Brett: Marilyn, you’re known for your math interviews, and, Jen, you do a tremendous amount of work in conferring. I’m curious about how these two approaches overlap from a math and literacy perspective. Marilyn, do you want to start us off?
Marilyn: In preparation to have this conversation with Jen, and, Jen, it’s really a pleasure to finally “see you” at least online. I’ve been reading some of Jen’s books and thinking about how the connections between math and literacy, what those connections are, how they might exist. It seems to me that the interviews that I’m working on now, that I’m just completely passionate about… Well, more than passionate, I’m sort of obsessed for quite a long time. And they’re, I think, Jen, like your assessment conferences, where I’m there for me to learn.
I mean, the mantra we have is, “I ask, I listen, and I learn,” so it’s not a test of the child as much as it is an opportunity to hear how they think and reason so I can be a better teacher.
Jen: Yeah. I want to start off by saying it’s an absolute honor and pleasure to be chatting with you. I read your, I think it was first edition of About Teaching Mathematics as a college student, and I’ve followed your work somewhat since. It was really great to read some of your work and watch some videos of you working with kids and see what you’ve been up to. Yeah, I do think there’s a lot of similarities. I love your emphasis on the importance of listening as a really key part of whether it’s an interview or a conference, listening and taking every opportunity with kids to really assess and, I think, evaluate what’s really going on inside their heads, how they’re processing things, how they’re working things out. I think that’s the same with literacy and with math.
I was watching today a video… I don’t remember where it was. But you were working with a child, and then you were talking about all the different ways that kids can add, I think it was four and nine, and all the different ways that you’re surprised by kids thinking and by kids processes.
I think what you’re doing… And you can tell if I’m wrong about this. But I think what you’re doing is you’re trying to map a child’s process and their answers onto that network of ideas. I think about it as hierarchy of goals for reading and writing and that there’s progressions within each goal. So it’s not just about listening, which is so crucially important, but it’s also about, I think, the evaluation. What am I doing with the information as I’m hearing it, and what’s the work in the teacher’s mind that helps me place where a child is, what they’re doing, and then what’s the next step for them so that we’re always working from a place of growth versus looking for deficits, looking for what they cannot do?
Marilyn: It’s so important. I get nervous when we say we focus on kids’ gaps or we focus on kids’ misconceptions. I want to find out about where I can start doing. Where are their strengths? What do they understand? What do I have to build on? So there is a progression I have in my mind.
But there’s two things. First, when I’m listening in an interview setting, I don’t have the extra burden of trying to figure out, “Well, what might I do to intervene? What might I do to help?” So I’m just listening to learn, but that is hard because first of all, keeping your mouth closed and not talking as a teacher is not natural. That’s not what we’ve been trained to do. The other thing is I’m trying to listen, not for what I hope to hear, but listening to the child, and that was a huge shift for me.
So the problem that you mentioned about, we ask kids how much is four plus nine, and that’s what we’re interested in thinking about, addition and subtraction within 20. So there is a progression. When kids first learn how to add, they count. Now, some kids will count starting with a nine and count on some. Some kids will start with the four and count on. Some kids will count from one, one, two, three, four, and then keep going up through nine. That progression of counting is there, and we want to help kids move from counting to using more reasoning strategies.
When I’ve interviewed kids, I have the progression in mind, but whatever they say is what’s important to me. Whatever they understand and how they explain their reasoning is what I’m listening for. And then when I get to a situation where I’m planning class instruction, then I’ll know that these are the kinds of things I need to incorporate in my number talks or in my small group work, or even my class lessons. I don’t know if that answers that question, but four plus nine, I was bowled over. I mean, how many ways are there to figure out four plus nine? A lot.
Brett: Marilyn, what is it you always say about correct answers?
Marilyn: I don’t know if this is what you’re thinking about, but correct answers can mask confusion, just like incorrect answers can hide understanding. The answer is just the starting place. It’s really how you got to the answer and how you reason that is just as important. So people say, “Well, the right answer really isn’t important?” No, it’s very important, but what’s important is how the student reasons to get to whatever answer they come up with because sometimes wrong answers are the right answer to a different question. My job is to think about, “What was the kid thinking about?”
Jen: And when I think about literacy, of course, when we’re talking about reading accurately, there’s a right word and a wrong word each time you read it. There’s a right way to spell that and a wrong way to spell that. But beyond that is the craft of writing and how I organize my sentences, what I’m choosing to focus my piece on. There’s not a right and a wrong there. How I understand things from a story, from a non-fiction book, maybe there’s a wrong sometimes if it’s really not based in text, but there’s a lot of possible right answers.
