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Dedicated to Teachers

Let's Talk Math! Purposeful Math with Kent Haines and Steve Leinwand

Copy of Lets talk math! Episode Four

What do we want students to get out of math class? Proficiency? A love of math? Job prospects?

Today we are passing things over to Kent Haines. Kent is a Heinemann Fellow Alum and middle school math educator based in Alabama. He is joined by Heinemann author Steve Leinwand. Steve is the author of Accessible Mathematics and Sensible Mathematics, and most recently the co-author of Invigorating High School Math.

Kent and Steve discuss the current status of math instruction in the United States and some long-overdue transformations that would benefit our students.


Below is a transcript of this episode. 

Kent: If you're a math educator and you've been around for a few years, you've likely heard of Steve Leinwand. And if you've ever seen him speak, you'll never forget him. Steve has been in the math education world for over 40 years, but he still speaks with the fire and conviction of someone who just can't wait to share the latest idea they've been chewing on. He's a principal research analyst at the American Institutes for Research, and he's written several books for Heinemann, including his most recent, Invigorating High School Mathematics: Practical Guidance for Long Overdue Transformation, co-authored with Eric Milou. He's worked as a math consultant for the Connecticut Department of Education, served on the board of the National Council of Teachers of Mathematics, and was president of the National Council of Supervisors of Mathematics. Just last year, NCTM presented him with their 2021 lifetime achievement award. Steve, welcome to the show.

Steve: Thank you, Kent. It's a pleasure to be here.

Kent: Now, by sheer coincidence, after we set up this interview, you came to my hometown of Birmingham, Alabama last month to speak at a conference focused on revitalizing Alabama's math education system. And since you've been around the country, you've met everybody. You've talked to everybody. You've spent so much time thinking about the big picture. I thought it would be fun to touch on some of those major areas of focus. Hopefully, even though most people listening aren't secretary of education or state superintendent, we teachers and math coaches and principals can find some ways to align our practices in our classrooms and our schools with some of the vision that you have. So let's start with the core of my work personally, which is teaching. How do we help teachers become more effective in the day-to-day work of instruction?

Steve: First and foremost, we break down the isolation within which almost every teacher I know works and operates. So few professions allow people to remain as isolated as education allows teachers to remain isolated. I first watched teacher collaboration way back in 1983, when I was blessed to be able to do site visits for a study of exemplary math programs with Mark Driscoll out of EDC. And I just came away from these incredible schools, one in Louisiana and one that I spent time with in Maryland and another school in North Carolina. And in every case, there was a math department that collaborated, a math department that worked together. I watched teachers watch each other teach. I saw teacher faculty meetings that were amazing. I saw teachers who saw themselves as mentors to younger teachers. I watched teachers in each other's classes, and it's amazing that 37 years later that's changed so little.

We don't provide adequate coaching. We don't provide adequate support. We don't provide adequate time. We don't allow teachers to grow together, and I think that it's best to flip it around to the positive side. When we walk into, when I walk into some of the most powerful schools that I spend time on or powerful schools that I spend time in, in every case, you have a case where people are collaborating, where people are working together. And I think that that's what's missing. And we operate in isolation, and there's no way that when you are isolated in a business that is inherently social, that you can be as powerful as you need to be. We create moats around our classroom. I'm in schools where I'm told, "Oh, so we're really glad you're here. Just so you know, you are really not supposed to go in the room 220 and 274."

Well, I mean, I don't give a damn. I mean, those are the rooms where there are problems. Those are rooms where teachers don't want to be observed. Those are teachers who in general are hurting kids that everyone else in the department has the following year. You know what I do. I write them down. And the first thing I do is I walk into room 220, and it's just this embarrassing of... And I'm not supposed to be here. I said, "Oh, are you teaching math?" And the kids will go, "Yeah, this is math." And I go, "Good." And I just sit down. I mean, what are they going to do? Throw me out? But seriously, I mean, you need to know what's going on in a school. And when people say, "You can't come into my room. I don't want to be coached," you have a dysfunctional school.

