Pam  00:01
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris, a former mimicker turned mather. And

Kim  00:11
I'm Kim Montague, 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  00:19
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  00:34
In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships. 

Pam  00:42
We invite you to join us to make math more figure-out-able. Hey, we did it, Kim!

Kim  00:50
I thought for sure I would forget. 

Pam  00:52
Alright, so if you've been listening to the podcast at all, you realize we just recorded a different introduction to the podcast because, Kim, it's our 200th episode!

Kim  01:04
I mean, if we had celebration emojis, we could shoot them off fireworks. Pam, that's a lot of talking. It's been almost four years. Can you believe that? 

Pam  01:17
Ah, yeah.

Kim  01:18
Almost three years of this.

Pam  01:19
I mean, we've been working together for a while. And yeah, four years of talking is a good thing. 

Kim  01:24
Yeah. 

Pam  01:24
And it has been good. Ya'll, we want to give credit to our wonderful podcast. What do we call Craig? I don't even know. Craig, thank you for putting the podcast together

Kim  01:34
And making us not cough and sneeze. And...

Pam  01:37
Yes, taking out all the dumb noises that when we're gagging, and...

Kim  01:42
We love Craig.

Pam  01:43
When I'm tapping, he used to go, "What are you doing? What is that tapping sound?" And I still don't even know what it was. But whatever it was, I stopped it. So, now he's not so mad at me anymore for (unclear) But really, Kim, I want to give credit to you. You are kind of the taskmaster to make sure that we actually record. "Put this on your calendar. We're going to like set aside this time. We're actually going to make it happen." You help us make sure that we planning and have things that we're going to talk about, keeping it all straight, making sure... This is probably the best part. You make sure that it's not me just in my ivory tower, talking about all the things that I'm kind of thinking about and interested in. It's not just theory, but helping make it applicable for teachers and parents to actually go from there. So, I think I think we're a good balanced that way. (unclear) about all the kind of ideas and theory. And you're like, "And how does that help anybody?" (unclear)

Kim  02:26
Yeah. Yeah, I mean, I do think it's a good balance. Because, you know, you have brought Math is Figure-Out-Able to the world. And you're really forcing people to reconsider what math really is. I mean, that's been...

Pam  02:44
Forcing. I mean, inviting.

Kim  02:45
No, forcing, reconsider. I mean, really, which is a huge undertaking, and it's a big job. And when we first started thinking about a podcast, I thought, "I mean, why would that be valuable?" And I feel like we've heard so many times how valuable it has been to people. So, you know, I think the way that you invite listeners to take part is not just you spouting off ideas, but you ask people to consider and try things. And you also do a really good job of slowing us down to make sure that we're making sense, and that we're communicating clearly. You know, sometimes I just start talking and you're like, "Wait a second. Just... Like, we're on a podcast, Kim, we need to slow it down." And I think that's been really helpful. I also think that one of the things you do really well is think K-12. Right? That's huge value to our listeners to have this global perspective across the math continuum. So, I appreciate that part that you bring. Otherwise, I would only talk about teacher stuff. So, anyway, it's a nice balance to bring our thoughts together and to collaborate. And can I give a shout out? You give a shout out to Craig. Shout out to Sue for all the long car rides, of listening to us banter back and forth as we travel around. I mean, I think sometimes about that, and I'm like, "Does she ever get a chance to speak?" There's absolutely no way. We probably like, "Hang on, Sue."

Pam  04:10
(unclear) Kim and I conversation, it's pretty hard to get a word in edgewise. But we appreciate you Sue. And Sue probably was the one who pushed us the most...

Kim  04:17
Yeah.

Pam  04:17
...to say, "People would want to listen to this. Like, that half an hour of you guys just going back and forth and beating out what you think, and pushing each other, and clarifying, and what do you really mean, and how's that going to help, and for what grades, and all of that. You know like, I disagree, and this is why. Wait, what do you..." Yeah, all that back and forth, really appreciate Sue then pushing us to say, "I think people would want to listen to this. It took her a while to convince us, but we really appreciate that.

Kim  04:44
So, we're here almost four years later, still doing the thing. 

Pam  04:47
Alright. So, Kim, we started today's episode with a new intro. 

Kim  04:51
Yeah. 