So I think in similar ways in math, it seems like there’s a lot of right processes. There’s a lot of right ways to think about a problem. I think that maybe that’s a parallel to literacy, that there’s a lot of right ways to, for example, infer about a character, to take what you will and come up with ideas about a character and say, “This is the kind of person who…” And based on who I am as a reader, it can change my read on that character.
I can have a different idea because of the people I’ve met in my life or the other stories that I’ve read. In math, one of the videos you sent me… So amazed by this. Was she a fifth grader maybe that you were working with trying to figure out how many notebooks she could buy? I was amazed by not only what she was saying but also what she wasn’t saying. When she was hesitating, I can almost see in her head she’s saying, “That can’t be right. That can’t be right. That can’t be right.” Did you take the same thing away from that video?
Marilyn: In fact, I’m about to write a blog about that, because then she came back later in the day with her whiteboard in hand to show me how she figured it out. This is interesting when you say that kids can put together sentences in any way, and it’s up to them. They have that agency, and we support that. We applaud that. We encourage that in literacy. But math, I worry that too often the kids are taught a paper and pencil method, and that we don’t expect them to be creative.
We expect them to apply this procedure to get this answer. There is an important role of procedures and algorithms and math, but somehow that becomes the goal. That’s what concerns me. That’s why I say the answer is only the starting place. Paper and pencil is a tool that you’ll use, but I want the thinking to be there the same way you want the thinking to be reflected in a child’s writing.
Jen: The emphasis on mental math in your interviews is really interesting to me. Can you talk about that?
Marilyn: If we think about all the ways we do arithmetic in our heads as in our lives, counting the change, figuring out what time to leave, figuring out the tip, we did so much in our heads that it’s a life skill. But in school, it doesn’t get the emphasis, and I think partly we have nothing to send home as evidence of what the child’s doing.
I think that the movement to having number talks is really a big push towards getting kids to think, reason, and explain without paper and pencil. I see paper and pencil ideally as a way for students to keep track of their thinking rather than to reproduce a procedure, but to me, mental math is what it’s all about. It’s all about reasoning in your head and explaining, communicating, reacting. So I think all the same skills that you’re doing in literacy are there. It’s just that the content area is very different.
Jen: The ability to visualize is something else that comes in literacy as… I think of it as something that’s so key to my own literacy. I’m reading a story. I feel like I’m right there in that world. I’m seeing the characters’ facial expressions. When I’m writing, I’m either imagining the audience I’m speaking to… Literally when I write, I write it like I’m speaking to people, and I imagine my audience there. When I’m writing a story, I can imagine the characters coming to life, and I write down what’s happening in my head.
So I wondered about this emphasis on mental math, and in particular with that fifth grader whose video I saw. What was she seeing in her head? Was it dollars and money? Was it change and money? Was she moving that around? Was she seeing the actual numbers stacked and she was adding and carrying or regrouping the… Right? I don’t know. What does that make you think about?
Marilyn: Well, it’s interesting because we find that some kids do visualize the actual paper and pencil problem and visualize doing it. That’s what this girl on that video tape was doing. She was actually trying to add $1.39, $1.39, and she was seeing nine and nine. She was carrying in that situation. When we interview kids, we always have a way for teachers to capture how the student is thinking, and one option for certain problems is use the standard algorithm. Now, this is all mental math, and that means that they visualize the paper and pencil algorithm and apply the procedure.
But it’s so interesting. I read your writing. I feel like you’re talking to me. So if you’re visualizing me as the audience, I think that’s the way I write. We do, in our math classes, we do a lot of writing. Sometimes you’re writing for your classmates as the audience, but sometimes I want the kids to write to me because if I can’t interview them all the time, then tell me what you’re thinking and describe your thinking.
And that’s one of the math standards. Create viable arguments. Critique the reasoning of others. So I think there are so many overlaps that way, even in how we think about writing and bring that into the math class, but the visualization is so important. There’s no such thing as three. It exists in your head. A kid has to have a picture of something. I had a hard time at calculus, and I have a degree in math. I think it was because I didn’t realize how important it was to visualize these curves and visualize this change happening.
Brett: What Jen’s asking you here. It really makes me think about the math anxiety that many of our K5 teachers feel. I think you talk often about how our teaching can be more flexible as we teach math, and that we can make space for curiosity in teaching math. Can you talk a little bit about that? And Jen, I’d love to hear your thoughts on that, too.
Marilyn: It’s so interesting to think about this level of math anxiety. I think that for many people, children, and probably some adults, they don’t come from the point of view that math is supposed to make sense. They come from the point of view that you’re supposed to know, and if I learn how to do this, then I would get the right answer. Then I would be okay in math. It’s supposed to make sense.
