Ep 135: The Challenge

Pam: 0:01

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

Kim: 0:07

And I'm Kim.

Pam: 0:08

And you have 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 mathematicians as we co-create meaning together. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keeps students from being the mathematicians they can be.

Kim: 0:38

Okay, Pam, super excited! The challenge starts tomorrow. The "You Can Change Math Class" Challenge is tomorrow. We're super excited. It's not too late to register. On the podcast, we've talked about the free ebooklet that you put out. And literally thousands of people have downloaded it, and we have heard how helpful it's been to parse out the major strategies, and really all the parts of this resource. So, listeners, even if you have already downloaded it, and made use of this PDF, we still think it'll be worth your while to join us as Pam shares her thinking beyond different parts and we gather together to discuss how it can change your classroom. You can still join us. You can register today at mathisfigureoutable.com/change.

Pam: 1:28

And if you're listening to this at a different time, the dates for that are January 18th- 20th, 2023 is when the Challenge will be if you're listening to different time. You can check out mathisfigureoutable.com/change to find out when our next Challenge is. But we are super excited because January 18th, we will be having one of our Challenges. And you might be like, "What is a challenge?" Well, literally, we get a chance to meet together live on Zoom. And if you register, and you can't make those times, you get the link to the recordings. But we get a chance to be together live on Zoom. I can see 50 of you at a time. It's a really high energy.

Kim: 2:10

Get in early!

Pam: 2:11

Oh, yeah. That is actually. Should we say that? We have people that join in like an hour before because then they're the ones that get to be one of the first 50 on the screen, which means... I'm super interactive. I don't know. You probably can't tell that on the podcast. But anytime I do anything virtual...or in person, for heaven's sakes...it's very interactive. I'm not a 'talk at you' kind of person, which I don't know if I can. This is so not in the plan to say. It's one of the reasons why, Kim, I begged you to be my co-host because I was like, "There's no way that I can sit here and talk at people on a podcast. Our colleague Sue. How long did she? It's forever.

Kim: 2:51

Oh, forever.

Pam: 2:52

She kept like, "You should do a podcast. You should do a podcast." And she was the brilliant one who said, "Really, it's the two of you talking together." Like, we would go and do workshops together and stuff, and the three of us would be in the car, and Sue would be like,"I'm just going to record this right now, just you two beating stuff out, and that can be a podcast." And we just laugh at each other. We're like, "Right, who would want to listen to us talk to each other?" But in a huge way, it's the interaction. So, I'm super interactive. That really gets me. And the challenge is that way. We'll definitely... You'll hear lots of questioning. We'll be doing examples of math. And for this Challenge, we are really going to focus on the behind the scenes, the reasons, the underlying stuff that went into, that goes into, that has everything to do with that major ebook. We won't be talking through all the parts, but we will be giving you an inside glimpse of the importance of certain parts. We will be doing some parsing out of some of the places where people have asked questions, and that they weren't quite clear on some of the things. We'll be giving you insight about the order, and why the order is the way it is. So, lots of really important and interesting pearls of wisdom will be coming out about that free ebook. Let's see, we will put the link to that free ebook in this podcast. But, y'all, join the Challenge because then you'll get the links for the ebooklet in that, and you'll also get all the other stuff that comes with being part of the Challenge. Like, we have a super cool Facebook group where there'll be lots of interactions. When we give you some short action things to do for some quick wins, we'll have those reminders in the Facebook group. (unclear). You can report on how they went, and that helps us all learn together and stay accountable, and we can sort of comment on each other's. You can ask questions. So, lots of really cool parts, things that happen when you join in our You Can Change Math Class Challenge because we can all reach more and more students. I mentioned a special guest. So, our special guests for this Challenge, we're super excited to announce, is a teacher extraordinaire, Michelle Chu, who has some amazing things to say about assessment. Because when you're teaching in a Math is Figure-Out-Able classroom, assessment can be tricky. It can be a thing that you are grappling with and parsing out, and we're going to get some helpful advice from Michelle. So, check that out. And Kim, in the last Challenge, we had John San Giovanni join us, and he said something. He was fantastic, right?

Kim: 5:28

Mmhmm.

