John: Many students don’t think as flexibly about numbers as we think they do, so this is a really bad example but it’s the best one I’ll come up with for the listener right now. For the number 50, we’d like to think that they can break 50 apart in infinite number of ways, but if you were to poke at it, you’re going to find that they really only think about it in four or five ways and those ways are very limited, such as 25 and 25, 49 and one, et cetera. And I’m talking about whole numbers right now, but it applies to really any type of number.

John: And the point with that routine, broken numbers or express it, we want students to play with, get dirty with numbers and look for patterns on how you break them apart. We know that when you do this, and you decompose numbers frequently, they because [crosstalk 00:00:38].

Jon Orr: That there is John SanGiovanni, a math supervisor from Baltimore and an author of the book series, Daily Routines to Jump-Start Math Class. In this episode, we chat with John about why your traditional warmup bell ringer activities need to change, how to build number sense at any grade level and save time doing it.

Kyle Pearce: Why traditional homework take up doesn’t work, how to avoid creating math sheep, and you’ll walk away with five specific routine activities to jumpstart your day. But before we get to all of that, let’s queue up the music.

Kyle Pearce: Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce.

Jon Orr: And I’m Jon Orr. We are two math teachers who together.

Kyle Pearce: With you, the community of educators worldwide who want to build and deliver math lessons that spark engagement.

Jon Orr: Fuel learning.

Kyle Pearce: And ignite teacher action. Are you ready for this awesome jam packed resource filled episode, Jon?

Jon Orr: Of course, of course, of course. Before we begin, the Making Math Moments That Matter podcast is excited to bring you the make Math Moments with Corwin Mathematics book giveaway. That’s right, we’ll be giving away 10 books from Corwin Mathematics, including John’s book, the guest we have on our show today, his book; Daily Routines to Jumpstart Math Class, the middle school edition.

Jon Orr: Plus you’ll receive a special Corwin discounts and digital downloads just for entering the draw. You can get in on the giveaway by visiting makemathmoments.com/giveaway by Wednesday July 31st 2019.

Kyle Pearce: Listening after July 31st 2019, no sweat, we would never forget about you. We’re always actively running giveaways, so make sure to check out the same link, makemathmoments.com/giveaway to learn about the current giveaway we have running.

Jon Orr: Don’t miss out, dive in to makemathmoments.com/giveaway.

Kyle Pearce: That’s makemathmoments.com/giveaway.

Jon Orr: Without further ado, here is our chat with John SanGiovanni.

Kyle Pearce: Well hello there, John. Welcome to the Making Math Moments That Matter podcast. How are you doing this mighty fine evening?

John: I’m going great. Thanks for having me.

Jon Orr: John, could you help our listeners understand a little bit about yourself, where you’re from? Take us a little bit on your kind of math education journey, if you will, please.

John: Sure. So here’s what I do right now. Currently, I’m a math supervisor in Howard County, Maryland, about halfway between Baltimore and Washington. We have 70 some schools in our school district and I am fortunate enough to work with all of our teachers through professional development and curriculum development and what have you.

John: But I think what we really want to talk about is my math story, I guess. I have a dichotomist background. I learned math in school and I did math in the world as a student. And those two things did not always intersect.

John: So I learned a lot of procedures and steps in my math classrooms and I practiced the hell out of those things. There’s my first curse word, I apologize.

Jon Orr: Let it flow, let it flow.

John: Keep them coming. Anyhow, no. I mean just like many of us, I had a very proceduralized do the math and plug it out and figure your answer output. In the real world, I love sports and I compared Karl Malone’s foul shooting percentages to Mark Aguirre’s.

John: And I guess my point is, is that I learned to do math in the world differently than I did in my classroom. And that actually inspired me to think about what it meant to teach math. And as I evolved and became more comfortable, I learned that we could do better things and apply and practice new strategies.

Kyle Pearce: Right, right. It sounds very similar to … Jon and I talk about it all the time on the podcast, we were very good at the game. Learning about math, we were told we were good at math and I was happy with that. I know I was. I thought, “Hey, I’ll ride this as long as I can.” I didn’t have to think and I just had to try to memorize as much as I could and eventually, it kind of fell short when I tried to actually get a degree.

Kyle Pearce: So that was something that sort of rocked my world. I want to back up a second. And you’re a math supervisor, I’m wondering, your district is 70 something schools and my district is just over 70 schools. And I’m just curious like what is the day in the life of a math supervisor in your district look like or sound like?

John: Well, it’s different every day, which is really great. Unfortunately that I spend a lot of my time in classrooms, which I think is important for my work and helping teachers, not just in my district but in other places throughout the country. So a day in itself could be a meeting with my math coaches, reading and learning together. It could be visiting a first grade math class and working with students. It could be visiting a team planning session and listening to challenges that they face.

John: It really goes all over the place. There’s ebbs and flows to the school year. So right now, we’re in the process of getting ready for curriculum writing. We develop our own and make that available to the world for free. So we’re looking to polish it this summer. So we’re in that throw of getting ready for a next school year but day to day is different, and that’s a good thing. But most of the time I spend my time in classrooms and that’s where I’m most at home.