Now, the ultimate way, we want to make sense out of black marks on pages. I mean, that’s reading, and in math, I suppose, it’s making sense of those symbols on the page. But the sense-making is in your head. So the source of the knowledge for me with kids is how they’re thinking, and so everything I have to do has to be to stimulate their thinking. That’s why mental math becomes so important. I think that people who have fear of math… And I know so many teachers I’ve worked with have can tell me the time I got sent to the board. The time they felt humiliated. The time they worried. It’s like, “Yours is not to question why. Just invert and multiply.” That’s what they were taught. They were never really taught to think reasonably, enjoy, be creative. Those words don’t seem to go along with math, and that’s one of my goals in life.
Jen: You know, I think I’ve seen a lot of math anxiety in children, and I think that part of it is about speed and some emphasis on speed and problem solving quickly. Then if kids can’t, they feel like they’re not good at it. I think we can make a parallel there to literacy as well.
Also, you said the publicness of getting things wrong versus being involved in math talks where you’re genuinely interested in other people’s thought process. That’s a huge, or maybe subtle, but very huge shift.
Jen: I think the speed is one thing. Thinking that faster reader is a better reader or someone who writes more is a better writer is not true. Sometimes when kids feel like, “I’m not good at this, this isn’t for me,” it’s because they compare their work to others and they see how quickly they can get it done or how easily it comes to them. And I think if they have to work at it, it’s not good. But there are so many writers who have to really work at their craft who have to really puzzle over every sentence and do a lot of revision and a lot of work.
And the idea of revision is something too in math. You revise your thinking. You have a first draft at something, and then you go back at it and you look at it again. And I think the more across disciplines that we can emphasize that for kids that there’s excitement and joy and interest in the work and in the process, not just in the final product or getting the answer. And I love what you said too about how at the end of the day, of course, it’s about making sense, that math has to make sense. And I think about the parallels to reading and writing. Of course, yes, what we write must make sense. What we read must make sense.
And part of the way that we control for that in the classroom is we help to provide kids with opportunities to practice that are within their reach. So I’m not going to stick Tolstoy in the hands of a second grader because that’s just going to shut them down and they’re like, “I can’t read this, therefore I’m a bad reader.” And I think the same thing in math. I think sometimes what happens is maybe all kids get the same problems, but that problem is not right for everybody. If some are still working on adding and subtracting within 10 and others within 100 and others within 1000, the kid that’s still working within 10, being presented with a within 1000 type problem, then maybe they’d shut down because it doesn’t make sense anymore. It’s not close enough to what they’re able to do.
Marilyn: That’s so true. In fact, I was working on a piece this morning about the numbers matter, the magnitude of the numbers matter because four plus nine was within reach of some of those kids you saw on the video tape, whereas 35 plus nine wouldn’t be. When a kid gets out of their comfort zone, then they seem to resort back to the earlier skills in their progression, like they’ll start counting. So if I have 39 plus six for example, a kid will tend to count rather than kids will say, “Well, 39 plus six, it’s 40 plus 45.” I mean, decompose. So once you get out of your comfort zone with the numbers, then you sometimes have something to fall back on.
And as soon as you get through with learning how to add and subtract, then along comes multiplication, which is a whole different animal. And then come fractions, then come decimals, then come irrational numbers. It goes on and on and on. So in some ways the reading and the math analogy is different. And I can see why teachers or adults would feel fear of math, because there’s some point at which they fell off that ladder and they never got back on. And so you have to be able to just like in reading, find something that’s accessible to the child to build the understanding, to build the strategic thinking, to build the ability to reason so you can then inch them up towards where they haven’t gone. So it’s subtle, it’s tricky.
Brett: Jen, that brings me back to something you were saying, I think closer to the start of our conversation around goal setting and some of the work that you do in conferring. So I guess I’m wondering, how do you use the information in either Marilyn with interviewing Jen and conferring, that information that you’re gathering to how you each identify the goals. And then Jen, I think we talk about this a lot, responsive teaching.
Jen: Yeah. It’s all about responsive teaching, right?
Marilyn: Talk about that, because that’s not a term anybody in the math world uses.
Jen: But isn’t that what you’re after with the interviews?
Marilyn: Seems like it, from what it sounds like it, so tell me a little bit about it then.
Jen: Well yeah, so I wrote down some notes about this graphic that’s on a website for … What is it called? The Listening to Learn website, right? And you have this series of boxes and then there’s this list beneath each one. And so it starts with numerical reasoning. Then it moves on to addition and subtraction, and then beneath addition and subtraction to 10 to 20 to 100. I’m just saying this for listeners who may not have seen it. Then it moves on to a multiplication and division and then beneath it foundations and extensions. And I think it’s similar way of thinking about, of course there’s overlaps and there’s times when kids might do something later on, but when they’re not yet doing something earlier on, but it’s the way I think about literacy and I have what I call a hierarchy of action for reading and for writing.
