice? And what do you wonder? They’re safe questions. You can’t get that wrong but those aren’t the most common questions. The most common question is what else? What else? What else? Develop this neutral voice of… because eventually, as I’m saying, what else? What else? What else in the class? And I’m honoring everything they say and I’m noting it. I’m saying, yes, it’s red. Yes, it’s a curve. Yes, there’s axes.

Sara VanDerWerf:
Eventually some student will say, “Hey, there’s a high point.” And I teach a lot of students with low language or whether they’re in poverty or they’re immigrant students. And I will say, because I’m always building language, one of my other passions that I speak about in my state a lot is that intersection of best practices from ELA and math is as they notice that there’s a high point I like, yes, there’s a high point that’s the maximum point, or if a student who already has that language says, “Oh, there’s a maximum point.” To invite in the other learners, I will pair that with the casual definition.

Sara VanDerWerf:
Yes, there’s a maximum point and I’m annotating this on the graph and having them annotate it with me and I’ll say, “Yes, there’s a high point.” And I’ll pair that idea of a maximum point and eventually they start to notice there’s places where it crosses the axes and we’ll name those as intercepts. That whole process of them starting to make meaning takes somewhere between two to four minutes, and then I say, okay, let’s take all this stuff and let’s try and see if we can make meaning out of whatever the intended learning for that day is. Whether it’s writing an equation or trying to describe how the change is happening in that event, but I’m connecting the stuff that we’re doing to other representations that we will connect that with, but it starts with a moment of giving students the space to make sense of the structure that’s there before we jump in to that.

Sara VanDerWerf:
One that I’m super passionate about that I personally had some ahas with this year is, I’ve been doing some work with a curriculum that’s a new open resource curriculum out there in their pilot, the super high school, and there’s a series of activities where students are beginning to understand this idea of trig, but they haven’t said the word sine, cosine, or tangent yet. The students have just been measuring all these different types of triangles with angles at different sizes and we put this all into a big table and this table, we then say, “Well, what do we notice and what do we wonder?”

Sara VanDerWerf:
What are the patterns or relationships that exist in this huge table and all these adult learners started saying as I was working with them and then they reported back to me, this is where I [inaudible 00:31:38] have a classroom this year, because I couldn’t go do this with students this year, but they… never once did the phrase sohcahtoa come out of our mouth or sine or tangent and all of a sudden we were seeing that there was a relationship between the sine and the cosine of angles that were 20 degrees and [inaudible 00:31:55] and we saw that because we had made these triangles and we had put this information in an organized way and done some notice and wonder, and I’ve never put this… I use this a lot.

Sara VanDerWerf:
In the last couple of years, just this table that gets created and said, “What do you notice and wonder?” And nowhere on the table does it say sine, cosine and tangent and nowhere does it say that these ratios that are created in this table that are increasing and decreasing and there’s inverses and somehow our brain… well, not somehow we’ve had this from birth, the ability to look at this and start to compare and contrast and see what’s the same and what’s different and do this, and I’m like, I’ve never taught trig without sohcahtoa. Like I could do this. Like I could make meaning out of this.

Jon Orr:
It’s amazing because it adds like this whole where trigonometry comes from. For so long kids think it’s just a black box. It’s like there’s a button on my calculator that says sine and if I punch this number in here, it gives me this number. I’m supposed to use this number and I think back to how I taught trig when I first started, and I think that that’s exactly the way kids thought it was. It’s this mystery number that you’re getting about a triangle, but not understanding where this ratio actually comes from.

Jon Orr:
I think I’d use the phrase the primary trig ratio but kids are like, well, what ratio are we talking? Like where’s the ratio? It’s a number of my calculator. It’s such an eyeopening way to teach trig and you’ve kind of articulated almost the way I’ve changed my teaching about trig for the last five years, about we have the make the trig table and we actually use the trig table for most of the year and it’s only until the end of the year where we’re like, okay, let’s give it a name, let’s take that whole black box mystery out of there, and then… well we can bring in the calculators at the end to say like, this calculator does what your trig table does. It’s just condensed into the calculator.