Pam  04:52
And sometimes people will say, "You re-record that every time?" And we're like, "Yeah, we do. I don't know that that's a good or bad thing." But for the 200th episode, we have been... We are always learning, right?

Kim  05:03
Oh, yeah.

Pam  05:04
And so, one of the things that I'm aware of, you're aware of is that we've been kind of rethinking that people push back sometimes, and we've been discussing. And so, we thought we would put some of the things we've been thinking about recently to tweak the intro. It's not that we don't like the last intro. But some things that we're thinking about, and maybe we'll change it again soon. But we thought we'd take this episode to talk a little bit about some of the things that are on our minds, top of our heads, and why. Because the changes we made were not just because it's the 200th episode. We actually want to make some points. So, you might have noticed that when I started today, I didn't say, "Hey, fellow mathematicians!" I said, "Hey, fellow mathers." I got to tell you. When I first started saying mathers instead of mathematicians, I got a little pushback on the team. They're like, "That sounds dumb." And I was like, "Okay, but let me..."

Kim  05:55
We're nothing if not blunt here. 

Pam  05:56
Yeah, we just say it the way it is. And so, I kind of wanted to defend that just a little bit. 

Kim  06:01
Yeah. 

Pam  06:02
I'm not saying that it was bad that I said, "Hey, fellow mathematicians." We'll probably still say that. But I'm aware that there is a distinction that might be helpful, that I want to sort of honor and respect that there are people out there that are mathematicians as an occupation. 

Kim  06:19
Yeah.

Pam  06:19
That, you know, that's what they get paid to do, and that's their sort of full time thing is this creating math or proving math. And that is different than what we're suggesting. We're not... I will often say it's not necessarily that we're trying to get kids to be mathematicians in the future, like mathematicians to be as an occupation. But we want them to math in the here and now. So, there's a difference between a mathematician as an occupation and mathing as something that you do. Like, I could compare it to we can say, "Hey, fourth grade writers," because they're writing, right? We're engaging them in the work of writing. But we might not call them published authors because they might not be published authors. There's a difference between my... Hey, I'll usually shout out to my old college roommate, who I've talked about before, who mentored me in writing. I think she just published her fourth children's book. Well, she has two YA novels or middle grade novels. Anyway, she's a published author. There's a little bit of difference between her and a fourth grade kid who's, you know, writing stuff. I mean, they're both engaging in the work of writing. But I'll sort of give her the onus, the respect of being a published author. That's like a big deal. So, I just want to be really clear that I'm not claiming professional mathematician status. What I'm suggesting is, is that what we want to do, what we're suggesting in this podcast, that Math is Figure-Out-Able, is that Real Math is doing math the way mathematicians do it, the way a professional mathematician today, the way they were thinking about math in fourth grade, the way they were thinking about math in seventh grade. That if I have Algebra 1 students, I want to Algebra 1 math with them the way mathematicians math that Algebra 1 math. That's the change. Mathematicians don't mimic. They math. Right?

Kim  08:14
Yeah. Well, and I think if somebody's taken your workshop or, you know, seen you present, they've heard you say "mathematician", and you've had a chance to elaborate the part that you just said about mathematicians in the here and now, where they are in that current grade like writers in fourth grade or mathematicians in third grade. And if you hear you talk about it, you know that you don't mean in the future. But sometimes it doesn't come across on a piece of paper or, you know, just when you casually say a phrase. And so, you know, it's an action to be a mathematician or a mather. And that's the point. That it's doing the work of mathing. And so, I think it's a nice change.

Pam  08:54
Nice. And what you just said was "mathing", right? It's doing the work of mathing. 

Kim  08:59
Yeah. 

Pam  09:00
And there's kind of a fun phrase that are kind of kicking around, kids have been saying for a little while, where they're like, "The math isn't mathing." And so, for a while, I've been using the word "mathematize". And I'll give credit to Cathy Fosnot. I think that's the first place I saw "mathematize". I think there's a few other people that are using "mathematizing" out there now to describe what mathematicians do when they math, and all of us can mathematize, that mathematics begs this verb form of, that it's an action to do. It's not this body of dead stale stuff, but it's actually what your brain is doing. We want to describe the actions your brain does when it maths. And so, I'm not dogging the word "mathematize". But I think we can also use math as a verb. I think, like you just said, that we want kids to math. We want to engage in the work of mathing. And we can kind of create a verb for that. I am aware that our international friends don't say the word "math". They say "Maths". And they're probably correct. Like, more correct than we are because it is mathematics. And so, "mathematics", the short form should be "maths". I just don't know how to turn that into a verb. So, international listeners, would you prefer that we say mathsing. Like, we just said we're going to math, mathing. Hey, we're doing the work of mathematician, so we're mathing, we're mathers. Would you prefer that we were mathsing? Math... How do I? (unclear).

