Steve Leinwand: Just look at those tests, how come there are so few applications? How come so many of these questions are just mindless regurgitation of procedures? And why is there so little alternative approaches? Why is it that when I do testing for fourth and fifth and sixth graders... So, I mean, I start with those things and then people push back and they say, "Yeah, but the test's a test." And I go, "Well, there's more to life than just a test." But you no, in part, the tests are changing a little. We've learned about the Advanced Placement test was able to crosstalk-

Jon Orr: In this episode of the Making Math Moments That Matter Podcast, we chat with Steven Leinwand and Eric Milou about strategies to create an invigorating high school math program.

Kyle Pearce: Yes, Steve served as a Mathematics Supervisor in the Connecticut Department of Education for 22 years and is a former President of the National Council of Supervisors of Mathematics. Most recently in 2021, that's this year, right now, he was awarded the National Council of Teachers of Mathematics Lifetime Achievement Award.

Jon Orr: And Eric is professor of mathematics, Rowan University in Glassboro, New Jersey. Eric served as the President of the Association of Mathematics Teachers of New Jersey and on the board of directors, the National Council of Supervisors of Mathematics.

Kyle Pearce: Stick around my friends, and you're going to learn what content in our high school curriculum needs to go and what we can replace it with, why sixth grade is harder to teach than calculus and what change you can make tomorrow to make a difference in your career and in the lives of your students. Jon, are you ready to dive into this one?

Jon Orr: Cue up the music.

Speaker 3: (singing)

Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. We are from makingmathmomentsthatmatter.com and together-

Kyle Pearce: With you, the community of Math Moment Makers worldwide, who want to build and deliver problem-based math lessons that spark curiosity.

Jon Orr: Fuel sense making.

Kyle Pearce: And ignite your teacher moves. Jon, I don't know about you, but I've been looking forward to this conversation for quite a while. You and I got our hands on this book right here, and we've got the authors today who are going to be hanging out with us. And I'm afraid we're not going to be able to get to nearly half of the questions that we had lined up for them today.

Jon Orr: Yeah, and we didn't. And as we're recording this, after we had the great conversation with the two, you're going to hear some great passion from these educators. You're going to hear some great ideas of how to change high school mathematics. One of the biggest takeaways I think for me is this reinforcement that there's been a lot of work. And I think everyone agrees that K-8, K-5 have such a great change in way math is delivered there, what conversations are happening down there, but high school math remains mostly unchanged if you talk to the average student, the average teacher. And the book gives a great guideline and roadmap of exactly the moves you, teachers need to make, principals need to make, district leaders need to make, which is exciting as a brand new book that came out. It's like a COVID baby, they call it. Right, Kyle? This came out of the pandemic. So really excited to get into this conversation. Let's do it.

Kyle Pearce: Hey, hey there, Math Moment Makers. We are hanging out with Steven and Eric today. I want to thank you both for hanging out with us. Eric, dare I say, it looks like you're getting ready to go on a flight somewhere. The background there looks great.

Jon Orr: No, that's like a campus or something.

Eric Milou: Yeah.

Kyle Pearce: It looks like Steven's just, he's hanging out at home. Probably the cat and dog might kind of roam by. So in very different places. But I want to thank so much for joining us here tonight on the Making Math Moments That Matter Podcast. How is things going in your world? Let's start with Eric to get us going.

Eric Milou: Well, thank you both for having us. It's just a pleasure to join both of you. So I'm in New Jersey, Southern New Jersey, right outside of Philadelphia. You know, in our state, we have had a tough time in the beginning of the pandemic. I think we have come through it with much better in the last few months. All schools in New Jersey are back 100% in person. We're excited to try to get some sense of normalcy back into the state. Obviously, politics has played a role into this and it's always been messy. One of the things I think you take out of this pandemic though, is that if you think about mathematics, it's all of the data analysis that we've had to look at that not just we but our students and teachers and parents and politicians, and just the important role of data analysis has become bigger than ever before, due to the pandemic.

Jon Orr: Steve, how are you doing over there on your end of the world?

Steve Leinwand: I'm doing great. I mean, I've spent most of the last 18 months between our home here in Washington, DC and our other place down in North Carolina, where we have two grandchildren. And so we did a lot of hovering for the kids. We've got a daughter who's a physician and a son was an attorney and they tried to work. And that meant that our kids have moved in with us sort of during the week while they were doing distance learning. But that's not what's important. I mean, what's important is that I was up in Vermont last week and I was in real schools with real teachers and real kids for the first time in 19 months. And I could not be happier. I saw some incredible teaching. I got to work for an entire day with a group of teachers redesigning Integrated Math 1.
I got to use some of the stuff in the book, but I also got the playoff of just some wonderful professionals who just knew that they needed a facilitator. They needed a nudge. And so it was like that 19 months disappeared overnight. It was like nothing had changed. And I did a three-hour sort of workshop. I wasn't as rusty as I thought. So I'm in a great place. I think that the only important thing here is I have the luxury of being 72. Oh, I mean, I'm sort of retired, but I'm not retired. I'm still working. I'm doing a whole lot of pro bono stuff, but I spent some time this whole pandemic wondering as we were writing the book and then after writing the book and doing a whole bunch of other stuff, what's really important, what have I really accomplished? And so I think that the perspective that we all ought to share is that I've been doing this for 50 years.
I mean, I walked into a high school math classroom 50 years ago in a month in 1971, you look back and it is incredible how far we've come resources and tools and technology. It is incredible what is immediately available now. It's incredible what this world is like. Because I remember when there were no calculators and no computers and they really were blackboards. And if you were lucky, you had an overhead projector. I think that anyone that has my 50-year perspective remembers that we really had a serious gender gap. I mean, it was no question, but there were not females in my calculus class. There were nowhere near the number of kids in honors classes and things like that. But clearly, we've made significant changes with that. And I think that more than anything, we've really won K-5. The improvement away from computation and towards thinking and reasoning.
But I mean, as by way of introduction, you can't help but look at that list and then say, "Yeah, but I've been a complete failure." I mean, any teacher who looks at what's happened in the world, but particularly in the United States, I think to a similar degree in Canada, and stops and says, look at the ignorance, as Eric just spoke of ignorance about data, ignorance about reproduction and infection ratios, ignorance about making sense of the data, ignorance about what exponential change is. High school is a mess. We have not improved pedagogy and the teaching to the degree that the research tells us we need to and can. We have in no way, shape, or form addressed the unbelievable inequity the way in which math still sorts and anoints and therefore destroys kids at the other end.
And so what's really been need is when people say so, "All right, where are you going now?" Partially because of this book and because of Eric, I'm worrying about high school and it goes hand in glove what I'm worried about detracking. Those are worth fighting for. Those are worth all my so-called experience and big mouth dealing with. And so it's fun doing a podcast like this, talking about the book, working with teachers like I did last week. And I was just reading the agenda for some work I'm going to do in Cleveland in November, and it excites me because it's not just after school mindless workshops. It's not moving the needle a teeny bit. It's taking on the big challenges, and that's really what floats my boat.

