What does it mean for math to be figure-out-able? What will you teach? How? Why? In this episode Pam and Kim discuss their thoughts to changing the "how" and "what" of math education around the world and explore the "why".
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Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able! I'm Pam.
And I'm Kim.
And you found a place where math is not about memorizing and mimicking, where you're waiting to be told or shown what to do. But we can make it be about sense making, and noticing patterns, and reasoning using mathematical relationships. Let's mentor students to think and reason like mathematicians. Not only are algorithms really not helpful in teaching mathematics, but roughly repeating steps actually keeps students from being the mathematicians they can be. Alright, Kim. Ya'll, we record a few podcast episodes at the same time. And I'll just say right now, Kim and I are a little punchy.
It's always the best ones.
So, it should be the best one here, if we can make sense of what we're doing. Neither of us slept well last night, and so this is going to be amazing. I can't wait to tell you. Kim, hey, I want to start off by talking to you. I was just in Florida. I had a blast in Florida. (unclear).
You've been traveling a ton.
I have been traveling a ton, yeah. And about to travel some more, which is. I like to travel. I love meeting new people. I really like hearing about how math is going in different classrooms around the world. It's super, super cool. And I worked with some amazing educators in Florida.
So, I had a great time. I was at the Florida. It's FAMs. I should know what it stands for. But it's their supervisor. It's their leader conference. So, I gave a couple of sessions at their leader conference. Saw John San Giovanni. He's great guy. We had a chat. And Alisha Charbonneau is one of their leaders in the state. And I had mentioned in one of my sessions, and maybe both of them, that I am both the "how" and the "what". And we'll talk about that in just a little bit. But she came up to me afterwards. And, Alisha, shout out to you. You did a great job of organizing everything. And thanks for treating me so well in Florida. She said, "Hey, Pam, Pam. You got to add to your bit here. It's not just the 'how' and the 'what', but you also have to add the 'why'." Well, Kim, I've been thinking about that.
I've been think about that a lot. So, let's parse out what I talk about with the "how" and the "what". And then, let's kick around this idea of adding the "why".
So, the reason that I've been talking about "how" and "what" is that I think it's kind of important to acknowledge that in math professional learning, it's important that we not only talk about how to teach, but that we also talk about what to teach. Right. So, what do I mean by "how"? I think a lot of good people are talking about how to teach. I think there are some fantastic number talks, people out there that are talking about how to do number talks well. I think that Peter Liljedahl in Building Thinking Classrooms is really talking about how. If you think about his Building Thinking Classroom, it's all how. It's, you know, vertical nonpermanent surfaces, and how you answer questions, and randomly grouping students. And there's a lot of really good things to consider about "how". I'm trying to think of some other examples. Some other instructional routines that are out there. We're talking about how. So, there's a lot of questioning. There's a lot of really good people talking about how to teach.
The teaching practices, the eight essential teaching practices are all about how to teach, right? The Mathematical Practice Standards for students are all about kind of the things that students are doing, as they're thinking and reasoning like mathematicians.
Yeah. A lot of teacher PD from their schools is about strategies for teaching, like grouping students. And yeah.
Yep, yep. Even looking at data, it's all about "how". And there's lots of that, and I think we need it. I think I'm also about "how". I think you and I have talked lots about how, especially in the last couple of podcasts that we've just put out, episodes we just put out. We also talked about "how". In fact, in my online workshops, we have seven module workshops. Oh, that's funny because we have seven right now, seven module workshops. We're about to have an eighth. In those seven modules, we devote a whole module to "how" in a really unique way. I'll maybe just mention really quickly. When we create those online, asynchronous workshops, I do a live workshop with real people.
Both Pam and Kim 04:26
Not fake people.
As opposed to fake people?
Both Pam and Kim 04:28
You always make fun of when I say that because it's always dumb when I say it. Alright, so I got people, like teachers in the room, and we do a two-day live workshop, and we film it, and then we turn that into the async workshop. And that turns into five of the modules of those seven.
And of those other two modules, one of them is completely devoted to teacher moves. It's completely devoted to the "how". We talk about equity moves, and talk moves, and identity moves, and questioning moves, and we really parse out. And we do it in, I think, are super cool, unique way.