Kim  10:24
That sounds like a song. Math-sing

Pam  10:27
Math-sing. Ah, mathsing? 

Kim  10:29
Yep. 

Pam  10:29
Nice, nice, nice.

Kim  10:30
I think for a while you thought that I didn't like "mathing".

Pam  10:33
I did. Yeah, I thought you were saying, "Pam that's dumb. Don't

Kim  10:36
Or the phrase, "The math isn't mathing." But I actually think that when somebody says, "The math isn't mathing," like when they're a kid saying that, it's that they're considering that something's not adding up. Like, it's not making sense. So, I actually don't hate the phrase, "The math is not mathing." I know it's done kind of tongue in cheek, and you know, they say it to be silly. But I want kids to be considering if the math is mathing. Like, does it make sense? Does it jive with what I know about number or operation? Yeah.

Pam  10:36
say mathing." So, when we're going to go film in middle school in a few weeks, I could ask kids, you know like, "Does this make sense? Everybody tracking here? Is the math mathing?" 

Kim  11:15
Yeah.

Pam  11:16
I could say it right there?

Kim  11:16
Go for it.

Pam  11:17
Okay, okay. Ah, I like it. I like it. Alright, cool. So, another thing that you might have noticed in our new introduction is I said, "I'm Pam Harris, and I'm a former mimicker." So, "mimicking". What does "mimicking" mean. I'll just say from my background, I bought into the myth that math is about mimicking. It's about waiting till the teacher tells you what to do, rote memorizing a bunch of steps and facts, and then repeating, mimicking in parrot fashion those steps. I say "repeating in parrot fashion" because when I traveled to South Africa, and I was speaking with audiences whose native language was not English, I was trying to bring out mimicking, and I said like a robot, and the people that I was talking to, like, kind of push back on that. They were like, "We're not sure we know what you mean." And at some point somebody said, "Do you mean like repeating in parrot fashion?" And I was like, "Um sure." Like, that's not a phrase I would typically use. And, Kim, after I started saying that, people's eyes would like, "Oh, okay. I get what you mean. Yes. That's..." Like, repeating like a parrot, right? Like, being a parrot and just saying it back because I've heard it. If you think about a parrot, a parrot doesn't really know what's going on when they're saying those words, right? They're just repeating it back. That's not what we want in math class. So, I am a former mimicker. Like Peter Liljedhal, he'll say, "We want to build thinking classrooms." We usually say we want to build reasoning classrooms. But I would suggest that both Peter Liljedhal and us here at Math is Figure-Out-Able, we are both against mimicking. We're going to say mathing isn't mimicking. And, Kim, I've been thinking a little bit lately about the perspectives thing. We've talked a little before where I've had this perspective that I was a mimicker, and you had a different perspective when you were a learner growing up. But we're actually shifting that language from perspectives to distortions. 

Kim  13:15
Yeah.

Pam  13:16
Because as we talk about perspectives, I've had a lot of teachers come up to me and say, "Oh, okay, so if a kid was like you, then I need to teach them differently than if a kid was like Kim then I need to teach them differently." I'm like, "No, no, no. No, we teach everybody Real Math, and then nobody has those..." I would say, perspectives, but now I'm going to say, "Then, nobody has those distortions."

Kim  13:26
Yeah. Yeah.

Pam  13:36
What we want to do is eliminate the distortions. We want to help everybody see math the way it actually is, that it's actually this mathing thing, not this mimicking thing. And, Kim, you were not a mimicker. So, how did you introduce yourself today?

Kim  13:52
Yeah. So, I'm saying, "I'm a reasoner who now knows how to share my thinking," because, you know, I always messed around with number. But frankly, I only mess with what I could see by myself. So, you know, if I bumped into something, or if I had a conversation with somebody, and it was within the realm of my understanding at that time, then, you know, I saw connections pretty easily. But what I didn't do or know was that was a desirable thing. You know, I didn't have a language to talk about it with somebody or have other people to talk to really. So, it kind of just lived in my head. And I think what's, you know, the Math is Figure-Out-Able movement is really about is talking about the reasoning that we are doing and having a way to communicate that, so that we can all get stronger and we can go further in math. 

