Pam  0:01  
Hey, fellow math-ers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam, a former mimicker turned math-er.

Kim  0:09  
And I'm Kim, a reasoner who now knows how to share her thinking with others. At Math is Figure-Out-Able, we are on a mission to improve math teaching.

Pam  0:17  
Because we know that algorithms are amazing historic achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.

Kim  0:33  
I was going to ask if you did it in one breath.

Pam  0:36  
I did. 

Kim  0:36  
I think you did.

Pam  0:38  
Could you hear me take a deep breath? 

Kim  0:39  
Yes, I did. It was...

Pam  0:41  
I was like, "Do I have the singer's breath?" You know, because when you take a singer's breath, you take a huge breath, and then you use your core to like keep it going. And I was like, "I got core. Keep going, core, core, core." I made it. I made it till the end.

Kim  0:55  
Hey, in this podcast... Oh, man. We teach you about breathing and math-ing, building mathematical relationships with your students, and grappling with mathematical relationships.

Pam  1:07  
We are so glad that you join us to make math more figure-out-able.

Kim  1:11  
Oh, man. I feel like today's going to be a mess. In this episode, we're taking a look back at some episodes where we've chatted about important topics for you, leaders. We're digging into why we believe so strongly about creating experiences between teachers and between teachers and leaders. Why names matter. And our take on algorithms and manipulatives. Keep listening to find out more. So, we recognize how important it is to have these shared experiences as we've kind of grown together. And as a coach, right, you have the benefit of getting outside of the walls of a single classroom. And because of that, I had the opportunity to see all kinds of different teachers and how they were continually improving their craft. And so, when someone would talk with me about wanting help in a particular area or some specific part of their classroom, I had the benefit of knowing who on their campus would serve as a great model of that particular thing. And so, sometimes it took some scheduling, but I would go in with that teacher who wanted to grow, and we would observe together the teacher who kind of excelled in that particular area. And I'll be honest with you, Pam. It took me some time to learn this. That I couldn't just watch that teacher who wanted to grow in an area. I couldn't just watch their classroom and send them off to watch alone. And as much as I wanted to be helpful, I finally realized that that wasn't the most important thing. Like, let me watch your classroom and you go watch them.

Pam  2:39  
Okay, I just wanted to clarify. So, you're saying that in the beginning, you actually thought, "I'll just take care of your kids."

Kim  2:45  
Sure, yeah. 

Pam  2:45  
While you, "Here, go watch that teacher do that thing."

Kim  2:48  
Right.

Pam  2:48  
"And now, you've got it. You saw it happen. Bam, instantly you've, you've achieved that thing."

Kim  2:53  
Right.

Pam  2:53  
Tell me more. Like, so what was it about you and the teacher doing it together that made the difference?

Kim  2:58  
Well, so I think it's really interesting because sometimes again people don't not do something because they go, "Oh, I just want to be less than in that area. You know, I mean, it's a thing. I kind of just don't want to do that."

Pam  3:14  
"I refuse. That would take too much energy. No, I can see it's better, but nah."

Kim  3:19  
Yeah. That's not what's happening with teachers. So, it took me a moment to realize, oh, so I need to be alongside them, and we need to have some conversation. So, like sitting in the back of the room and pinpointing certain moments where those small things are happening that make the big difference.

Pam  3:43  
Like calling out those small moments. 

Kim  3:45  
Yes.

Pam  3:45  
Making them a thing, putting some words around it, having that shared conversation around it helps sort of solidify and create that move as a thing. 

Kim  3:56  
Yeah, and so then once we've had this shared experience, we could watch together. We could whisper together. We could pinpoint different things. We could take notes and confer. And then we could go back. And because we had this shared experience, we could make a plan. We could talk about how we were going to implement into that classroom the things that we saw together. There was no discussion to be had if I just sent them off alone.

Pam  4:23  
Right. And having that shared conversation reminds me of what we've talked about, where we all know we can do more than we can say clearly, and we can talk about more than we can represent clearly. And even sometimes when we see things and we have some ideas in our head, but talking about it, having that shared conversation and putting words to it and descriptions to it, and having the conversation and creating that shared meaning makes it more of a thing. Now, it's a thing we can talk about. Now, it becomes those keywords and code words and quick descriptions that then you can say, "Okay, so now that we know it's..." Well, it probably doesn't come in that soon. But it starts to gel, right? Starts to gel into a thing that now you can make the plan, like you said, to actually have it happen. And then when the teacher gives it a go, you can go, "Oh! Now, I see what you heard, not what I meant." 

