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

Kim  0:10  
And 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  0:19  
Ya'll, we know that algorithms are amazing human achievements, but they are terrible 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  
In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:40  
We invite you to join us to make math more figure-out-able. 

Kim  0:44  
Hey there! 

Pam  0:44  
Hey, Kim. 

Kim  0:45  
It's school time. 

Pam  0:48  
Indeed. School is on. 

Kim  0:49  
I

Kim  0:50  
sometimes forget that you aren't in the day to day of that because I see you all the time.

Pam  0:55  
Because my kids are old? 

Kim  0:56  
Well, and yeah, and I knew you with your kids. So, anyway, school has been going on with us. I just said I knew you with your kids. Like, you don't have kids anymore. I mean, like (unclear)

Kim  1:06  
(unclear). 

Pam  1:07  
I have grandkids now.

Kim  1:09  
I know. 

Pam  1:09  
So, my kids are too old and my grandkids are too young. 

Kim  1:11  
Yeah.

Pam  1:12  
No, yeah, they're on in school at the moment. 

Kim  1:14  
So,

Kim  1:14  
It's been going on for a little bit. And it struck me the other day. I sent an email to my kids teachers. And when my kids were younger, like in elementary school, you know, when I would walk into campus with them with supplies and whatever, and I would meet the teachers, I would say to them. You know, when I (unclear) classroom, I would say to them, like, "I get it. Like, the beginning of the year is nuts. And, you know, but like, I teach math." And, you know, would kind of form a relationship with them and maybe would like say, "Hey, if you want to come in, I can do something." But now that my kids are in high school, the email is more like, "Hey, I know that you teach high school and you get nothing for school supplies. What do you need? And the

Kim  1:54  
funny thing is...

Pam  1:55  
Aww, that's nice of

Pam  1:56  
you to do that. 

Kim  1:56  
Well, I mean, it's... You know like, I want them to know that they can. Listen, but I think now this is... 

Pam  2:02  
What do they

Pam  2:02  
ask for? I got to know.

Kim  2:04  
Tissues.

Kim  2:04  
I heard back from a couple of teachers. Every single one of them said tissues. Nothing

Kim  2:09  
else. 

Pam  2:09  
Like Kleenex tissues. Like. 

Kim  2:11  
Nothing else. 

Pam  2:13  
(unclear) Central Texas allergies are so bad. Is

Pam  2:15  
that? 

Kim  2:15  
I think it's because they don't have anything, and nobody wants to watch kids wipe their snot on their shirt. It's gross.

Pam  2:20  
Well, that that would be true. Yuck. Yum.

Kim  2:23  
Yeah, so nothing else. All they want is tissues. Anyway.

Pam  2:26  
So, do you send tissues? 

Kim  2:27  
Oh, yeah. I'm going to go to like

Speaker 1  2:29  
Costco. Which is like, if you don't know Costco, it's like a big warehouse thing. 

Kim  2:33  
And I'm going to buy bulk tissues and drop them off. Yeah. 

Pam  2:37  
Well, they'll be very grateful. 

Kim  2:39  
Anyway, but you know part of it is also just say like, "Hey, I'm a, you know, I think, kind of normal parent, and if my kids are acting a fool, like let me know. I'll fix that."

Kim  2:49  
Anyway. 

Pam  2:49  
You support them. It's good to start

Pam  2:52  
a relationship. Yeah, nice. 

Kim  2:53  
Huge teacher fan. Anyway. But what I... You know, I would kind of talk to the elementary teachers differently because I had been there. And, you know, I kind of engage a little bit in math conversation with them. But with high school, I realized like I don't sometimes know how to describe what we do. Or like Math is Figure-Out-Able. It's like it's I guess a cool name, but that doesn't really tell anybody anything. So, anyway.

Pam  3:18  
I mean, it's kind of a cool. It's more than a cool name. 

Kim  3:21  
It is. It is very cool.

Pam  3:23  
Math is not rote memorizeable. It's figure-out-able.

