Episode #255: Math Is Figureoutable – An Interview With Pam Harris
Pam Harris is here and she’s changing the way we view and teach mathematics. She is a mom, a former high school math teacher, a university lecturer, an author, and a mathematics teachers educator.
In this session Pam is going to share how and why you need to use problem strings to get your students thinking and making connections among strategies. She’s also sharing insight into her 2023 Make Math Moments Virtual Summit session: Talking About Talking.
What You’ll Learn:
- Why and when you should use problem strings in your math class regardless of the age of your students;
- Why you should use already created problem strings before attempting to create your own;
- How to create your own problem strings for an upcoming topic;
- Learn 2 key teachers prompts you need to use when teaching with problem strings;
- How do you create discourse in math class that is not trivial;
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00:00:00:06 – 00:00:20:15
And that’s the beauty of math. If we’re doing what I call real math for really mapping, there is that interconnected deep things over here that maybe not everybody is going to get to, but it’s open enough that kids are ready for it. Have that experience. One that’s on my mind right now. You guys know your listeners might know I’m really interested in problem strings as an instruction routine.
00:00:20:15 – 00:00:22:17
So I think probably strings are.
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Hey, hey there. Math moment makers. Pam Harris is back and she’s changing the way we view and teach mathematics. That’s right. She’s still a mom because she was here last time. It was mom back then. She’s still a former high school math teacher, a university lecturer and an author and a mathematics teacher educator.
00:00:43:04 – 00:01:04:10
Hey, stick around. In this session, Pam is going to share how and why you need to use problem strings to get your students thinking and making connections among the strategies that you want them to learn. She’s also going to share some insight into her 2023 Make math moments, virtual summit session. That’s coming up this November. Her session is called Talking About Talking.
00:01:04:10 – 00:01:11:13
We’re going to unpack that session here for you so that you’re like, hey, I got to get over there. I got to get that free session that’s coming up. Let’s do this.
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All right. Let’s do some talking about talking. Welcome to the Make Math Moments That Matter podcast. I’m Kyle Pearce.
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And I’m Jon Orr, we are from makemathmoments.com.
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This is the only podcast that coaches you through a six step plan to grow your mathematics program whether at the classroom level or at the district level.
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And we do that by helping you cultivate and foster your mathematics program with strong, healthy and balanced tree. If you master the six parts of an effective mathematics program, the impact of your program is going to grow far and wide.
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Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence and get back to enjoying the planning and facilitating of your mathematics program for the students or the educators you serve.
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All right. We’re excited to dive right in. So let’s go. Here we go with Pam. Hey there, Pam. Welcome back to the Making Math Moments That Matter podcast. We had you. Oh, it’s been a while. You presented and a few of our make math moments virtual summits over the years but stretching back I think it was episode 7071 which is a while ago because this is episode 255.
00:02:36:06 – 00:02:44:05
So it’s been a while that we’ve chatted with you here on the podcast. We thought, Hey, we got to bring Pam back. How are things going in your world?
00:02:44:07 – 00:02:58:15
Well, I’d like to thank you guys for having me on. You guys do a fantastic job. I don’t recommend too many people watch, but you guys are on my list, so that’s a job. Thoughtful people. And I really appreciate that you think about what you’re doing. That’s excellent.
00:02:58:17 – 00:03:09:03
I love it. I love it. We always love running into you. I know the last time I saw you, I think in the flesh was, I think last year, what, NC S.M. Maybe or something.
00:03:09:03 – 00:03:11:02
You didn’t see a smile on when.
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Ran into each other at a restaurant?
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Yeah, we were at the restaurant, we were out, and then of course, we had some laughs that evening, hung out for a little bit and then I got to check out your session as well, which again I always love your approach. You’re real and always great to catch up with you. So hey, tell the math moment makers what the heck is new in your world?
00:03:32:19 – 00:03:37:07
I mean, has math changed since the last time we talked or is it still figure out a ball? Tell us about.
00:03:37:07 – 00:04:00:18
That. Math is still figure out of all. I got them. Yeah, maybe more and more. Part of what I’ve done is I started as a high school teacher and thought I knew high school math and then really got into technology and graphing calculators and was able to play around a whole lot more with things and test conjectures. You can’t do that when you wrote Memorizing and Spitting out rules, which is what I did as a student.
00:04:00:20 – 00:04:18:11
And so it kind of figured out secondary math more so, and then had this huge experience where my own child was growing up really around kids. But my oldest for sure was blowing my mind with how he was thinking about math. And I’d never thought about math that way, and I didn’t understand why he wouldn’t mimic the teacher.
00:04:18:13 – 00:04:20:08
Right. What do you do? What he says.
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Isn’t that the right way to do it? That’s the way you’re supposed to do it, right?
00:04:24:07 – 00:04:40:02
Isn’t that the only way to do it? So he would invent his own. I was like, That’s not a thing. You don’t do that in math. And so that sent me into the research where I could really I was curious, can you teach arithmetic differently? Can other people do what he does? Can we actually teach kids to do that?
00:04:40:02 – 00:05:03:06
And we can. And I know you know that the universe opened up to me in younger math. And so then I kind of became an expert about building numeracy and from someone who had no numeracy at all. Then I learned to think and reason myself about numbers. And then I kind of grew up with my kids, learn to think and reason additively first and then multiplicative really.