Kim  5:13  
Right. 

Pam  5:13  
Right? Like, "Let's talk about that." And now, gives you a chance to sort of go back and forth, and continue to build, and all the things. But the part we want to emphasize today is that there's the part of shared experience.

Kim  5:25  
Right.

Pam  5:25  
That we need to have a shared experience that we then put descriptions around that we can talk about, so we can refer to a shared experience. I cannot tell you how many times I listen to a keynote, I listen to an expert, I read something, and I think to myself, "Oh, that's wonderful! Yes! Yes! Yes." And then the rubber hits the road, and I see the math, I see the example, and I go, "Oh, not that. No. No," because words can have lots of meanings, and even descriptions can have lots of meanings. And because we come with different experiences, we could read the same thing, hear the same thing, and completely talk past each other.

Kim  6:05  
Right.

Pam  6:05  
And one of the things that we're trying to do in this podcast, Kim, is give all of our listeners in the world really some shared experiences around some vocabulary and the math. Like, I feel like what's one of the things we're trying to do in this podcast is do math and not just talk about it, so that as we talk about it and do the math, we have these shared experiences that we actually know what each other are talking about. So, we would encourage. It's one of the reasons why when I say Number Talk, like then we describe and do some math, so that everybody knows what we mean because there's so many different ideas about just even that one kind of thing. Alright. So, y'all, consider when you're helping teachers and colleagues, be in it with them, so that you can refer to that shared experience.

Kim  6:52  
Yeah, so we have three things for you to consider to help create these shared experiences. One, get into each other's rooms, so that you can have a common experience. Even if you don't have a coach on your campus, right? Teachers, you're listening, and you're like, "Great, I don't have a coach to do that with me." Or, "My coach is doing something else." You can work to get into your friend's classroom, your partner teacher's classroom. At least then, right, you have a shared experience that you and that teacher can work together. But even better, two, coaches, if you are listening, take a teacher into a room together, discuss what you see, and create some shared time that you can refer back to.

Pam  7:35  
And three, we've created a system to help us all do this with each other. All around the world, we can do this shared experience together. A, in this podcast, but also in our support system we call Journey. We release videos of expert teachers and facilitators and discuss the high leverage teacher moves. We call them out. We name them and describe them, and they become then a discussable shared experience. Not just a heard one, but also a viewed one because you're actually watching video. And, for leaders, we're announcing what we call JourneyLEADER, where we are providing leaders with helps like this as they lead teachers to more and more figure-out-able math. That is debuting this fall 2021. We are so excited about it. We think this is an amazing addition to our cadre of things that we offer to help us all teach more and more math that is figure-out-able. So, check out the mathisfigureoutable/leader section. So, if you go to mathisfigureoutable.com/leader. We'll put that link in the show notes. You can get more information about JourneyLEADER, so we can help all leaders on their journey to make math more and more figureoutable for them, for their teachers, and then, of course, for teachers' students. We are really excited to provide our teacher colleagues with more. Whoo! So, if you want to learn more mathematics and refine your math teaching, so that you and students are... 

...and be a little vulnerable about some things that we've learned. To be clear, teaching is a profession where you're never done. And teaching teachers is teaching. And that we recognize that there are things that we learn. There are things we improve, that we tweak, and we thought we'd be a little clearer about that today. We'll just sort of talk about some things that we've done early on that we don't do anymore, and that we do better now. So, one of those things has everything to do with some of the language that we use now, the way that we talk about math. You'll notice that in the intro we talk about mathematizing. Sometimes we'll talk about real math. So, one of the things that we learned really early on when I very first started on my journey into numeracy. I was teaching high school math. My kids were growing up, and I started working with my kids' teachers and just really doing things in my own personal kids' classrooms. And then the school got wind of it, and I started doing some professional learning with the school. And then the district got wind, and I started doing professional development with the district. And we had about, what, I think 11 elementaries at the time?

Kim  10:25  
Mmhm.