Kim  3:26  
Well, so anyway. What I was realizing was that I... Without a longer conversation, I don't really know what to say to a math teacher in high school. "This is what we believe or what we do." So, anyway, it was occurring to me because I just sent the email, and I knew we're going to talk about today. So, this episode is going to be in part, for leaders of professional learning, professional development and also for teachers of math. And you've had some experiences lately that I think would be important to share.

Pam  3:57  
And I think maybe you're getting at like when you just said you're not quite sure how to describe what we do succinctly. What do we do here at Math is Figure-Out-Able, maybe succinctly? And, yeah. That's not trivial. I think when people recognize. Listeners, you can tell us. When you hear the podcast, you might be like, "Oh, yeah. These guys. You know, they do some math, and we chat about some math. And it's, you know, it's just I don't know. We have good banter. And so that's... You know, it's a pleasant podcast. But maybe if you've listened for a little while, you realize that what we do is a little different. At least from the way we were taught math growing up. And when you realize that maybe we're a little different than, I don't know, the way you were taught growing up, you might be tempted to put us kind of in a camp, like a group of people. You might be tempted to say, "Oh, okay. They're like, inquiry based or constructivist." And you might even think, "Oh, they're fluffy, and it's all about play." Or, you know, "We don't actually have to get kids, you know, to do anything. Whatever." Many of us learned more when we became teachers. We became teachers, and we made connections and got some conceptual understanding if that's the way to say it.

Kim  5:06  
Mmhm. 

Pam  5:06  
And so, we as teachers were like, "Whoa! Like, we can understand more. We want to give that to our kids!" But yet still have the goal of the kids getting to the steps, memorizing the algorithms, that the goal is to get answers. And so, sure, let's get some conceptual understanding, but because then they'll do the steps better. They'll perform the algorithms better. And you might think about if you're like, "Oh, but you guys are a little bit different. So, yeah, you're in that camp that says, you know, get some understanding first, and then you can." But your goal is still to then get to mimicking steps.

Kim  5:43  
Mmhm. 

Pam  5:43  
However. Kind of like Kim, like you were just saying. Succinctly, what would we talk about what we do? We are different in a major way that our goal at Math is Figure-Out-Able isn't to get some conceptual understanding, so that kids can then answer questions, performing the steps, mimicking the steps. Like doing the steps of algorithms. Not our goal. We think that that as an end goal, that landing there, making that the goal, that mimicking steps to get answers, that actually is detrimental. And so, this is subtle. It's a subtle kind of if what you think about math education is to get, of course, you're going to get there. But hey, we're going to get there better. Then you might think that we're in that camp. And so, I... Oh, go ahead.

Kim  6:27  
Yeah,

Kim  6:29  
I want to hang for just a second that on the fact that you said "detrimental". Because you're not saying just like, "Hey, make sure kids understand, and then give them the choice" or "Be okay with however they land." You're saying it's actually harmful to their mathematical journey to propose that that's what they do is land on a series of steps to solve problems.

Pam  6:56  
Yes. And as you were saying it, I wondered if I was going to say it can be detrimental. But I'm going to say it is detrimental. Like I could have,  softened that a little bit to say, "Well, it might not be. You know, some kids. But I'm going to say even those students who see that your end goal is to be algorithmic and choose or that you show them the steps and say, "Our end goal is that you mimic these steps to get answers." They could have been doing more real mathing if you hadn't spent time doing that. 

Kim  7:23  
Mmhm.

Pam  7:25  
If you had spent time differently, they could have done more real mathing sooner, faster, and better if we'd done other things. So, yes, I'm going to say categorically detrimental.

Kim  7:38  
And one more clarification.

Pam  7:40  
Mmhm.

Kim  7:42  
When your goal is conceptual based, and you want an understanding, and then you say, "Maybe my goal wasn't to teach algorithms, but the kids came with that," or "They were taught that at home, so I'm just gonna say, okay, so they're good. I'm going to like, we've got something."