And it’s the stuff I do first and then the stuff I do later. And then within each of those potential goals, and I’m calling goals things like print work, fluency, understanding plot and setting, understanding characters. Those are big categories. Within each, I’ve got this progression just like you have within the addition and subtraction, this progression within it, that lists the kind of work that you’d see as kids move into more and more sophisticated texts and reading, or learn more and more skills in writing. So for example, if I were to sort of crack open fluency, reading fluency, you might say at the beginning, I’m just trying to read words with automaticity. It might sound choppy word to word. Then I’m going to read two or three word phrases at a time.
Then I’m going to make sure I’m paying attention to ending punctuation and I’m reflecting with expression what the author wants me to. Then I’m paying attention to medial punctuation and pausing at the commas. And so if I, as a teacher and listening to a sample of a child reading aloud, I can sort of map onto that skill progression, where is the child now? And then look ahead to see what’s next. And if there’s a need within that goal, then that becomes the child’s goal. That’s what I’m going to focus my strategy instruction on, but I’m still seeing, where are they strong within that goal? And then what’s next. So it’s both looking for an area of opportunity for me to support the student’s thinking or their skill work, but it’s also looking at their strengths and then trying to move them ahead to what’s next.
Marilyn: And it’s so true that the only way you would know that would be sitting with a child and hearing him or her read.
Jen: Or collecting samples of work. So, I don’t really need to hear a seventh grader read aloud most of the time. I could sit down in a kind of interview or an assessment conference, ask a series of questions to probe, how is the child thinking about the plot? Are they visualizing the setting? How are they thinking about the characters? And so I’d ask a series of questions that aligned to each of those possible goals. Or I could ask a child to hand in some writing that they’ve done about their reading, or I could look through their notebook to see what kind of writing that they’ve done. And I’m looking at their writing probably the same way in math you could look at their written work.
Marilyn: Well, no, that’s the whole thing. If the written work is just a worksheet of problems to solve, you don’t know anything. You only know that the child did or did not apply the procedure and did or did not get the right answer. And you don’t have any idea about how they were thinking, and how they were reasoning. So it seems to me that in the reading community, especially with young children, you listen to them read, and that’s the only way you know they are going to pause it a comma and take a breath at a period.
So interviewing, it seems to me, has become an integral part of teaching reading to young children. Why not in math? We never thought we’d give them a paper, pencil, let them “work the problem.” And working the problem is very different from the kind of work you’re expecting from a child who’s doing a piece of writing that’s integral to who they are and what they want to communicate. But we do have writing and math, but that’s not really the norm. The norm is get the right answer and get it fast.
Jen: So if you notice through these interviews that you have a wide range of different needs in your classroom, which I assume you would, it’s like, “Oh, these three over here really needs help with this. These three really need help with this.” A question I get all the time is, how do I reconcile the differing needs in my classroom with what the curriculum tells me I’m supposed to be teaching in October? And how do I balance the curriculum and the scope and sequence with what I know the kids need and really supporting them responsively? What’s your answer to that in math?
Marilyn: All right, and the snarky answer is, you’re teaching children. You’re not teaching math.
Jen: I maybe have said something similar in literacy.
Marilyn: But that doesn’t help. But the thing is, here’s what I want in my classroom, I want kids to be excited about all their learning. I want them to be excited about math. I want to have a community of learners that treats each other with respect and kindness and curiosity by modeling how I’m treating them with respect and kindness and curiosity. And then I want there to be problems that we’re going to solve together. And we’re all different, so we’re going to have different ideas and we’re going to value these ideas. So if I’m going to talk about the path to the old four plus nine if I’m working with first graders and I put this problem on the board, and I say, “I wonder how many ways could we think of figuring out the answer to four plus nine?”
First of all, let’s get the answer out of the way. “In your whisper voice, when I say three, tell me what you think the answer is. I’ll give you a minute to think.” And then I whisper, “One, two, three.” So finally we say 13, that’s the answer. So we’re getting that out of the way. Now how could we explain to somebody? How could we justify that answer? How could you prove that answer to somebody who agreed with you or didn’t agree with you? So that’s the nature of the work.
That’s why I love number talks, where we have the entire community. That’s where we do lessons, where the problem solving and you come to it and you work cooperatively. And then in the independent work, would you be working individually or with partners, then that’s where I can tailor it more. But I don’t want to give up the sense of community. I don’t want buzzards or Bluebirds.