00:05:03:06 – 00:05:30:18
And I built my own proportional reasoning and then I looked at secondary math again, high school math especially. And I was like, well, I thought I was really reasoning about math. And so a current interest of mine is that I’m really diving into, I’ve just done a whole thing at linear functions and I’m really diving into exponential functions in there, and then I’m going to go into quadratic functions and I’m just really thinking about sequences of tasks which I know you guys are interested in as well.
00:05:30:18 – 00:05:58:11
I think that’s one of the frontiers, is we’ve kind of had textbooks, we’ve kind of had done some textbooks, gave a shot at sequencing things, but not the way we are now. I think that’s a bit of a frontier to really think about having an open enough task that everybody can answer, but that everybody grows from. And then what does it mean to have the next task that everybody can still enter and can still grow from?
00:05:58:11 – 00:06:30:05
And then what’s the next? And I’m super interested in that. In fact, I was listening to one of your podcasts this morning, and one of the conversations was if you have a student who’s absent for a week, how can you make up that learning, make up the learning? And one of the thoughts that I had in that moment was that’s one of the things I’m seeking for, is not that I necessarily have something to hand that kid, but that I’m actually teaching in such a way that he folds kind of naturally in because there’s a place for him to enter where he is, and we’re going to keep cycling back enough anyway.
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I’m kind of doing.
00:06:31:00 – 00:06:46:12
I know I love it too, because your task that you’re describing, we’ve built our task. So that day two is a little bit of a math talk at the beginning, which is got some skills from day one. Students are naturally folding in whether they’ve missed a day or maybe even two days. They’re coming into that because they’re so low floor.
00:06:46:12 – 00:06:57:00
So what would you say? It sounds like you’ve done a lot of thinking over the last little bit. What would you say is the most surprising thing you’ve discovered in the last 12 months?
00:06:57:00 – 00:07:33:16
While Pam’s thinking about what I started to play on the number line with and it was funny how you described it because you you’re talking about additively the multiplicative the that proportional reasoning and understanding proportion relationship. When I started to do that on a number line and over this past year and really went down the rabbit hole of solving systems of equations in different ways on a number line where the type of division actually is, where the context drove the type of division that you’re using at the end to get rid of the coefficient that blew my mind.
00:07:33:17 – 00:07:53:02
I can tell you that because of this type of division that it’s going to look like that on a number line and you’re going to use that strategy. And if it’s that type of division, then you’re going to do this one over here. That to me was like, Oh my God, blowing experience and took a long time to do so.
00:07:53:04 – 00:08:09:05
You said you had three, but at least share this one. What was one that maybe? I think what John’s getting at is when you’re going down this rabbit hole and you’re trying to keep tasks low floor enough, it’s almost like you want them to be almost like wide, where you have this big idea that you want to focus on.
00:08:09:11 – 00:08:32:17
But the task allows for this width so that some of those students who miss some can still enter. And then the students that maybe are a little bit further ahead than others can still continue advancing. Everybody’s benefiting there. There’s got to be so many things that you kind of bump into and you go like, Oh, I didn’t recognize that or I didn’t realize or maybe I didn’t see how important that one thing was.
00:08:32:17 – 00:08:53:01
And that’s the beauty of math. If we’re doing what I call real math for really mapping, there is that inner connected deep things over here that maybe not everybody is going to get to, but it’s open enough that kids are ready for it. Have that experience, one that’s on my mind right now. You guys know your listeners might know I’m really interested in problem strings as an instructional routine.
00:08:53:01 – 00:09:14:22
So I think probable strings are super important and very helpful in helping kids. Really math, helping the average student know the way that math people think and the way that Matthew people kind of learn relationships maybe on their own. We can do that with all kids. And a way to do that is by using a string or series of problems to teach well.
00:09:14:22 – 00:09:36:06
So lately we’ve as a team at math is figure out all have been talking about structures of problem strings and I’ll give a lot of credit to car M and Rachel Lambert they did a session oh five years ago or so and CSM, I believe it was about probably string structures and I kind of hadn’t thought about it and a car left it alone.
00:09:36:06 – 00:10:05:21
Since then I’ve written a lot of problem strings, but we’re currently writing at our team here. We’re writing ak5 series of problem string, so there’ll be a third grade problem, string of fifth grade problem string and kindergarten book across strings. And as we’ve been writing them, we’re realizing that it really informs what we do. So when we say to ourselves, I want to talk about this strategy, this main strategy for multiplication, how can we really help kids develop the relationships necessary to be able to do that?
00:10:05:21 – 00:10:23:04
Strategy is kind of a natural inclination, and then it’s been super helpful to go, Ooh, do we want an equivalent structure? What does that mean? That means where the problems in the string are equivalent to each other. So an example might be we’ll see if I can give you a good one where I might say the first problems 15 times 18 go.
00:10:23:06 – 00:10:41:19
Students are 15 times 18. I might share a couple of strategies. It’s a rich problem. There’s lots of nice strategies. Of the five main multiplication strategies, you can use four of them at least, maybe even the fifth of the four of them to do that. So you might share a couple of those and then the next so 15 times 18, the next problem might be 30 times nine.
00:10:41:23 – 00:10:42:19
And like it.
00:10:42:19 – 00:10:55:05
And so you want kids to go, same answer. And the teacher goes, Huh, Probably just a coincidence. And then you give another problem. And at this point, depending on the numbers and I don’t have a memorize, but you might give a third one that’s equivalent.
