If you could re-imagine math instruction, what would you change?
Hi, this is Edie, welcome back to the Heinemann podcast.
Today we are going to revisit a podcast from 2019 on re-imagining the math classroom. My colleague Steph speaks with Heinemann author Steve Leinewand.
Steve’s work revolves around fostering authentic math fluency in students, valuing deep understanding over memorization and speed. By challenging long-held ideas about how math is taught, Steve says we can re-imagine instruction that better serves our students.
The conversation started on the topic of math homework, and why it’s just not working.
Below is a full transcript of this episode!
Steve: Just the way we do homework as an opportunity to practice, practice, practice, practice, practice. When in fact I know when I watch a student do homework that if they can do the first two problems, they understand it. And all I do is I ask them to continue to waste time. So the first order of business is we have to assign it and we have to have the five minutes with the kids who've got to write it down. In a world where we ought to email every single kid the homework assignment, we ought to email the parents the homework assignment so that everyone is clear on what problems need to be done and we don't spend any classroom time doing it.
And then the kid is sitting there doing homework at 8:30 at night. All I can do is relate to you that I spent a lot of years as a single parent, which means that my kids were in after school programs, which means that they then had sports and soccer and school and piano lessons.
And so I didn't do a whole lot of cooking during those years and we'd go out to the pizza place or we'd get some sushi. And so that meant that we had quality face time, but it also meant that we didn't get home until 7:15 or 7:30, at which point, obviously, in every household, reading, language, arts homework needs to be done first. Reading, language, arts is more important than anything else. It creates all the right habits. And now it is 8:15 and my kid has got to do one to 19 odd of long division of the same problem over and over and over again.
I'm sorry, but there's bedtime coming up. I talk to parents all the time. I talk to parents on planes as I fly around the world and everyone says, "Oh my God, homework at my house is such a nightmare. I don't understand it. I can't help my son, I can’t help my daughter." Plus they're bored to death. Plus it's the same problem. And so we see untold time at home and it creates all kinds of tension for no good reason.
And that doesn't happen in social studies. That doesn't happen in science. And it certainly doesn't happen when kids are reading and writing essays. And then we come into school and I've been in classrooms where 20 minutes is wasted going over homework when there are so many other better ways to do it. So that's why I wrote that. That's why I believe it. And I think that there are lots of answers and alternatives.
Steph: And so I think there may be a common conception that practice makes perfect. The more you do it, the better you get. Why is that not the case with math?
Steve: It is exactly the case with everything, except that it's not clumped practice, it's distributed practice. And I don't practice until I engage someone in the game. So I don't start soccer on a fall beautiful afternoon in the elementary school playground or soccer field by saying we're going to spend the next 40 minutes doing left foot, right foot, left foot, kick, left foot, right foot, left foot, kick. And then will switch order and then we'll throw the ball in over our head. We sit there and say, "Hey, you guys are blues. You guys are reds. You know you don't touch the ball unless you're out of bounds and you throw it in," and then all of a sudden the kids are playing the game and we sit there and go, "Well we have some problems. Let's do some practice after that." Piano, singing, everything that everyone gets coached on, we have a reason and we play the game first.
And so in mathematics, we tend to give kids the odd problems after the first day because the answers are in the back of the book, certainly in middle school and high school. And then we move to the even problems because the answers are not.
Why wouldn't the answers be there? I mean, I want to see the work and I want to see different approaches and so I want to give kids answers to all those things. And so we waste untold hours by going over that homework. We have kids still writing on the board where only the teacher and the kid squinting can see it and no one else in the room can do it and meanwhile there's a document camera sitting there. And so I think that when we assign homework, number one, it has to be distributed practice that makes some sense.
And what distributed practice means to me is that every night, Monday night, Tuesday night, Wednesday night, Thursday night, four nights a week, I don't think we do homework on the weekends and we do projects or other kinds of things. Every student beginning in second or third grade at whatever point you sort of feel that some homework makes sense, get eight problems. That's it. Everyone knows, math, eight problems. Two of them are on the new skill, four of them are cumulative review. That means that there's a problem from yesterday, a problem from last week, a problem from last month, and a problem from last year that is diagnostic for what we're going to do. That's distributed practice. That's keeping skills current. That's recognizing that last week, my fifth graders did not remember that there are 16 ounces in a pound and 16 ounces in a pint. Well kids don't remember that. Well, we sit there and go, "Hey, homework, how many ounces are in two pints?"