John: But I want to go back to something you said as a matter of fact, playing the game, I call it being a math sheep. I think [inaudible 00:06:08] math sheep, right? And my motto is, “No more math sheep.” And so I’ve been working hard to help our colleagues and other teachers think about how can we help students think and reason?

Kyle Pearce: That’s great. Yeah, that’s great. I’ve never heard that phrase yet. So that’s a new one, the math sheep, I really like it. I mentioned that brings up some memories here and being this the Making Math Moments That Matter podcast, we have to ask you this question, if you think back to your experience, you’ve shared a little bit about that already, but if you think back more to your experience as a student or even as a teacher, what would be something that sticks out to you as the memorable moment from those math classes?

John: Well I have three or four. Let me share my student ones first. I remember very vividly the first time I got to apply mathematics in a real situation, or at least it was to me, and we were working with ratio and proportion and I want to say it was maybe seventh grade, and we took small comics and blew them up to be the size of poster board by gridding in and creating these proportional representations. And I thought it was the coolest thing.

John: But what was even more cool was later that day or maybe that week, whatever it was, riding around our town, I saw these billboards and it was the first time I recognized that I knew how they did it. And the math is actually how they did it. So that’s actually a really poignant one for me.

John: Another one is in high school, so this is a math phobia I got to tell everybody about, I don’t like writing with pencils, which is ironic because math people do nothing but use pencils. Anyhow, my point is, I had a high school teacher, and like it got to the point where it was really uncomfortable and she let me use pen in math class.

John: And there’s two reasons I share this story. The first, that was maybe the first time I realized there really weren’t math rules. I call them the math 10 commandments and they really didn’t exist. That was the belief, but I was shattered. I realized you could do math with a pen. And the other cool thing that came about was that I actually saw my mistakes because I no longer tried to erase them. And the point is that you learn a lot from your mistakes, but when you use a pencil and erase them, you don’t actually see what you did.

Kyle Pearce: I was immediately, as soon as you said pen, that was, the second portion was what I was jumping to right there was just this idea like I was the kid who, even with pencil, if I didn’t know and feel confident that I knew how to get to the answer, I would just skip it. I was considered a good at math student based on those fake rules you just described and yet I still didn’t have the confidence to like try something that I didn’t have like 100% certainty that I knew I was going to be able to get to the end. It was like I was ashamed or just too scared to fail.

Kyle Pearce: And I think even just that idea of using a pen and sort of like how awesome is it to celebrate those mistakes? And as teachers, I always think back like how often I would have my lessons so carefully crafted that it would look as though I never made a mistake as a teacher.

Kyle Pearce: And that’s another thing I felt like we just got to break away from that, and it’s like a bad habit, is not showing students that we actually have to think through things in order to do interesting math anyway.

John: That’s really, really well said. And again, I want to say dichotomist for me and my experiences. There was this perception of what math had to be and then like I was doing math all the time at home and never really realized that the two needed to intersect. But your point about making mistakes, like we did that at home all the time, right? Playing games in the backyard and keeping score and like, I don’t know, you got over mistakes really quickly, but boy, they had a different lasting appeal so to speak in the classroom.

Kyle Pearce: You did mention you wanted to share a few moments. You have a few more that you want to share?

John: Yeah. This one probably sums it up for me the best in terms of those awakenings that you have, like your math awakenings or awakenings in your career. So I was teaching, it was third grade and we were working with multiplication. And long story short, I had a pretty traditional math education, yada yada yada.

John: So we’re working with areas, and a third grade student said, “Did you see? Do you notice that each time it has the same factors?” Granted, she didn’t say factors, but each time the numbers are the same, they’re squares. And I was like, oh yeah, I see that. And she’s like, is that what a square number is? And at that moment I realized that’s what a square number was. But here’s my point, I never understood what square numbers were. I mean, don’t get me wrong, I could find square roots, but I never knew why they were called squares. And at that very moment also then I was like, is that why they’re called cubes?

John: And I had the great math awakening teaching elementary school and realizing that I was fooled for a long time.

Kyle Pearce: Well, you know what’s crazy about that, and Jon and I have talked about this, now that I am a K-12 consultant, which sounds as though my role, going back to you sharing about your day in the life of a math supervisor, it sounds like a very similar role where I’m in classrooms sometimes, I’m in PLC, sometimes I’m working with coaches sometimes, all of those things, right?

Kyle Pearce: And it wasn’t until I came out of the secondary classroom and I started in this K-12 journey where I’ve been spending so much time in K-eight, I started really exploring the nuts and bolts of addition and subtraction and multiplication and division. And when I was doing that exploration to prepare myself in order to deliver a workshop that I sort of made that connection myself, right? Like playing with arrays and doing all these things and going like, wow, this would have been really helpful for all of those kids that I had in my high school class that were always way behind and I just never knew what to do with them.