00:10:55:07 – 00:11:00:03
To like 60 time or I guess four and a half wouldn’t be as fun. But yeah, but it would work.
00:11:00:03 – 00:11:16:20
Or go to the four and a half. Yeah. Yeah. So now you have another equivalent now that you would probably not do that in fourth grade, but you can do it fifth grader, sixth grade, and then you might do another set of two or three that are equivalent. And then you ask students what’s happening. That’s a structure in a problem string that kind of allows some things.
00:11:16:21 – 00:11:40:11
In fact, that equivalent structure is the one that we now have realized you use to help students develop equivalence strategies. What I mean by that, strategies like doubling and having an equivalent strategy is I solve the problem by creating an equivalent problem. It’s easier to solve. So another example might be if I have something like 72 -37, I might say to myself, I don’t want to solve that problem.
00:11:40:11 – 00:11:51:19
72 -37, I’d rather subtract 40. So if I think about the subtraction problem as the distance between those numbers, I’d rather solve an equivalent problem that when I say 72 minus.
00:11:51:20 – 00:11:52:11
00:11:52:11 – 00:12:13:12
37. Yup. So if I bump those up both by three, then end up with 75 -40. Bam. And is your problem to solve? That’s an equivalent strategy. So the shocker for me was, hey, to help students develop equivalent strategies, you use an equivalent structure of a problem string, but there are other strings. I want one more structure.
00:12:13:12 – 00:12:37:02
Well, you know what? Before you do, I do want one more. But I want to make a comment, too, because I think it’s interesting in the first string that you use because you were doing an off the cuff like on the fly, but it just shows how important to when you design a problem string. What’s really interesting, what I think is really valuable, you’ll notice in our problem base units, our math talks, our problem strings as well.
00:12:37:02 – 00:13:03:04
And some are structures that bring out this equivalence idea. Some are just seeking out a different behavior in the math. Whatever that purposes. The goal, though, is that as you design it, you would have probably in third grade, like you said, you want 15 and 18 year old go, okay, that works. And then 39 that works, and then you want 60 and four and a half and you’re like, Hmm, I guess I’m going to adjust that first one and I’m going to go back and I’m going to fix, you know what I mean?
00:13:03:04 – 00:13:22:14
So it just shows how with a problem, string all of the numbers, at least in a chunk, because sometimes the string might be long and then it might be in different chunks and some might be related and some might not. But when you do that, it’s all about that intentionality. And like you’re saying, you want kids to almost like bump into it, right?
00:13:22:14 – 00:13:40:14
And I loved your sort of nonchalant I do that sort of thing all the time where you just sort of like, Huh, that’s weird or that’s odd. And it’s like, Hmm, I like how you said, must be a coincidence. I’ve not used that one. But you use some of these ones where you’re talking to the kids and you’re playing it up like you have no clue what’s going on.
00:13:40:14 – 00:13:48:10
When in reality you thought long and hard about this exact string and why I’m doing it and what I’m going to say this. And it’s so, so helpful for kids.
00:13:48:13 – 00:14:12:03
We just did one that we were just talking Kyle, in our live Q&A session last night about working with exponents and the exponent laws and thinking about the quotient rule and how normally for a long time I just taught the rule, right? It was like, Hey, here’s the rule, use the role. And then it was me. Then these carefully crafted strings where, hey, when you simplify this or kids would just normally crunch the numbers with their calculator and put to the power of but they all came out to be one.
00:14:12:03 – 00:14:29:22
It was like 1111. It was like, oh, must be a coincidence that three to the power of four divided by three squared times three squared is one. That’s weird, everyone was one and it was like everyone’s starting to go like, Something’s up here. And let’s explore why it’s always one.
00:14:30:03 – 00:14:33:03
Mister or is pretending like he doesn’t know what’s happening.
00:14:33:03 – 00:14:46:11
Again, we have a super video of a string very similar to that, where the teachers walking around as the students are doing something. And her name is Abby Sanchez. She’s an amazing teacher and one of the students on camera goes, Look at that. Look. She’s doing it again.
00:14:46:13 – 00:14:47:13
How do you.
00:14:47:13 – 00:15:03:20
Have this look? Like noses that look on her face. It’s brilliant because we have the kids saying and then we have the camera on the teacher going, Right, That’s awesome. Kind of an inquisitive, kind of like you’re curious with them. You said a minute ago you kind of like, I’m kind of clueless. You can’t pull that sometimes, but you can also pull.
00:15:03:21 – 00:15:06:21
You think, Let’s dive into that. I’m curious about the two.
00:15:07:01 – 00:15:24:03
What exactly you think that there’s a pattern happening here that’s interesting and it’s like, you know what I love about math is that it’s all about patterns. What do you notice? What do we see here? What’s going on? Is is this related? Is this not related or how is it related? Or maybe there’s more to the story. And you said you had one more.
00:15:24:03 – 00:15:31:05
I want to make sure before we Segway, we’ve got a Segway idea here to chat with you about. You said you had one more string for us, so hit us.
00:15:31:09 – 00:15:49:21
So one more structure. I think we’ve identified about five structures. One of the other structures we often use, typical one we call helper clunker. I think we got that term from Kathy Falls. Now maybe where you get a helper problem and then one that’s harder to solve, but you could use the helper to solve it. So for an example might be give me an operation.