Kyle Pearce: I'm loving it. And there's so much that I want to jump in and say. The first thing I'm going to do is say, I know the feeling after that pandemic, the first time I got to go into a class and do some co-teaching with a teacher in my district. And it was awesome too, because it was a bunch of kids who I had taught in a virtual environment that I had never met before that were in this class. And I was just so giddy, so excited to get up there. And it was so interesting to see how the kids were even leaning in so much more so than the way you could experience in the digital world. So, that was a fantastic experience. But you're bringing up such a huge concern. And I agree with you. Like, I'm so happy that we're mindful of how far we have come, but there is so far to go in secondary.
And Jon and I are both secondary teachers. I'm now in a K-12 consulting role. Jon's still in the trenches doing the work, and there is so much work to be done. And I still think so much work to be done in elementary as well. And we keep hacking away at it. But before we dive in any deeper, let's give those who are listening a little bit of a backstory here. Tell us a little bit about our journey. I'm going to flip it back to Eric. Eric, what got you here? And coauthoring this book, this fantastic book, that I think it's going to really at least get teachers thinking differently, that we can do this differently, and that we need to do this differently.

Eric Milou: I'm going to flip it back to Steve. Steve tells the great story of how we came to writing this book here. I'm going to leave the story to him.

Steve Leinwand: Yeah, well, I mean, we have different pieces that we do better than the other. I'm honored to be able to simply tell you that whether it's true or not, my story sounds good, just like all stories. Eric has sat in my workshops. I've sat in his workshops over the years at regional and national meetings. We both do a whole lot more than just high school, but we both have in different ways, sort of talked about high school is really a problem. And so we knew we had that affinity. About three years ago, Eric said we really have to do something about it. And I said yes. So what do you mean? And so we wrote a proposal that went to like NCTM, didn't go very far. That went to NCSM and for all kinds of good reasons, it didn't work.
We know Mike Steele at NSF, and he was wonderful. And he really gave us some great guidance. And we worked with Skip Fennell and we put a proposal together for like $100,000 to run a conference. We thought that we could get some money into a study group and write a report. And then Mike Steele at NSF sort of said, the National Science Foundation, said, "Well, I've got this kind of money." And then the pandemic came, and there was some problems in the organization. And so it fell through. And so about three days after it falling through and probably April or May of 2020, I get a text from Eric that says basically, "Well, screw all that. Why don't we just write the book? Instead of a report, we'll write the book." And it was like, duh, I'm dying there. I mean, it's like, what am I going to do with my life?
I mean, all kinds of trips are canceled. I'm flying 150,000 miles a year and I'm saying that is never going to happen again. And so I said, "Let me write a table of contents." And so I did a first draft table of contents in about two hours. I sent it on up to Eric and I said, "Phase, fix it, change it." And Eric did some changing to it and he added some things and he moved some things around and we knew that we had a pretty decent table of contents. And then we said, "Before we even talked to my friends at Heinemann, let's write some of it. Let's see." And so I did the introduction and chapter one.
Eric started working on chapter five to try and capture some things. He started outlining some of the other chapters that are just so important about assessment and modeling. And the bottom line is we had four chapters that, again, an iterative process. One of us would write. One of us would adjust it. We tried to develop a common voice so that you couldn't tell who was saying what. Heinemann said, "We like this." Basically, we got a green light in June. And then there was some changes there. And we finally did get a green light and a contract and all, and it didn't take long to spit this baby out. That's how we ended up with crosstalk-

Jon Orr: You know what-

Kyle Pearce: All on the tip of your tongue, eh?

Eric Milou: Let me add that-

Steve Leinwand: Well-

Eric Milou: ... there's a story there. It's a great story.

Jon Orr: Hear what Eric's saying. He's like, "Steve, you didn't tell it right. I got to tell it crosstalk-"

Eric Milou: All right, all right. No, no, but that's our typical. That's our typical inner place. You see the point there is that we got rejected so many times. We got rejected two, three times from national agencies, from the National Science Foundation.

Steve Leinwand: From our friends.

