Ep 145: Transforming Teaching: Small Shifts, Big Impact

Pam: 0:01

Hey fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.

Kim: 0:08

And I'm Kim.

Pam: 0:09

And you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But, ya'll, it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. We can mentor students to think and reason like mathematicians. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be.

Kim: 0:37

Okay, so if you know Pam at all, you know that she is full of ideas. Always the ideas, right? Like, there's always a new thing. There's a great idea. So, much so that we're constantly busy trying to get things done. And some of our Journey members or people who have been in a workshop, when they hear her talk about something that we're working on, they will send a little message that says, "Hey, Kim, is that like a coming out in six months thing or like a coming out in two years thing?" Because they know that there's always something going on. So(unclear).

Pam: 1:15

Because I'll be like, "Hey, it's about to come out." And they're like " 'About', this time. What does that mean'about'?"

Kim: 1:21

Right.

Pam: 1:22

Yeah.

Kim: 1:22

Right, right. Well, we are super excited to announce that we have just launched something brand new, and we're very excited about it. So, we decided that in this episode, we were going to just spend a little bit of time talking about the new thing. And I'm going to just ask, Pam, you some questions about our new thing. And we'll get to it in just a second. But I'm just going to ask you some questions, and, if that's okay with you.

Pam: 1:47

Yeah, absolutely.

Kim: 1:47

And just to give us a little bit of insight about what it is, and why we're doing it, and a little bit about what's going on, so that the listeners will know what's new and current in the world of Pam Harris. Okay?

Pam: 1:59

And, ya'll, I'm so excited about it!

Kim: 2:02

Yeah!

Pam: 2:02

I'm so excited. I'm brimming over, overflowing with excitement for this super new. Can I announce it? Can I say it? Can I say?

Kim: 2:10

Yeah, go for it. Yep.

Pam: 2:11

We have launched a new mini workshop, an online workshop for everyone to take. But it's a mini workshop, so it can be bite-off-able. And it will help you address the most, the main important things to get right as a math teacher. Yeah, absolutely. I'm so excited about it.

Kim: 2:33

I'm glad you said that because it is about kind of the main things. And (unclear) if we have a great word for what the things are, but kind of the major components or the major things that you have to think about. So, that's actually a little bit about what I'm going to ask you about. So, first of all...

Pam: 2:49

Yeah, let's dive into it.

Kim: 2:50

...why is this thing a mini workshop? And not you... You absolutely have some full blown workshops and longer ones. Why a mini workshop?

Pam: 2:59

Yeah, so we created deep dive workshops because we realized that I wanted to help teachers really dive deeply into content, and so my deep dive workshops are very specific. It's a specific kind of content. Building Powerful Multiplication, Building Powerful Division are a couple of examples of where we really dive deep, and so they are longer. And we take the time to really develop those big overarching, major ways of thinking, ways that mathematicians reason about problems. But we also realize that there are some very important things that we could get the ball rolling, that there are some things that could help teachers clarify those major points, where we're missing in math ed today. There's these major things that people are just kind of not quite clear on and because of that are missing a mile wide, and we're not getting the results that we want. And so, we wanted to give a mini experience, so that more people would have an opportunity. It's shorter. It's much shorter. So, it's a short burst, it's less expensive, and it will give more people an opportunity to get started in the Math is Figure-Out-Able movement. But not only get started. I don't want to sound like it's an intro. Though, it is. But it's also a way to focus on the major, important things that people are missing, so that we can get those right. Then, it makes where we're able to dive into those deep content areas even better.

Kim: 4:31

Yeah, absolutely. So, one of those things, those topics, those ideas that people sometimes miss just a little bit is the idea of why strategies versus algorithms, and that's going to be a portion of this mini workshop. You want to talk about that for a second?

Pam: 4:49

Yeah, we're going to dive into the difference between algorithms, mathematical algorithms, and strategies, sometimes called alternative strategies. This is a place where... It's kind of odd actually. There are some really good math teacher educators out there that are using the word"algorithm" wrong. They'll say,"Oh, you know, student generated algorithms." I'm like, "No, you don't mean that, you...""Algorithms" is a very specific definition, and when we muddy the water, and we don't understand the difference between strategies and algorithms, then we don't know when to use which. And we also don't know why strategies are so important, and why algorithms are amazing historical achievements but not really very good teaching tools. And if we don't understand the difference between them, then we don't understand the reason to lead away from algorithms and to dive into strategies. So, we're going to parse those out.