00:15:49:21 – 00:15:53:18
If I was subtracting, I might say something like 42 -20.
00:15:53:24 – 00:15:59:02
You start off with the lob ball, I call it like throw the beach ball and then you throw the curve.
00:15:59:04 – 00:16:09:14
And then you throw the curve. So 42 -20, 42 -1973 -30, 73 minus. And then I pause and people are like 29.
00:16:09:16 – 00:16:10:17
00:16:10:19 – 00:16:38:10
And I’ll say coach 28 like Exactly. You keep the kind of spark alive. You don’t want it to be too predictable. I want to say one of the thing before we leave this problem, strings, like you said a minute ago, are you’re super deliberate in the design or the questions I get asked a lot is hey Pam to just a bright problem strengths and we do do that in my journey membership we talk about how to write problem strings but the first step is do someone else’s pre-written problem.
00:16:38:10 – 00:16:39:02
00:16:39:04 – 00:16:41:03
Yeah absolutely. And that’s how what.
00:16:41:03 – 00:16:44:20
It means for how the facilitation works, why they wrote it the way they did.
00:16:44:20 – 00:17:08:13
100%, 100%. And one of the reasons is not only because you then get to experience and see these different structures, these different approaches, but one of the other things is like you’re going to learn a lot. That’s, I think, the reality. I learned so much when I started doing Problem Strings and you’ll notice in this conversation, for those listening, hopefully there’s more than just the three of us listening right now.
00:17:08:13 – 00:17:29:20
Hopefully more will listen. I I’m sure there will be a handful that will those who are listening, their math moment makers. You’ll notice we do talk a lot about how there’s number talks, there’s math talks. Some people just think of them as warm ups. There’s all these different terms. But a problem string to me is so specific and so important and so intentional.
00:17:29:22 – 00:17:55:10
You’re helping to emerge these ideas, which oftentimes were like things that you knew. It’s like, Oh, that’s obvious that that was true, but you never thought to use them to help you to solve problems. And that for me, was a big epiphany, especially when doing, say, subtraction problems like you just gave us there, where a nice little fastball down the middle and then the curveball comes.
00:17:55:12 – 00:18:16:03
That for me was a big epiphany and going like, Wow, I would have never used that strategy. I would have always use my go to strategy. And this is one of the other things that I didn’t recognize for a long time, but is really important when we do math talks. And I think this is going to be a great Segway to start talking about your summit session coming up in November.
00:18:16:05 – 00:18:56:20
But when we do number talks, often times what happens is and I noticed this was happening for me is I would do a number talk and I would ask students to solve these random problems, oftentimes disconnected, not structured in a problem string sort of way. And what you’ll get is you’ll get kids sharing various strategies and you almost get students where like they think the goal is to be as creative as possible instead of actually trying to be, dare I use the word efficient, but more or less like looking at what is happening and use what’s happening to their advantage.
00:18:56:22 – 00:19:31:08
And what you find is if you actually pay attention is you’ll start to recognize that kids start to sit and they start to use the same strategies over and over and over. And sometimes those strategies in scenarios that are not actually helpful, that they’re actually hard and actually making it more hurtful for them to use. But if we just have this loosey goosey number talk that everybody’s just sharing whatever, instead of having something intentional, What I recognized after doing Problem Strings was like, You know what?
00:19:31:10 – 00:19:51:05
I’m going to let you solve the first couple problems with any strategies you want. That’s the low floor ness of it. But now I’m going to push you to try this new one. We’re going to hone in on this new one. So if you didn’t fall for, like you were saying, doing the 72 minus or 42 -20, and then the 42 -19, like the adjustment.
00:19:51:07 – 00:20:08:07
The adjustment, that’s a strategy we’re trying to get them to do. If they’re not doing that, then it’s almost like you want to be explicit, or at least that’s what I would want to do. I go, okay, now I want to challenge all of you to try this new strategy. How many people can see this strategies working? Amazing.
00:20:08:10 – 00:20:26:19
Awesome. You’ve recognize it. Now I want you to actually do it because unless you do it, you’re just kind of using the same old wrench, chatty or tool belt, right? You’re pulling the wrench out every single time, no matter what it’s like. I want to give you another tool for the tool belt. You don’t have to love it and you don’t have to use it all the time.
00:20:26:19 – 00:20:44:18
But there will be times where you go, You know what? That one’s actually a whole lot easier to use than this one over here. What are your thoughts on that? Do you always have an intent to make sure that we elicit this specific strategy? Sometimes you’re like, let’s just kind of let them go. What’s your thinking on that?
00:20:44:20 – 00:20:48:05
So if it’s a rich task, then it’s a bit more let them go.
00:20:48:06 – 00:20:49:12
Yeah, for sure. I agree.
00:20:49:12 – 00:20:52:00
Yeah. If it’s a problem string, you’ve got intentionality.
00:20:52:04 – 00:20:52:18
00:20:52:20 – 00:21:10:14
Yeah, for sure. I tell you my two favorite ways to make it happen. Kyle, your way’s a fine way. My two favorite ways is as we’re going through the problem string, I might say. Did anybody use the problem before to help you? And then I might look. And if no one did, or if a few students didn’t, I might say, could you.