Eric Milou: Yes. From friends and people we knew very well and yet, we... Perseverance. We still continued to persevere. We had an idea. We wanted to move forward with it, and we just decided to keep going until we found the right venue to make it happen. And eventually, we did. And that's how this book came about. And it wasn't something that was just an overnight thing. It was something that we had talked about so many years of seeing each other, we got to do something. We got to do something. And in some respects, the pandemic made this happen because we both had the time to sit down. We've ripped out over 200 pages in just a few months.

Jon Orr: That's a such a great example of like perseverance, right? I think you're not the first story. Like, I think we've talked with other people on the podcast and books are coming out of the pandemic. It's like this episode, this podcast, not this podcast, but I heard someone else who created a podcast because they had time during the pandemic. Your book came out of the pandemic. Lots of resources are coming out because it's like, okay, now we have the time to do the things that we've been always saying we would do. And what a great example of perseverance here. And I know that we are definitely going to dive into the elements of the book and we want to talk about some of those kind of common excuses teachers have. We want to talk about some of the content changes you want to make. We want to get in and all that.
But before we do that, we do have to ask each of you a question that we ask every one of our guests, which is, when we think back to our experiences as students in school... And thinking back, way back, it's like when Kyle and I do our live workshops and we ask teachers to think about like, when you think back and we say math class, and you think when you're a student and we say math class, there's like an image that pops in your head and it sticks with you. And it's like something you've carried forward with you. Like I've shared my math moment here a number of times, so is Kyle, about some of these kind of good events and sometimes bad events, but they always kind of shape a little bit of our path. And I want to ask each of you what your math moment would be. Steve, let slip it back to you. What would be when we say math class and you think way back, what stands out? What is a moment that has always stuck with you through the years?

Steve Leinwand: I think more than anything else, it was when ice cream was dripping out of the bottom of the cone in calculus. And you had to deal with the related rate. I mean, it was like, "Oh my God, that's why we learned all that crap." One of the things that we do in the book, and we talk about the problem solving and the modeling is that what we spend a whole lot of time trying to do is say that should be happening all the time in high school. That kids need to be given a reason for why they're learning it. In my case, it really was so much no calculators, no technology. And so you did all this symbol manipulation, but then you get to the real problem of something as stupid as a hole on the ice cream, the ice cream coming out, and how fast is it dropping in the cone? In some ways, that changed my mathematical life. I loved it. It gave meaning and purpose to everything we've done.

Kyle Pearce: It really makes you think, too. Like the way you've stated that, it seems so obvious now. And I know we always talk about how Dan Meyer had a huge influence on both Jon and I. We fumbled our way through for many years, not really capturing what was important about the work that he was doing. And now it's like for us, that big word of curiosity, it's like, you just think of how curious you would become. Even though I don't really care about the ice cream all that much, it's like, but I am kind of curious. When you put it in that way and you give students an opportunity to estimate and make predictions and argue, and then reassess and all of these things, that's an awesome, awesome moment. I'm wondering how about for Eric. Eric, what is popping into your mind when you think about that math moment for you as a student?

Eric Milou: Before I even mention a moment, just take a step back and think about, like, if you ask that question to most people on the street, their moment would not be positive. Steve and I talk about that a lot. You know, it's like our moments were... I can remember so many of them. I remember in the '80s when the first TI-81 came out, it was unbelievable to me that first Texas Instruments graphic calculator. I don't know if you remember that TI-81 at all, but you had to set up this tripod thing that sat on top of the overhead projector. I'm showing my age here, but it was really this crazy thing you had to build on top of the 81 to project a calculator to the classroom. And that was just unbelievable. I could show what I could visualize to my students. There's actually people in the classroom go, "Wow, I finally understand it for the first time."

Jon Orr: You still have chills, don't you? I could see it.

Eric Milou: Because I build that thing. If you never built the TI-81 tripod on top of the overhead inaudible... That's a moment.

Jon Orr: I still have the TI-83 one that sits on top of the overhead projector in the closet.

Eric Milou: But that was a paddle. That was a paddle. You had to build this thing up.

Jon Orr: That's right.

Kyle Pearce: You had to build. It's like a computer you had to construct.

Steve Leinwand: Yeah. It's interesting, when you talk about calculators and stuff, I go back to Bert and Frank, Bert Waits and Frank Demana, and the Casio FX-7000. I mean, that was the first graphing calculator and you had to be a nerd to have any appreciation for it. And then along comes TI, and 81 was pretty amazing and it certainly was so much stronger. But everyone who lived through that stretch of time knows that the difference between the 81 and the 82 was the single greatest jump. That's when you could trace. You couldn't trace on a TI-81. You could trace and therefore solve everything you needed to do with the trace thing on the TI-82. And the TI-82 has been sort of tweaked and all, but it still stands there as the machine that changed the world.

Jon Orr: The first, I remember TI-83 while I was a high school student, but it was like introduced while I was in calculus. But not before that.

Steve Leinwand: Jon, let me just throw one more thing in. And that is that when Kyle just jumped in about that we are talking about making a difference for kids and for teachers. The operative word here is empowerment. I mean, we have done a whole lot of disemboweling. I mean, we have deadened math in so many ways. And I just think that everyone is listening to this, it is as a teacher, your job is to empower your students. And I think more than anything else, that's what we're saying is that right now, middle school empowers kids if done right. It's the right curriculum, the right content. It is absolutely critical that builds so many things. High school doesn't yet empower, and we think that that's a critical missing people. And then everyone who is thinking about themselves as a teacher, the question is how are you empowered?
Who empowers you? Because it isn't until we all feel empowered to make a difference. And that's really what drives so much of we try to do in this book, provide guidance. What was so neat last week working in Vermont is it's the first time I took some screenshots, and I took some Xeroxes of pages in the book and actually did what Eric and I have said all along. We do not believe this is the answer. We made changes. I already want to go rewrite part of the chapter four. No, I don't really want to rewrite it at all because it served its purpose of teachers saying, "I don't understand why you did that. That doesn't make any sense. We're going to do this. This is what we've done before, it's working." And so just that notion of empowering people that we're not spoon feeding them. We're saying, "We worry about this, work with this, do it collaboratively." And then empower yourselves to empower kids. End of speech.