Pam: 5:29

Fantastic. Everybody super enjoyed him. John, thanks so much for coming on. We had a super time with you. But he said something I have been thinking about for quite a while. And you and I beat this out a little bit, and I thought it would be good for us to sort of beat it out a little bit today, kind of off the... How do you say that phrase?

Kim: 5:49

Off hand?

Pam: 5:49

Off the cuff? Off the cuff, just kind of as a mention. It wasn't like a major point he was making or anything. He just kind of said, "Well, you know, there's the math you do at school. And there's the math you do everywhere else." And he went on, and he kind of talked about some of the things, and I was like, "Wait, wait, wait. Backup. Say that again?" And he goes,"Well, you know, there's the math..." Maybe I should say, John and his co-author, Jenny Bay Williams have a fantastic book series out there called"Figuring Out Fluency." And John is a numeracy expert. And both of them are one of the only people out there that I'm aware of that are doing similar work that I'm doing, which is parsing out what are the major strategies. And they have started that work, and I'm doing that work, and not a lot of other people are doing that work. To say, if we're teaching relationships and connections, not algorithms and step-by-step procedures, what are the major relationships and connections that are important? And I really value their work. And in the midst of discussing that, he said, "So, you know, there's the math you do at school. And there's the math you do everywhere else." And I want to push back on that just a little bit. And I said to him, "Wait, wait, wait. I think maybe that was true for you." He's like,"What do you mean?" And I'm like, "Well, maybe for you there was the math you did at school, and you did something else everywhere else. Everywhere else, when you ran into a math problem, you didn't actually just repeat a procedure that you learned at school. You didn't just mimic what the teacher had shown you. You did something else. But that's not true for all of us. And John, I love ya. He kind of looked at me like,"What?" And I was like, "Yeah. Like me. Like, my perspective was I repeated the procedures at school, everywhere." And he goes. He kind of chuckled Like,"Really?" Like, "Well, no, yeah, actually, really. Like, that was..." My perspective of math was so ingrained that the definition of math, the nature of math was you wait until the teacher gives you something and it shows you the steps, and then you mimic those steps. That was what math meant to me as a high school math teacher. Now, I think I was a pretty good high school math teacher, traditional high school math teacher because I helped make that fun and exciting, and I had great rhymes to help, you know which rule to do when, and then I had great mnemonics, and pictures, and stuff to help you know which steps were the ones in that procedure. I'm a fairly interesting storyteller, and so my students knew that, you know, my class was relatively interesting. But they weren't mathematizing. It wasn't a mathematizing class. I didn't know what that meant. There's no way that I could do it. So, it made me think about some perspective work that we've talked about on the podcast before, where I think there are these... I think there's at least three. Well, let me say four. I think there's four main perspectives that we could have had as students, and I think those perspectives impact your teaching. I think they have to. The way that you were taught, the way you view math, the way that you view what math is, and therefore what it means to teach math, it has to affect the way that you teach.

Kim: 9:05

Sure.