Kent: I certainly agree that this isolation is really inhibiting my development as a teacher, because I have so few opportunities to hear from another adult who knows what they're talking about. Hey, I love how you did this. Did you notice that the kids kind of missed this element of the class. Or, oh, have you thought about structuring your warmup this way or what have you? Is this something that other countries have a better model for? A more effective-

Steve: Absolutely. I mean, this goes back to some of the original work that was done with the TIMSS, the Trends in International Math and Science Study, where we had videos of Japanese classrooms and every one of those classrooms had five adults in the back of the room. You saw people learning from each other. That's the way it goes. I have worked with people who teach at the American Embassy School in India. AES is an amazing, amazing place. And the head of the largest school in New Delhi, 10,000 students and there are about 400 parents in the building every day. There are always adults and parents in classrooms. I mean, number one, it just makes people more accountable. But more importantly, it's an incredible feedback mechanism. So yes, we are, along with Europe, pretty problematic when it comes to these issues of isolation.

Let me just say that... So I'm doing work in Cincinnati a bunch of years ago, and so I did one of these large sessions with... I had 120 secondary math teachers, and you got people that are slouching around and they could care less. And so I went back to the table and I go, "Is this really that bad?" And they go, "No. But I mean, please, we should be teaching our AP calculus class. And this is just getting in the way." And I said, "Yeah. You know what? I understand that." And so the next day I happened to be in that school, and so I walked into that AP calculus class to sort of see. And the teacher says, "Oh, this is the guru that cost us yesterday. He's the guy that came and talked."

And he says, "This is a national math leader, and we should be really honored he's in the classroom." And so I sat like I always do on the side of the room, because I never sit in the back of a room. I'm always a co-participant, a co-teacher, and a co-student in the classroom. And you can only do that from the side of the room. And so he's doing his class, and I jumped up and said, "That's really cool." I said, "Turn and tell your partner why that is." And the teacher realized that, "Oh my God. I mean, I should have asked that question." That bottom line is we co-taught the class for 45 minutes. And when it was over, he said, "Why don't you stay the whole rest of the day? This is the professional development that we didn't get yesterday that I would so value." It says it all.

Kent: And so let's say, all right, we're waving our magic wand. My school, every school in the country, we get that sort of common planning time and also I guess the attitude among teachers that it's okay to come in my room. It's okay to give me feedback, positive, negative, constructive feedback, I should say. What should we be talking about? What should we be focusing on?

Steve: I love this. I mean, Kent, you're asking all the right questions. Means I don't have to go back and interrupt and all that stuff. I think it is as simple as a 20 minute collegial discussion at the end of every observation. I mean, if I have been observing you, I have a responsibility to give you my thoughts. If you are being observed, you're sitting there going, "Well, what do you think? I mean, can I grow from this experience?" And so it starts with... I got to tell you. What really impressed me was it always starts positive because psychologically, that makes sense. But it also sets the tone that there's always something that's positive. I want you to go search for it. I've done hundreds of these discussions afterwards, and sometimes it's hard to find something positive. But you can always find, I mean, something micro often. I got to tell you. The high point in this lesson was when Emma... Was that her name?

And they'll go, "Yeah. I mean, the one sitting over in the side of the room?" And I go, "Yeah. When Emma raised her hand and you handled that discussion and her confusion," I go, "That's when I just said, 'This teacher really gets it.' And every kid in the class benefited from that interchange, and I imagine you worry about spending too much time on it." I mean that or the way that technology is used, it was seamless and all. It always starts with something positive, and the second point is so here are the questions I have. I mean, I wasn't sure about or can you give me more information as to why you did this? It's not critical. It's simply a matter of so help me explain some of your actions.

And then the discussion always ends with the observer saying, "On the basis of this discussion, on the basis of the observation, this is the one thing I'm going to try and do differently tomorrow." So it's action oriented. Those are the three things. Anyone can go to my website. There are a whole bunch of slides that are there. My presentations are posted. There are probably 20 different presentations, and there is one about professional development. And the one about professional development says that it's not professional and it doesn't develop the way in which we are currently doing it. And then the alternatives are, among other things, these collegial visits. And it has a slide that sort of says, "So at the end of the collegial visit, these are the three discussion questions for two professionals who have the same purpose: improving the mathematical lives of the same set of kids in this school. Well, go and collaborate." So that's where people can go for a visual copy of what I just gave orally.

Kent: Fantastic. Now, something that I'm noticing a lot, and I think it's becoming particularly acute after the turnover with post-COVID, there's a lot of teachers leaving the profession. And so I see a lot of states working on alternative paths to certification, eliminating requirements, eliminating content area tests. And I understand the rationale behind this because we need a sustainable amount of teachers in the profession, but I worry about teachers who don't necessarily have content area expertise being asked to teach in front of these students. So I'm curious your perspective on how important you think that subject area expertise is to know the mathematical ideas. And secondly, how good do you think we are? And I guess there's 50 different answers for 50 different states, but how good do you think we are at determining when a teacher truly does understand the math that they're teaching?