Jen: I’m thinking about how the act of doing these kinds of interviews changes the teaching that happens in the classroom and changes the learning that happens in the classroom. Yes, it’s assessment, but if you assess kids by asking them to do a sheet of problems and then correcting them as right or wrong, it changes what you value, what you emphasize, how you spend your time during math class, how you talk to kids about what math is, and how mathematicians think and how they work. And I’m thinking about that from a literacy perspective, when we have a state or a district that is very bound by these standardized tests where it’s about choosing the right of the multiple choice questions. It changes the way that you teach comprehension because you’re teaching kids to get a answer.
But like I said before, there’s many possible ways to understand anything, a character, a plot, a setting, a theme in a story. So I’m thinking about just how exciting it is to think about the way that this real inquiry mindset, I think, that a teacher has to take on to do these interviews and to benefit from these interviews, what implications that has for the classroom.
I think it’s so exciting about how it changes the inquiry mindset that a teacher needs to adopt to do an assessment conference, to do an interview in math, that kind of thinking and the kind of genuine curiosity of how a child’s brain works, what implications that has on how a teacher budgets their time during the classroom, during the math classroom, during the reading classroom, and how the instruction changes because of what you’ve now learned.
Brett: Jen, you mentioned fluency, and it reminded me that we have a lot of overlapping terms in math teaching and literature teaching. We’ve got fluency, prompting, searching for information. Jen, and I guess Marilyn, however you want to approach this, how do you see these terms overlapping in math and literacy and the connections that they build for teaching both?
Marilyn: Like you’ve talked about, responsive teaching, what do we… Can you talk about comprehension? That’s not a word we use in math, we use understanding. So comprehension equals understanding. I can write a little equation like that. But responsive teaching. I get it, you’re supposed to respond to who the child is. The child is the starting place, not chapter three. So in that way, I don’t know if we have… I think the language is important because if we want to help literacy teachers build on their own strengths to feel more comfortable with math and vice versa, then we have to find the common ground of language, I think.
Jen: That’s right. I think, just like we’re saying, the advice we’re giving about teaching children is to see what they can do, see where their strengths are, see where their understandings are, and help them grow from there. Same thing with teachers, with any areas that feel less comfortable. So I think the terminology, sure, that’s one way, the common language. And I think about the moves you can make as a teacher, the kinds of structures you use in the classroom, whether it’s small group strategy lessons, you can do that in math or an assessment conference is like an interview. You can do both in math and literacy. So finding commonalities with structure and then finding commonalities with content.
Marilyn: That’s harder.
Jen: That’s harder.
Marilyn: That’s where the rubber hits the road, when I’m struggling with this. Like in writing, the kids are doing their own work. Even if they’re all writing a how to, or they’re writing a memo or whatever genre they’re writing in, it’s their work. What’s the work in math?
Jen: To learn the algorithm to learn the…
Marilyn: Long division had a birth. It can have a death. You heard it here.
Jen: Without long division, what is there?
Marilyn: No really. If you want to be efficient and accurate, the last thing you want to do is paper and pencil. That’s a mind shift.
When I grew up we had to learn how to take square roots by an algorithm. You had to put numbers in twos… It was sort of related to division, but it was very complicated. I loved it. But nobody figures out square root of a number by paper and pencil. In fact, I was talking to a math colleague who’s a real math person. He said, “I can’t remember how you do that, because you just punch it in your calculator.” But you have to know what to do with the number. Once you get the number, first of all it doesn’t make sense, and second of all what problem are you solving with it, and what are you going to do with the information? That, to me, is math.
I had a kid interview, we have it on tape, and I asked her a question, and she said, “Can I use my fingers?” I’m thinking like, “You have to ask permission to use your fingers? They’re your fingers.” Doing it under the table or they’re using the tongue on their teeth counting. Why are we taking these things away from our kids? You shouldn’t be counting on your fingers. Yes you should. They’re your fingers. Maybe we can think of some ways that… Besides that, that’s it. What you’re doing is fine, let’s change the game. Let’s think about what other ways could we think about this?
Jen: And I wonder sometimes if it’s a matter of spending more time with concrete manipulative, fingers, counters, something. If it’s a visualization thing. Or just spending more time with the numbers, playing games, rolling dice, subtracting, adding, subtracting, adding.
Marilyn: It’s what they value as being important to know. And the important thing for me to know is what do you do when faced with a problem you’ve never seen before? So I got really good at long division. I got good at taking square roots. But the question was, think about… That’s what math is all about. Thinking about problems you haven’t seen before and wondering. So what do you notice? What do you wonder? Let’s talk about it.