Where what we do is we take video of those two live days that were in the five modules, and we grab moments where I did those teacher moves. And we can exemplify those to say, "Hey, you actually just experienced all these teacher moves." And we put them like right in a row. Bam, bam, bam. Like, we pick a teacher move, like getting students to talk to each other, not just to the teacher, and we'll put together moments that they just experienced over those two days, where they'll hear me say, "Oh, so you disagree with James. Well, tell James. Tell James that." Like, and I'll actually move my hand like, "Turn, and talk to James." And then, the clip will stop. And then, it will be a new clip, and I'll say something like, "Can you restate what Elise just said? "Oh, you can't? We'll, go ahead and ask Elise what she said. You don't remember what she said? Well, go ahead and ask her. Or you're not sure what she said. Go ahead and ask her." And then, it will stop and go to another one. And so, they'll see like a montage of seven different times in those two days, where that teacher move happened with them. And then also, in one of the modules we'll also always put a student, at least one or two classroom examples where it's happening with students. So, the thing that we're... If it's Building Powerful Multiplication, multiplications happening with students. And then, we'll also include not just me doing that teacher move, but that classroom teacher doing that teacher move. And so, they've already seen it, to get at the math, and now they're seeing it to get at the "how" and the teacher moves. And so, we think that's kind of a unique way of really doing the "how". So, we do the "how", right? We also advocate that it's important to talk about the "how". But you might have just noticed, when do we do the "how" in those workshops? After we do the "what".
So, first, in the workshops, in those two days of the live workshop, in those five modules, we get into the math. What do I mean by "what"? I mean the mathematics. We actually build participant mathematics. Ya'll, it doesn't matter what grade level I'm working with, I really try hard, I plan purposefully, that everyone in the room will learn some math. And so, let's say that we're doing Building Powerful Division. We don't start the workshop with, "How should you build division with students?" We start the workshop with a Problem String, where teachers are diving into division, and they're thinking hard about solving problems, and we build relationships about...like in that particular workshop...in Division. Or if it's proportional reasoning, proportional reasoning. We really dive into the mathematics, and we get clear about the landscape of learning. Thank you, Cathy Fosnot. We get clear about the landscape of learning for that math in that workshop. So, if it's Building Addition for Young Learners, we get clear about the math that students need to own to build counting and counting strategies into additive reasoning for those young learners. If it's Building Powerful Linear Functions, we get at the math of what students need to know and own to build powerful linear functions. So, when I say to people, "Hey, I'm about the 'how' and the 'what'," I would suggest that we're kind of unique that way. The workshops that we do are a bit unique in that we are really helping teachers build the mathematics for them, so that then we can talk about how they can build it for their students. But we get really clear on the big ideas, models, strategies, concepts, properties that are involved in the mathematics they teach, so that they are clear in their heads. Now, we don't do that by telling. It's not about, "Hey, here's this pre-created chart that I've created. Now, just stare at it. And there, you got all that? Did you just like by osmosis get all that learning?" No, no. We dive into problems, solve problems. We do what we want them to do with students, where they are actually doing the same kind of work. Solving problems. We make it visible. We point at it and discuss it. Compare. Next problem. Rich Tasks. All of that discussion to really build teachers mathematics, so that then they can build their student mathematics. So, we're all about the "how" and the "what". But then, Kim, then Alisha said to me, "Pam, it's not just about the 'how' and the 'what'. It's also about the 'why'."
I'm thinking about that. What did you think when I first said that?
Yeah, when you first mentioned it to me, I wondered if she meant like when kids say, "Why am I ever going to need this?" Right, like that could be a question. And older the students get, right, some of them are snarky, and they're like, "Why do I need to know this?" And so...
"When am I ever going to use this?"
Yeah, right. And so, you and I got talking a little bit about like how we respond to that. And I think I shared with you that, for me, it's less about the specific topic or question that the kids are learning about in that moment. It's kind of more about mathematics in general and how things are connected. Or maybe it's about kind of the eight practice standards, and the behaviors of problem solving, and tackling something, and finding connections between what we're doing.