Pam  8:03  
"I'm going to leave them there." 

Kim  8:04  
Would you say that's also detrimental?

Pam  8:08  
Yeah, because that was me.

Kim  8:09  
Okay. 

Pam  8:10  
Like, I had the algorithms down cold.

Kim  8:13  
Yeah. 

Pam  8:13  
Like well. And not only was I... Because I often say mimicking steps of the algorithms, I was thinking through the steps of the algorithms. Like, I couldn't have told you why they worked and how they worked. 

Kim  8:23  
Mmhm.

Pam  8:23  
But I wasn't mathing. I wasn't doing the mental actions that I now know I could have been. 

Kim  8:29  
Yeah.

Pam  8:29  
And that's the goal that I'm trying to help everybody. And this became a whole lot more clear recently, and I wanted to chat with you about it, at some conferences. So, I've been in a lot of conferences. You know, there's a lot of conferences over the summer. And to be really clear, I've been at a lot of conferences, so nobody is going to be able to pin down. 

Kim  8:52  
We've missed you! 

Pam  8:52  
Yeah, it's been a busy time. Great time. Fantastic time. I've had a wonderful time interacting with a lot of really cool people. So, I'm going to kind of do an amalgamation. I'm going to pull together a lot of experiences. 

Kim  9:00  
Mmhm.

Pam  9:01  
So, you might have been at a conference with me, and you might have been sitting in a session with me, and you might go, "Ooh, I wonder if she's talking about this session." And the answer to that would be no. Because I'm pulling together lots of sessions that I was in. I'm also not talking about lots of sessions that I was in. So, to be really clear, nobody can tell who I'm actually referring to because it's a  combination. Does that make sense? 

Kim  9:22  
Yep.

Pam  9:22  
But the combination, there was a pattern, and I'd like to talk about that pattern that I saw. So, in that pattern, I want to share it, so that we can all get more clear on our message at Math is Figure-Out-Able and how it's different than some of the other messages that you might be hearing. So, I'm going to kind of talk about a specific session I was in as if it was a session, but again, it was a combination. So, picture a session. It's a featured speaker. It's right before the featured speaker that I'm about to do. So, I'm in the room to kind of get a feel for the room. You know, I'm looking at the connections and stuff. Am I going to be able to get my tech set up? You know, and what's the room look like. Making sure that I'm going to look right. Kim, you know that if I'm going to do anything wrong in a presentation, I won't look right. So, I'm telling myself. I have these little notes to myself. Look right. In other words, I will call on people more on my left than I will on my right.

Kim  10:10  
Yeah.

Pam  10:10  
If I don't think about it. So, that's one thing that I'm trying to be. Anyway, so I'm looking around the room, whatever. And I'm excited. Hadn't heard this particular presenter before, kind of an up and coming. And this could be true for... Again, this is a combination, right? Combinations of sessions. So, often I see that a feature speaker might do something like this. Tell us the math. So, if they do any math at all, often the presenter will tell us the math. They'll say, "So, you know, we know that this is true," and then they will sort of state some math. Then, the person might say something like, "Here's a really cool student task that I've used that could work really well to get kids to actually understand, get some conceptual understanding." And then I'm thinking of a particular one. It was actually not too bad. Like, the student task. But it was really interesting that the presenter shows us the student task. Rather than engaging us in the student task. "Hey, everybody. Do this. Try this." Now. I get that because sometimes it doesn't work really well. You might not have the... I was going to say, equipment. Is that the right word? You might not have the manipulatives or the graphic calculator, or the like pick your thing. The graph paper. Whatever it is, you might not have that handy, and so it might not be, you know like, the particular task that you've chosen to do in a big Ballroom with a lot of people. But it's kind of noteworthy. You've chosen a task that you tell us about.

Kim  11:34  
Yeah. 