Jen: It changes what math is. It’s not about just doing a sheet of problems. It’s a totally different way of approaching math, which I think maybe contributes to some teachers’ discomfort. Here’s another literacy parallel. I find that teachers in general, there are more teachers comfortable with teaching reading than there are teachers teaching writing. Some teachers feel very uncertain, especially when we’re talking about creative writing, like story writing or poetry. They’re like, “I never had to do this myself as a child. I never really learned. I don’t do it for fun. I don’t do it because I need to. It’s something I just don’t do. And here I am trying to teach four weeks’ worth of lessons to kids on how to write a good free verse poem.” So it feels uncomfortable. It’s so different than how they were taught.
And I think back to how I was taught math, and I’ll be honest with you, I think I understood math better when I taught it when I was an elementary school teacher than how I was taught as a child, because as a child, it was only about the right answer and doing over and over and over again the same type of problem until it just stuck. Rote memorization. And now you’re asking teachers to… You and other math programs that are popular nowadays are asking teachers to really understand how numbers work, the whole number bonding, and taking apart numbers and moving them around or really working on developing a conceptual understanding before they get to the algorithm, or concrete understanding before get to the algorithm.
I wonder for how many teachers that feels really different than how they were taught to do math, and that’s part of the discomfort. You see the jokes all the time on social media from parents. “Oh, now that kids are home, I’m just going to teach them this way. The good old way, like I learned.” And just the unfamiliarity with this way of teaching makes it challenging.
Marilyn: But what you said about when you learned to teach you then understood it.
That’s because you had to take it apart and put it back together in some way so that you could explain it to the kids. You do all the work. I walk into classrooms and I see teachers doing all the work. And I want the kids to be doing the work. So I think that I… This was a painful lesson for me. I prepare my lessons, I get it clear, and then I’d give my explanation. I was trying to make it plain to the kids. Well, I was doing not only the preparation of thinking it through, I was doing all the talking.
So if I want to shift my teaching of math, then I have to shift it so that they’re doing the thinking, they’re doing the talking, and I’m doing… So instead of I do, we do, you do, I want to reverse it. You do, then we’ll talk about we do, and then I’ll tell you what I think and see if I can help you move a little bit farther. And that’s completely a shift that that’s turning it upside down, I think.
Jen: I visited Japan as a pretty young teacher. I got a Fulbright scholarship to go to Japan and study the schools there. And I will never forget one of the, I think it was a middle school classroom, a math classroom, just as you described. The teacher put a problem on the board. One problem. All of the kids moved their desks into groups. They talked, and almost the entire class worked. The teacher circulated. The last 5, 10 minutes of class they turn their desks back to explain their thinking, how they got their problem, the different ways they went about it. And the lesson was at the end.
We do this sometimes in literacy. We’ll put up a text, a poem, let’s say, and say, “Well, what is the author doing? What do you notice? What are you wondering about? Why do you think the author made these choices?” Katie Wood Ray’s book Wondrous Words was really foundational of making this a regular practice in classrooms. And at the end of it all, “Oh, that’s called show not tell, and here’s how you do it. Here’s a strategy for trying it in your own writing.” And the idea of flipping that, of starting with the students, starting from what the students can do, starting from their thinking, and then having the explicitness of the teaching or the strategy or the lesson come at the very end of the class.
Marilyn: It puts a lot… It’s hard, because as a teacher, when the kids are working, your job is to figure out how they’re thinking, so you select the students who are going to present. That means you really have to understand, first of all, this thing about the progression, second of all, what are your kids doing, and third of all, how am I going to do this paying attention to the fact that I can’t always call on the same kid and in what order? It’s problem-solving teaching that’s of the highest order and very, very important. So I think that you’re lucky to have had that experience.
Brett: It makes me think about that question you always get, Jen, about the teacher that may not know the plot of a particular book that the student wants to read. It makes me think of that, because you always have a great answer for that.
Marilyn: I read that. I want to hear it from the voice, but I’ve been reading your books, and I say, “What do you do if you don’t know this book?”
Jen: And that happens a lot. If you are running your classroom in such a way that kids have choice of what texts they read, and especially once you get to end of second grade up through middle school, they might be reading these really thick books that you don’t know. How do you evaluate their thinking? How do you evaluate their comprehension? And I think the first piece of advice I have for teachers is to let go of the idea that there’s only one “it” to get. That getting it could be a lot of different possible… There’s a lot of right answers.
There’s a lot of right ways to think about it. And instead, what I look for and what I advise teachers to look for is the quality of the response. So if I ask you, “Tell me about your character,” and you say, “She’s really kind. Well, except when she’s with her sister, then she seems really bossy.” Then what I’m thinking right there is the child’s understanding that characters can be complex, that they’re not just one way.