Steve: So I had this discussion yesterday. I mean, one of the beauties of being 73 and of being quasi retired but not really retired and being able to do whatever I want, part of the way I give back is I'm just doing an immense amount of pro bono stuff, a whole bunch of mentoring. I get these emails and it's, "Can we talk? Can we pick your brain?" And so one of the really stellar math leaders in West Virginia, I mean, she's been doing some incredible things over the years. This is a kid that I met in an elevator 10 years ago, and I don't know whether I said something or she said something. And the next thing you knew, we were talking for 10 minutes and then we've carried on a working relationship for almost 10 years. And she was saying that the hardest thing they're facing in West Virginia, and I hear this across the country, is the warm body problem.

We have to have a warm body in the classroom for all of the right custodial reasons, but either they have serious content knowledge deficiencies, or they have no idea what it means to teach math other than to just tell kids how to get answers. And so there is where this collaboration and, more importantly, where the coaching and the mentoring is so important. So, let's just go back. We like to think, "Rah-rah America. America's so amazing and everything." I love this country. This is a given. I wouldn't trade it for anything, but that doesn't mean that we've got all the answers and we need to recognize that there are other places on this planet that are doing things a whole lot smarter than we are.

So in Singapore, the reason why Shanghai and Beijing scores are so high is there is a very simple understanding that teaching is like becoming a physician. You have teacher preparation, like you have med school. Our daughter went from Princeton to Yale med school to a residency at Duke. She could not even work in the VA hospital in New Haven when she was going to Yale med school. It just doesn't work. Everyone knows that you become a doctor during a three year residency. Why is it that we think that somehow four years of education, one methods course and a couple of weeks of student teaching, and you're going to be able to walk into the classroom? It's insane. So in Singapore, the very first year, all you are doing is you are observing. You are in classrooms. You are doing no teaching by yourself.

You are co-teaching at most, just like a first year resident. The second year in Singapore, you have your own class, but you are mentored the entire time. You have someone who is observing and someone who is helping you at every step of the line. You really are not teaching alone because there's somebody who is also responsible for those kids. It isn't until the third year that you are finally, still with great supervision, being able to teach, and the people who watch you the most as a third year teacher are the first year teachers who are seeing you in your classroom and watching as you struggle and you grow and all. And so, I think that the way to handle the current situation is to stop and say, "If you have to have a warm body, and if there is a serious teacher shortage, the first order of business is you've got to pay people more money."

It's no different than Walmart is now going to pay people 17 and $18 an hour. The 15 isn't attracting people. That's what the inflation is all about. We are finally paying people a living wage. Well, we couldn't do a minimum wage, which would've done it. We were all screaming and yelling they would've put people out of business. Well, now they're raising their prices. They're getting away with raising their prices. But that's the economic system working in all the right ways. The second thing is you've got to make people feel like they're part of a profession. That's where back to the culture you're in, so people don't run because they're completely abused and bombarded, and they have no life work balance. There are ways that we can support each other. We can have slides that are available so I don't have to create those slides.

I can adapt them. I can amend them. There are so many things that we can do to make things easier for teachers that all require collaboration. And then we have to be able to provide that kind of induction and in internship, that opportunity for the first year teachers who come from all over the place to have the opportunity to grow and learn. And that is obviously the role of a teacher who's teaching four classes or three classes, and the other two fifths of the day, they are the mentor, the support person, for the two new teachers. But that person really has not just a fake mentor, not just someone to go and help, but somebody who is charged with them coming along and when they don't make it, that failure is a collaborative failure. So, again, it requires us to be creative around things that we know work and things that we know make a difference.

Kent: Let's shift a bit and talk about assessment because I did something very scary. A few weeks ago, I sent you a couple of tests that my colleagues and I had given to our students, and you wrote back with a ton of excellent feedback about which questions you liked, which ones you thought I could do without, and what you thought was missing. So if you don't mind putting yourself back in that mindset, when you opened up my test for the first time, what were you looking for?