Jon Orr:
I really liked that example for sure about noticing and wondering like you’ve hit a whole bunch of great stuff here and one of the things that Kyle and I’ve talked about before about the best question you’re asking your students is the, what else? We’ve referenced this book a number of times here on our podcast, which is called The Coaching Habit, which is Michael Bungay Stanier and he has a ton of tips on how to listen more and be curious more as a teacher. Actually, it’s not even a teacher book, it’s just a coaching book and how you can be more curious a little longer and then be less answer giving and it hits home as a teacher.

Jon Orr:
Like what else is one of his main questions when you’re coaching someone, it’s kind of saying like let them talk about what they want to talk about and then you would just ask what else and asking what else gets down to what they really want to know and what they’re really looking for and it works perfect for noticing and wondering. That’s a great connection between that book and what you’re doing in your classroom for sure.

Kyle Pearce:
We definitely want to talk about stand and talks. We should talk about that. We know that’s something that I’ve picked up from you and we’ve been very high proponents of standing while doing math. Talk to us about stand and talks. What is it? Where’d you come up with this idea and how can teachers get started with them?

Sara VanDerWerf:
Well, I got really lucky. I don’t know, probably 15, 17 years ago in my career after I’d been teaching high school for 12 years. That’s where I started my career was at the high school level. I decided like I can only put so many bandaids on students at the high school level to like they arrived to me just like with so many deficiencies and attitude and I hadn’t really figured out how to address their identity around mathematics in those early days and I’m like, I really want to go become a middle school teacher and that it wasn’t really common. Most of the people in my district… I was in a large urban district were trying to get into the high schools and here I was trying to get into the middle schools and I’m not going to go into the whole story about how hard my district made it for me to get into middle school even though we had tons of openings in the middle school.

Sara VanDerWerf:
But the only middle school that I could get into, because I had been working at the high school with the highest poverty rate in the district and I got into a K-8 that had the lowest amount of poverty in the district, and I’m like this is not where I want to be. I want to be where I’ve been hopeful but the universe knew this is the school I needed to be in for a season of my life and it was just hippy dippy trippy school where all these middle-class wealthy, and then there was also students in poverty in the school where this art is infused school and it freaked me out because in high school all I had done is taught math and now I was expected to teach all this other stuff in addition to math and at the school there was one other math teacher and her name was [Allie 00:36:30] and in Minnesota to this day, Allie Ruben is the only person in our state that is certified to teach both dance and mathematics.

Sara VanDerWerf:
The day she would teach these middle school kids dance and they would all dance because she was so passionate and so enthusiastic and then she would teach math. She loves mathematics. She would teach algebra and geometry to her eighth graders and they like so passionate and you’d walk into her room and she was moving and like how all these movement activities in her classroom. At the same time, I was also doing some leadership stuff at our district level and the fiat person and our district level had become a friend of mine, and he was talking to me about how kids and like have all this data about how sedentary students’ lives and schools had been.

Sara VanDerWerf:
Recess had gone away and that the kids needed to move more and he was passionate about convincing content area teachers to incorporate movement and he put in my head that students need to move and had the research to back it up every 20 minutes, and I’m like, my students need to move every 20 minutes and as a math educator I was freaking out because like I don’t have time to move. I’ve got all these standards I need to teach. I don’t have time to take a brain break and like do all this [soshy cushy 00:37:45] things.

Sara VanDerWerf:
I agree with you that they need to do it, but I don’t have time. I got to teach them how to multiply binomials. Like I got… like I have all these things to do and I think a lot of us math teachers don’t know what to do and I knew my friend Allie had done all this movement, but I was scared. I’m not a dancer and I’m like, I don’t know how to creatively do this and she had taught me a few things and luckily like she had given me some things to do, but when I really was in a school without her, because I only worked there at that school for four years and then I went and worked with teachers.