Are you saying that when kids say to you, "Mrs. Montegue, when am I going to use this?" that you would say back to them, "Well, it's not about this particular..." I don't know "...problem that we just solved. It's not about knowing that the answer is 42."
Which is the answer to the question of the universe. But it's more about that you can now do this thing. You could have looked at this pattern and you've noticed a relationship. Hey, you'll be able to look at the patterns and use them, you know, later in your life. Or, you could say, "Hey, it's more that you can now model with mathematics."
Like, "We've been working with this model, so now you have gained something that you could use in the future modeling with mathematics."
Or, "Hey, in this problem, we just solved this problem using tools strategically. What you just learned is how to use this tool strategically. Now, you have some sense of, 'Hey, when I'm solving a problem in the future, I could use a tool strategically.'" Something like that?
Kind of what you're saying?
So, an answer if student students ask you "why", you're saying, Alisha's 'why' to me could have been when students say, "When am I ever going to use this?" Or, "Why are we learning this kind of thing?"
We can say back to students, "Oh, it's about your brain." In fact, Kim, I am thinking hard right now trying to remember. Somebody just said. I can't think of who it was. Just a day or two ago, I was talking to somebody. Who am I talking to? Hmm. Somebody just said to me that when kids say, "When am I ever going to use this?" And it was a guy. I know it was a guy. So, guy, whoever you are out there said, "I answer students, 'You will use that every single day the rest of your life because your brain just grew.'"
"And so, when are you going to use this? That brain you just created, because now your brain is thinking more sophisticatedly, you're going use that brain the rest of your life every single day."
I kind of like that answer.
Yeah, yeah, yeah I do too.
Man, I can't remember. I can't believe I can't remember who that was. So. Well, maybe they can contact you. Yeah, whoever that was. Please let me know. I want to give you credit. I want to give you credit for saying that because that is brilliant. It's a really nice way of answering that question that I think a lot of us get, especially the older that you teach.
Well, older you teach, and if you are teaching math as fake math, you're going to get that question a whole lot more often.
Yeah. I'll just say, Kim. We don't get that question anymore.
Like, ever. Like, yeah. We don't get it from students. We don't get it from teachers. Ever. Because we're just diving in and just having so much fun with it that they're not... It's not the drudgery of, "When are we ever going to use this?" They're like, "Oh, ask me another one! Give me another one!" Like, that's more, yeah, kind of we are.
But you said you didn't think that that's what Alisha meant?
Right, you were like, "I don't think so."
I don't think that was her "why". I don't think that's what she meant by "why". Yeah.
And I think the next thing I asked you was, do you think she might mean "know your 'why'?" Like.
Like, Kim, we almost didn't do this episode. Because you said, "No, Pam."
I was like, "Absolutely not."
"We're not talking about that." And I was like, "What? Why would we not talk about the 'why'?" So, tell everybody why you were pushing back."
Well, because I mean it's just a thing, right? Like, teachers do the hardest, hardest job. And, you know, in times of struggle. Like, when people say, "Just remember your 'why'." It's a little like vomit inducing. Like, teachers are great people, and they like love kids, and they whatever. But you shouldn't have to take on just an unimaginable amount of junk just because you like kids. And people... It's my opinion. It doesn't have to be yours. That people should not just throw out the phrase, "know your 'why'," so that you can have to suck it up for more stuff. Not alright.
Absolutely. And I think especially now, where we're just all kind of coming out of the Covid crazy, where teachers were asked to do untenable things. And the expectation was crazy. And I think what you were telling me is that you saw a lot of teachers kind of being patted on the head, and almost like kind of spanked a little bit like, "Remember your 'why'. Come on! Suck it up! Do the thing!" And so, let's be really clear, that is not what we are suggesting that we're going to do in this episode. We are not telling you teachers "Just remember your 'why' and everything will be okay." I do think that when life gets hard, it can be helpful to remember why we went into education. But that's a helpful thing for us to dredge up inside ourselves. I don't know that it's ever a helpful thing for someone to pat you on the head and say, "Remember your 'why', sucker. You went into teaching."