00:21:10:17 – 00:21:11:22
Kind of that push? Right.
00:21:12:02 – 00:21:28:08
And so even if they didn’t, then I’m going to say you saw the thing where you wanted. Did anybody use the problem before? I’m going to point out, and flashing did anybody use the problem before? And then I’m going to like, could you that’s one method. A second method is I’m going to be circulating as much as I can and be seeing what kids are doing.
00:21:28:14 – 00:21:45:12
When I see kids like you said, that are kind of stuck, they’ve got away. That got the answer that I might say to that student, Did you understand, John strategy? Yeah. And they’re like, Well, I got the answer. And I’m like, All right, we all had the answer. My question was, Did you understand John’s strategy? And they’re like, Oh, I wasn’t listening.
00:21:45:12 – 00:22:04:06
They’ll say, Oh, you can go and ask John, it’s okay, go ahead, ask John, and then I will do everything I can with all of my turn and asked John Fine, John, how’d you do it? And then as John starts to explain, I’ll be watching that kid. And when that kid’s like, and I’m like, You actually have to listen to John because I’m going to ask you I’m going to ask you how John did it.
00:22:04:06 – 00:22:11:19
And they’re like, No, I told you already got the answer. I’m like, Well, that’s all we do here. What we do here is we listen to each other. This is a good segway into my. It is.
00:22:12:00 – 00:22:13:14
Yes. You’re going with that?
00:22:13:17 – 00:22:30:00
Yeah. We listen to each other. And our job here is to understand how each other are thinking about it. And John used the problem before. You didn’t have to, but he did. And so can you explain what John was doing? So that’s a way to get it to be a little bit less of. All right, everybody do this strategy.
00:22:30:00 – 00:22:39:12
Okay. I’m going to command you now to do it. I’m going to say, no, no, you can do it anywhere you want, but you have to understand how John was doing it. So can you explain how John’s doing it? I don’t care how you did it.
00:22:39:12 – 00:23:01:10
That’s the other piece, too. I’ll say something very similar to that as well. When someone shares and having that pause moment and asking everyone saying, I’m not interested, if you did it the same way, can you see do you see how John did it? Do you see how John saw it? Do you see how John approached it? And it’s all about again, not about us mimicking each other.
00:23:01:10 – 00:23:20:20
That’s not what it’s about at all. If you did it in a unique way, amazing, we might share. But today I really want to hone in on John’s method here. Maybe you’re a thinker like John, but if you’re not, guess what? We’re going to try to help you think like John, at least in this moment, and maybe it’ll help you in a future scenario where you’re dealing with problems like this.
00:23:20:22 – 00:23:35:05
All too often I hear teachers say, No, no, no, this kid’s got a way. We’re going to let them do their way. We’re going to honor their thinking. And I’m like, Whoa, whoa, whoa. I honored their thinking because when we started off, we let them solve that any way they wanted that We honored their thinking. Now we’ve got to move the math forward.
00:23:35:07 – 00:23:43:00
They want to help them have choices. So like you said earlier, we don’t want kids sort of stuck in one method of thinking.
00:23:43:01 – 00:23:55:11
Getting really, really, really, really, really, really, really good at one way versus being really good at multiple ways. Flexibility, right, is what we’re after here. We want to get you flexible and fluent.
00:23:55:13 – 00:24:15:12
I think that’s perfect to talk about your session, Pam, because I want to talk about intentionality for a sec. When you’re saying this is what we do here in our class and these are the things that we want to emphasize, and it’s not just about doing the thing that everybody wants to see. Like, oh, I got discussion in my class, my kids are talking, but are they talking about the strategy?
00:24:15:12 – 00:24:40:01
I think talking about the math, are we pushing the math forward? That is a really important distinction, I think, about making sure that we’re engaging our students in, say, discussion, but also we’re making sure that we’re helping them make that connection to mathematics, that deeper understanding to mathematics with strategies and also in models. So your session coming up in our summit that’s happening in November is let’s talk about talking.
00:24:40:03 – 00:24:55:16
And it’s perfect because I think what I just said is that lots of people think we should get our kids talking, but it’s like, Well, how do I do it? And like, what are the most useful strategies to get my kids talking if they’re talking in class? Is that good enough? Or what is the best form of talk?
00:24:55:19 – 00:25:00:09
Fill us in on some of the insights that we’re maybe why you want to do this session at the summit.
00:25:00:11 – 00:25:18:00
Yeah, absolutely. So I’m going to tell you a quick story. When I was a high school teacher a minute ago, there was a movement in Michigan to write across the curriculum. At least it hit sort of high school big and hard. And we were supposed to write across the curriculum and these were in the days where I was still really pretty stuck in what I would call fake math.
00:25:18:00 – 00:25:29:07
Math was about mimicking. I was trying to help kids. We had lots of songs and rhymes and raps, because if you’re going to memorize stuff, I won’t help you memorize it. Well, then in that mode we had to write. So everybody was supposed to write in classes.
00:25:29:10 – 00:25:30:03
00:25:30:03 – 00:25:46:23
Like produce a written product. Guys in fake math land guys. I had no idea. I was like, What in the world are they going to write about? So to me, that is a very similar question to why are we talking in math class? Is math moment makers? That’s what you call you guys, right? Yeah.
00:25:47:00 – 00:25:50:21
They could be math majors, things, lots of atoms, lots of AMS. Yeah, all the EMS.