Pam  10:25  
And so, it was doing a lot of professional learning with a lot of teachers, and I started hearing teachers say things like "Pam math". Or, "Oh, you know like, I'm doing Pam math." Or, "I'm not doing that Pam math." Or we were at that point in time, the best resource that we had found. What was really sort of guiding a lot of what we were doing was Investigations in Data, Number, and Space, which is a fantastic resource. And especially at the time, I think it was the best thing that was out there. And we started hearing teachers say, "Oh, Investigations math. Yeah, we do Investigations math here." And, for a while, it bothered me, and I wasn't quite sure why. I was trying to figure out what was sort of tweaking me about that. And I began to realize... This sounds kind of, I don't know, too much hubris or something. But that I wasn't going to be there forever, and that I wanted this movement to continue, that I wanted the idea of teaching real math and actually teaching the mathematizing, that we could mentor students to be mathematicians. That I wanted that idea to continue on past me. That if I wasn't going to be there doing professional learning, I needed to have, I wanted to have an informed citizenry enough that the teachers really understood what was going on enough that when, for whatever reason, I wasn't there anymore, that it would continue. You know, I had four kids. They were in the district. They were still growing up. I wanted... And not just for them, but, you know, for my community, and  frankly, for the world at large that I want it to be. It can't be about a person. It has to be about real math and mathematizing, and that we can mentor teachers and students to be mathematicians.

Kim  12:08  
Yeah.

Pam  12:08  
And I learned that a little late in the game at the district, but I started to tell teachers and be much more clear about how this is not Pam Math. It's Math is Figure-Out-Able. It's not about Pam Harris math. The name of the website, the URL, all the things is Math is Figure-Out-Able. It's about math, and real math, and mentoring mathematicians. It's not about me. It's not about you. It's about all of us changing the way that we view math to be the real view.

Kim  12:39  
You get asked a lot, "What about manipulatives?" And it's kind of an interesting question because people will say, "What about manipulatives?" Question mark. It's like, "Wait, what's the question here? What?"

Pam  12:48  
Yeah, what about manipulatives? 

Pam and Kim  12:50  
Say More. How, when, which one?

Pam  12:53  
Yeah, yeah.

Kim  12:54  
You'll need a long answer, but in brief.

Pam  12:58  
So, I have to tell you. The first thing that comes to mind is Gail Burrill was a former NCTM president.

Kim  13:06  
Yeah.

Pam  13:06  
And when I was a young teacher, she was NCTM president, and she did a president's message. And it was when the Wendy's commercials.  I'm totally dating myself here. The Wendy's commercials had come out, "Where's the beef? Where's the beef?" Their whole thing was, you know, we have big hamburgers, I guess, and where's the beef in everywhere else? But her thing was, "Where's the math?" And she said, as she was traveling around as the NCTM president, she saw a lot of manipulatives out in classrooms, and her concern was, "Where's the math?" And so, I share that concern. And here's where I would add to that conversation. We do a lot of talking about developing mathematical reasoning in that we need kids to learn to count and solve problems using counting strategies. But then we want to advocate additive reasoning and thinking in terms of bigger chunks of numbers. If we give kids one to one manipulatives all the time, kids will not necessarily be nudged, be encouraged to build their brains to think in terms of chunks of numbers because they're counting one by ones. If we give them one to one manipulatives, they will continue to count one by one. So, the biggest caution that I would give. It's not the only one, but the biggest caution I would give about manipulatives is to think about what is my goal here? And is the manipulative supporting answer getting only? Or is it supporting the goal of building reasoning? And what kind of reasoning? So, then we actually have to identify what kind of reasoning we're trying to build. I'll give you a quick example. Early, early, when I dove into elementary. So, I was a secondary teacher. I got super interested in elementary. I started diving into research. One of the things I did was volunteer in my kids' school. And one day they said, "Hey, today? Today, we're not going to give you that group of kids you've been kind of extending." I had had a group of kids, and I was just experimenting and trying some things with them. And they said today, "We don't have time for you to do that. Sorry, we didn't, you know, tell you ahead of time. But today, can you just help this one student? She's just really struggling." And I was like, "Oh, I don't even know what I will do with the second grade student, but sure." And so, I started chatting with a student, and they said, "Help her add." And it was like, add two-digit numbers. And they gave me base 10 materials.

Kim  15:19  
Yeah.