Jon Orr: I think that sets up a lot, like, gives a good context to kind of like why you've written a book. And first three chapters of the book you outline the reasons that the system has to change our high school math curriculum. The way we teach, the way we assess all have to change. That's what we've been doing here on the podcast has been for the last three years, every week, talking about how to make changes in our classrooms that empower kids and empower teachers. Maybe this is different for you, but when Kyle goes into a classroom or when I work with some of my colleagues, I would say that those colleagues still don't think or see that math class needs to change. And I think this is why you wrote the book.
So we've got this huge group of math teachers that aren't seeing a need to do anything different. And so what specifically can you say about the beginning of your book to the teachers listening here? Because a lot of the teachers listening here are coaches, are trying to make changes and trying to help people with those changes. So what are some of these big things that we need to change, but why do we need to change these? Like, what reasons can we give these teachers to say, hey, these are the things we need to change and here's why we got to change these things?

Steve Leinwand: The fact of the matter is nobody is factoring trinomials anywhere. It's done with the machine. Nobody is doing trig identities. No one is doing synthetic division. There are so many things that we have built into the program that serve absolutely no purpose. And then we teach it all as if technology didn't exist. And it's absurd. I think that what we do is I ask teachers to think about their students and their own children at home. How would Google and Alexa and Desmos do on the last test you gave kids? We're hearing now that people can't wear a smart watch because the kids cheat. Well, wait a second. They're using the available technology. You know, I say to these people, if they're under 40, good, use the square root algorithm to go find out the square root of 527. And they just look at me like, I'm crazy. I mean, I have a calculator.
Well, why is that? Well, a calculator, but you're going to tell kids they have to do all the things by pencil and paper and hand. It just makes no sense how much time we spend doing that. So I start with the world has changed. Technology has changed every piece of our existence. And right now it's not just the pandemic, but it is the fact that the pace of the workforce and of what's required to be an effective citizen, what's required to be able to maintain a mortgage and a budget and a house, requires a depth of knowledge that was not required even 40 years ago. So we start with that and we look at what we're still teaching. And the only way I know how to do that so that it makes sense is I say, look at your tests. Just look at those tests. How come there are so few applications?How come so many of these questions are just mindless regurgitation of procedures? And why is there so little alternative approaches?
Why are there so few pictures? Why is it that when I do testing for fourth and fifth and sixth graders, I scroll through it and ask, are there graphics attached to more than half of the items? When I look at the tests that we give kids, there are graphics on 15% of the items. It's a lot. That means it's just all symbolic. So I mean, I start with those things and then people push back and they say, "Yeah, but the test's a test." And I go, well, there's more to life than just the test. But you know, in part, the tests are changing a little.
We've learned about the Advanced Placement test was able to get by without part one. I don't think that's the end of the world. Of course, the college mathematicians go crazy because they believe that everything begins and ends with using pencil and paper to do stuff that no one does with pencil and paper anymore. The argument about the ACT and the SAT, I mean, look at the fact that the scores are mediocre at best in part, because we haven't taught kids to think or do anything other than regurgitate. So what kind of a society do you want? That's where I start. And then I ask them, what do you want for your own kids?

Jon Orr: And when I go back to you, where you said, like the idea of eliminating factoring, eliminating some of these skills that we have paper and pencil, because computer can do that. So I'm wondering, like those pieces of a content, you want to get rid of them because the computer can do it or it's because like we've been teaching it so robotic. Is it the content that needs to change they are specifically? Or is it the way we need to teach it?

Steve Leinwand: The world changes and our curriculum wouldn't change. I love some of those things. I mean, I used to love the puzzles or trig identities, but now I just enter them into, in the Desmos. And lo and behold, I find that it's the same graph. So why would I do that? But it's also a matter of, I have to throw some things out because I don't have enough time to do the statistics and the modeling. And that's what's critical. I want kids to look at the data for Ontario, Canada, and look at over two different time periods. What happened with the number of cases? I want them to say, "So, what would you learn if that's all you saw?" "Well, it certainly looks linear." "Well, let's go see." And sure enough and they think it's linear because it's a linear thing. And the R-squared is like 0.9, and they're so happy.
It's nice and easy. And then I give them the next month... Oh my God. Well, maybe it's an outlier. Well, then I give them the month after that, all of a sudden, I don't think it's linear anymore. I need time for that. I need kids that understand that things change in different kinds of ways. I don't have the time if I'm still doing so much of the things that we used to do.