You know like, "Suck it up!" No, that's never helpful. So, that's not. No, not what we thought.
So, what do you think Alisha meant when she...
Well, when she said it to me, my first wonder was if she was saying, "Teachers need to understand why to change. Why algorithms are not our goal. Why they're not good." Like, we even say in the beginning that rotely repeating steps actually keeps students from being the mathematicians they can be. But they need, teachers need, to understand that. That why teaching for reasoning is better than answer getting. And something about the change thing. You know, Kim, I was just recently in a workshop where somebody suggested, "Never tell people to change. People don't like to hear that." Like, just the word "change" people kind of bristle. I don't know, listeners, do you agree with that? When I say, "Hey, change," do you go, "Who are you to tell me to change?" Like, "What do you think you know?" Or you might, even if you respect the person, you might be like, "Don't tell me to change. Like, change is hard. And life is hard enough. And I'm doing the best I can." And you can almost have kind of the response of "Don't you believe I'm doing the best I can?" Like, "Don't tell me to change." And so, that I kind of took that to heart. You know, I've started to think about some of the ways that I say things. Because I was kind of usually up for change, but I know that not everybody's kind of crazy like me. They don't like to change everything on a dime. Like, if I ever saw something that I really thought was a good idea. I'll give you a short example. I was a very young teacher. I went to my first NCTM regional conference. I heard Gail Burrell give a workshop. I didn't know who she was at the time. I walked into her session. I had just been to two or three sessions, and honestly, I'll be clear, I was not that impressed with. So, as a young teacher, I was really hungry. I had been in a really amazing environment in my first school that I taught in. And I had just moved. I was in my third year of teaching. I was in a brand new school. They were very nice people, but it was not quite the collegial, generative, where we were working together and kind of coming up with ideas. It wasn't collegially working together atmosphere. And I was missing that. And I thought, "Well, I'm going to go to this conference, and I'm going to get it there." And the first few sessions were not that, and I was kind of disappointed. And, you know, I was like, "You know, I really want to learn." I don't know that I would have said I wanted to change. But maybe. I wanted to change math classroom the way it had been, the way I had taken it, the way, you know, been taught to me. I'll never forget sitting in her session, where she started to do the "guess your age" task. So, if you've been in our Building Powerful Linear Functions online workshop, you've seen us do that "guess your age" task, where basically you throw out a famous person, then you say, "How old do you think they are?" and then the person guesses. And then, you throw out another famous person. Now, you've got a list of a few famous people. You've guessed how old they are. And then, she started to then after we'd guessed, I don't know, 10 or so famous people's ages. Then she said, "Well, did you know that this famous person is actually this old? And then, this famous person is actually this old?" And you can kind of almost hear the room, you know "Ooh", "Ah", or "I got that one right!" or "Woah, I was way off!" and "Who even is that?" And, you know, kind of people are back and forth. And then, at the end of that, she said, looked at us with that calm, Gail Burrell. Oh, I love Gail. She's awesome. She's calm, quiet, kind of cocked her head, and she goes, "Ya'll, how would you..." I don't know if she said "ya'll". She's from the north. Probably didn't say "ya'll". But she said, "How would you know if you're a good guesser?" Kim, I was like, "Oh my gosh!" Like, instantly I just had this flash of insight, and I was like, "This is an amazing task!" Because we could talk about you know, you're a good guesser when your input is equal to the output. And if you could see my hands right now, I just went over the same amount I went up. And I was like, "That is like the line y equals x. She's going for line y equals x. Like, the parent function of all parent functions. She's going to build the line y equals..." And I had thought about the fact that all the functions were built off of the parent function, the line y equals x, but I'd never considered how I could build the line y equal x. I just started there. I was like, "Hey, here's the line y equal x. Let's build the rest of them from there." Kind of what we don't advocate, right? Like, just telling kids something. But I never even had thought about how you could build the line y equals x. And in that moment of mathematical insight, I was willing to change. I went back to my classroom, and on a dime, I did that activity for like three days. Now, it didn't take three days to do Gail's version of it. But I did it, and then I built on it, and then I built on it. I