Pam  14:43
Yeah, so we can all math the way you are mathing but not alone, not solitary.

Kim  14:48
Right. 

Pam  14:48
Not only with the things that you can kind of grasp on your own. But we can do it intentionally. We can bring it out for everybody. 

Kim  14:54
Yeah.

Pam  14:54
Nice. So, another phrase that we said is, "We're on a mission to improve math teaching." Which is true. But let me make sure that if you're a parent or a student who's maybe listening in the car with your parents. High five them right now. "Bam, that's me! I'm in the car with my parents." If you're someone else, you're not maybe a math teacher, but you're still listening, you are welcome here. We love having you as part of the Math is Figure-Out-Able movement. We're so glad that you are here learning with us. So, just because we said we're on a mission to improve math teaching doesn't exclude anybody who wants to dive in and math more themselves.

Kim  15:31
Yeah, I think it's also really intentional that we mentioned algorithms in the intro because I think, you know, you've mentioned so many times that their historical achievements. They're really pretty amazing. But they're not amazing for teaching. And I think this is so important to you, and to teaching Math is Figure-Out-Able is that there's so much to it, right? A lot of education is about doing some work, and then ending up with the algorithm. But you are saying, that's not what it's about. And it's so much so that you have an entire book. It's the premise of your upcoming book. And it really matters because we've been so focused on algorithms in education for so, so long. And when we first started thinking about the podcast several years ago, talking about this was one of your highest priorities. And the first episode that we did, in fact, was about algorithms. Like, it was so paramount to you to say, "This is the message that we need to be spreading to the world," that episode one introduction, episode two, let's talk about algorithms.

Pam  16:31
Bam. Yeah, because it's so important. And I am knee deep in the thick right now of writing, Developing Mathematical Reasoning, Avoiding the Trap of Algorithms for Corwin. And super excited. It's going to be available for preorder and NCTM in September. I believe... I know it's announced. Is it available? I'm not sure exactly when it's available. I'm pretty sure it's... Well, okay, Corwin's killing me right now. But for sure we're going to announce it in September of 2024, and like I said, I'm in the thick of writing. It's so much fun to get it all down. It's going to be so amazing to everybody have this resource. Yeah, and it is such an important part that yeah, we thought we would kind of say it a little differently in this new introduction for the podcast. 

Kim  17:17
And frankly, it's been really fun to see math education take a bit of a shift and watch others take notice and begin to wonder out loud about how unnecessary they are.

Pam  17:28
Unnecessary algorithms are. 

Both Pam and Kim  17:30
Yeah.

Pam  17:30
Absolutely. And one of the things that I've been grappling with a little bit as I'm writing this new book is what is the purpose of math class? So, as I've been writing, I'm becoming aware that if I can tackle that idea head on, if I can help teachers sort of say to themselves, "What is the purpose of math class? Is it getting answers? Is it getting kids to do a bunch of stuff that they'll need for higher math, for physics, for engineering?" If that's the purpose of math class, then we're going to do, we're going to teach math one way. But if we believe the purpose of math class is more than that, if we believe that the purpose of math class is building mathematical reasoners, which includes content, but it really means that we're using that content to develop brains that think mathematically?

Kim  18:27
Yeah.

Pam  18:28
Then, we have a sort of different outcome. Then, math class becomes a different place. So, yes, there's still content. We're definitely still hitting content. But we're hitting content not as the end goal. Content is the vehicle to create mathematical reasoners. And I think the more I work on that, the more think about it. I think the more helpful it is for people to start to make that shift, to then understand why we're emphasizing what we're emphasizing, and de-emphasizing what we're suggesting to de-emphasize. 

Kim  18:59
Yeah. I told you this, but I'll say it here that recently I had a conversation with my oldest who's a sophomore. And he said to me, "You know, some of these math classes that I'm going to be taking, you know, I wonder if they are appropriate for all kids." And I was like, "Well, tell me about that. What do you mean appropriate?" And he said, "Well, at some point, you know, the math that we're going to be doing isn't in the career field or in the area of interest for some students." And I said, "Well, yeah. That's a lot of times why kids say why do I need this? And how does this help me in life?" And he said, "Well, you know, teachers often say you need to know this thing, so that next year you can use it." And he said, "You know, at what point do you say I don't need that next thing, so I could be done now. Like, where's the stopping point?" And I said, "Well, you know, it's different for every person maybe. But here's the thing that is important is that, you know, if we believe that all of the basically the practice standards, constructing arguments, and modeling thinking, and whatever. Grappling..."