Steve: Great. So let's put this in context. We have to live with a whole bunch of tests. I think we live with too many tests. I think that the quality of the state assessments is mediocre in many cases. I think that when we lost the [inaudible 00:17:05] Smarter Balanced and all that came along with the Common Core. We lost a tremendous amount. The fact that it was $3 more per kid, or even $7 more per kid for quality assessment and for open ended items and for creative approaches to these things, we lost a tremendous amount. And so we've returned to multiple choice drivel that just diminishes the quality of teaching, that doesn't tell us nearly enough. So I have come to believe that, first and foremost, every teacher needs to practice formative assessment. It is always asking questions, it's listening to kids, and there is an exit ticket or an exit slip every single day, every single classroom.

Now having said that, it means that we both know that one out of five days, I don't need an exit ticket because the last task the kids did conveniently serves as my exit ticket, and I didn't realize that was going to happen. But I knew everything was going on and I knew the kids were successful and I didn't need to go any further so I could spend time on it. I also know that one out of every five classes, the class sucks. It didn't work. I blew it. There was an interruption and I don't do an exit ticket. So as part of my teacher evaluation says, "You used an exit slip." Well, yeah. But it really means that three days out of five. I've been in thousands and thousands of classrooms in the last 30 years. I don't believe I see a formative assessment in more than 10% of the classrooms. We run out of time.

It's not built in. We don't have a slide for it. So we fail the fundamental test of, "How successful is your lesson?" which means, "Did the kids learn what you wanted to learn?" when we don't have that data. All the work that I do in New York at The Success Academy Charter Schools, which are the highest performing school network school system in all of New York state, they outperform Scarsdale. They outperform Bronxville. They outperform Chappaqua. How is it possible that a school system that's 95% black and brown kids, mainly in Harlem and Bed-Stuy and the worst parts of the city in terms of support and the public schools are doing so amazingly well? The answer is, "Quality instruction." The answer is, "A formative assessment that they act on, where it is a deliberate part of the day." So I start with, "That's instruction. That's not assessment. But it is assessment built into instruction."

The second piece is I believe that the very best programs are driven by a set of high quality, common unit assessments. It means that beginning in second grade, there are eight units and there are eight unit assessments. In the best world, there are two forms. A form for us to use, and then a cloned form that we use for a retest or a makeup, or for an opportunity to show that you didn't get it the first time, you can get it the second time within five or six days or something like that. But these unit assessments are done collaboratively. They answer the question, "We are successful as a unit grade level team, as a course team, when our students do well on this unit assessment."

And when they don't, we know we need to build in some reteaching before we get to the final. It's really common sense. It's, again, why less is more. We have to have time for the reteaching. We have to know what our focus is, and so I just think that a unit assessment is a place that not just answers the question, "Were we successful? Did the students learn what we know?" but it's my fundamental planning guide. The week before the unit, I come together as a math department, there is a grade level team, and the issue is, "All right, fine. Next. Fractions is next. No. Linear functions is next. Okay, fine. Let's talk about it. What are the hardest parts of it? What are the parts that drive you crazy? Where do you need more time? How did we do it better last year? How do we build off of that?" And, "What is it we're looking for?"

In other words, "Let's all look at that unit assessment. Is it still appropriate? Does it still work?" And so when I looked at your assessments, like I have looked at literally thousands of assessments of that sort, the first question is, "Is it balanced?" That is, does it ask for the core, basic skills that are non-negotiable for that unit and for any future further learning of mathematics? Two, does it get at conceptual understanding? Does it, in other words, move from depth of knowledge, one, the core, the recall, the vocabulary, the understanding that is enabling, and then does it ask, "Do I have evidence that students understand the key concepts, that they are not falling into the misconceptions?" And then thirdly, do I have knowledge that they are able to do some reasoning and solve some interesting kinds of problems?

And so, that to me is an assessment that also differentiates. This idea of differentiation says we need to build in some of the enrichment. Differentiation to me, great teaching is, and we'll talk about this perhaps under instructional quality, but to me, differentiated instructions says, "We ask kids, 'Why? How do you know? Can you explain? How did you picture that? Who did it differently?'" Those are those key guiding questions. Our assessments need to say, "Show another way. Do it in two ways." Our assessment need to say, "Show it symbolically and show it graphically and we don't care what order you do it in." So what I look for in your assessments was, "Does it go beyond just a procedure and an answer?" and so my feedback to you was saying, "The skill stuff was all there. I think you could have reordered it. You want to put that stuff up front so that you have it, and it's clear and the kids can sense, get some cues, about what they need to know in that first part."