Sara VanDerWerf:
When I was without her though, I was like, I got to find an easy way to do this and so I said, if I’m going to move every 20 minutes, I was already a passionate believer in turn and talks and giving students space to think but then turn and talk to their neighbors and really… when I do a turn and talk, I would notice that only some students, the ones I happen to be standing next to would be the ones talking to each other [inaudible 00:38:38] somebody was dominating that conversation and so, because I was trying to do movement, I just like decided that one day you know what I’m going to have, rather than have them turn and talk to their neighbor, I’m going to make them stand up and I’m going to have the walk across the room so that they get some energy and movement going.

Sara VanDerWerf:
I said something silly that day, like take 17 steps and I’m at a high school at this time. High school teachers often will be like, “Well, my kids just won’t do that.” I’m like, well, they will if you just say this is what we’re going to do and when I was really explicit and said something silly, like a number like 17 and you have to take 17 steps and you can go in a circle, they walked across the room and all of a sudden, like every student… I looked around the room and it was a happy mistake. It’s like when… those old commercials from back in the day where chocolate fell into peanut butter and [crosstalk 00:39:25].

Sara VanDerWerf:
All of a sudden I’m like, oh my God, my students, like they’re talking so much more when I have them standing up. They were so engaged and later the research from, I know [peanut Lilienthal 00:39:37] and like all these other people about like when kids are vertical they talk more. I kind of happily got into that and then one day I was being observed by some teachers, and I get this all the time when people are in my classroom and I have tons of people in my classroom throughout the year, like hundreds of people observing me and I always get the same three comments when people are in my room. They say, “Sara, where are the cell phones? I don’t see the cell phones.” Which is funny because I’ve written a blog post, that’s title why I believe cell phone should be in the American classroom.

Sara VanDerWerf:
I get that but I also get like, I’d never been in a room where kids talk so much about mathematics and where kids move so much because I started… I got addicted to doing these things and I had to give them a name. The first time people observed me, they’re like, “What are you doing here?” And so I just called them stand and talks to give them a name for the people. I’m like, yeah, this is what we do in my room. We stand and we talk and it’s just a play on turn and talks and they’re like, this is brilliant. We should have more people doing it and I started teaching this to other people and I started doing this in all the professional development I did because adults need to move in development as well.

Sara VanDerWerf:
It’s amazing, we’re no different than our students. We will talk about the mathematics that are in front of us more, and so the more and more I got better and better at them, and I’ve gotten better and better at being able to say out loud what makes them this successful the first time. There’s a lot of people who will go and try them and it won’t work the first time, and so there’s some little tricks of the trade that I’ve learned along the way. Even now, like when I blogged about them the first time I get contacted almost every week through social media with people saying these are like a game changer. Like why didn’t I do this? And I felt that way about the vertical non-permanent surfaces.

Sara VanDerWerf:
Like when I started making those in my room and I would do it the first time and oh my gosh, my kids are talking even more and [inaudible 00:41:23] do it for several weeks because I don’t know, like I just wasn’t comfortable with it yet and that I would do it again and even more engagement stuff. There’s something about being vertical and moving to radically change your engagement in your classroom.

Kyle Pearce:
Yeah, we couldn’t agree more. I’m glad you referenced Peter’s work. Peter Liljedahl and he was on our episode number 21, so we’ll put that into the show notes. If folks are listening and they want to learn more about Peter, we’ll also include some links to some of the white papers about that and John and I started doing the vertical non-permanent getting students standing and oh my gosh, like what a difference and something you’ve mentioned here, just talking about the stand and talks I think is great is that by taking your turn and talk time, which you said you were already using, and for some people maybe they’re not.

Kyle Pearce:
They might still have to make an adjustment to get that into their teaching practice and make it a routine as something that you do in class but once you’re doing that, I see it as hitting two birds with one stone because now it’s like you’re getting some of the benefit of getting kids up and active, just like some of the research you had referenced earlier, but then also even if you have a student who in turn and talk time, like you said, isn’t talking unless you’re near them or someone’s dominating as you had mentioned, like here it’s like at least you’re getting one of those two things minimum, right?