Eric Milou: If you read the literature in the last 10 years, every single math organization from NCTM to the Math Association of America to the association of mathematics of two-year colleges, every one of them has used this phrase "The status quo is unacceptable." Back in 2016, when Matt was NCTM president, Matt stood up and said this, he said, and I quote, "Today, it seems as nearly everybody agrees that high school math needs to change. For far too long, high school math has not worked for far too many students." We start the book with Matt, because Matt had the courage to say 50 years and no change in high school math. Has society changed since 1970 but yet, our Algebra 1 and especially our Algebra 2 courses have not. I would say they are 95% of what they were 50 years ago, we've just tinkered at the margins of them.
And that should be totally unacceptable to everyone. That society's needs, what a student needs to function in society today, whether they're going into a vocational career, a two-year college, a four-year college, their needs are not what they were 50 years ago, but yet their curriculum is getting the same thing from 50 years ago. We have to look at ourselves in the mirror and say, yeah, there might be all these excuses, but what are we doing to our students? Steve says it so well about data analysis and data science being more important before. And we're going to say it again and again and again, how many times and how many weeks do we have to factor quadratics before we can say that's enough?
And there's time for data analysis and data science and math modeling in 21st century skills that are... We're 20 years into it, 21st century, but yet we're still factoring quadratics for six weeks, doing difference of squares and doing some other method. And none of those things are as important as math modeling and the 21st century skills that kids need to be successful in the world. Kids know that the crap they're being asked to do in Algebra 1 and Algebra 2 is nonsense. And they look at you and go, "Why are you making me do this? I know I will never do this ever again. And if I have to do it, I can Google the damn answer. Can you at least make my math class meaningful to me?"

Kyle Pearce: I'm going to just deal with it then, right? There's always the, you know, kick the can further down the road. It's like, "I don't care about it now, I'll care about it when it matters to me." Which they know is quite often never, unless there's another test coming, right? Go ahead there, Steven.

Steve Leinwand: I think what really becomes key is it's not just the content, but it's the process. Yes, there's probably a content and there's absolutely content, but regardless, whatever we're teaching, I need teachers to be saying, "Why? How do you know? Can you explain? How are these the same? How are they different? Can you convince the class as to why you think that's so? Who did it differently than that? How did you picture it? Show up your whiteboard, let's see it a different way." That is what goes on in every single classroom where everyone knows quantity of learning is higher than it is next door. We have the answers. We know what works. You can take principles to actions based upon all of the research, and know that kids learning depends far more on the questions that their teachers ask than on anything else.
It's not the great lectures. It is the questions that enlisted that kind of thinking. And so when you talk about why these changes, I need time to do that. I can't sit there and ask kids to do 12 problems of regurgitating something when I know that four problems where the last one is a independent, interesting situation and problem. I need to recognize that that's what prepares kids for this amazing, crazy world that we're living in.

Kyle Pearce: Here, Jon and I are in Ontario. We are currently undergoing a curriculum change. We just had one from grade one to eight. Much improved, still a long way to go. Much the same as in the US. You had mentioned already, Steve, from K-5, that we've seen a lot, like a really positive shift. But it's interesting because then you hit these middle grades and when things become multiplicative in nature, when things become more complex, it's almost like we don't have a handle on the simple idea of proportional relationships and ratios and rates. And what is a ratio? What is a rate? What's the difference? Is there a difference? There's so much confusion and muddiness in those middle grades. And I feel like there's this battle there. That's almost like the battle zone in middle school where, like Jon said, they're looking up going, I got to get them ready for this.
And then they're looking down going, like, I want to continue what they're doing there. Teachers know deep in their hearts and souls that they want students to understand this mathematics. They don't want to just regurgitate it. And there's a bit of a tug of war going on. And soon as that content knowledge piece wanes a bit where we're uncertain about something, then we tend to go right to the procedural. And I'm wondering maybe if we throw this back to you, like, what are your thoughts on the impact that changes made? As you mentioned, like data science and all of these changes that we could be making, what sort of influence or impact do you see that having on the middle school grades, which might set students up to have a better understanding of fractions, of being able to problem solve and work their way through problems that maybe they're unfamiliar with?

Steve Leinwand: It's not just K-5. I mean, certainly in the United States, the Common Core for K-8 is equivalent to mana from heaven. Did we really have finally got a teachable, coherent, rich, you don't need to accelerate a middle school program? You can go to my website and read my beliefs that sixth grade is the single hardest to teach and the single most important grade in the entire continuum. Six to eight is harder to teach and more important than calculus. It's more important and harder to teach than probably anything except kindergarten only because in kindergarten, it's not the content. It's just the amazing diversity of the kids in the room. But if you think about sixth grade done right, and you follow the Common Core, for example, in the States, it means that it's one quarter of the year's operations and problems. That is what you're doing is you're saying we taught you all the computation. Now it's time to apply it.
The only thing that's new in sixth grade is division of fraction by fraction. Everything else is already been "covered", but what's important is what operation and why? What's a reasonable answer? So that's a quarter of the year, it's the culmination of number. You then turn to what you just said, multiplicative reasoning and the idea of ratio and proportion. And so we've a quarter of the year in sixth grade, a quarter of the year and seventh grade. That's not one chapter. That's not the old two chapters that you race through. That's using the whole range of paths and depth of understanding to do that and do it right. And you don't have to race through it. And then we know that kids' life is not just on ratio and proportion, but is on the foundation to equations and expressions.
25 years ago, even work that I did, we have 40 different things we asked teachers to do in fifth grade or sixth grade or seventh grade, but a quarter of the year to launch this idea of algebraic thinking and of representations of the equations and of expressions and evaluating them and where they come and creating them. And then if I have not been very effective, like I got kids that are weak... You know what? Screw the geometry and the statistics. I can get away with it, or I could round out the year with a quarter of the year on geometry, which is a lot of vocabulary, you know, done. And then the statistics. But in seventh grade, I don't have the order of the operations anymore. I'm going to repeat the... Not repeat. I'm going to build on the ratio and proportion. I'm going to get the percent, which as everyone knows is a disaster for so many kids.
We know how many kids go to community colleges and they screw up because they can't do any ratio, any proportion, any percent. And they get put into remedial math. We then build off of the equations and expressions because we know in eighth grade, we're going to do functions. And we're going to do probability because it's different that it reinforces the pressure. What I guess I'm saying to you is that we made the assumption that middle school, when done right, following what most states have been doing, and a lot of provinces as you well know have done as well, then you fall off the cliff. Because then, you move from all of this richness and the possibilities into algebra. And whatever happens to statistics? and where's the geometry? And do you really believe you need a whole year for geometry?
So all of that really says that we have said, and it worked again as recently as last week, let's say that there's one level at eighth grade and it is this integrated eighth grade aligned with the Common Core. Now, what happens next? Well, we ought to continue to be integrated. We ought to build off of that. I think that goes hand in glove, but the gap finally between and what was proposed and what the reality is, is just too giant. Does that make sense?