Pam  15:20  
And so, I wasn't even sure what to do with base 10. And so, I said to her, "You know, we got this problem, 28 plus 37, like what are you going to do? And she goes, "Well, I think I'm supposed to grab these rods." And I said, "What's a rod?" Because like this is me early, right? I'm like, "I don't even know what a rod is." She goes, "Well, you know, it's this thing right here." And I said, "Well, what is this?" expecting her to say it's 10. And she goes, "It's a rod." And I said, "Right. But, you know like, if this is 1, what's this?" And she goes, "It's. A. Rod." And now you might be like, "Well, Pam, that student misunderstood," or whatever. But when I pulled out the 100, and she said, "That's a flat." And she goes, "I think it's called a flat." And I was like, "Um, but like how many of these little guys are in that?" She goes, "I don't know. I'm like, "Well, how many of these little ones are in this 10?" And I think I literally said, "How many of these ones are in this 10?" And she goes, "It's a rod." And I'm like, "Right. I know." So, then she took the little one, and she lined it up against the rod to see, and she goes, "Well, I guess in this one there's 10." So, yeah. So, my point is that I'm not sure what the teacher had tried to do. Obviously, you could do a better job of that. But in manipulatives, we have supposed, we've... How do I say this? We've created manipulatives to represent the mathematics that we have created in our minds and supposed that students can see the mathematics in that manipulative. And that is not true. Students cannot just look at this preconstructed rod that we've stuck together and all of a sudden go, "Oh, yeah. That's a 10. And see, there's 10 of those in that flat, and there's 10 of those in that cube." And so, we can't... I'm going maybe longer than you wanted me to. But we can't just assume that because we've created the relationships, and we now know what the mathematics that are involved in that manipulative, that then therefore it, whoo, magically appears to the students in the manipulative. So, I don't... There's four other things I can think about manipulatives, but we won't make this too, too long. 

Kim  17:20  
Yeah. Sometimes people say that you say algorithms are bad.

Pam  17:28  
Sure enough. I got an email the other day from a delightful person that I have been back and forth on Twitter. And Brad Ballinger said, "Pam, I agree with like 90% of what you're doing, but why do you call algorithms bad? We have got to talk." And I was like, "Brad, let's get on the Zoom. Let's talk." So, we connected. Ae found a time that we could get on Zoom. We got on Zoom. We started to talk, and he showed me some amazing algorithms and some connections between them. We had a blast doing some math together. And then he looked at me and he goes, "See, this is my point." And I said, "Brad, are you clear, I am not saying that algorithms are bad? What I'm saying is they're not really good teaching tools." And he said, "Oh. Well, then I agree with everything you're saying." I mean, I'm not quite... Maybe I'm misquoting him a little bit. But he was like, "Wait, you're not saying they're bad?" And I said, "No. Like, the work that you and I just did..." So, basically he said, "You know like, here's a really cool algorithm. And notice, how it's connected to this algorithm, and what does that help us bring out in the math? And then what if we did it in base 2, and there was a connection between base 2 and everything." It was a super fun sort of trail for us to go down, where we could talk about math that we knew, talk about relationships that we knew. And he said, I think there's a place for this kind of thing in math class." And I said, "I do too. Absolutely, we can talk about how algorithms work, why they are general, and how the meaning is all kind of stuffed in there. It's like behind the scenes. You can't really tell what's going on. I think that's a very fruitful conversation. But not as a step-by-step procedure that then kids use every time to answer questions." And he's like, "Well, yeah. Of course, not." And I was like, "Okay, then we agree." Like, then we agree. So, algorithms are not bad. They're not evil. They are amazing historic achievements. How did mathematicians create these amazing historical achievements? And here's where I don't know if I can do this under the time I have left. But mathematicians ran into patterns in their life, and they played with relationships, and they felt out like how are these all related, and they created strategies, and they solved problems using those strategies. And over time, as they got really good at the relationships, they created algorithms that could generalize the relationships that they were seeing and feeling, and it could be a method to solve problems of any problem in that class, any problem in that type of problem. That is a super cool achievement to create something that's general enough that no matter what the input is, you can crunch it, and then you can get the output. But it was never the intent that that becomes, then the way that you teach people how to make the same relationships and connections that they made in that journey. It was never intended that we just hand them. Flat out, we can hand kids a calculator. Everybody knows that's a terrible way to teach kids. It's a terrible way to help brains, kids' brains develop better. To just hand the calculator... [Timer sounds]. We can end on that.

Kim  20:27  
I like it. 

Pam  20:28  
We can end on that. Yeah.

Kim  20:31  
Leaders, we know you're doing fantastic work every day to create opportunities for teachers to make math more figure-out-able for their students. We'd love to work alongside you and invite you to check out our Math is Figure-Out-Able Solution program where we work with schools and districts to support both you and your teachers to make math more figure-out-able. You can check that out at mathisfigureoutable.com/solution.

Pam  20:55  
Alright, y'all. 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!