That's all. That appears for three weeks, once a week, until it's like, "Oh yeah, I remember. I have a means to do it." So the distributed practice and then we believe in problem solving. I don't understand why we don't have two problems every night that are related to the skills that are going on or maybe the older skills, but it is solving a problem. It is showing your work. It is explaining your answer. It is using English. Explain or define isosceles triangle. That's a homework problem. Okay. You need to know it. We did that before. No, we did it in class. I want to see that you can do it. I don't care. Go pick your notes up. Go and figure out. Go Google it.
But the point is that parents who are told help your son or daughter as needed with a homework assignment that is this, monitor what they've remembered and what they've forgotten, and then the kids walk into class and on the whiteboard or on the flip chart or on a document camera, all eight answers.
It's not about answer getting, it's about understanding how you got the answer. And so the answer is there, and teachers that I see say to the kids, "Okay, you have three minutes with your partner to see if you agree on the problems and if you have different answers, see if you can agree with what the right answer is." "Okay, class, which of those problems gave you the biggest problems? The biggest trouble?" And I've already walked around and I've marked these papers with an A, with a B, those are the ... Where's my A up on the document camera? It's sitting there. Everyone can see it. It's not scribbled on the board.
To me, that just makes so much more sense. It abides by the research of a distributed practice. It doesn't waste time. It does this balance of skill and concept and application, and it undermines the, thank God, the stupidity of mindless regurgitative practice, which is what homework has been.
How many damn quadratic equations do you, or trinomial expressions do you need to factor? I mean, the fact is go factor two. How'd you get it? One's easy. One's a little harder. And now we'll do another one tomorrow. We'll do another one next week. Oh yeah, that's easy. I remember how to do that.
Steph: So to backtrack a little bit, we talked about reviewing homework the next day in class. Why is that also not working right now?
Steve: Well, it doesn't work because all it is is just a search for answers. I am in lots of classrooms where, "Okay, take out your homework. Good. Number one, 37. Number two, 15.5. Number three, 86. And all you have is kid's going check, check, X, check, check, X. I mean, where's the learning? I mean, I got it right. I didn't learn anything. I got it right. That's wonderful. I want to know that.
But the question is, if I got it wrong, what do I do? And that's why I want kids to interact. I want them to become each other's teacher, because we all know that when you teach something, you understand it much more. And so that is a four minute chunk of time that is doable and is productive that to me makes so much sense. And we're not worried about simply the answer. We have an opportunity to say, "You're right. I know number seven, I probably didn't win any friends by putting number seven on our homework. Good. Let's talk about it. Okay, where's my B paper? Let's put it up there. Turn and tell your partner what Stephanie did for this particular problem. Okay, good. Nice. Who did it differently? Oh my goodness."
And now we're talking about the essentials of differentiation. So I believe that number talks are so completely essential and valuable because a number talk gives teachers and kids a structure to focus on all the important elements of good teaching. I want to do the same thing with homework problems. We know that the word differentiation is bandied around in this business so much. We know that most people have no idea what it really means and we know that you read all these articles and all these books. To me, in mathematics, differentiation is as simple and as hard as there are 26 brains in your class. Every teacher knows that that means that when it comes to mathematics, the kids are processing that mathematics in three, four, or five different ways. They're seeing the mathematics in three, four, or five different ways.
One kid sees the abstract, another kid sees the number line, another kid sees a bar model, another kid sees a jar that's half full. I mean they're all seeing it ... Differentiation honors those ways. Differentiation gives all kids access to a strategy, to a way to see it that they themselves didn't think.
All they have is "What's the rule, what's the rule?" And we need to break out of that and talk about what's the making sense of this? What's so ... So when I have that problem seven, I smile and say, "Let's see if we can find four different ways to get that right answer." "I've got one, I've got two. Can we get another one? How did Mr. Steve do it?" I mean that is the way to start a class that has us going. And after 10 minutes I'm going, "Nice, are you ready? Here's our launch for today's lesson."
Steph: And so that kind of segues into alternatives for math homework. What are they?
Steve: So I think that we build the alternatives into our eight problems. Other days, it may just be go gather data, of course. I mean, but I would do that on top of the eight problems because I just need to extend it. I think that that we need to basically have an hour a day for math kindergarten through 12th grade. I'm aghast at how many schools I am in where teachers are given 42 minutes and 45 minutes and you can't do it. I've taught about 40 classes, 40 math lessons from sitting on the rug with first graders at the American School of the Hague to doing five days of geometry classes outside of Phoenix in five different high schools. I mean, and everything in between. When you give me kids sitting in rows and 45 minutes, I'm dead before it even starts.