Kyle Pearce:
Like you get that stand time now it’s a little bit of a brain break but really now you’re walking around as well and you’re trying to kind of maybe jump into some conversations as well, try to push kids to get on and actually do some of that talking. I love that. Now you did mention that now you’ve got a few little tricks up your sleeve of what kind of is important in order for a successful stand and talk because we get the same emails all the time, tweets, things like that from people asking about vertical non-permanent or any of the other things we talk about on the show.

Kyle Pearce:
Help folks who are listening. If I’m going into the classroom and I want to try to actually make this thing work, what are some like go-to strategies you have to make it a little easier for success? Like you said initially, it can be hard, right? Just to motivate kids change. We humans don’t like it a whole lot, but what are some things that might help someone take a step in the right direction?

Sara VanDerWerf:
Yeah, well okay. First of all, this is all related to the stuff I talked about earlier. You need to start with something in their hand that they can talk about. I frame something… like I’ve created a mathematical experience that’s something they can notice or wonder or something they can talk about what’s the same or different so they’re convincing me. I haven’t uploaded this into my blog post on stand and talks yet, but I’ll upload because I’ve created it because people have wanted it. My three favorite types of stand and talks to create. Like I have some little tips on how to create them a sheet and I have… I’ll put that post up today so that it’s in there if you want to look at what you create to put in front of their kids in place, but let me give you my best tips because I really feel like stand and talks are kind of your entry point.

Sara VanDerWerf:
If you’ve always wanted to look at what Peter is doing with his work and start doing some longterm… like getting up and having students at whiteboards for a longer amounts of time, stand and talks might be your thing that you can do on your journey to making it happen, because it’s a really short time commitment in your classroom and so it’s a good way to just try something and do it. The directions are super important. If you’ll allow me, I’m going to just like model for you really quickly my directions, the first time I ever do a stand and talk because everything I do in these directions is intentional and the tips are in those and there’s some psychology with kids. I’ll just do it really quick. Are you guys cool if I do that?

Kyle Pearce:
Yup. Take it away.

Sara VanDerWerf:
All right. All right, students. Today we’re going to get up and talk about mathematics because we’re mathematicians. We’re going to notice and describe. That’s what I want you to do. When I say go, I want you to stand up and I want you to take 13 steps away from your desk at least to go find a partner. When I say partner, that means two people. You’re going to make a group of two, not three. It’s going to be two. If you’re the odd man out, you’re going to come and see me and I’ll tell you what you’re going to do then. When you find that partner, I’m going to come and find you and give you something to look at. You’re going to get one sheet of paper for the two of you and I want you to talk without stopping for two minutes.

Sara VanDerWerf:
You can’t stop. You’re going to take turns and you’re going to talk. Your questions are going to be what do you notice and what do you wonder? I want you to notice like 12, 13, 14 things. Keep noticing and then wonder a couple things. What do you wonder about this picture? If you run out of things to say, I want you to repeat the things you’ve already said, but without talking, I want you to just get up and go and make it happen. Students like, what do you need to do? Like somebody tell me what you’re going to do and then I wait for students to repeat back some of these things. It’s two people. It’s two minutes. We’re going to take 13, 14 steps. What are you going to do if you find the person you want to be with and they’re not from your group on step six. We’re going to keep walking together until we get to the group across the room.

Sara VanDerWerf:
And so I say, “All right, do you have any questions?” And then I say, “Go.” And I, Sara VanDerWerf want to be the one that goes out as they make partners because they get up right away because I say… the one thing I forgot to say in my directions is nothing in your hands. You don’t need anything with you. As soon as I say nothing in your hand, students will drop it. I will then walk around and give each partner, it’s often a half sheet of card stock with something for them to notice and wonder. Usually the first one I do is a notice wonder. It’s a good safe thing, you can’t be wrong and then I hand that all out as they’re going and then it’s amazing.