Pam  11:35  
So, now we're all sitting there, and we're being shown. I would have the kids do this, then I would have the kids do this. And to be clear, one of the ones I'm talking about was a high school task where we all could have dove in and found some patterns. So, the way the task was set up was, the kids dove in, did some things, found some patterns, had an experience, collected some data. In fact, I should have said, collected some data and noticed some patterns, and then made generalizations based on those patterns. And I was like, "Huh, it's not actually too bad of an experience, an activity for kids. And in the moment, I thought to myself, "Oh, it's almost too bad we didn't do that. I would have liked to have done that. I would have liked to have seen what my brain would have done when would I have noticed the pattern? What kind of generalizations would I have made? Even though to be really clear, I knew that math, but I think it would have been worth doing. Anyway, so then several these presenters kind of did the same thing, told us some math, then showed us something that we could do with kids, kind of told us what we could do with kids. And even though that thing might have been pretty good, then said say something like, "Now, that we have conceptual understanding, now it's now time to memorize the rules. And I think if one specific literally said something like, "Okay, now that we kind of understand what's going on. Now, it's totally fine to just here are the rules. Now, I'm going to give kids these rules. But, ya'll, there's a lot of rules here, and so since there's a lot of rules, now we're going to help kids memorize the rules."

Kim  13:01  
Mmhm.

Pam  13:01  
And I just kind of sat back in my chair, and I thought, "Okay, good. Like, right now in this, we are clear on what you think teaching math is."

Kim  13:12  
Mmhm. 

Pam  13:13  
And several these presenters said something like, "You know, when I was a kid, I was just given the rules, and I was just told to memorize the rules. It is better if we get some conceptual understanding first see, how we do this? But then we're going to memorize the rules. We're going to repeat those rules. And so I was like, "Okay, at least I'm clear now on this person's perspective."

Kim  13:31  
Right. 

Pam  13:31  
And, Kim, I think I would agree that if I think the end goal is for kids to rote memorize these rules and mimic them. Then, yes, it would be better to get some conceptual understanding, and then do that. 

Kim  13:44  
Yeah,

Kim  13:44  
yeah. I think...

Pam  13:45  
Not my goal. Not our goal. 

Kim  13:45  
Yeah, and I think it's really important. You know, I was just sitting here thinking like why is it so important for you and for me to make sure that people understand or have heard us describe why what we're talking about is different. And I think it's because if you have a different belief, then maybe it's okay that you do something different. But we want to make sure that people understand that what we're doing matches maybe a different belief system than... You know like, you said earlier. There's like maybe this giant camp of like maybe not traditional but a whole bunch of other stuff, and we want to make sure that the belief and the intention matches up with what we're doing. And maybe there are some people in this kind of giant camp of some inquiry that also have a different belief. There's maybe like a little bit more of a separation. And so,

Kim  14:34  
I think it's important... 

Pam  14:39  
So, don't lump us all together (unclear).

Kim  14:43  
Right? And I

Kim  14:44  
think it's important for people to know like even within that, that there's more to just to dig into. And it's maybe not like, you know, "Oh, they're wrong or they're right." It's like, dig in more, find out what you believe, and don't assume everybody's the same.

Pam  15:03  
Yeah, and maybe another way to put that is you might listen to our podcast, read your books, do our workshops, join our coaching group, and you might initially go, "Oh, yeah, these guys are great. They have some ideas. They have some tricks. They have some things to try. They have some ways to tweak," and then have the completely understandable because then it will help us gain some conceptual understanding, so that the kids can memorize (unclear)...

Kim  15:25  
Right.

Pam  15:25  
...the rules better. What we're suggesting today is we invite you to consider that that's not actually who we are, what we do. We're not just a bit of get a little, do a little bit better here, and our end goal is still the same. We have a different end goal.

Kim  15:40  
Mmhm. 