Pam  19:58
Generalizing from you are examples. Yeah, the whole. Mmhm, mmhm.

Kim  20:02
So, and I said to him, "That's what you should be taking away. Like, there are some mathematical things content wise that, you know, you're going to be using. But what I said to him was, "You really haven't had to grapple, really grapple hard yet. So, you, in particular, sir, are going to keep going because you can experience why you need to create arguments and represent your thinking." And that is a different place for all kids. Not everybody is going to take, you know, Algebra 2 or precal or whatever. But it's really about when do kids have to experience those math practice standards? And we can start that very early. But for many kids, you know, and for all kids, we need to be speaking to them about I think the math class is really about the behaviors that are involved in the math practice standards. 

Pam  20:54
Yeah, for example, we want kids to learn to use tools appropriately. 

Kim  20:59
Yeah.

Pam  20:59
We want kids to learn to reason abstractly and quantitatively. 

Kim  21:02
Yeah. 

Pam  21:03
Well, like you said, we want them to construct viable arguments and critique the reasoning of others. Those are important life skills. We want them to attend to precision and look for and make use of structure. Like, those are things that we need kids to get better at, so that we can talk about data in the real life and be able to, you know, listen to political arguments and be able to help the world get better from a mathematics perspective. Those things are so much more important than maybe the specific content. We're using the content to build those things in kids heads. That we want them to know they can make sense of problems and persevere in solving them. Those things there's no deadline. "Oh, I won't need that next year." 

Kim  21:49
Right. 

Pam  21:50
We we definitely want those things to keep going. 

Both Pam and Kim  21:52
Yeah.

Kim  21:52
Yep. Can I share a review with you? 

Pam  21:56
Absolutely. 

Kim  21:57
You haven't seen this, but I knew what we're going to talk about today, and I thought what is something that is kind of like a message that we would want to send? So JYC... And maybe I've shared this before, but I think it's still appropriate. JYC wrote in and said, "Long time listener, first time reviewer." So, that's fun. 

Pam  22:16
Yay! 

Kim  22:17
And they said, "I've listened to this podcast for a few years now, and just when they think there are no more topics to cover, Pam and Kim keep coming out with more and more great topics."

Pam  22:27
Nice.

Kim  22:28
(unclear). One thing I most appreciate about every episode is the very personable and authentic dynamic between Pam and Kim. It feels like you're in a room with your favorite colleagues chatting about math." I love that that's... That's fun. 

Pam  22:40
That is super fun. 

Kim  22:41
"Just when I think I figured out one or two ways of thinking about a problem, one or the both of them will share a way with a different perspective or way of doing things that I had never even considered." This is the part I love. "I truly appreciate how these episodes really stretch my own mathematical thinking, gives me pause... Yeah. "...gives me pause to think about the intentional ways that I should structure my own instructional practices, as well as ways of lifting up student thinking about mathematics. Thank you for making each episode so engaging, inviting, and most of all, figure-out-able.

Pam  23:11
Aw, (unclear).

Kim  23:13
Right. That's exactly our goal, right? That's exactly what we're hoping for. (unclear).

Pam  23:17
Thanks JYC. Yeah.

Kim  23:18
We already have a platform with each other to talk and ramble. And having people take something away is super valuable to us. So, thank you for that.

Pam  23:26
Yeah. And we invite you to make math more figure-out-able is the way that we sort of ended that beginning introduction. And exactly that JYC. We thank you so much for listening and taking it to heart. We appreciate you giving us a review and leaving the rating. Doing that helps more people find the podcast, so if you want to help us keep making math more figure-out-able around the world, then right now while you're watching... Okay, maybe not if you're driving, but when you get to a place, you know, just drop a quick rating, throw in a couple of words for a review. It doesn't have to be as long as JYC but it will help us spread the word and make math more figure-out-able around the world. Ya'll, thank you for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com, and keep spreading the word that Math is Figure-Out-Able!