Kim: 5:46

Another topic that is going to come up in the mini workshop is one that we've actually addressed a little bit here on the podcast because we both recognize and have noticed that this comes up in teacher's classrooms a lot. And it's the idea of models versus strategies. And so, that's going to be another part of the mini workshop as well.

Pam: 6:07

Yeah, and I'll give Cathy Fosnot some credit for really helping me start to think about the difference between strategies and models. And this is a really important distinction for teachers to make because if we don't, then we have this muddy water out there where we might say, "How did you do it?" And the student says, "I did a number line." And a number line is a model. In that case, in that point, we want teachers to be super clear that they need to say, "Oh, okay. Well, what did you do on the number line? Which relationship were you focused on?" That's the strategy. Similar to other important models out there. And if we're not clear on the difference between models and strategies, and the difference between strategies and algorithms, then we might tend to just teach a model as a new algorithm. And that's a place, a miss, that we're seeing good teachers that are honestly trying to interpret what's happening in their textbooks and what they're being told to do by their leaders. They're like,"Okay, now I guess I'm supposed teach the steps with this box. Alright, you guys learn these new steps." Or they might be misunderstanding the purpose of models. And the purpose of models is to make thinking visible. And then, some good models we can then help them become tools for reasoning. Not tools for following a bunch of memorized steps, but tools for actually reasoning because it helps us illuminate the relationships, it helps make the relationships more clear because they're visible. If you can see my hands right now, my hands are in the air, and I'm like showing that we're making the relationships visible. So, understanding the difference between really those three terms. What's the difference between strategies and algorithms, and then what's the difference between strategies and models really helps teachers clarify, "Oh, that's why my textbook is asking me to do this or my leader is suggesting I do this kind of a thing." That clarity then helps everybody be like, "Okay, now. Now, I can move forward clearly."

Kim Montague: 8:08

Yeah. It's so good because I think sometimes it's real easy to throw out some of these words and expect that everybody is on the same page with what what they mean.

Pam: 8:17

Yeah, so often we're not.

Kim: 8:18

And use them interchangeably, but it's not true, right? So, another.

Pam: 8:22

Well, and it's nobody's fault just to be clear.

Kim: 8:24

No!

Pam: 8:24

It's nobody's fault. It's vocabulary, and it's tricky stuff. And so many good people looked at kind of what's been coming down the pike with new standards, and they're like, "I don't really understand what the..." You know, the words. if they weren't clearly elucidated... Well, let's be clear. If we don't own Real Math, then looking at Real Math is going to be... Or looking at words that mean Real Math. But we might read fake math because of our experience. Yeah, we just need to... We need to gain the experience in Real Math. And then, now, being more clear, we can actually move forward with the Real Math, not just attaching fake math to some new dressing.

Kim: 9:04

Yeah. I'm actually really glad that you mentioned the standards a few seconds ago because one of the other components of this mini workshop are going to be kind of what are the major strategies for each operation, right? And so, sometimes when people look at the standards, then they'll say,"And other strategies," and people are like "Which? What? Which ones?" And so, you're going to touch on that as well. Do you want to talk about that for a little bit?

Pam: 9:31

Mmhmm. There's this huge, really cool moment actually when people start to learn Real Math, and they realize there are alternative strategies. Or maybe their textbook says, "Here's a bunch of strategies kids should learn." Or, you know, maybe they're either in professional learning, and they're seeing that there's these alternative ways. Maybe they've done a number talk, and they're like,"Whoa, there's all these different ways that people are solving these problems." It could feel really unwieldy. It can feel like there's this innumerable, not clarified. My hands are kind of swimming in the air because it's like this vast universe of all these different relationships. Like,"How in the world am I ever supposed to teach that?" Especially, I think many people have been in a number talk when, you know, six different people share a strategy, and your mind's kind of blowing a little bit, and you're thinking, "I can't teach that." Like, "How do you... Am I supposed to teach the steps for them to be able to do all 18 of what just happened?" But what my work entails is that I've distilled down the major important relationships that mathematicians use when they actually solve problems. And there's just really a small set. It's just really this very definable set of major relationships that we need to help students construct in their minds, so that then major strategies become natural outcomes. And it's not a ton. It's not innumerable. There's not so many that we can't fathom them. There's really just this very small set of major relationships that then translate into major strategies. And once teachers realize that, then it becomes doable. Then I can go, "Oh, okay." Like, "For this operation, I just need kids to build these four major relationships, and then these four strategies will become natural outcomes. Okay." Like,"I can do that. Alright, now I can wrap my head around it." And all of a sudden, Real Math becomes this thing that we can actually attack and gain success.