00:25:50:21 – 00:26:13:24
I would invite you to consider that if you think about math as a disconnected set of facts to memorize rules and procedures to mimic, then the question what to talk about is, I think, super tricky. I thought what is there to write about? But if math is about using what, you know, relationships and connections you own to reason through things that you don’t know yet, then there’s lots to talk about.
00:26:14:02 – 00:26:30:00
So one of the interesting experiences I had not too long ago is we were working with a small school and we were working with a small group of the teachers in that school. And as we were working with a small group of teachers, we worked closely with them. They were again, phenomenal things happening, lots of good conversation in their classroom.
00:26:30:02 – 00:26:57:04
They were also telling their colleagues the activities they were doing and so the colleagues were getting the activities, the tasks, but without any of the experience themselves about actually doing the task and realizing what it means to math. So kind of the second hand thing, as we went in and we were kind of working with the teachers that we were working with, one of the teachers said, Well, you go and just kind of check out how it’s translating.
00:26:57:06 – 00:27:01:24
What’s it looking like in the classrooms that aren’t part of our Does that make sense? We’re not perfect.
00:27:02:04 – 00:27:05:12
Oh, yeah. I’m going to guess it looked different.
00:27:05:14 – 00:27:26:20
Yes, it looked drastically different. And the picture I want to paint for you is I walked in and I sat in the back, really liked this teacher. The kids like this teacher, you could tell, was just a really good human being. There’s lots of good sort of karma in the class and everything. And then math started and the teacher would walk up and down the aisles and was doing one of our tasks.
00:27:26:22 – 00:27:50:18
And this is how the teacher heard productive struggle and talking in math class. The teacher said, Nope, not yet, keep going, and then moved on to the next kid. Oh, close. You can do it and then moved on to the next kid. And it was the difference. Here’s how I kind of described it. I felt like I was listening to a cheerleader, not a coach.
00:27:50:18 – 00:27:57:18
Interesting. Yeah. Cheerleaders don’t really actually help the team do anything better on the field.
00:27:57:20 – 00:28:00:18
I mean, they they get you hyped up energy.
00:28:00:18 – 00:28:02:04
They help the fans get excited.
00:28:02:04 – 00:28:29:13
Yeah, that’s a good analogy. A good analogy. And you know what, though? I will say this, though, is that the fact that I’m going to guess based on that picture you painted for me, that that teacher probably wouldn’t typically teach with a task usually. So that teacher was probably so uncomfortable going like, how are they going to do this when I haven’t taught them everything yet that they need to know They.
00:28:29:13 – 00:28:33:21
Don’t know how to do it, right? Yes, it’s in my head. So I’m a chairman.
00:28:33:21 – 00:28:57:00
Well, yeah, I’m just hoping and praying here. But they don’t have the rules and the algorithms and all the things that I normally would give them ahead of time. And on the other end to the kids are probably trained as many are, that that’s how math class happens. So they have this belief that I mean, it’s not even a belief, it’s a reality.
00:28:57:00 – 00:29:19:11
This is what math classes for me. And that must have been such a awkward situation to be in, Right. Like I’ve been there. I know exactly how that is. And it can be so difficult because as a mentor or a coach, you’re there and you can’t really go very far without going, Hey, can I hop in? Which is potentially offensive.
00:29:19:13 – 00:29:43:00
Right? But that is really interesting because in your session you’re going to be essentially talking about exactly that. And I feel like through our discussion with problem strings, but then also through a task based approach to teaching. Right. Whether you want to call it problem based lessons, whether you want to call it just, hey, we’re going to solve through task, whatever you want to call it.
00:29:43:02 – 00:30:17:21
The reality is, is that the talking is all about the reasoning, the conjecture, doing, the estimating, the wondering. Just all of those pieces make real math discourse sort of happen. And there’s still a lot of teacher moves and facilitator moves required in order to navigate that world and keep that flowing and do all of those things dynamically. But ultimately, at the end of the day, it really makes you wonder if our goal is that we’re going to teach those rules and procedures, like you said, and that’s sort of how we’re going to do it.
00:30:17:21 – 00:30:47:12
We’re going to mimic it. Talking is almost a bit of a waste of time because unless the kids are just going to recite it to each other so that they can memorize it better. Right? But ultimately you’re kind of wasting time getting to that goal of just memorizing a bunch of stuff. Whereas on the other hand, if students are actually talking and inquiring and they’re trying to see how somebody else sees it and they’re modeling it and showing strategies or demonstrating strategies, that’s true.
00:30:47:17 – 00:31:08:23
MATHEMA discourse. So if someone’s listening right now and they’re like, Hey, Pam, session, Pam session is going to be on Saturday, November the 18th, it’s going to be in the morning depending on where you are, because people from all over the world are going to be joining in. But I think your sessions around 11 a.m. Eastern ish Time, the last 1030 Eastern are awesome.
00:31:08:23 – 00:31:32:16
So if you’re on the West Coast, you’re going to be looking at, ooh, it’s a little bit early for them. I apologize to those friends, but we will also have those recordings going up after. So depending on where you are in the world, make sure you check it out. What would you say would be your big or your hope for the big takeaway that some of those participants are going to get when they come to that session called?
00:31:32:16 – 00:31:36:07
Let’s talk about talking with Pam Harris.