Pam: 9:06

So, just quickly, I'll give you a quick recap on those four perspectives and how that could be impacting your teaching. And we'll put in the show notes the other episodes, if you want to go dive into that similar. Which is really cool. Especially if you're a leader, I would highly recommend that you dive into the quiz that we have that can help you and the teachers you work with identify what your perspective was and how that could be impacting, not only the way you teach but the way you're listening to PD, the way you're listening to what people say, the way you filter... It's all impacted by that perspective that we had about what math was and how that affects your teaching today. So, one perspective, I sort of call. I just gave them variable labels because I'm a high school math teacher. So, one of them is called the X perspective. And I consider the X perspective, the Kim perspective and the John San Giovanni perspective. Now, John, you can tell me that this is incorrect. But here's why. I'll tell you why. I think there's a group of people out there that sort of naturally play the game of math, that for whatever reason. I think often they had someone early in their life that played with mathematical relationships with them, and because of that, they made connections in their brains, and they were able to then build on those. They also might have a natural affinity for that. I think there's a natural affinity for things. I think some people are naturally more gifted basketball players without a lot of work than others. And then, whoever puts in the work that sort of falls out. I think that can be true in all areas of life, that we all have sort of natural talents that we can build on. So, I think there's this group of people that for whatever reason, maybe...Like I said, maybe they had people early in their lives that were influencing them, maybe they had this natural talent, maybe they had both...that naturally solved math problems using relationships and connections. And even when they saw the teacher show step-by-step procedures, they knew there was more. They were aware that when the teacher said, "Alright, to add 99 plus 47, line them up, and add these digits." people like Kim said, "I mean... you could do that for those numbers. But for those numbers, everybody's just thinking about 99, 100, and then add the leftovers." Or if you were Kim, you were thinking about 47 plus 100, and then backing up 1. So, there's this whole perspective out there that means you can see the steps, the teacher can show you the steps, and you can sort of see through them to times where you can actually use relationships. And then importantly, everyone else is also seeing that. That everyone else is also seeing these other relationships and connections, even though we're being shown the rule and we're expected to do the rule in school. It's kind of like what John said, "You do the school math in school, but you do this other math outside of math, outside of school." I think that perspective can impact the way you teach because it quote, unquote "worked for you," and so you are going to turn around and teach the way you were taught. And those students who did what you did will naturally pick it up, and you can have fun playing around with them with the math; and everyone else, I guess doesn't have the math gene, and so they must need the rules, and so you'll do the rules slower and louder, and you'll help them as best you can to.. Did you just totally laugh at me saying"slower and louder"? And I'm not trying to be ornery. I think that's an honest perspective. That if you honestly didn't see anything else. Kim, you've said before, you honestly didn't know there was another way to think that other people experienced math, right?

Kim: 12:44

I absolutely thought that there were many, many, many more people who saw relationships and patterns like I did. And so, when they didn't catch on to the things that I was saying, I was troubled. I was like, "Okay, well, let's try this. Let's try this." Because I just assumed that they saw what I saw and thought about what I thought about.

Pam: 13:10

And didn't have... None of us have experience in our... I shouldn't say "none". But most of us don't have experienced as a student seeing anything else, right? There wasn't anything else to try that maybe could help. Now, there's a lot of other things being thrown out there now, but if it's still your perspective that kids should be able to sort of get it on their own or were stymied, then that's tough. Yeah. Okay. So, that could be a perspective. We call it the X perspective. Just not for a reason, just because it's a variable. So, another perspective is the perspective that I had. And I call that the Z perspective. And it is the perspective that the nature of math is, you must wait until someone shows you what to do. Doing math means you're performing steps and procedures. Learning math means you're figuring out which rule to do when, and when you've remembered which rule, then you've got to parse out which step. Not parse out. That's too thinking. Then, you're remembering what steps to do in that rule. And so, until the teacher shows you what to do, you don't know how to do a problem. And the nature of math is mimicking. And those who can have a memory are going to mimic better because they can memorize stuff. And so, since it's all based on rote memory, how it might affect your teaching is you're going to help students memorize. You're going to help them realize which rule to do when, and once they've realized the rule, you're going to help them realize which one of those steps in that rule, and all that. Sometimes people will poke me and go, "I can't believe you didn't think at all while you're doing math." And I'm like, "No, no, no, no. No, I thought a lot. I worked really hard!" But all my thinking was about someone else's thinking. It was always trying to make sense of what I was just shown what to do when, and then what were the steps in there, make sure I didn't miss a step. So, I was doing a lot of thinking, but it was always someone else's thinking. It wasn't, "What do you think about when you see this problem? What relationships ping for you?" It was, "Which rule? What part of the textbook do you see in your head right now? Oh, that rule, okay. Now, remember the steps in the rule." So, if you relate to my perspective, then you're working hard to help students memorize. You're teaching them songs, and rhymes, and raps, and you've got pictures, and you're telling stories, and you're making. Now, I didn't do this. But you might be making math cute, so there might be like turtle multiplication, and the bat and the ball for memorizing the cross multiply and divide. That's a name I just heard. Pizza Steve for knowing what to do with integer operations. Like, you've come up with sort of these cute, catchy mnemonic kinds of things to help students rote memorize if that's the perspective.

Kim: 15:58

Yeah.