Sara VanDerWerf:
As soon as I give them stuff, they’re doing things but in that little moment of stuff that I told you, all those things that I said are intentional. Me saying how many steps you take, I don’t care what the number is. That number changes all the time in my life, but it gives them something really specific to do. If I just said walk to another partner, they struggle to stand up and walk to another partner, but when I’ve made it silly and that you need to do this many steps, they get up and do it.

Sara VanDerWerf:
It’s super important to say how long they’re going to be talking. When I say the first time they do this, you’re going to be doing this for two minutes. It’s… I’ve set the boundaries. I never have problems with students wanting to be with some other student in the room because if I had not said two minutes, go find a partner, they don’t know if they’re going to have to do a project with that partner and be with that partner forever and they’re less hesitant to do that and so when I’ve started saying it’s two minutes, they get up and go right away.

Sara VanDerWerf:
When I say it’s groups of two and not three, and I make the group of three, I used to not say that and then kids would wait because they want to be with their three friends and you know, like they drag their feet and it would just take forever, and then it’s super important. The first time you do this is that you demand that everybody does this. If you let even one kid lean on their desk or not do this, they just won’t and so the first couple of times you’ve got to have no opt out. I get asked all the time, like a couple of common questions. I got this asked this yesterday, “Sara, I have a student in a wheelchair, I don’t want to say you got to walk 15 steps.” I say, “Yes, I’ve had students in the wheelchairs.”

Sara VanDerWerf:
I just reframed my language and say you have to move 12 feet and I measure out 12 feet and I just have changed it and it’s no problem. What do you do if a student [inaudible 00:48:36] you know, a broken leg. I just… all those things and honestly I don’t have students who don’t do this. I’m always saying like I teach in areas where people say, the students I teach can’t and guess what they all do. I most recently taught juniors and seniors in high schools and guess what? They will do it if that’s just the passion that you bring into the thing and so I mean this is a routine that’s not specific to math.

Sara VanDerWerf:
The only thing that’s specific to math is what I’m putting in their hands of noticing and wonderings and it’s just as going to get your students moving and up and thinking and it shakes it up and it shakes it out of the… I think I remember Peter talking about the nature of the vertical just shapes you out of this normal thing where you will budge out in your seat and just like be either looking at your phone or be zoning out and doodling and doing stuff for other classes and when you’re standing with nothing in your hands, you have nothing else to do with but talk.

Sara VanDerWerf:
And I’ll be silly. I’m like, you can talk about your shopping list when you leave here to adults. No one ever does and occasionally some… [inaudible 00:49:37] funny when I say you got to talk for two minutes, they will talk for two minutes.

Kyle Pearce:
This is fantastic. I’m so happy that you’ve outlined just these different pieces and actually modeling it for us. Makes it super explicit and going back and essentially explaining why you’ve done what you’ve done. I love it, especially when you’re starting. My guess is as the school year goes on, you can kind of relax a little bit because the routine is set and now you’ve just got them out of this bubble and I know for myself it is so much easier for me to brainstorm, to work on ideas or even just to think by standing and I know we’ve seen that same experience in our classroom with our students because as you mentioned, when you’re sitting it’s just really easy for yourself to like get into that relaxed state. Your brain stops thinking. You’re just kind hanging out and when you get up and get that adrenaline, the blood moving.

Kyle Pearce:
I see kids that I’ve never seen participate while just sitting in their desks. I’ve seen them come to life. I think this is such a great opportunity for people to be able to grab something from this episode and be able to go try this and the beauty is they don’t have to actually restructure everything they’re doing tomorrow. They could actually just insert this through their lesson where they think is appropriate and give it a go. This is fantastic. John, what do you say my friend, we had so many more questions but I think we’re coming to the end of the episode here. John, what are you thinking?