Kyle Pearce: And it was like I had that aha moment myself too, right? Going like, Oh my gosh, I’m like picturing that. And something else too, even just going back and just thinking about fractional language and how we use language like quarters for fourths, and it’s like things that we could do to help make things more explicit for young children and even older children, right? Because obviously you were much older than a child when you realize that, and it’s like even though it’s right in front of our face in mathematics, oftentimes without being explicit, we completely miss it. It’s like it just goes right over our head.

John: Yeah, well said. And there’s one more thing I’d throw in there too and is a similar awakening, and it really goes back to elementary math and that’s the distributor property. And memorizing properties with letters and not understanding them because then when you grow up you have to memorize things like the foil method when you never understood [inaudible 00:12:33] just the distributor property. And I think that those are just prime examples of how we overlook the math. We can do the math, but that doesn’t mean we always know the math.

Jon Orr: Yeah. And you brought up the squares. That reminded me of my experience teaching the Pythagorean theorem, because I for years just taught it the way I learned it with A²+B²=C². And then when you actually … It wasn’t until only five/six years ago where I saw the visual representation. I think I had seen the visual representation of the squares drawn off all three sides, and in a book before but I’m like, I don’t know what … I’m just going to skip that and we’re going to just go right to the formula.

Jon Orr: But it wasn’t until later that I was like … And when you see the squares, you’re like, that’s why they’re called square numbers. It was eye opening to me. And again, as a secondary teacher not knowing that till later. And what a great way to explore the Pythagorean theorem is to look at that. Also, in the Pythagorean theorem, it was mind boggling to me that if you drew the triangles off the sides or like a regular hexagon off all those sides, those areas still add up.

Jon Orr: And then when you explore that with kids, it was awesome to say like, “Well why do we use squares then?” What is it about squares that makes it so much nicer to calculate those side lengths if we could use any shape. And so it’s like a great exploration for sure there.

Kyle Pearce: So John, I love the moments that you’re sharing. And obviously, you did a little bit of homework thinking about that or maybe it’s just it’s so fresh in your mind. I know for me, my moments like those are so fresh. I’m wondering if we could shift gears a little bit because recently I had the pleasure of coming across one of your books from your series called Daily Routines to Jumpstart Math Class. And I was wondering if we could take a little bit of time before we dive into that specific book, but we’re wondering like what sort of experiences in your career had an influence on you to take your passion and then find ways to actually share it with other educators?

Kyle Pearce: Like was there anything that had influenced you or inspired you? Like why did you feel it was helpful to start writing books? Because I know these aren’t your only books, but they are the ones that we’ll be talking about tonight.

John: It’s hard to say there’s any one moment. One thing that I’ve always lived by is take advantage of any opportunity that comes, say yes to everything. And I remember early in my career, I had opportunities to do some curriculum writing in our district and I just loved the process of diving into the math content and developing resources for our colleagues and then trying those things out in our classroom.

John: And that led me to a special lady in my life, a former supervisor and friend, Kay Sammons, who got me involved in the math in our district and took me to national conferences and took me under her wing, to speak, and sessions and just I had opportunities to be exposed to learning about math. And I saw this great community that we have. And at that time, we weren’t really connected as well as we are today, per se. But the point is, is that every time we went to a conference or a meeting, it was a revival. And those types of moments really reignite your passion for it.

John: So I guess, those moments in my career, I don’t know that there’s anyone that was like, this is math for me, but just … I don’t know, being involved, creating and then working with teachers to polish those creations, and then seeing, and this is probably the most important part of all, but like all of the things that I’ve created for our district or whatever, people buying books and using their classrooms, when you see kids, students using those things and having opportunities that we didn’t have, that’s the part that makes you come back for more.

John: So I don’t know how well that answers your question, per se, but that’s kind of how I got started and it becomes … I don’t know, a passion.

Kyle Pearce: Yeah, for sure. And I think too, and you mentioned national conferences, so I’m assuming like probably NCTM. Were there any other conferences that sort of like stuck out early for you?

John: Yeah, I mean, and it was NCTM. It was our state conferences, which was Maryland council of teachers of mathematics. It was, there were a couple of districts that worked together that had a thing called quad counties in Maryland. It was just these little different math gatherings that really got me to connect with others and to learn about other perspectives and the way that other approach math.

John: So that was it. And then I’d been really fortunate and blessed to have new opportunities and do other conferences. In fact, last week I was in Oklahoma during the Oklahoma Council of Teachers of Mathematics Conference, and I guess my point is, is that anytime I’m in those, I have an opportunity to sit in and hear what other people are doing. Yeah, those are the things that inspire me.

Kyle Pearce: Right. Like for me, I know very vividly it was the opportunity to go to our provincial math conference, the OAME conference, and I actually was asked to be a part of the planning committee because we were going to be bringing it locally and I had never been to the conference and I actually didn’t really know what the association was all about and I just sort of said sure, just like you said, like the whole yes man sort of thing, right? And gave it a go. And threw my hat in to do some help and then we had an opportunity to actually go to the conference.