And then I can say how will I help this child deepen their thinking about character? And maybe it’s to say that I’m noticing that the child’s talking mainly about one of the characters and I can help him extend his thinking to other characters, and how the interactions between the characters gives us new insight. Or maybe it’s to say, “You seem to have a really good grasp of character. So I’m ready to teach you, or I think you’re ready to learn some things about how the characters and their journey helps you think about big ideas in the story.”
So it’s again, placing it along this progression of skills, this idea of listening for a quality of response and trying to nudge them along to think more deeply within that same goal, along that same progression, or moving to a new skill progression. That’s one difference in math, you know what the right answer is.
Marilyn: But that’s where I’m trying to break that mindset. The right answer is only the starting place, because right answers can, as I said before, mask confusion, whereas wrong answers can also hide understanding. So what’s interesting to me is how do you think about it? Why do you come to that answer? And so that’s the shift that’s enormous. So if the grain size of your math teaching is correct answers are what I value and what’s important, then I’m trying to make that grain into a lump a rice, whereas it’s more complex than that.
I was really interested. I was interviewing this girl, Tova, and the problem I gave her to solve in her head was 36 plus nine. And she thought, and she thought, and she thought, and then she said, “I’m going to change the problem from 36 plus nine to 39 plus six, and now I can do it because 39 and one is 40, and five is 45.”
And I’m sitting there thinking, “She switched these two digits. Are you allowed to do that?” And I’m thinking, “Well, when can you do that? Could I do it if it was subtraction? Can you do it in multiplication?” I mean, it opened up my whole math mind, in a way, but it was her way of thinking about that, where she got the answer 45, and that was only a starting point to think about, how does this work? She’s adding the ones; does it matter if we have this one on the top and the bottom? Can you just change the quantities?
Well, if it was a contextual problem, it might not make sense to change 36 plus nine to 39 plus six. But it was fascinating. So I’m always amazed about answers are only the starting place. It’s how they get to answers that really give me windows into their mathematical minds and hints about how to help them grow.
Jen: Do you find that there’s a lot of kids that just aren’t that able to discuss their process?
Marilyn: Yeah like last year, I just did it all. I got it all right. I said, “Oh, that was third grade. That’s what you do in third grade and fourth grade. This is what we do in fourth grade math. We talk, talk, talk.” I mean, that’s the way I’ve always handled that. And you will have to do it in a safe way, so you’ll have a partner and you can practice. And I sometimes even so much will … One will sit and the other will listen. Then I’ll bing, and now switch roles. Teach them to talk to each other, teach them to talk to their class, teach them to listen and ask questions respectfully. I have kids saying, “I would like to respectfully disagree.” We’d all learn that phrase, so that you can participate in the discussion and we can be open to listening to each other.
So it’s just a question of shifting your culture, shifting the culture so math becomes everything. Probably, your literacy teachers are more comfortable doing this with reading and writing. Why not take those skills I have and move it into the math world
Jen: Oh yeah, those same sentence starters or discussion prompts: “I’d like to respectfully disagree,” “I see what you’re saying,” “But another way to look at that is,” or, “I would like to add another point to the conversation.”
Marilyn: Yes, yes.
Jen: Those same kinds of words that we use in discussing a picture book that we’ve read together can be used, it sounds like, to talk about math.
Marilyn: And sometimes I have kids talk in pairs and then I’d say, “Okay, now I want everyone to think about how you’re going to tell the class what your partner said.” So I’ve tried every way to get kids to really process information, verbalize it, communicate. And then later, it would be to go back and write what you think about this. So I think that it’s a question about … That would be really interesting, to take the skills … Like when I was reading one of your books and you had all these mentor people, and there was a whole spread on Marie Clay. And I said, “Was she talking about literacy or was she talking about math?” I wouldn’t have known if I hadn’t known it was in your book, not my book.
Jen: Yeah, I just think there’s so many parallels or could be parallels in a classroom to the moves that we make, like putting kids in a circle and having a whole class conversation, working with partners or working in a club and then coming together and sharing what you’ve thought about or spending some time independently and a teacher circulating around the room and doing one-on-one conferences with kids. The moves probably feel comfortable to teachers who are more comfortable with literacy than math. It’s the content…
Jen: And I think developing interest and curiosity and appreciation, recognizing the relevance of what you’re learning. The same with literacy, right? Not every child is going to go on to become a professional writer, but we want them to be comfortable enough to write a really well-crafted letter to their school board or to keep a journal because it helps them emotionally to do that, or whatever it is, to have that be a part of their life or have that be available to them. And same thing with math, right? I use math every day. I really do.