Kim: 11:32

Yeah.

Pam: 11:33

And not just success of right answers but success of actually mentoring mathematicians, students are actually thinking and reasoning more sophisticatedly than they were.

Kim: 11:42

Yeah. So, one other question that I have for you about the content of the mini workshop. We also hear a lot of teachers who talk about how they're doing number talks, or we call them Problem Talks. So, you spend some time talking in the mini workshop about Problem Strings versus Problem Talks and what you recommend as kind of the...

Pam: 12:07

Balance?

Kim: 12:08

Yeah, what you should do, and when, and how much.

Pam: 12:12

Yeah, so some really good people have written quite extensively about number talks, and I don't want to take away from really good stuff. But I think we can get more bang for our buck if we understand the distinction between a Problem Talk, a one time shot, one problem, maybe a couple of problems, where the goal is different than a Problem String, or a series of problems, where the goal is something else. And I suggest that if we parse out those two goals, that both goals are good and we need them, but we have somehow misunderstood that we can just do Problem Talks and get both goals accomplished. And I'm going to suggest not so. That if we want both goals accomplished, we need both routines, and there's a good balance that we need between the routines of what we might call a number talk. Well, I call it a Problem Talk. I call it a Problem Talk, ya'll, because I'm K-12. So, I don't just do talks about problems that have numbers in it. I do talks with problems that have graphs, and equations, and functions, and geometry, and statistics, and all the. Like, those are Problem Talks. We're talking about problems. So, we don't need to split that hair, but that's why I say Problem Talk. There's a difference between just... Not "just". But between doing a Problem Talk where I'm going to accomplish some things and a Problem String where really the outcome there is to build those major relationships that lead to those major strategies. That's where the construction happens. There's some other good things that can happen with Problem Talks but we really don't get those major relationships constructed. You might consider that if you are thinking about a number talk, or what I'd call Problem Talk that... I've thrown out a problem, and I'm asking kids, "How did you solve it?" and then putting all those different strategies on the board, that often an outcome is that this kid did way number one, and this kid did way number two, and this kid did way number three, and this kid did way number four. There's so much happening here because it depends. You have to understand models versus strategies to make sure that you're recognizing did you have really four different strategies? Or did you actually have two different strategies on two different models? Or were they all the same strategy, and they were all using different? Like, there's a lot of models and strategies to parse out there. But then, I need to ask myself, "Did kid one really construct kid fours strategy in that? By seeing one example of it, did that actually help them really develop those relationships?" And I'm going to say not most of the time. Sometimes some kids can pick up on that. But how can we get all kids to pick up on that? Problem Strings. That's where the series of problems come in. And we need to have Problems Strings not just Problem Talks. So, there's definitely a section on that in the mini workshop.

Kim: 14:59

Yeah, It's going to be great. So, let me just ask you a question that is probably on the minds of some of the listeners. And they might be thinking, "Hey, I know you just put out this major strategies ebooklet, and you've talked about it before, and you've shared it before. Why can't I just download that and call it good?"

Pam: 15:20

Yeah, because you're recognizing that each of the topics that we just talked about that's going to be in the mini workshop are in the major strategies, ebook. Bam! So,that's a super question. Well, we've had lots of people download. Thousands of people download the major strategies, ebook and love it, and we are getting fantastic comments back from it. But we're also getting a slew of questions about it. Because it's a mini ebook. Like, it's a free ebook that we put out, and it's all in writing. You're not hearing it live. You're not... Here's the most important part, you're not seeing it happen. You're not seeing the models being drawn. You're not seeing the order of the numbers in the model and what I'm thinking about first. You're not hearing the conversation about the "why", the kind of parts of what we just talked about here, and then the more in depth that we're going to go in the mini workshop. But in a huge way, it's the illumination of the concepts, and the ideas, and the strategies that are in the ebook now become live. In a way, it's a little bit of a comparison between say... Pick your favorite ebook that you've read, or a hardcopy book. You read the words, you do the thing. And then, picture that you get the audiobook. And when you hear the audiobook...especially if you've got a really good reader, or maybe the author is reading it, you can hear it in their voice and everything...you just get so much more out of it. But then, consider what if that was a full blown movie? Like, what if you're actually seeing it happen, and you're able to. You know, it's recorded. It's not live, but you're you're seeing the visual, and the sound, and the sight is making it all even pop all that more. That's why the mini workshop. So, ya'll if you've downloaded the free major strategies ebook, great. Like use, let's change the world with it. But if you'd like to have the film version of it, if you want to have the really the popped version, the boost that it can give you to... It'll definitely have more. It's not an audio book. I'm not just reading through the ebook. It's a lot of explanation. And mostly a lot of visuals, a lot of really being able to see what we mean. And again, more detail, more behind the scenes, more explanation. All the more. But to be clear, all keeping it within a mini workshop, so that you can do it in a reasonable, respectable amount of time and really gain clarity on those major misses that are happening out there that are just keeping really good teachers from getting the excellent results that they should be getting.