And then, I was surprised that in many cases, you didn't ask kids, "Why? How do you know?" You didn't expect them to show their work in any real way. So those are the things, and I think that you saw my comment that, "Yeah, but you only had one application of any of this, so you didn't help kids understand why is any of this stuff important? When would you see it in the real world?" So that's the lens that I use, and I believe that 10 items, some with multiple parts, is all you need. And I'm still screaming and yelling at my friends, The Success Academy, where I have invested a lot of my time and energy over the last five years, to release all of that stuff, and they're hung up on some copyright issues and they're hung up on other things. But I just would love to have the ability to say, "Hey, there's this website to show you a set of really impressive unit assessments."

Kent: I really appreciate that, and I think that it's really interesting to think about this because we actually, as a department or at least the seventh grade department wrote these together so it's a collaboration among colleagues and there's obviously, attention where we want this to be an assessment that everybody feels comfortable assigning, that sort of thing. And so a common response that I hear from my colleagues and feel frankly myself is, we have to put a grade from zero to 100 in for the assignments that we have at our school. That's not negotiable with our district. And so if I have a test with 10 questions, my students are like, "Oh, I missed one question, now I'm down to a 90. I missed another question. I'm down to an 80." How do you respond to that idea?

Steve: Why is everything worth the same amount? I mean, there is some things you should get wrong that are only worth a point that's all. It's not a big deal, I can reteach it. You didn't remember it, why am I going to zap you for something you didn't remember? A serious conceptual error, yeah. I mean, there's a problem there. But I respond to that first and foremost by saying, we ought to have a system of retesting. Every single kid ought to have an opportunity to go over that test, to figure out what they didn't know what they couldn't do and have a chance within the next five days to come back and retake the test, that's how I deal with it first. That's just fairness, that's just common sense to me, this idea of one shot. So I'm working in the highest performing high school at all of New Jersey a couple of years ago.

Well, how come you only have this one shot? These kids are so pressured in all those ways and I said, "All you do is contribute to that." "What do you think we should give every kid a trophy?" I mean, that's the kind of mindset that I run into. You could hear a person who's a good teacher who cares thinking about, "Well, I'm just making it too easy." Another says, "Where else in the world do you get second chances? I'm sorry." I said, "You said that? Where else in the world do you not get a second chance? We live in a society where you can kill someone and get a second chance. You can sin, you get another chance, we live in a world of atonement, in a world where... I mean, how can you even call yourself... And I have no religiosity in my body at all but how can you call yourself a religious or spiritual person? How can you go to church every Sunday or to temple or to a mosque and not recognize that there's more to life than just retribution."

So anyway, I think that there are lots of ways to respond to that and they require us to say, "We are going to do it differently. That we are about serving our kids and we lose nothing and the kids lose nothing, everybody gains by having a second shot at it." And then the whole point structure is really key, I think that we ought to have a point system that it's not 10% for everything but you know what? Here is a 40 point test and we have marks so we have points it's so clear.

This is one point, this is two points, this is four points, this is five points with partial credit and all those kinds of things. And then we simply convert the points... Geez, we're math people to a number that we need. So, I mean, I can live with a hundred system. I also think that we'd be a whole lot better off if we all thought about... Look, there is A, work and some work a little better and work that's a little worse, good. There is B work, there's work a little better but it's not A, level and there's work a little worse. In other words, it makes sense to me to talk about that we have 95, 98, 92, we have 85, that's B, work. I mean, you're going to tell me that there's a difference between one student's 89... And I'm sorry, let's be fairer. One student gets a 79 by making lots of careless errors and loses all those points but hits it out of the park on the two biggest, most important consolidating items. Meanwhile, the student sitting next to that person gets the 81.

They hit it out of the park and all the mindless, all this stuff, they can get all the skills, they regurgitate beautifully but they really cannot come into it. And on the big items, they get low partial credit and we sit there and say, "Well, 81 is better than that." No, we've got to find a way to be able to have our point structures so that we're not differentiating 79 and 81, we're differentiated between a B minus and a C plus. And so I think that would be a whole lot better. And then I don't have any ideas about failure in, Ds.

I know that basically, we have a system that has a bunch of A's a bunch of B's plus and minus, C plus and minus and then you fail. What is a, D? A ,D, is failure. So we have a lot to think about with that whole system. I do think that the British system with the marks or the points makes a lot of sense. And that way we don't worry about the points, we sit there as the department and say, "Hey. Look, all I can tell you is that these two items are really a quarter of what I'm gaining for. Good. So you know what? I have a 50 point test. So this one is six points, this one is seven or eight points." And then we go from there and we ended up at 50 points and it's weighted in a sensible way.