Pam  15:41  
One of the particular sessions that I was in after the presenter said something like, "Okay, good, now that we've got some conceptual understanding, now it's perfectly okay to give kids the rules because we know they're just going to repeat these efficient rules to get answers. That's our goal." I'll push back on that idea that they are efficient in a big, huge way. And then a couple of times the presenter did something kind of cute. So, I can think of one where the presenter showed us actually had us get up and do some kind of a dance to help us remember the rules. And it was sort of this physical thing. And that's like you could say, "Oh, look. That's using brain science because if we get physical, then we'll remember the rules better." Again, that's assuming that our goal is to remember the rules.

Kim  16:23  
Right. 

Pam  16:24  
To mimic the steps.

Kim  16:25  
Mmhm.

Pam  16:25  
And then in another session, the presenter had something similar with this kind of pneumonic memory device, and then said to the kids, "Go create your own mnemonic memory device and turn that in as an assignment. Now, that feels kind of cool because now the kids are able to use their creativity. Oh, finally, we figured out how to use creativity in math class. But again, all of that still was creativity toward how could you memorize these rules different or better, so that you can mimic, so you can follow the steps to get answers. So, what if our goal isn't to mimic rules to get answers? And that's kind of what I'm hoping this episode could be a little bit about is we could sort of parse out some of these sessions that I've just seen and heard. And, ya'll, you can listen to what we say, and you can go, "I don't know, Pam, and, Kim. I kind of like your fluff. You know, I kind of like your stuff. That little tricks that you do, it's making my class better enough. I do think that the end goal is for kids to do the rules, so they can get answers. That is the goal." Okay. Well, you're welcome here.

Kim  17:21  
Yeah.

Pam  17:22  
As long as you're kind of clear, we just want to... I would like to be clear that I've learned there is a different set of mental actions that mathy people actually do.

Kim  17:31  
Mmhm. 

Pam  17:32  
And the good news is we can actually do that ourselves and help our students do that. And now, we're all mathing, doing the mental actions that mathy people actually do, and then now we're all mathy people. 

Kim  17:45  
Yeah.

Pam  17:45  
There's not a math gene. We're all mathy people. We can all be mathy people.

Kim  17:49  
Mmhm. 

Pam  17:50  
And the good news is we can do that, so that is... I don't know if that is helpful. It's a huge sort of shift. So, Kim, I'd like to kind of dive into two ways that we could sort of learn from these experiences that I've just kind of had.

Kim  18:03  
Sure. 

Pam  18:03  
So, one is leaders. Now, teachers don't tune out quite yet. But, leaders, specifically, let's stay with you for a second. When you do professional learning, I invite you to consider that you could actually have your teachers dive into the same kinds of learning experiences that you want your students to dive, that you're you're telling them to have their students dive into. In other words, if you say, "Hey teachers, it's really better to have your students experience the math." Instead of telling them that, help them experience that. Help them just like we want teaching to not be telling. We want teaching, teaching to not be telling.

Kim  18:43  
Mmhm.

Pam  18:43  
We want teaching math to be helping kids experience. We want teaching, teaching to help teachers experience.

Kim  18:49  
Mmhm. 

Pam  18:49  
So, don't show, experience.

Kim  18:53  
Yeah. You mentioned in the examples that you gave.

Pam  18:57  
Mmhm.

Kim  18:58  
That some presenters showed the math and then said, "This is what I show the kids." And maybe they don't quite mean "show", but I'm struck by a comment that we just got in our coaching Facebook group that a person, incredible person, said, "My kids already know the algorithms. Do I still show them strategies?" And I think...

Pam  19:21  
That word ping for you? "Show". 

Kim  18:53  
It did. And it did. It's pinging for me now because I think that's another thing that we push hard on, that it's not about showing.

Pam  19:30  
Yeah, so what I think, what we would say is we kind of don't care what your kids come in with. We're going to develop in their brains mathematical relationships and connections, which leads to them using strategies.

Kim  19:42  
Mmhm. 