Kyle Pearce: And I’ll tell you like for me, that was definitely a game changer and it just totally reframed everything I thought about teaching. I mean, it took me a long time after that before I started to feel like I was actually changing my practice. But it was like a start to my belief shifts.

Kyle Pearce: I’m not sure if you could relate. Like when you were at the beginning of your career, were you like us, where we sort of came in and we were teaching the way we were taught and we weren’t really feeling too successful about it or did you have a different experience?

John: I had a slightly different experience in that … I mean, many of the ideas and ways that I approach math and that we believe in were very deep down inside me. I needed something to unlock it and let it out because I had these beliefs about what it meant to teach and learn math and it wasn’t until I was exposed to, no, you really don’t have to do it that way. And there’s research that supports new approaches and thinking and reasoning and so forth. And I guess for me, it was more about having an opportunity to unlock those and then to grow my ideas based on those exchanges.

John: But I want to go back to one other thing you said real quickly, and you said you got involved with a program. I think that for many colleagues, we don’t recognize there’s so many opportunities out there. And for some of us, I mean, just started as just volunteering at a conference and you work with somebody. And I guess my point is, is that our councils, our institutions, our organizations really want members to be involved, but it never feels like it’s like my voice matters or that I can. Does that make sense?

Kyle Pearce: Totally, totally. I know that it could be a struggle to … I mean, with the internet, you would think that we could find things easily or like we would know that these things exist. But I mean, it’s really hard. There’s so much out there now, right? Not just obviously math, but just everything coming at us. And once you find them, it’s sometimes people are feeling like, how do I get into the “club,” right? Or something like that.

Kyle Pearce: But I mean, I’ve experienced so many different conferences and it seems like all of the committees, it’s like they’re always waiting with their arms open. Even if maybe initially it doesn’t seem that way just because you feel like you’re just you and there’s this big conference or this big committee, you’re right, they’re always looking for more help and more support and all of those things. So anyone who’s listening who is kind of sitting on the sidelines, take a look around, like see what’s local and if there’s nothing local for you, then maybe this is an opportunity to maybe start something and start forming a group from the grassroots.

John: That’s exactly right. But I do know that organizations are always looking for folks to be involved. So yeah, anybody listening-

Jon Orr: For sure, for sure.

John: … Get involved. Small, your state, your local conferences, whatever, it doesn’t matter.

Kyle Pearce: John, we wanted to dive in and talk a little bit more deeply about the book series you’re writing, Daily Routines That Jumpstart Math Class. And jump-starting math class makes me think and a lot of us think about warmups or we call them warmups. I guess we want to know like what is it about warmups that led you to write a whole book about it? What are you seeing about warmups that you think is exceptional?

John: Well, let me actually go back to something you said or I said earlier about the math 10 commandments. And on those 10 commandments were I had to start math with a warmup that reviewed things and then I had to go over homework or I could do those in either order.

John: I guess my point is that warmups have become very mundane and homework too for that matter, and they became mini lessons. I hijacked my own class, my own lessons so many times because number three in the warmup was a mini lesson because no one understood it or remembered or homework number seven was just a jacked up problem that nobody could do. Or 20 people didn’t do their homework. And I guess my point is, I know my point is that I wasted so much instructional time doing things I thought I had to do. And the same time, there were so many things I wanted to and I didn’t feel like I could.

John: And one of those is developing number sense, right? And I’m going to get into that in just a second. But there’s one other thing that I had challenges with when it comes to routines and … Or excuse me, traditional warmups and going over homework to start a class. And that is, I told my students all the time that thinking and reasoning is what matters, right? I was interested in how they did math more so than the answer that they got. Yet, I started every math class with going over the answers.

John: So I told them one thing, what I believed in valued, but I did another. So they had this real big disconnect about, you’re telling me you care about our thinking, but you’re only going over the answers. We all have bad years or bad months or bad weeks, and I remember complaining about my students’ number sense and they just didn’t have number sense. And a teacher, a colleague called me out and said, “So what are you doing about it?”

John: And what’s funny about that is I was very angry with her, but it really stuck. Like, what was I doing about it? And number sense, it’s a perfect excuse, right? It’s not a unit in anybody’s textbook, it’s not a specific lesson. Number sense isn’t on a test, but it’s on every test. And so I started thinking about how do we restart, or how do I restart conversation thinking and reasoning in those first few minutes of math class? And I have a colleague, Heather Dyer, who helped me think about how we were going to go about reshaping the first few minutes of math class.

John: So that was work in our district and it evolved into those books.

Kyle Pearce: That’s awesome. And it aligns so well, we actually had a question all queued up. We were like feeling really good about it and you actually answered it, which is great. Which is like, why the traditional warmup doesn’t work. And that’s this idea that like homework tends to … I mean, your typical warm up, your mind’s on or whatever you want to call it. I used to call it a mind buster. It was like kids would do it, but it was like they knew it was coming every single day. There was nothing different about it. It was very like just a problem of some type and there wasn’t much to it. And then when we got to the homework it was the same deal. Like I plan for my 15 minutes of homework take up and then 45 minutes later we would start the lesson, right?