Kent: That's interesting. I had a system that I used for several years here. I didn't implement it this year because it's my first back at this school and it takes a lot of work as you'll hear. But I did a standard space grading system where I would break out. Well, Unit 3 has essentially six major ideas and so I would have a line at the top of the test and it says, I can and basically, each of the six major ideas are standards. And then I would give them a test and then I would grade item by item but then I would just go back and holistically say, "Do I feel that this student has mastered this standard?" And treat it a little bit more, I wouldn't say arbitrarily a bit more holistically, just trying to say, "Do I think that this student understands and can apply the Pythagorean theorem?" Let's say. And so I could actually, give the same test that I've been giving or the types of tests that I sent you or what have you. I just assessed it in a different way.

And then the benefit that I found from that is my students knew where they needed to study for the reassessment and then we could just reassessment that item as opposed to, "I have to retake the Unit 3 test." I have a daughter in preschool and I get a very thorough standards based grading report from her teacher that says, "Oh, she can identify letters. She can count, order the numbers." If my daughter's teacher said, "Oh, she has a B, in letter recognition or a B, in English or whatever," I'd be like, "I don't know what that means." And so I really enjoy the standards based system which my child's elementary schools uses it. It just isn't very popular in middle and high school, unfortunately.

Steve: So I think that we have some real problems and confusions with the term standards based part of it is the teachers are saying, "What are you talking about? All my tests have been standards based. Every one of my items is linked to a standard. So it's standards based so now what do you want me to do with that stuff?" If the language is confusing and it doesn't motivate me to change, I think that we all talk about less standards based and more balanced, common, collectively reviewed great task system of unit assessments. And so we look at it from the perspective as we set a balance and we do it together and we review it and we look at the student work and one person is a day ahead of everyone else and so we can make some many adjustments on the test so quickly.

But it is a set of items that are aligned with a set of standards. And then there is the opportunity to say, "Okay, so in terms of the basic skills and the vocabulary, very strong, you did well on items one, two and three." That's standard based, that's giving you feedback like your three year old gets. In terms of the conceptual understanding, there are some issues here, "You were not able to explain, you were not able to show how these things relate." So I think that we can accomplish what ideally standards base is about when we construct our tests with deliberate attention to what we're measuring.

Kent: I think it's interesting. I guess, what you're saying is if we're trying to leverage and have the most impact possible, getting teachers to collaborate on the same type of tests that's within their comfort zone is going to lead to a larger impact than trying to rejuvenate the entire system of assigning grades.

Steve: When I walk into an Algebra 2 class in a school, in any state in this country, and within four minutes it is obvious that half the kids were using a graphing calculator in Algebra 1 and half the kids weren't. I want to run, I just think that's malpractice. I think we have to have a common set of expectations for everyone who's taking Algebra 1, for everyone who's taking Geometry. No, for everyone who's taking fourth grade Math. I know that in fourth grade I have a teacher who loves reading, who I want my own kid to be in that class. I'm really to screw Math for that year because that person is so magical with reading and writing and all their shelf is filled with the best Heinemann products, it's so awesome. But that person needs to be assessing with the same way that the two other fourth grade teachers are assessing. We've got to have that kind of commonality. I just don't think that it's fair to the kids to have different standards as we roll across the grades.

Kent: So we've talked a little bit about how to help teachers improve their instruction by collaborating. We've talked about how to help teachers improve their assessment. And I really like those because those are things that I have a handle on things that I have at least the possibility of having an impact on it. It definitely, requires a bigger shift than any teacher is capable of implementing personally. But it could be very interesting. So let's just start quickly, what do you think is wrong with high school Mathematics in America?

Steve: High school Math teachers have not been given anywhere close to the level of useful guidance as K-8 teachers have been given. When I look back on my 50 years, I can tell you that I am proudest of the fact that there have been some real successes. We've won the gender issue in so many ways 20 years ago and 40 years ago. Math was a male domain, it is no longer a male domain, it is incredible the changes that we've seen. What I've seen at K-8 in the last 40 years is just an unbelievable shift from worksheets and computation. And little more than that done in 30 minutes a day to really teaching Mathematics and engaging kids. And the same thing applies to the technology, the use of technology and its ubiquitousness and even when it's used poorly, it's still there. But I see a lot of incredibly good use of technology.