Jon Orr: I think for Kyle and I, it is actually seems kind of foreign to not have integrated math because all of high school is integrated until we get to grade 12. Maybe grade 11 we have a full functions course, but grade nine and 10 for all of Ontario is fully integrated.

Steve Leinwand: We say that in the book that in fact, look around the world. I mean, that's the other problem. I mean, when I scream and yell and we wrote that, and I think in the first chapter that the Common Core screwed us. The Common Core didn't make it simpler. It didn't make it easier. Didn't make it more coherent. It's not intellectually internationally benchmark. All the things that provided guidance and coherence and trajectories and progressions in K-8 all disappeared with just a mishmash of the same old crap.

Eric Milou: Emphasize the importance of ratio and proportion in the world. Your friends asked you or even when my doctor asked me what I do for a living is math professor, the first in my doctor, all the various doctors I have, by the way say, "Oh my God, I was terrible at calculus. I just had to do it. It was just the gatekeeper for me to become a doctor. But what do I use every day? Ratio and proportion. Oh my God, that's what I use every day." And job after job after job will tell you that. That's what they use every single day, especially in the medicine field, especially if nurses and doctors with medication, it's what they use; rates, ratio and proportion. The importance of that. Can't be overstating. The other issue here that we're kind of talking about around the edge is we're mentioning a lot about content and curriculum.
We say this in the book with, you know, changes in curriculum mean nothing if there are not changes in pedagogy, okay? Because K-8 has done a good job. We both agree K-8 curriculum has done a good job, but so why don't we see more positive things coming out of there when kids come to high school? We have to look at pedagogy. You know what? The pedagogy changes that I see... Well, instead of a teacher giving out notes anymore, they give out guiding notes. Like, that's better. Oh my gosh, that's not a mathematical experience. Talk about this a lot. What is the experience kids are having? If they're filling in boxes on a worksheet, that is not a mathematical experience. No changes in pedagogy are going to make any positive successes without appropriate changes in pedagogy.

Kyle Pearce: Yeah.

Jon Orr: Yeah. For sure. Steve, you wanted to jump in?

Steve Leinwand: That's why we have to stop blaming teachers and recognize that they have not been giving adequate guidance. I mean, you don't learn this in teacher preparation programs, no matter how good they are. You learn this on the job, in the classroom, and without coaches, and without coaching, without the opportunity to have a culture where you can walk into each other's classes. We've all had the chance to walk into some amazing, amazing middle schools in high schools. And there's a department where people are looking at each other's tests. People are walking in each other's classrooms. People are sharing. People are stealing each other's ideas because that's what they do. That's the exception that are peril.

Jon Orr: Can I keep going with your book? Because I found, I really love about your book in particular versus lots other books about how to change mathematics and what mathematics should look like is you give such a practical guideline like here, we're going to do this, we're going to do this, and we're going to do this. You've outlined those in some of the guiding principles or you've talked about these domains of invigorating high school mathematics. You give it like such clear outlines of like what should change. And because we talked about how or why we should be changing, but now it's like, well, what has to change? And how do we do that?
Teachers who are listening right now are like, okay, I know this has to happen. I know. But okay, if I want to make a significant change in my classroom as early as I can, like, I want to like get some low hanging fruit here or spark... Because I know that when Kyle and I started to change, it was like one little moment that like trickled into many. So I'm wondering like, what would you guys recommend as like the change that teachers could make tomorrow that could lean them down this path?

Eric Milou: Simple answer is go observe a colleague. Talk about it, and then that colleague observes you. Professional growth begins. `Every high school math department, there must be practices that include video, video review, collegial classroom visits, follow-up debrief discussions. We close our door, we teach, and we rarely see another adult until lunch or after school. No other profession works like that. We need to open our doors and have our colleagues in our room constantly, no evaluation going on, whatsoever. Collegial digits between colleagues that are sitting in and trying to learn about what worked and what didn't work in your classroom. So then when I go do it in my classroom, I can improve on that and we can talk about it together. We always talk about our lesson, but we don't watch what happened, but worked and what didn't work. That's a structure that is missing I believe in almost all high schools, and we call it professional growth and collaboration. It's one of our 14 domains of invigoration. And I think it is the starting point. I know Steve has a couple of his favorites also.

Kyle Pearce: Before Steve shares, I want to make mention, because you do bring that up on, I think it's page 117 here. I had it earmarked, because you had referenced the Observe Me, #ObserveMe on Twitter. Some people know it as like the pineapple chart, right? You put the pineapple on the door and all of those things. And the thing I love about that and encouraging people to do it is because just that, again, like what Jon was after is that spark. And I think you just nailed it there, Eric, was you start observing each other. And okay, maybe that first time, okay, maybe you noticed a few things, but then you start to talk with each other. And then when you have a problem, then you go to that person and then that person comes to you. Oh my gosh, I tried this, but it sort of just continues to grow from there. So I love that. That's a great takeaway. And I want to hear from Steve. Steve, what pops into your mind as something that could kickstart someone who wants to get down this path?