Kyle Pearce: Like it would always turn out to a balloon into this huge thing. We felt like this, like you said, like a rule that we had to do. And when in reality, the kids who did the homework, they were the ones who had to sit there and they were actually listening but they didn’t need what I was giving them. And then the students who I was doing it for often were the ones who were disengaged immediately. So it was like just not helping anyone. So I love the alignment there and that was why we wanted to frame up that question. So Jon Orr, why don’t you tee us up for our next question, my friend?

Jon Orr: Sure. You have a number of routines outlined in the books that are all fabulous. I’m wondering if, do you know how many routines in total are spanned across those three books? Like maybe you can fire out an estimate if you’re certain or uncertain.

John: If I was to estimate, I would say about 45 or so across the three books. They play out a little bit differently but it’s important as teachers that we have a collection of routines for lots of reasons, right? And so even though there are middle school routines and high school routines and elementary, what have you, they could be changed out very easily to be used in a different grade level or grade band by changing the numbers or the approach or strategies, what have you. But why it’s important to have a lot is this, so we create math sheep but sometimes we’re math sheep too. And so if you do the same routine over and over and over again, it just becomes a different procedure.

John: So it’s important to keep the first few minutes of math dynamic. And when we’re growing and engaging in number sense, you have to do it in lots of different ways or it just becomes, again, another procedure. So there’s a little over 45, I guess I’d say, over all three of the books.

Kyle Pearce: Awesome. Now I’m wondering, thinking about this, so there’s 45, I’m wondering are there some that are sort of like more of your go-to strategies? Do you have maybe a couple of favorites that you wouldn’t mind giving us a little bit of background in? Maybe something that someone might be able to hear this, they might be driving to work right now and something they might go, “Wow, I’m inspired to at least check out or look into some of these routines.” I’m sure if they Googled some of them, they may even pop up, they might have some sort of variation of a few of them. Are there any that are further like up your sleeve that you wouldn’t mind sharing?

John: Yeah, sure. Well let me say one more thing about that too, there’s different ones that have different memories that are favorites for different reasons, right? But number sense it’s such a complex idea that the routines, they do different things. So one of my favorite routines I call picture perfect where we prose a picture to the students and ask a provocative question.

John: So they might see part of fare so we don’t have to estimate how many people could ride it at one time or they might see a plate of brownies and know that one brownie is 125 calories so how many might be on the plate? What I discovered in my own students that live upstairs in my house and those that I taught, they don’t see the math in the world around them. They’re not constantly engaged in thinking about like, I want my real kids, my flesh and blood to walk into a room and say there’s about 50 people in here, right?

John: I want them to see numbers and push back on them. And so picture perfect is one of those routines that starts and helps them start to see the math in their worlds. I like other routines like ones … I mean, I’m not really creative when it comes to titles. One of them is called more or less and it’s real simple, it’s about estimating if something is more or less … If you’ve ever had a student do a calculation and not recognize that they’re not even in the ballpark, this routine and a bunch of others are really good for you. And that is having students think about let’s do two and seven tenths times 14 in five tenths or something like that. We give kids or students some expressions and we have them determine if it’s more or less than a certain benchmark.

John: So in that case, the numbers I use might be compared to 50 or something like that. More or less is one of my favorites because I remember vividly telling students to put their pencils down, we weren’t doing math like that anymore. And so I come back to that because it’s just a really cool routine for kids to estimate solutions and then compare them to a benchmark.

John: One more for you, one of my favorites. If you’ve ever played $20,000 pyramid or math headbands … Or excuse me, not math headbands, but the game had bands where one person’s giving another person a clue about something and they guess it. Math yapper is a version of that. I call it math yapper because you’re sharing ideas through your yapper. But we do it with vocabulary, but then we pivot and do it with numbers. And every time I do it with adults, in fact I did it with adults this morning in another part of Maryland, they could give clues for vocabulary like nobody’s business but as soon as I changed the targets to be numbers, they couldn’t communicate about numbers at all. Those are three of my more favorite, so to speak routines. But I think the thing that I hope the listener hears is that they’re designed to get kids engaged and thinking and talking.

Kyle Pearce: Yeah, for sure. And we’ve talked a lot about that here on the podcast too. And we’ve referenced some very similar strategies, what we’ve called starting a math fight, has been kind of like my go-to for the last year or so of like, how can I create more math discussion in my room at any time in the class? A lot of times, it’s at the beginning. And I’ve used the headbands one that you referenced for sure with math. Like any topic can be great. Like put a number up, up on the kid’s head and they have to ask questions. I’ve had high school students putting rational functions up on their head and they have to figure out what the equations or even parabolas.