Pam  19:42  
And a way that we develop those relationships and connections is by helping develop the strategies. We develop those relationships and connections, so the strategies become kind of their natural inclination, their natural outcome. And that, yes, we would absolutely do that because our goal is to develop kinds of reasoning, not just having them get answers. So, it's almost like this very good person that you're saying said something like, "But if my kids can get answers, do I still help them develop the necessary mathematical reasoning?" And the answer to that is yes. Just because kids can get answers doesn't mean that we've done our goal of helping them create reasoning.

Kim  20:19  
Yeah. And that doesn't happen by showing them things. 

Pam  20:23  
Yeah.

Kim  20:24  
You're not going to show some strategies and say like, "These are great and you can use them." We have to develop them within students.

Pam  20:32  
Yeah, which is not trivial, and so we're not going to do a lot of in this episode of what we do to develop. But we'll give you some ideas. But so, leaders, we would suggest that you involve, engage teachers in the experience of learning about teaching. And one way to do that is to watch video of expert teachers in classrooms. One things that we do in our Journey teacher coaching is that we reflect on teachers in classrooms with kids, and we reflect on that teaching together. We do that. It's one way that we do that. Another way that we do that is when we plan our Building Powerful Mathematics, asynchronous workshops. We... It's not me sitting at a computer talking to a screen, and so that when you're involved in that workshop, you're just listening to me talk at you. It is literally a live two-day workshop where I'm interacting with teachers, and it's as if you are there. We're doing the mathematics. We're diving in and building teachers... Pick it. Additive reasoning, multiplicative reason, proportional reasoning. And then as we're building that reasoning, then we step out and review what we've just done to then talk about the teacher moves that I just used in that mathing, and we identified then those pedagogical kinds of things. And so, when we plan PD, leaders, highly encourage you to think about engaging your teachers in mathing and getting them engaging in the mental actions of mathing, and then step out and talk about the pedagogy and what they've been doing, and how to teach that way.

Kim  22:11  
Yeah. And so, why does that matter? Well, we have to acknowledge that many of the teachers who in classrooms today have not had the experiences that we're talking about. They were probably very often taught pretty traditionally. And frankly, it's unfair to have them teach what we're talking about without giving them experience of what that can look like and sound like. And even more so, they deserve to know mathing the way that we're describing for their own personal

Kim  22:39  
lives. 

Pam  22:39  
Absolutely. Yeah, nice. Alright, let's shift a little bit. So, that was to leaders. So, teachers, I'm really clear that several of these speakers that I'm talking about were excited. They were like, "Let me tell you what I've learned. I've learned that if I get some conceptual understanding, man, everything makes more sense. I'm able to..." Well, in fact, we're going to talk about this on an episode coming up, Kim. We were just planning. "I'm able to read word problems better because I'm actually understanding the concepts better, and so everything's making more sense." It's a whole lot less guess and, you know, pick and stuff, and it's more I'm understanding. I love that. I love the fact that that that could be part of a Journey to realize that if we get conceptual understanding, algorithms make more sense. I invite you to consider there's more to mathing than that, that there isn't this weird dichotomy, this weird split, this weird separation of conceptual understanding, procedural fluency, that it's not, "Let's get some conceptual understanding over here, and now we have kids perform these steps, so they can get answers," that mathing is actually logicing your way through using real mathematical relationships and connections like content. And yes, getting answers. But the goal is to develop that kind of reasoning, so that you own the math, you own the the facts, and you own ways of getting there, and you have a dense connection, a dense web of connections that you really actually own. So, in class, we want you reasoning not mimicking.

Kim  24:21  
Yeah.

Pam  24:21  
And sending the message all the time that Math is Figure-Out-Able. It's not, "Hey, let's do some conceptual stuff. And actually, you can wait me out during this fun time because later I'm just going to give you the rules that you're going to mimic and get answers." Teachers, I invite you to consider that if there's ever been a time where kids go, Just give me the rules. Tell me how to do it," that that you have probably inadvertently set up, that they know they can kind of wait for that because you've, for whatever reason... Well, and probably because this way we were taught, they know they can get away with not doing and not really doing any of the conceptual understanding part of it because they can get to, "I'm just going to memorize stuff. Just give me the stuff to memorize. I'm just going to repeat it. I'm going to circle the answer. We're going to move on. That's what I know is going to matter here in class. We're offering an alternative.