Steve Leinwand: Find a partner. Find a partner, that's all. It is absurd to take people who are as busy as they currently are, teachers who are stressed to the max, and then say, go do all this additional stuff without... You just, you know, you have a breakdown. And so you have to find a partner. You got to share the loads. You've got to recognize that the collegiality is just missing. The professional isolation of the professional, as Eric just said in a different way, is greatest obstacle to change and growth. And so we've got to build professional cultures. Having said that, I think that the beauty of the guiding principles is you read that and you decide. Some of them, you're already doing. Your department's already doing. It's great. I'm happy for you. Some of them you say, "Yeah, but I'm not ready to do that now. Maybe later." Then you get to the ones where, you know, that's something that's both important and doable.
Eric and I are so proud that Heinemann did what Stenhouse is doing. And they are releasing chapters, and it's like the loss leader. And so this is available. Chapter three is available for free to anyone that goes to the Heinemann website, goes and looks up integrating high school math. And chapter three ends with, "Of these 14 domains, which ones do you think your department comes closest to meeting? In what ways is this the case?" Great. So, I mean, that doesn't mean there isn't work to be done, but they are not critical focuses for, as you said, really changing the game. Of these 14 domains, which ones do you think your department is furthest from meeting? Why do you think this is the case? What specific steps can you take to change that? And we don't think that's the right place to start either because you're so far away.
I mean, and so of the domains, which ones do you think you can turn to and begin to make changes? Because if you go to the chapter that in some way I'm proudest of, it's chapter 10. It's the implementation. It's the game plan. I mean, it's the five-year plan. We are saying, we know what Michael Fullan has said. We understand that change is hard, that change takes time, that change needs to be done top down and bottom up, that change requires monitoring. You can't just say, "Okay, good. Back inaudible, you know, next year, you're going to have this new program." And it's absurd. There are five tables in here that lay out a five-year plan from moving from a year of study to a year of recently full implementation. And then you start all over again with revision.
And we tried to ground it. Remember this whole thing, we didn't quite say it this way, but this whole book grew out of the sense that Eric and I have been so frustrated that the Common Core didn't provide any effective guidance to nine, 12 teachers. NCTM came along with catalyzing change. I mean, you know, lots of background. I helped Matt Larson actually draft the position, not the position, but the charge that the board approved. It ended up becoming close, but not really providing the kind of detail that every teacher that Eric and I worked with is saying, "Well, yeah, but you fell short. You didn't tell us this." And so when say guidance, we put guidance in the subtitle. We think that it's guidance because that's what people need. Not all the answers, but guidance. And every chapter in this book is an opportunity to envision, an opportunity to draw from it in terms of guidance and steps. I assume that people are going to demand the time to do it.

Kyle Pearce: I must say, as you kind of take us through and give us some big ideas that sort of pop out, I do want to say for those who are listening, it's definitely this book is worth grabbing. We talk about excuses and a lot of times, there's excuses we tell ourselves. But ultimately at the end of the day, we need to realize that there is a problem and that you give them some guide or guidance throughout the rest of this book on things that you can do to start. And for those who are listening, the messaging I'm hearing from both of you here is that don't put the pressure all on you. Make a team of it. Come at it as a department. Work on it. This isn't quote "our fault" as educators. We are coming in here underprepared to do one of the hardest jobs in the world, right? Aside from kindergarten and middle school, high school math, I would say is an extremely, extremely difficult subject area.
And probably even more so because usually, the people end up in high school math are people who thought math was cool, right? Like, they get all geeked out about the first graphing calculator they had, like Eric did. And that's not all students in our classroom. So that's a huge, huge hurdle that we have to sort of break through. And I think this is such an awesome way to see what's wrong, start making some progress, and to really start small and build from there. Jon, I know that a lot of these things resonated with you. Before we wrap up, what's one big takeaway for you and for the Math Moments crowd to check it when they pick up the book?

Jon Orr: I definitely had a big takeaway from the book for me, which was the chapter seven, I believe, chapter seven on assessment. Assessment for me has been kind of like my obsession, like, how do I assess high school students? A deeper, how do I assess for growth? I've been doing a lot of learning on this over the last few years and a lot of coaching with other teachers on this as well. And I really appreciate your detail on the different types of assessment, different formats, and also some of the examples you provide. Like you said, teachers need guidance. Teachers need to see it.

Steve Leinwand: Yes, you're absolutely right. It starts with why, because that's what we hear. I mean, this book is a response to years and years and years of work that Eric and I have done in real math departments with real teachers who are struggling with this stuff who have a sense of, I need to make some changes but I don't know where to start and all. And so it starts with why. Why do we have to do this? Build a compelling case. Study those things. Build the kind of agreement about it. The question is, yeah, okay, I understand you need to change, but like, what might it look like? And I use that phrase "what might it look like" for chapters four and five about the integrated courses and then the pathways.
But when I talk about chapters six, seven, eight, nine, what must it look like daily? Because the non-negotiable here is, your pedagogy has got to be better and different. Your assessments have got to be better and different. You've got to build in modeling and you have got to recognize that... Look at that. I just drew a blank. What's the fourth one? inaudible, that's great, pedagogy assessment. Oh, this is so... Oh, of course, and then technology. And then you've got to take... That's so embarrassing, right? It's perfect. crosstalk-

Kyle Pearce: Hey, now they're going to remember it. So it's good.