Kyle Pearce: That one’s a good one. There’s a couple more in our kind of math fight. We use Andrew Stadel’s Estimation 180, which kind of goes along with like the picture perfect one that you’ve referenced here, which is always great because it’s always like too high, too low. Those are some good ones.

Kyle Pearce: I’ve used one quite frequently called two truths and a lie, which is kind of that game, the, tell two true statements about yourself and one lie about yourself, and everyone else has to figure out which one’s the truths and which one’s the lie. And you can easily mold that one into a math one. You could put an expression up on the board or a statement and have kids end three statements and they have to figure out which ones are truths and which ones are lies, or have them … And the best part is you could have them come up with the truths and the lies and have them try to fool each other.

Kyle Pearce: So those are some good ones for sure, which always I’m trying to start a math fight in our room, for sure. Yeah. And it’s funny because I look back and you know I’ve got the middle school version of daily routines right next to me here and I’m sitting there going like, which book did I see that one in? And I saw it in the middle school book there. A lot of these other ones too have different names, but you can see how they sort of can be easily modified, right? And you referenced that in the book a number of times about the idea that like nothing’s set in stone. I really liked that.

Kyle Pearce: You’re not saying like these routines have to happen the exact same way that we’ve put them here. But you’ve done a great job giving people a great starting point. So I’m going to push you just a little bit further and say like you’ve mentioned three here but let’s imagine that someone’s at home and they’re thinking about this and they’re going, cool, okay, so there’s these three. I’m wondering, could you hook them up with like two more low hanging fruit routines that you think would be like, okay, I’m just getting started and I don’t want to overwhelm myself, I can’t learn all 20 and use them all tomorrow obviously, but let’s say I was like planning out five days in a row, what might be those last two routines?

Kyle Pearce: And I’m sure that some weeks you’re going to repeat some in the same week, it doesn’t have to be all unique, but just so that people have five in their back pocket before they head out for the evening.

John: Yeah, no, that’s good. And you made a really good point, right? We’re not … And maybe that I do one routine for a whole week before I shift and move to another routine, I’m thinking about where I am and how I want to modify it to best meet my students’ needs is important.

John: So two others that I like a lot is … And really pretty easy to run with, and that is one called, where’s the point? And I discovered that my students had very narrow perspectives about how numbers were related, especially through number lines. They believe that number lines had to end with zero and something, zero and one, zero and two, 10, what have you. And so where’s the point is a routine where students are given an empty number line with two end points. They could be decimals, fractions, whatever you might want to have. And you just place a point on that number line and ask them to make an argument, a math fight as you say, which I love, about what that value might be.

John: And then right below that, so after you have that conversation about what it might be, then you offer another number line right below it with a similar missing location, but you change the end points in some way so that now they have to reason about how that value has changed based on the value of the end points changing. And I discovered that students didn’t recognize … Well, they didn’t think dynamically about numbers. In fact, with integers, every number line they ever worked with had a zero in the middle, like zero was in the middle of every number line with integers and didn’t realize that I could have a number line with negative 33 and negative 55 as end points.

John: So where’s the point is a really nice, easy place to start. I think one other one is called broken numbers, or there’s a different one similar to it, and that’s called express it, where students are given a value and they just have to decompose that value in a collection of different ways, share it with others and then you build a record of ways to decompose numbers. But here’s something I discovered, many students don’t think as flexibly about numbers as we think they do. So this is a really bad example, but it’s the best one I’ll come up with for the listener right now, for the number 50, we’d like to think that they can break 50 apart in an infinite number of ways but if you were to poke at it, you’re going to find that they really only think about it in four or five ways and those ways are very limited, such as 25 and 25, 49 and one, et cetera.

John: And I’m talking about whole numbers right now, but it applies to really any type of number. And the point with that routine, broken numbers or express it, we want students to play with, get dirty with numbers and look for patterns on how you break them apart. We know that when you do this and when you decompose numbers frequently, you become a better computer in general, you have new strategies and see new relationships.

Kyle Pearce: Those are great ones. I got a question, I’m wondering about how you specifically set this up in your room. So when the students come in, were doing one of these to begin class, are they at their desk, are they standing, are they in groups? Could you fill us in on what that might look like for those teachers that are like, I want to try this in my room, like how is it set up? What do you think is optimal here?

John: I think whatever’s best for that individual is optimal. And I don’t mean that to be coy. So anytime students are in proximity to each other so that they can talk with each other, that’s really important. Standing up, I don’t know that I would necessarily, if that’s a great idea, but it could work for some classrooms. So I do want to share this, once students are trained on any one of the routines, those routines should become, well routine. Students should know how to interact with it without a lot of prompting and what have you.

John: Most, almost all the routines are designed so that they’re not paper pencil activities. There’s intended to be observations, reasoning and discussion activities. So I would want my classroom to be conducive to having students be able to talk to each other and share out. But however, you set up your room should facilitate it pretty well.