I start to think about cutting corners. I start to think about rushing. I get shrill, I don't follow up on kids, and I do turn and talk and no one turns and talks because they're in rows. Two days later I have the same set of slides. I plan the same lesson with a group of teachers and the kids are in groups of four and I have 60 minutes and the class is twice as effective. And so I've got to be more efficient with my homework and I want the kids to come in with gathering data.
I would love that on weekends kids come back and they talk about the math at McDonald's. I spend a lot of time with parents and tell them their job is not to teach their kids how to divide and how to add fractions. Their job is to make math commonplace. And so some of the homework are family projects, like how much paper does McDonald's use in the 20 McNuggets? That's middle school. That's exactly what I want kids and parents to be doing. So that's a different kind of homework.
But if I could get a balance on all my tests and all my homework between skills that are essential, conceptual understanding, which is essential, and applications which are essential, and I can have kids saying, "Look at what I've learned, look at what I now know. Okay, I still have a problem with this. Okay." As opposed to who learns anything when all you do is regurgitate a process eight times? Show me you can do it twice. So that's what I think about homework.
Steph: Why is this not commonplace? Why is homework still being assigned the way it is? And then what steps could teachers take to start shifting?
Steve: Steph, you pressed all my buttons because in fact, so much of what I say, do, and write is interpreted as teacher bashing. There is no teacher bashing. Teachers are so set up, teachers are told, do this, do this, do this, do this, and they're given no guidance. Teachers are told differentiate. Nobody knows what it means. Teachers are told change how they homework, they are not told how to do it.
It is happening in the school and teachers don't have the opportunity to go and visit another classroom. Teachers don't have the opportunity to come and plan a class together and watch each other teaching the class. We have no quality vehicles in most schools for people to envision something that is different. And you know people can't do what they can't envision. They won't do what they don't believe.
So I mean practice, I was practice. That's the way I learned it. Then you forget how painful it was. And so until we have one teacher trying it, we videotape it, we bring it to the faculty meeting, we talk about look at what Sarah is doing in her class. Why can't some of the rest of us think about that? We look at the middle school math department, I don't give a damn about the rest the school. My job is to worry about the six people who are teaching math in the middle school, that nine people who are teaching math in a high school, the third and fourth and fifth grade unit team. Those are the people who have to stop and say, "Yeah, you know what? This is not working. This is ridiculous."
I look at all the districts that are using Engage New York, too many of them think that it's the Bible, and so they do all of that insane workshop, worksheet math sprint that only destroys brain cells. They try and do every problem. They only do the application stuff with the application problem, and then I'm another schools that look and say, "Wow, I got an application problem. I've got six problem solving problems. I've got six homework problems. And I've got a formative assessment. Yeah, but that third problem is really the best one." They take that and they do the application. They start with that problem as a launch.
They say, "That formative assessment isn't the best one. It's a little too easy.” So they take a different problem. And what that is they build ownership of it and they take that and they say, "Super, are you ready? We know our lessons, we know our numbers. They're all set. Homework tonight, you're going to do number seven and number 12 on this page. You're then going to go back to the previous lesson and do number four that we never got to."
That's the way it becomes. I think math becomes a scavenger hunt of go find it, but it's there, it's published, and so what if the kid does number three instead of number four? That's what I think has to happen and it won't happen until a school decides. It's not a district that can impose this policy. A school has to have a principal and a math coach, a principal and a math leader who says, "It's time for us." A teacher stands up and says, "You know that I have a son or daughter in this school. I'm embarrassed that I have contributed to what I see at my own dining room table." And then we have a discussion. We act like professionals. The principal says, "That makes perfect sense. We're going to send a newsletter home to the parents about how we're changing this stuff."
And it just becomes the way we do it. I'm in schools where the principal and the teachers have simply outlawed worksheets. They are outlawed. They are deemed to be, you never, ever, ever give a kid a chance to do a mad minute so that the kids who already know it, oh, I'm so smart because I can get right answers quickly.
And I'm sitting there watching the struggling kids. They can get answers, but they need more time. But no one is talking about the strategies. No one is having the kid articulate. All that stuff is answers. And I want to break out of all that. And so you and I can have a talk about number talks and how that works. You and I can talk about a launch and a good problem and accomplish this. We happen to be talking about homework as one piece of quality instruction.
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Steve Leinwand is the author of the bestselling Heinemann title Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement.He is Principal Research Analyst at the American Institutes for Research in Washington, D.C., where he supports a range of mathematics education initiatives and research. Steve served as Mathematics Supervisor in the Connecticut Department of Education for twenty-two years and is a former president of the National Council of Supervisors of Mathematics.
Follow Steve on Twitter @steve_leinwand