I see interactive whiteboards being used in ways that are clearly supporting, learning in so many ways across all disciplines. I only tell you that because when I look at where I failed, when I look at where there's been no change, we still track and group in ways that are just nefarious. We screw more kids by telling them, "You can't do it. You don't have a math brain. You don't have a math gene, you can't do it." And all too often, those are kids of color or kids of lower economic class and it is just disgusting and pathetic the way in which the system systematically, preserves privilege at the detriment of the entire society.

And high school sits there still with an 1894 committee of 10 model of Algebra and Geometry, that it is about getting kids ready for Calculus today. And when you look at guidance, NCTM has never really provided anything close to what the common core did for K-8. And the common core itself ran out of time so where high school starts, it is a systematic sorting of kids out with overwhelmingly obsolete stuff, poorly organized and a total outlier in the world. And so I just think that when you look at Eric and my book, we sit there and say, so it used to be K-6 that was common and then you'd differentiate in some ways and then it became K-8 that's common.

Well, we think that the world is such that K-10 has to be common, that we need to continue the integrated math of sixth, seventh, and eighth into ninth and 10th. Ninth grade is part algebra, part geometry and part statistics. That we have to do statistics like we do in seventh grade and eighth grade, and continue it in ninth grade. That the idea of a common curriculum for all kids, and I think without levels or without all kinds of tracking, and all that, that entails is the right way to push the quality of common appropriate, important math for citizenship. And for the workplace through the end of 10th grade. That means that Algebra 1 that is currently in eighth grade, thanks to the common core continues. It's important, but it means that Algebra 1 has to change. And it hasn't.

I mean, if it's taught right in eighth grade, then we review it and we build on, and we expand it in ninth grade. The idea of this Algebra 1 with quadratics and simple manipulation, with an Algebra 2 course that every teacher says is a nightmare to teach. Unless you just love telling kids how to do something without thinking, or reasoning, or applying it, that's Algebra 2. You talk to the calculus teachers to say, "I don't know why they're doing synthetic division. I don't expect kids to do that even when they're doing Newton Quotient in calculus." We've got a screwed up obsolete curriculum that has to change. And this linchpin is twofold. Algebra 2, and everyone going to calculus is simply misguided.

The lack of attention to statistics as co-equal to algebra and geometry is a societal nightmare. We're the only country in the world that does this stale geometry sandwich between two rotten pieces of algebra. You sit there and say, "But wait a second, everyone leaves fifth grade, everyone goes to sixth grade. Everyone leaves eighth grade, everyone goes to ninth grade. Everyone graduates from high school will know we're only at 90%," which is amazing that we've gotten that high. I mean, in the last 10 years, that's been the biggest change in all of education, is that we've moved from 75 to almost 90% high school graduation rates. But when you graduate, or even if you're part of the 10 or 15% that don't, you go to community college, you go to a high school, you go to a selective school.

You are a math major, you're a physics, you're a STEM person. You are going into medicine, you're going into nursing. You're going to be a construction person. You're going to a community college. You're going into the job force. You're going into the military. My goodness, it's all over the place. We ought to be able to say somewhere around February, March, April of sophomore year, "Here are the pathways." Most importantly, now is colleges increasingly have got a calculus pathway, a quantitative literacy pathway, and a statistics pathway. The math departments have been pillared at so many of the major state institutions, because all they have is calculus. Half of the departments say, "We don't need calculus. We need statistics." You have this move towards pathways there, high school's out of step. There's just a mismatch that has wonderful things going on in K-8, and some really cool things going on in college. High school sits there as this block, as this barrier, still believing that the answer is calculus.

The answer for about 25 to 35% of kids is calculus, but we don't need precalculus and calculus. We could easily have this common curriculum, and then 11th and 12th grade, there is a pathway that is an intermediate algebra precalculus. It is really intermediate algebra. It takes the best of what's currently in Algebra 2, and it adds some of this stuff from precalculus and then low and behold, the kids are ready. There are dozens of school systems in the United States that do not put kids into eighth grade Algebra 1 solely so that they can take calculus. I need every kid to be able to take calculus. If you blossom, and it comes alive in ninth grade and 10th grade, great. All of a sudden you want to go do STEM stuff. I love it. We have this intensive calculator computer based course. It doesn't do a lot of statistics, but it is about functions and polynomials, and about a range of functions, and gets you ready to do calculus.