Kyle Pearce: Yeah, no, for sure. And I appreciate you always, we use the word, it depends all the time on the show. There never is like the perfect scenario and every class is different, every grade is different. And something I want to kind of go back to it, I really like how when you hear the word routine, you really, it could be anything. So like if someone’s sitting at home and they’re thinking about classroom routines, it’s like, okay, it could be like routines of what we do in the class but it could also just be like fun little, I’m using bunny ears here, activities, that where you could fall into the activity trap. So I’m really happy that you got very explicit about this idea of number sense.

Kyle Pearce: And I know you’ve said it a number of times here, but just this idea that when we do things like number talks at the beginning of class, I think number talks are great if there’s intention there. And I feel like the same is true here, like these routines are such a great way to be able to essentially like I’m going to call it like almost like morph a number talk and do it with different approaches so to speak or different routines to especially help students, as you get into the middle grades and then to high school, you have to work a little harder. Like I don’t want to say that we’re there to entertain students, but we do need to have their attention. And how do you gain the attention of anyone?

Kyle Pearce: Like think about adults, adults are some of the hardest crowds. Imagine, and you know this John from doing workshops, like teachers are the hardest group to try to engage because they know a lot of stuff and it’s like their time is valuable and you’ve got to make sure that you captivate them somehow. And through these routines, I feel like that’s such a great entry point. And then to do the actual working with numbers, because I think number sense is like you’ve referenced, it’s where it’s at and a lot of the rest of the curriculum I feel like are put there with intentions to give you like the opportunity to play with more number sense. And I think we often miss that, right? When we rush to calculators and we’re just proceduralizing everything, it’s like, let’s look at these topics, even the ones that you know kids are probably not going to use in their life ever again, let’s use those as a way to access the number sense and to build that fluency and to help students really see numbers a little bit differently.

John: Yeah. You said so many things there that I want to respond to. I’m just going to pick a few. So number talks are fantastic, right? And number talks, especially, designed as they are, serve very specific purposes usually about computation or what have you. They’re fantastic. There’s so much more to number sense though, right? And that idea of estimation and relationships and all these other things that we want to poke at and play with. And that’s why I think these routines kind of balance number talks and similar things to engage students because anything as great as it may be, 180 days in a row, it’s going to get boring and folks are going to want to punch themselves in the face.

John: And so we’ve got to think about like how do we engage our students? So you made a really great point about that. The other thing is, number sense is the underlying thing in all of mathematics, but it’s never one lesson. And another good point that you made was this notion that number sense is such a critical part of mathematics but yet it’s not a specific lesson. And the other thing is number sense is developed by lots of practice and play and we don’t always feel like we have the time to do that. And so regardless of the program or the tool, the textbook we use, what have you, these routines and things like number talks help complement those pieces to develop that number sense.

Kyle Pearce: I love how the approach you’re taking is that … And it sounds like I’m hearing balance coming from you in everything you’re discussing tonight, which is great, and it’s not this idea that it’s like only use these daily routines. It’s like this is to compliment some of the other great things that are going on out there. And I couldn’t agree more. Finding those ways to just access number sense and give students the opportunity, I feel like once they feel like they have a command of number sense and they feel like flexible and fluent, students can do anything in math.

Kyle Pearce: Once they get to that place where they just feel confident, we can ask them and we can do all kinds of crazy things because they know that they actually understand how things work.

Jon Orr: You know what I loved about that you have so many warmups to dive into in the book is that when I first started doing warmups in the class, that I had the exact same … I imagined the exact same thing, it’s like I got to get a bell ringer, I got to get them going right away. And I developed five different ones, but I did the same five, like Mondays was always this, Tuesdays was always this and it became too much of a rut. And I’m really looking forward to spicing it up a little bit more with the variety and to build the number sense skills up in a variety of ways.

John: And I think what’s most important is that you take them and you make them your own. These are ideas, these are seeds, but you take it from there and make it your own. And the other thing that I have to really stress is that routines really aren’t designed to teach new content per se, it’s more about revisiting ideas about number that students should own to some extent already, but they’re not really … The word you used was fluent, but they’re not necessarily fluent or comfortable. So that’s another thing to keep in mind is this is a really good way to touch on number sense skills that haven’t been seen for maybe a month or 10.

Kyle Pearce: I was wondering if we could switch gears here a little bit and I’m wondering what you’re working on now. Do you have a new work in place? Are you working on something new? Could you share a little bit of what’s next on the horizon for you?

John: Yeah, thanks. So I am currently working on a new project which is called five actions for productive struggle. And that is a labor of love with some colleagues. But the thing is, is that productive struggle is so important to all of us, but we’ve had little training about how you grow it and deal with it. And for many of us, our experiences, our own math identities, tell us to stay away from struggle as much as possible.

John: And so this project was critical for me to help me unpack my thinking about what does it mean to struggle? How do I prepare for it? How do I help students navigate it? And then how do I help students reflect on it in the lesson or during the week so that we can honor and value it and not just pass over it?