00:31:36:09 – 00:31:56:12
Yeah, one of the biggest things to walk away from are those teacher moves that you just talked about. What are the talk moves when we really want students reasoning and I’m going to employ several of them. The first thing that we’ll do in the session is actually do a problem string. As I do it, I’m going to kind of enacted a little bit and call out some of the things that I would do.
00:31:56:13 – 00:32:18:19
That’s a short experience. I’d also like to how I might use principles to actions and the move opposing personal questions, the difference between focusing questions and funneling questions. So I have a really nice task. We’re going to watch a video of an interaction, of an excellent focusing pattern of questioning and contrast that with a funneling pattern of questioning.
00:32:18:19 – 00:32:42:16
So a funneling pattern is where you funnel a kid to an answer and kids got it. But if you remove that funnel so the kid has a choice, they can either memorize your funnel or they’re lost the next time they get there. But if you can use a funnel in pattern of questioning, then students own that reasoning that they’re using and they can then use that reasoning the next time and they learn from it.
00:32:42:18 – 00:32:46:02
Those are probably two of the biggest things that are going to happen now.
00:32:46:02 – 00:33:07:14
If a teacher comes to the session and they’re going to get everything that you just said, what would you say is prerequisite? Imagine what would I need to know? What would I need to be able to be good at? Or what should I already have experience in or might be a barrier for me as a teacher to get the most out of the session that you’re.
00:33:07:14 – 00:33:11:14
Giving the listeners homework before the session? Kind of. Is that what you’re.
00:33:11:14 – 00:33:21:12
Yeah, right, exactly, exactly. I want to make sure that I’m prepared enough so that when I come to Pam’s session, it’s like, Hey, I’m ready to dive right in.
00:33:21:14 – 00:33:42:09
I would suggest I make this short homework. John So we’re not going to, like, turn anybody off? No, no, no. I would invite you to ask everyone you run into between now and then, the partners of 100. So and then your task is to listen and ask them how they think about it. So you literally just said, Hey, we need 100 and I’ve got 83.
00:33:42:13 – 00:34:01:06
What do we need? Total 100? What do we need to make a hundred? And then just wait. So if I’ve got 83, we need wait, wait, wait, let them figure it out. When they say 17 back, you say, how do you know? And then your task is to just listen. I didn’t know kids were thinking anything. I thought they would line those up and do some subtraction, and.
00:34:01:06 – 00:34:04:05
Some adults will, too. That’s the interesting part, right?
00:34:04:07 – 00:34:15:02
Especially if they kind of panic in math was all about mimicking the teacher and they don’t whatever. And then at that point, you can say, I mean, you can do that, but I’m wondering if you could think about getting up to 90 and then what would you need to get from nine?
00:34:15:04 – 00:34:16:10
00:34:16:10 – 00:34:18:15
Then and part.
00:34:18:17 – 00:34:19:06
00:34:19:08 – 00:34:45:01
So the more you can ask a fairly figure out question and then the task to get ready for the session is then listen and open up to the idea that you can gain from how other people are thinking about numbers. So see what happens when you try to nudge that person to tell you what they’re thinking and you’re going to have some successful experiences where people will actually tell you what they’re thinking and you’re going to have some experiences where they’re going to say, I was never good at math.
00:34:45:01 – 00:34:59:20
And then how do you handle that in that moment? What kinds of ways can you help settle their anxiety and help give them just a nudge for reasoning? Like when I said 83 and what can you get up to 90 or do you know 80 to 100?
00:34:59:20 – 00:35:07:12
Yeah, I was just going to say I’m like or like, do you know 80 or does 85 make it easier for whatever? Which super cool.
00:35:07:14 – 00:35:14:11
Was in between each of those and give you a chance in a low stakes environment to get better at eliciting thinking.
00:35:14:13 – 00:35:37:16
I love it. I love it. So something we talk about all the time in math class is about listening and observing and you giving this very manageable homework before your session I think is going to be so powerful for those who are listening and those who actually take you up on that offer. Because when you go down the rabbit hole with them in that session, they’re going to have all that experience, right?
00:35:37:16 – 00:36:02:20
And everything is so much better when you have the experience in doing something yourself. Hint, hint, just like our students gain more experience, more value when they’re doing math themselves and actually reasoning improving through it. What a cool, cool way to set up for that session, which once again Friends is going to be at 10:30 a.m. Eastern time on Saturday, November 18th with Pam Harris.
00:36:02:20 – 00:36:26:14
She’s going to help you show or understand or believe that math is truly figure out a ball. Pam, for those who are curious and want to maybe do more homework, maybe explore thing more about Pam, where can they find you? What else do you have out there that they might want to explore? In the meantime, as we look ahead to the virtual summit coming up in just about a month?
00:36:26:15 – 00:37:00:13
Yeah, absolutely. So math is figure out a little dot com has all sorts of free resources you can click on at the top of the thing. It’ll say free resources or learn. Now lots of free problem strings. We also have other instructional autism. I call it as close as it gets in relational thinking, some kind of opener quicker problem talks nice so math is figure out table dot com and announcing the day this podcast dropped so you guys told me October 16th 2023 I am opening a brand new mini workshop called Teaching Place Value.