It is not all that different than the IB system and program of two years that includes calculus. It also includes statistics, but it can, and must be done, for some percentage of the kids. Well, then you've got somewhere between 60 and 80% of the kids who, what are they doing now? What we propose in the book, and what states like Oregon and Ohio and others, are really pushing towards is this notion of a statistical pathway that is data work and statistics work. And allows kids to take the AP stat course and test if they want as seniors, and a quantitative literacy financial literacy test. I mean, why is it that we don't allow every kid to understand after a week of exploration and spreadsheet work, that when you pay the minimum balance on your MasterCard, you are screwed.

Why do we not have kids understanding that when you don't pay the speeding ticket, and you just ignore it because you just think you can ignore it. It's like the ticket on the windshield for the parking fine. Well, but when you look at what happens to that accelerated fine, it is incredibly discriminatory. "I mean, fine. You know what? I end up having to pay $500. I can afford that." You've got people who don't have $500 to go spend on that. They don't even have $100 to pay the damn thing in the first place.

I mean, we've got to be able to have people understand the ways in which exponential change works, and the way in which it plays out in our society. You've got the Dana Center Quantitative Literacy materials that could easily be adapted. You've got some of the data science materials. Some of it comes from YouCubed at Stanford. Some of it comes from UCLA. The point is that those materials are out there. They are free, they are online. It's to me, the only way that we can invigorate high school math, which means that it's no longer deadly. Which means that it's no longer, "Oh, God, this sucks," but it's actually engaging.

Kent: Thank you so much for sharing that. I hope everybody can hear what I was talking about, that fire and conviction. What I really appreciate about this is in all these areas we discussed today, you're not just focused on identifying the problem, but you're giving us ideas for a solution. That even if we don't necessarily implement exactly what you're talking about, it gives us, it's much easier for me to think about how to improve something if I have a framework to look at. I really appreciate that. I should mention if anybody is particularly interested in Steve's work on high school mathematics, we do have another great conversation with Steve and his co-author Eric in our podcast archive. Everybody should check that out. Steve, thank you so much for coming on.

Steve: I just want to.-

Kent: Oh, yes.

Steve: If we've got three seconds.-

Kent: Please.

Steve: I just want to say that, I mean, obviously there is a soft spot in my heart for Heinemann. It's been a wonderful relationship, but of all the books that I've written, and the one that I understand second, only to Tom Carpenter's Children's Mathematical Thinking, the Accessible Math is the book that I turned to first. Because before we even talk about curriculum, what happens when you close your classroom door? I think that, we didn't spend a whole lot of time on Instruction and Instructional Quality Day, which is perfectly fine. We can't do it all in an hour. But the first thing you asked me is, what do I look for in a test? The real question is what is it that every coach, every principal, every parent who visits a school. And every support consultant needs to look for in a classroom is, how do you get the kind of engagement and the kind of thinking that is just so critical? And that is not, is nowhere close to uniform.

In fact, the variation in instructional quality within schools, between schools, continues to be gigantic. I mean, particularly in math, you can't get away with that in reading to the same way that you can get away with it in math. I believe it's even worse in science, but that's a whole nother discussion. It's not like I'm selling my book. I'm just reminding people that the real solution, the way in which we prepare kids for all these things, is we're doing cumulative review. We're asking kids, "Why?" We are using context. We are doing the kinds of things that we know research tells us make a difference. I just, an unabashed shameless plug for a book that's still out there called, Accessible Math.

Kent: Absolutely. Thank you so much, Steve.

Steve: My pleasure. Thank you, Kent. This was just a great discussion.



KentHaines-1Kent Haines is a National Board Certified middle school math teacher in Birmingham, Alabama. He has spent 10 years in the classroom, as well as two years as a visiting instructor at the University of Alabama at Birmingham. Kent is a 2016 Heinemann Fellow and has helped develop curriculum for The College Board's Advanced Placement programA+ College Ready and Citizen Math. He writes about math games for parents and kids at Games for Young Minds

steveleinwandSteve Leinwand is Principal Research Analyst at American Institutes for Research in Arlington, Virginia and the author of Accessible Mathematics and Sensible Mathematics, and coauthor of Developing Numerical Fluency. Steve served as Mathematics Supervisor in the Connecticut Department of Education for 22 years and is a former president of the National Council of Supervisors of Mathematics. In 2021, he was awarded the National Council of Teachers of Mathematics' Lifetime Achievement Award.

Topics: Heinemann Fellows, Mathematics, Podcast, Heinemann Podcast, Math, Steve Leinwand, Kent Haines

Date Published: 05/12/22

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