Kyle Pearce: Productive struggle is something that comes up in a lot of the workshops that Jon and I do. It’s a part of our online workshop that we run as well as our online academy. And it’s one of those things that as a teacher, I’ve said it before and I’ll say it again, that I would design my lessons hoping to make it as easy as possible for everyone. Like I thought the key to being a good math teacher was to take all of the struggle away and it was almost like coddle everyone so that every student felt, and it was all out of the goodness of my heart, like I was trying because I want them to feel successful.

Kyle Pearce: But in doing so, I actually got the opposite, right? It’s just like when you coddle your children and they don’t learn how to like survive in the real world because we’re doing everything for them. It’s like we’ve got to put them into that struggle. So I’m really looking forward to diving into that when that comes available.

Kyle Pearce: Maybe I missed it, maybe you said it, maybe I didn’t. Do you have an anticipated launch date for that book?

John: Yeah, it should be out next winter, spring. I think your target is March, April 2020. But at the moment with everything else going on, I’m a little behind. We won’t tell my editor to that, but yeah, you just summed up. I designed lessons so that I would be successful and didn’t recognize that success came from their struggle. And so maybe we have to rethink that.

Jon Orr: John, I’m wondering where we could find more about you. Is there a place that our listeners could go and read more about you or do you have a social media that we could follow? Could you share us a little bit about that?

John: I should probably have a website and all these other great things available to everybody, but I’m so busy in it that I haven’t taken the time to curate it and put it in one place. I’m on Twitter @johnsangiovanni. I’ll spell that for you later, but [crosstalk 00:41:57].

Kyle Pearce: We’ve already got your Twitter handle, don’t … But just for those listening, just for those listening, we will link it up in the show notes though.

John: Sweet, thanks. No, but there I don’t really … It’s not that I don’t want to say much, I just listen and grow my own thinking that way. Works through Heinemann and Corwin Press, you can read more about my work there. And then I’m fortunate enough to speak at most conferences and things like that, so hopefully I’ll see folks in those capacities.

John: There’s a web page place in design, but it’s going to take a little while because doing other things like everybody else, right?

Kyle Pearce: Well listen, Jon and I have a website, but something we don’t have is a book. And it’s like when you say yes to one thing, you got to say no to something else, right? We would love to be able to take some time and actually sit down and try to put a book together.

Kyle Pearce: My mom and dad would probably say like, you’re crazy, right? I’ve never been one for something like that. But we totally get it, that you’ve got a lot of things going on and I think the beauty is, is that you are still sharing with the world. So maybe not through the website, right now but through the print form, which I think is great.

Kyle Pearce: So we want to really thank you for taking the time to join us tonight here on the Making Math Moments That Matter podcast. And actually for those listening, we’re actually going to be running a book giveaway. So your book is one of the books we’ll be giving away here on daily routines. So that will be coming in and we’ll have some more information right after we hang up with you here, John, for folks to get their names in the hat so that they can get their hands on a fresh copy.

John: Nice, that’s great. Thanks for that.

Jon Orr: Thanks a lot, John, for joining us here and we hope you enjoy the rest of your evening.

John: Hey, thanks again for having me. And for everybody out there, thanks for listening. Investing in ourselves pays dividends for our kids. Thanks.

Kyle Pearce: All right, all right, we want to thank John again for spending some time with us to share his insights, not only about daily routines, but just mathematics class in general. It was awesome and I hope you folks in the Math Moment Maker community felt like you had some big takeaways just like we did.

Jon Orr: As always, how will you reflect on what you’ve heard from this episode? Have you written ideas down, drawn a sketch note, sent out a tweet, called the colleague? Be sure to engage in some form of reflection to ensure that the learning sticks.

Kyle Pearce: Don’t forget about the Math Moments with Corwin Mathematics book giveaway. That’s right, we’re giving away 10 books from Corwin Mathematics, including John’s book, Daily Routines to Jumpstart Math Class: The Middle School Edition. Plus you’ll receive special Corwin discounts and digital downloads just for entering the draw. You can get in on this giveaway by visiting makemathmoments.com/giveaway by Wednesday July 31st 2019.

Jon Orr: If you’re listening to this after July 31st 2019, no sweat at all. We are always actively running giveaways, so check out makemathmoments.com/giveaway to learn more about our current giveaway that we have running.

Kyle Pearce: That is makemathmoments.com/giveaway. Don’t miss out.

Jon Orr: That’s makemathmoments.com/giveaway. In order to ensure you don’t miss out on new episodes as they come out each week, be sure to subscribe on iTunes or your favorite podcast platform.

Kyle Pearce: Also, if you’re liking what you’re hearing, please share the podcast with a colleague and help us reach a wider audience by leaving us a review on iTunes and tweet us your biggest takeaway, tagging @makemathmoments on Twitter. Show notes and links to resources from this episode can be found at makemathmoments.com/episode31. That’s makemathmoments.com/episode31.

Jon Orr: We release a new episode every Monday morning. Keep an eye out for our next episode.

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

Jon Orr: And I’m Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high fives for you.