00:37:00:15 – 00:37:22:11
We recognize that place value so often in most of the resources looks like place labeling, which is necessary but not sufficient. We do all work to do all the stuff it’s called place value. And then we’re like, guys, kids only know place value. And so I would suggest that’s because really that work was all about labeling places and not really helping students and.
00:37:22:11 – 00:37:25:24
Not really valuing what place value is all about.
00:37:25:24 – 00:37:44:07
Yeah, exactly. Yeah. So they love it. It’s the short mini workshop that we’ve got out. You can find that at math is figure out a bill.com slash mini. As for many workshops, yeah, mouth is forever dot com slash mini is where you can find that. And you guys know I also have a podcast so you can join me on the math is figure out a whole podcast.
00:37:44:07 – 00:37:59:16
That’s a fantastic place and I think we will see each other and CSM and CTM, so that would be fun. If anybody wants to come and hang out there. As Kyle said earlier, that was a fun place. John I know I saw you at a conference about a year ago. I thought, Well, yeah, those are always fun to catch up there.
00:37:59:16 – 00:37:59:22
00:37:59:22 – 00:38:18:09
Awesome. Awesome stuff. Thanks, Pam. We’ll put all of those in our show notes page and the next time we see you will be in November or before that actually be at NCC. But after that, we’ll see you over in November at the Make That Moments virtual summit. So, Pam, thanks so much for joining us here this evening. And have a great rest of your week.
00:38:18:11 – 00:38:19:01
00:38:19:03 – 00:38:47:05
Take care. Well, they’re math moment makers. Wow, what an awesome episode. It was great to dig in, dive down the rabbit hole, starting with this idea of problem springs, but really leading us towards the big topic of Pam’s virtual summit session, where she’s going to talk about talking and really some of the big, big pieces that I took away from this conversation that I know we’re going to come out through that session are that, you know what?
00:38:47:10 – 00:39:19:04
Talking is all about the reasoning, the proving, the conjecturing, the call it math fights that ensue in our math classroom. And what I think about our math program and the tree that tree we’re trying to nurture, that getting balance strong, trying to get this thing nice and nurtured. I’m thinking about a number of things here. I’m going to argue, though, when you think about problems, strings, while there’s a pedagogical approach, so we could talk about the branches of the tree.
00:39:19:10 – 00:39:47:23
So of course, that’s one part of the tree we could talk about. Problem strings is like resource because as Pam mentioned, starting with other people’s resources. So there’s intentionality is really key. But I’m going to say the part that is probably most important to me and I think one of the biggest things that shines through when you use intentional problem strings like we were discussing today, is the roots of the tree that were actually explicitly emerging.
00:39:48:04 – 00:40:24:05
The ideas, the big ideas, the behaviors of the mathematics were eliciting strategies. And most often we’re trying to use a specific or a particular model to try to bring that strategy and those behaviors through. So today we talked about a lot of our math program tree, and hopefully our math moment makers are excited to continue nourishing their math program tree when they join us November 17th, 18th and 19th, 2023, at our fifth annual virtual summit.
00:40:24:05 – 00:40:56:02
If you’re hearing this after the fact after November, guess what? All of the 30 plus sessions are available Insider Academy and that puts us at over a 100 past virtual summit sessions inside the academy, along with our ten plus make math moments courses and our 60 plus problem based units and full teacher guides. I’m telling you that Academy is bursting at the seams with mathematical amazingness, and if you’re not a part of it, I think you’re missing out.
00:40:56:02 – 00:41:13:03
So join us at that virtual summit. If you’re hearing this before, before it begins November 17th, 18th or 19th, or make sure that you are an Academy member so that you can experience it at your own pace any time after the fifth annual summit.
00:41:13:05 – 00:41:33:10
So be sure to head on over to Summit Dot, make math moments dot com, Get yourself registered and you’ll be thanking us later. So we want to thank you, though, right now for joining us here, taking time out of your day. Put your earbuds in. Listening now while you’re driving. Maybe you were on a run or on a bike ride and you listen to us talk with Pam.
00:41:33:10 – 00:41:50:02
We want to thank you for joining us here. If you haven’t yet already, I know that you probably have like a bunch of people. You’ve left a rating and review on your favorite podcast platform was on Apple Podcasts. Or if you’re listening like I do over on Spotify, you’re leaving a rating and review over there. Leave us a rating.
00:41:50:02 – 00:41:56:02
Review It helps us out, helps teachers out, it helps students out. So please do us that solid.
00:41:56:04 – 00:42:32:00
I love it. And friends you can head over to make math moments dot com forward slash Episode 255 because guess what? It’s the 255th episode of the Making Math Moments That Matter podcast. So once again head over to make math moments dot com forward slash episode 255. You’ll see all those links, all those resources, those transcripts and hey, we’ve got a link there for you to enter the share the summit giveaway if you want to jump there right away to win up to, I should say, over $15,000 worth in prizes.
00:42:32:01 – 00:42:32:17
00:42:32:18 – 00:42:49:05
Yes. Wow. $15,000 of prizes you can head over to make math moments dot com forward slash giveaway and that will bring you directly to enter that draw. Well, my friends, until next time I’m Kyle Pearce.
00:42:49:05 – 00:42:50:13
And I’m Jon Orr.
00:42:50:15 – 00:42:53:08
High fives for us.
00:42:53:10 – 00:42:59:23
And a high five for you.
00:43:00:00 – 00:43:03:02
The opera singer
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