Jon Orr:
Yeah, we want to talk about name tents and the [MTBoS 00:51:07] and play tables, like we had so much to talk about but just before we do wrap up, is there anything you’re currently working on or anything you’re passionate about lately that you want to slip in here to let the math moment maker community know about?

Sara VanDerWerf:
Yeah, the two things I’m really passionate about because I’m always wanting to learn more. It actually relates to what I’ve talked about today. The first of the two quick things, and that is movement. I am working with [Chris Lesniak 00:51:30] who’s out of California. He’s a debate guy and we’re going to be doing some PD together this year around movement, because we are just like on a mission to get all teachers up and moving and so we’re super excited about some of those things. I’ve also filmed my friend Allie Ruben’s classroom and those will go on my blog of her students doing some of her other dance movement activities that are connected to the algebra that she teaches. It’s not like they’re just dancing to dance, so if you’re looking for more ideas, look for that on my blog at saravanderwerf.com. Even if you spell my name wrong, you’ll find me out there.

Sara VanDerWerf:
I also am just really passionate right now in my personal learning around why change is so hard for teachers and a weird thing about me, I won’t go into it, is that I taught myself how to ride a backwards bike several years ago. It’s the only bike that I know how to ride and that journey to learn to ride a backwards bike is the best professional development I’ve ever done. I did it in the hallways of my school along with another teacher, Morgan and it just radically changed and gave me empathy for my students in a way and for other teachers but it also made me think about why in American teaching, like why do we keep going back to teaching in a way that we know isn’t what we want to be doing and then what do we do about that? And so those are the things that I’ll be speaking and writing about as I move forward in the year, so yeah.

Jon Orr:
Awesome stuff. Awesome stuff. We’ll put the links to your website and your Twitter and some of the other things. I think there’s even a YouTube backward bike kind of journey video that I’ve seen. Great for you to mention that. I think we can put all those links in there for where people can learn about you, but we want to thank you so much for joining us here today and we hope you enjoy the rest of your summer and I think this’ll be airing later after summer’s over but everyone will be like, oh, I wish it was summer again when they hear this, but-

Sara VanDerWerf:
I know, I know. I know. I know. Happy fall. It’s the most beautiful time in the year [crosstalk 00:53:27].

Jon Orr:
Right. Yeah.

Sara VanDerWerf:
Come visit us [inaudible 00:53:29].

Kyle Pearce:
But thanks so much Sara, for joining us.

Sara VanDerWerf:
All right.

Kyle Pearce:
Thank you, John. Thank you Kyle. I love what you guys do.

Jon Orr:
Thanks Sara. We’ll talk to you soon. Take care.

Kyle Pearce:
We want to thank Sara again for spending some time with us to share her insights with us and you, the math moment maker community. As always, how will you reflect on what you’ve heard in this episode? Have you written ideas down? Have you drawing a sketch note? You sent out a tweet? Talk to a friend or a colleague. Be sure to engage as some sort of reflection to ensure that the learning we’ve done here sticks. All right, and don’t forget to check out our three part framework math moment maker post where we’re going to help you deliver math lessons that students will not only love but will also learn from. You can learn why we created the three part framework and the necessary pieces that you need to know so you can run your classroom lessons without a hitch by visiting makemathmoments.com/framework. That’s makemathmoments.com/framework.

Jon Orr:
In order to ensure you don’t miss out on new episodes as they come out each week, be sure to subscribe on Apple podcasts or your favorite podcast platform.

Kyle Pearce:
Also, if you’re liking what you’re hearing, do us a huge favor and share the podcast with a colleague and help us reach an even wider audience by leaving us a review on Apple podcasts and tweet us your biggest takeaway by tagging @makemathmoments on Twitter.

Jon Orr:
Show notes and links to resources from this episode can be found at makemathmoments.com/episode55. Again, that’s makemathmoments.com/episode55.

Kyle Pearce:
Well, until next time, my friends, I’m Kyle piers.

Jon Orr:
And I’m John Orr.

Kyle Pearce:
High fives for us.

Jon Orr:
And high fives for you.