Marilyn: Like, we were getting some work done in the house that required a contractor coming in and he had to make a bid and I’m thinking, “Wow, this guy is doing so much math to estimate what his costs are, estimate what his time is, come up with a number that’s fair.” He doesn’t want … “I don’t want to be greedy.” He’s not going to get the job. He doesn’t want to feel used. He’s going to feel awful. That’s a lot, a lot of math.
I had a friend who an interior designer who said, “I’m not really good at math. That’s why I went into interior design.” And her eyes are darting around the room, and she’s saying “there, and you have to have so many yards for that.” And I’m thinking, “What are you telling me here?” And I met another woman who was a ballet dancer, and she really wanted to be a choreographer and said it’s because she’s so bad in math that she couldn’t.
Jen: But she’s counting. She’s keeping time to know she has a rhythm to the music.
Marilyn: … and music and the movement. I’m sure music is all math. I mean, the cross between math and music is very strong. So there’s math, it’s everywhere. So how did we get to this terrible, “I hate math”? I mean, the first book I ever wrote was called The I Hate Mathematics! Book. And I come into the class, and I wrote it in 1975, and I said, “How long ago was this?” And that’s a good because they can do that in their heads because from 1975 to 2000, and then they only have to go … That’s a long time ago that I wrote this book. In fact, I think it’s quite amazing. But I think the reason why it’s still in print and successful is because children don’t buy children’s books, adults buy them. They look at this book and they say, “Yeah, that was me. I’m getting this for my kid.” So it’s pervasive. The, “I hate math” syndrome is pervasive.
Jen: Do you think that the standards or … I mean, you don’t have to speak specific to today’s standards, but any standards, do you think they push too much, too soon, and that’s part of what’s challenging? Like if we slowed down and focused more on depth…?
Marilyn: If you saw your job as uncovering the standards, rather than covering the standards, you’d be on your way to thinking about how to teach, in your language, what would be responsively.
If I’m covering the standards, I’m doing what you and I did as teachers, we were explaining it. We figured it out, we’re going to explain it. If I’m uncovering, I’m giving you a way to engage with it from which I can help you see the structure, see the big idea. It’s that, “I do, you do, we do,” shifted to, “You do, we do, I do.” So I don’t want to cover the standards, like, “Check, I taught that.” It’s like the used car salesman who said, “Well, I sold that car. The problem is he just didn’t buy it.”
So I taught it, they just didn’t learn it. Who was it? John Goodlatte said there was the written curriculum, the perceived curriculum, that is how the teachers thought, and then the taught curriculum. I liked there were four different, sometimes not even intersecting, worlds.
Jen: What do you think about grading and tests as being another impediment to kids being comfortable with math or teachers being comfortable with math?
Marilyn: Yeah, timed tests are mean-spirited, useless, cruel, demeaning, and horrible. You got that clear? I think tests, it’s like, are they motivating? I don’t see how they’re motivating. They’re just ways of sorting and labeling kids. And I think that’s mean. I think it promotes deficit thinking. I don’t know how to get around that, because it’s huge. The thing about accountability and the importance of knowing that we’re doing our best as teachers and our schools are serving our kids best as we can.
And like now, they say the kids are falling behind because there’s COVID. I said, “Behind what?” I mean, where is it written that every child in the third grade is supposed to learn multiplication? That’s a construct. So they’re not going to learn it for another year? I mean, really? The question is, you’re learning the importance of what the interaction is. But, “I don’t want them wasting time when they’re home.” You think they didn’t waste time in school, and how much chatting was going on? We’re in such an unnatural world right now. And I think that maybe it’ll help us reset to think about what school can be. To me, I want play, work, and learning to all be the same.
Jen: I agree with that, and I think the challenge is going to be when things get back to normal, whatever that means, right? When we’re back in brick and mortar schools, the whole class at the same time, five days a week, how do we approach students and how do we approach curriculum? And if we’re just going to open up to the first page of the teacher’s guide and teach whatever it says is aligned to that grade level standard for September, that’s when people are going to feel like the kids are behind, there’s a huge gap, we need to catch them up, but if…
Marilyn: Yeah, and then how do we get that language out? Okay, so my remedy is how about when we all come back together … or that the first three weeks of school is you learning to know who your kids are and how they think.
How can you start teaching chapter one, page one, when you don’t even know who your kids are? You don’t know what they’re thinking, you don’t know if it’s appropriate, of interest. What can I do to make them curious about math, and me learn as much about them, and them to feel my interest in them before I say, “Okay, I’ve got an idea. We’re going to now spend the next three weeks learning about division. This is going to be so exciting.” That’s the attitude I want.
Jen: Yeah, I agree from a literacy standpoint, as well. The more we can get to know our kids first, the better the teaching is going to be from the beginning, and then just working efficiently to support kids with what they actually need to learn.