innovated, innovated, innovated. And then, I took a deep breath, and I was like, "Okay, back to what I usually do." Because, you know, I could only stretch it so far. But in that moment, I was totally willing to change. So, when Alisha said, "Why do teachers need to change?" I thought, like how do I tell? How do I help teachers understand that for me I'm... I don't know. I'm always on the look for that flash of insight, where I go, "That! That would help everybody own this thing! Oh, let's do that!" Like, "I want to own that the way this person just kind of helped me own it." Like, "Ooh, I could do that for my students." So, I kind of got excited about, well, could I help teachers understand? If that's what she means, could I help teachers understand the "why" to change is well, frankly, so that they can help their students math, the way we just math. So, Kim, when I do a workshop, when I do a presentation, even a keynote, people are always telling me, "Your keynotes are really different." And I'm like, "What do you mean?" And they're like, "You're so interactive. Like, you do math with people." Oh, hey, that's back to the "what", right? Like, I always do some math. But in that doing that math, it is to build content. It is to really get like the math out there, the "what" of the content. But in a huge way, it's so that people have an experience in mathing. It's not just so that you learn another strategy for multiplication. It really is so that you... If that's my first task that I do, you know, in the presentation, in the keynote, or whatever. If the first thing I do is a multiplication Problem String, my goal at the end of that Problem String is to be able to say, "Hey, this last problem we just solved? This last problem? If when you walked in the door today, if you wouldn't have solved it this way, you just mathed." Like, "You just did real math because I didn't tell you steps to do. I gave you problems in a certain order. We did a Problem String. And you found a pattern as we were doing that string of problems because of how we were making things visible and how we were discussing and sharing strategies. That by that last problem, your brain was thinking in a different way. You literally we're creating new connections, and you were able to use that pattern to solve that problem in a way you'd never thought about. Bam! That's mathing." So, I always do that first experience A, to get at content. But B, to get at that "why", so that teachers can go, "Wait a minute." Like, "That's mathing?" Like, "What we just did? That's what mathematicians do? Huh. Well, I just did that. Are you saying I could do it with my kids?" And then I say, "Yeah, you can do it with your kids just like that. Like, you can teach..." In fact, I'll boldly say. You can teach all math that way. Like, all math, as long as it's not social. So, we've talked about that a little bit. As long as it's that logical math, which is most of math. We can teach all math by having kids reason, building their brains to think and reason more. So, if her "why" was that teachers need to know the "why" to change, why algorithms aren't good, why teaching for reasoning is better than answer getting, I would suggest because it's Real Math. It is the thing that mathematicians do. And so, I am about the "what", and the "how", and that "why". That "why" because we can actually math the way mathematicians do. So, Alisha, what did you mean when you said the "why"? Were sort of curious. Either way, though... Well, Kim, before I was going to kind of finish up. Is there anything else you wanted to add in?
I was just going to say. You kind of went there. But what you are trying to do for other people and with other people in workshops, and presentations, and whatever, is kind of duplicate that experience that you got as a young teacher, where somebody put you in a position to find your own need to change. You saw something that moved you. You latched on to that. And instead of you telling people why they need to change, which never works, you're also trying to do the same thing. And in whatever setting they're in, put them in a position where they are motivated to change because they see a different outcome that's possible.
Absolutely. Yeah. Yeah, I really like how you said that. Because I was able to have experiences that actually changed the way I thought, that is exactly what I'm attempting to do with the "what", the "how", and the "why" is give teachers that experience. Yeah, nice. Alright. So, Alisha, what did you mean? But either way, whatever you met, we need to think about the "how", the "what", and I'm thinking my version of "why", but for sure some "why". Ya'll, let's affect the way we teach. See, I just didn't say change. Let's tweak. I don't know, I'm trying to say "change" because I don't want to make it this big whole thing. Let's all help our students grow their brains to think and reason like mathematicians just a little bit better than we were yesterday. How's that? Is that better than "change"?
Alright, cool. Ya'll, thank you for tuning in and teaching more and more Real Math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able!