Steve Leinwand: I know. Exactly. Technology. I mean, normally, I'd put them out. I can still do the eight mathematical teaching practices, but I've had more practice on it. And then in the very end, it's how. What else would anybody ask but why, what, what, and how? And I think that's what grounds it is terms of both guidance and practicality. And we try to make it conversational too, and not a big whole bunch of high pollutant stuff. And yet, there are enough citations. Thank you, Eric, because he adds them and he knows them inside out, forwards and backwards. And it does add some heft to them, not just two pipers telling you what to do.

Kyle Pearce: Gentlemen, it's been an awesome, awesome conversation. As I mentioned before we hit the record button, I told you guys we could probably go on this all night and not be anywhere close to done the conversation. But I want to give you both one last opportunity here. I'm going to start with Eric. If there's one thing, if there's just one takeaway that you're hoping that the Math Moment Maker Community walks away with from this conversation... I'm thinking of all kinds that they're going to walk away with. But what's one, if it's the one thing that they walk away with today, what would you say to those educators now?

Eric Milou: Every single mathematical organization out there, whether they represent elementary or high school teachers, or whether they represent four-year colleges or two-year colleges, everyone uses the phrase "The status quo is unacceptable." It's unacceptable the way we teach math, the how we teach math, and the what we teach math today. We have to believe and examine that. What can we do? What's our little part? Whether it's a change in curriculum, whether it's a change in pedagogy, whether it's mathematical modeling or technology, those four things that Steve just mentioned. What is our little takeaway? What is our little change that we can do? Because right now, the status quo is unacceptable. And our kids deserve better and better mathematics than they're getting right now.

Kyle Pearce: Awesome. Thanks for that. And Steve?

Steve Leinwand: If it was easy, we would've done it a long time. And it's just really for us to understand we're talking about upsetting the apple cart. We're talking about goring a whole lot of oxes. We are talking about throwing out things and changing things that have been near and dear to the hearts of the power structure in too many ways. And so I just want people to recognize that this is hard and if it's hard, we've have to be given the time to do it. We've got to be given the resources to do it. We've got to be given the support to do it. And we need to generate buy-in because those are the things that we've known for years. Without time, it doesn't work. Without resources, it doesn't go anywhere. Without buy-in, we end up with enemies winning the battle. And without support, we just feel like we're little islands in this. And so to the degree that, that this book doesn't just honor the fact that it's hard, but it also makes a strong case for what it takes to make changes that are hard. I think that those are the critical takeaways.

Kyle Pearce: I love it. Well said, gentlemen. It has been an honor having both of you here on the podcast today. I know people are, especially our high school friends are loving that they had an episode especially for them. However, I'm going to argue this is a K-12 discussion, right? I mean, there's a lot of similar problems happening in K-8. However, in high school, we really do need to make that long due transformation. So friends, here's the book right there, Invigorating High School Math, and it's a practical guidance for long overdue transformation. Steve and Eric, it has been awesome. Awesome to have you here. We can't wait until we get to bump into friends like you folks at a face to face conference at some point in the near future. But I want say thanks a ton and we really appreciate you joining us.

Steve Leinwand: So Eric said thank you at the very beginning, and I saved it for the very end. Kyle and Jon, you guys are just a pleasure to work with. You bring energy and spirit. You ask important and deep questions. This was an absolute pleasure for us to do, but I thank you for the contributions that you make every day and with these podcasts to move the whole enterprise ahead. So it's been a pleasure for us as well.

Jon Orr: Thank you. It was a definitely pleasure here. So thanks, everyone. And have a great evening.

Eric Milou: Thank you.

Kyle Pearce: As always both Jon and I learned so much from these episodes. And just like Steve had mentioned in this episode, how are you going to hang on to this learning? Steve recommends getting a partner, like do this learning with someone or maybe with your entire department. Both Jon and I have been doing this for quite some time. And through the doing of this podcast, we get to do so much learning and so much reflection as we create the show notes and as we prepare for our interview questions. So what are you going to do at home? Are you going to do a sketch note? Are you going to call a buddy? Are you going to do maybe a listening party and get together at somebody's house or in someone's classroom on your prep time? Hopefully, you're going to do something that's going to help you remember and act on some of the ideas that you heard here today.

Jon Orr: What Steve said and Eric said is do this with a buddy, or both do this with a partner. And actually, Kyle and I, that's how we met through social media. So if you've not yet followed us on Twitter, @MakeMathMoments, or on Instagram over there, or in our free private Facebook group, maybe there's someone there who will also be like, "Hey, I'm in the same place as you. Let's chat. Let's connect a little bit more." That's exactly what Kyle and I did. Make sure you get on over to those social media accounts if you're also looking for some more connection.

Kyle Pearce: Awesome. And if you found this episode helpful or other episodes helpful, you are doing us a huge solid and every other educate are a huge solid by going and leaving a rating and review in Apple Podcasts or Google Podcasts, Spotify, wherever you're listening, because that's going to help other people find this content and make some of the transformational changes that you're making in your classroom here with us today. And just remember, this episode and most of our newer episodes are available on YouTube. So head on over there, hit subscribe, leave a comment, hit the like button. Hopefully, we will see you face to face on YouTube sometime soon.

Jon Orr: In order to ensure you don't miss out on new episodes of this podcast as it come out each Monday morning, you sure to subscribe on your favorite podcast platform.

Kyle Pearce: Show notes, links to resources, and complete transcripts to read from the web or download and take with you, you can find them over at makemathmoments.com/episode155. That is makemathmoments.com/episode155. Well, Math Moment Makers, until next time. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high five for you.

Speaker 3: (singing)