Kim  25:08  
Mmhm. So, the students that we want to create who are reasoning rather than mimicking, why is that better? We would argue that because we need students to make sense of the world around them. We don't need mimickers. We have tools at our disposal. We need, in our world, thinkers, and creators, and problem solvers.

Pam  25:30  
Oh, that's nicely said. Yeah.

Kim  25:31  
Okay, so let me see if I can summarize all the things.

Pam  25:34  
All the things. 

Kim  25:35  
Okay, so it's not... In PD, it's not about, "Hey, let's do some things where I tell you the math, and then I tell you how I would actually do it with students." You're suggesting that we should experience math with our teachers, and then they can take that that they've learned and help their students experience the math as well.

Pam  25:57  
The only thing I would tweak in there is experience the math and the teaching. 

Kim  26:01  
Okay.

Pam  26:01  
So, it's not like, "Hey, teachers, go do the math," and you walk out of the room, presenters. 

Kim  26:05  
Yeah, yeah. 

Pam  26:05  
PD. You're actually... What's the word I want? Enacting. Enacting the teacher moves. 

Kim  26:12  
Yeah, that you want them.

Pam  26:14  
That you want them to do, so they get a chance. Ya'll, in the minute to minute decision making, we rely on our personal experiences. And most of our personal experiences were teachers who had end goals of repeating steps of algorithms to get answers, and so we lean back on that. We need to give ourselves and teachers different experiences that they can lean back on. So, in the moment to moment decision making, when a kid says something, does something, reacts this way, the task goes this way, they can go, "Oh, well, I just experienced in my PD where the facilitator of the PD asked me just this question, and walked away."

Pam  26:48  
Yeah.

Pam  26:49  
Or said, "What are you thinking" and walked away. Or said, "Ooh, that sounds like what they were doing over in that group" and walked away. Or, "Ooh, this feels familiar like the string we just did. I wonder if that could be helpful here," and walked away. Like, now you've experienced moves that you could go, "Ooh, now I can draw on those experiences to pull into my classroom. 

Pam  27:11  
Yeah.

Kim  27:11  
We actually have a another episode about knowing your beliefs that I shared recently because it's a great way to start the year. Just reminding yourself like, "What do I believe? And in what I doing. In my day to day work, is my belief showing in the actions that I'm doing? Okay, and so with students, we're not suggesting that it's about, "Hey, let's do a bunch of great activities and then tell them." 

Pam  27:33  
To get you engaged.

Kim  27:34  
Yeah. "To get you engaged. And now, we're just going to have to practice some algorithms because that's what you're always going to actually be using.

Pam  27:43  
And but

Pam  27:44  
make it cute. And fun 

Kim  27:45  
Yeah.

Pam  27:45  
And musical. And dance. And now, I'm not saying we don't want kids physically involved. What I'm suggesting is is getting them physically involved in rote memorizing and mimicking procedures is not the goal of math class.

Kim  27:58  
Yeah. So, what we really want is to help students recognize relationships, and then use those relationships to develop strategies, and help them determine when to use those strategies in the work that they're doing. Not only in math class, but in their

Kim  28:14  
life. 

Pam  28:15  
And those are the mental actions of mathematicians. And if this is your first episode, we invite you to listen to some other episodes where we actually do some math and talk about teaching. We'll do some more of that in future episodes. But today, yeah, we just kind of wanted to dive in. You might think that when you go to a feature speaker presentation at a conference and you hear somebody say, "Yeah, I do some conceptual understanding, so that then you can do this goal of rote memorizing and mimicking," you might think we fall in that camp, and we don't. So, we invite you to just know that. And maybe if you're curious about that, keep diving in. Then what do we mean? And what does that look like? And how can we help kids math the way mathy people actually math? 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!