Kim: 17:56

Yeah. So, one other really, really important question for teachers, for schools, for anyone in the field of education is money. So, why did you pick such a low price point for something with such great value?

Pam: 18:12

Yeah, and we've put a lot of effort, and thought, and time, and all the. Like, it's a decent experience. You are going to learn a ton, but we wanted it to be affordable. We know that you're teachers. We know you have both limited funds and also limited time, and so we packed punch into this short, really powerful experience. We want to have the opportunity for schools to get lots of teachers on board, so that there's common knowledge across systems, so that we can start having common understanding, common language, common uses of models, and the vocabulary we use. So, we really wanted to make it affordable, so that we can really spread the word that Math is Figure-Out-Able. We really want to make it happen. Yeah.

Kim Montague: 18:59

Okay, so Pam, the last few questions that I have for you are like a rapid fire. We're talking about mini workshop.

Pam: 19:06

Oh, I love rapid fire. Okay, taking a deep breath. Here we go. Mmhmm.

Kim Montague: 19:09

(unclear) Okay. Favorite mini Blizzard flavor?

Pam: 19:13

Mini workshop, (unclear) blizzard. Okay, so Blizzard for those of you out of the country is as ice cream treat that we get around the country. Yeah. At the moment, I'm a Reese's girl, but I put chocolate syrup, so it's got to be chocolate ice cream with Reese's. It's all the chocolate (unclear).

Kim: 19:29

Okay, all right. Ready?

Pam: 19:30

Yep. Yep.

Kim: 19:31

Mini Muffin flavor?

Pam: 19:33

Chocolate. Do you hear a theme? Yeah, there you go.

Kim Montague: 19:40

Alright. What about a mini candy bar?

Pam: 19:45

Ritter Sport.

Kim: 19:47

What? What is that?

Pam: 19:48

Yeah, that's a German. It's kind of expensive, but it's super yummy.

Kim: 19:52

Okay, I never heard of it before.

Pam: 19:53

I mean, yeah. Yeah, they're kind of mini, and they're really... And way too expensive but super good. Mmhmm. Yep.

Kim: 19:58

Chocolate, chocolate, chocolate. Alright, ready?

Pam: 20:01

Yep.

Kim: 20:01

This one's not chocolate. Minnie Mouse or Mickey Mouse?

Pam: 20:05

Oh goodness. Alright, since we're in the mini workshop mode, let's just go Minnie Mouse. Why not? Woah!

Kim: 20:09

Alright, sounds good.

Pam: 20:10

Go Mini! Okay.

Kim: 20:10

Alright, you got any other mini? Any other minis in your life?

Pam: 20:13

Oh minis. I drove a Mini Cooper once does that count? Is that a thing? Let's see...

Kim: 20:18

Yeah, sure. Absolutely.

Pam: 20:20

Hey, my son had a Mac Mini that served him well for many years. That was a good thing.

Kim: 20:25

Mini, mini years.

Pam: 20:26

Mini, mini. mini. Ha, ha, ha.

Kim: 20:27

Alright, alright, last thought. Any last comment about this fantastic mini workshop.

Pam: 20:33

Ya'll register for this mini workshop at mathisfigureoutable.com/mini Ha! Do you see that one coming? mathisfigureoutable.com/mini is where you can register anytime. It's open all the time. We call that an evergreen. You can get in, and dive into helping you clarify what could be the thing that could be keeping you from being as successful as you deserve. There's just these few major important things that if we clarify, everybody can get more clear, and we can have more and more success. Alright, ya'll, thanks 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!