Pam: 15:59

And then quickly, I'll describe a third perspective, which I kind of came across a bit later and mostly happened because of my daughter. Bless her heart. And I'm super glad God gave her to me because she's helped me understand this perspective. The perspective that she had was that she could not do the math unless she understood why. So, I call that group the Y group. And often, that group gets super frustrated because they believe they can know why. That's different than the perspective I had, the Z perspective, where I believed I could know which rule to do when, but I believed I had to wait until somebody handed it to me. And I wouldn't ever really understand why that rule, I just... Yeah. But the Y perspective, it's almost like this psychic break thing where they're like, "I will not. I believe I can understand what you're doing, and I want you to explain it to me, so I understand it. And until you explain it to me, I'm going to put my foot down, and I'm going to go, 'No, I want to understand'. Because if I don't understand, I'm not going to be able to do your thing. And so, I want to..." And they believe they can understand. And that group, I have to work the least with because that group once we get them into Team Real Math, once we get them mathematizing, and Math is Figure-Out-Able, and we help them learn the math, they just soar. Because they always believe they can understand why, and now they understand why, and they will happily teach that way to help kids understand why. So, if you relate to that Y perspective, all we do is just help you learn more math. And then, we set you free. And once you're like, "Oh, that's how I just learned that through you. I'll do that with my students." And they happily do that with their students.

Kim: 17:34

Yeah.

Pam: 17:35

So, the fourth perspective that I'd like to share is different than those three. The fourth perspective is where I hope to nudge all of us into believing that math is Real Math, and that Math is Figure-Out-Able. And that we can all learn what those X's were doing sort of naturally in their head if we get it out, if we understand what it is. If we make it visible, and discussable, and comparable, we can all think that way, and we can all then teach math that way. We can teach math as being figure-out-able, not rote memorizable. So, I call that team R, that's the R. So, if we have to put a variable to it, we kind of have the X's that were sort of doing all that math on their own, we have the Z's that it was kind of all about rote memorizing. Well, actually, let me back up. So, X is math was learned on your own, and then therefore teach the way they were taught because it works for them. And they don't know, like Kim said, "I don't know what else to do. Like, it was troubling." And so you try, but you're not sure how to help kids do what you kind of did naturally. We can help with that. If you're a Z perspective, and everything was rote memorized, and so now you're trying to make math cute and memorizable, we can help you learn the math that's figure-out-able, and then teach math that way that you're learning. And if you're a Y, good gravy we just such we're just such a loose, We just set you loose to help the world know why. And we all know why. And then, we can all be on Team R, Team Real Math.

Kim: 19:02

Yeah. And you and I have experience because we have different members of our family. Even if we hadn't worked with a ton of teachers, we have varying perspectives in our family, so we know they exist. And you and I have talked about this a number of times because we had very different perspectives. And so, the implications for teaching are that teachers have these kids with different perspectives, these students with these perspectives in their class. And I think the major point is that, your teaching is likely to be impacted based on your perspective that you had growing up. And while you can't change the perspective that you had growing up, there are things that you can do to get a glimpse of some of these other perspectives. My kids have had teachers who have all these different perspectives in their... You know, being raised in school. And sometimes they have teachers who have the same perspective as them, and that sounds great and lovely and let them fly, and if they're an X, then yay for them! But that also means that there are other students in the class who had different perspectives or have diverse perspectives at that time. And so, you know, I've had my kids land in classrooms where the teacher had Z perspectives, and I've had my kids come home and say, "It's all about memorizing. And I think with you, and I've thought in classes before. But now, I'm in this classroom." They don't say Z perspective, but what they mean is, it's all about mimicking. And, you know, they struggle a little bit with this idea that now what's honored is not their thinking and reasoning. And so, your idea here, your work is that we can be aware of these perspectives, and we can help everybody flourish.

Pam: 20:59

Absolutely. And really, I want to lift everybody out of those three perspectives into the fourth perspective because once we teach math as Real Math, as figure-out-able, then everybody has the R perspective, and we're just all on Real Math, and everybody flourishes in that atmosphere. Everybody does more math, learns more math, is more successful at math in that R perspective. Even the X's because. Let me just clarify something that you just said, how somebody might have heard when you said that your kids have had teachers in the past that might have had the same perspective. What you don't mean is that if you had an X perspective where you kind of were naturally, and then you have a kid who has that perspective, that that's super. No, actually, it isn't great because anybody who is teaching from that X perspective, not the real perspective, the R perspective, isn't helping the students and themselves go as far, as fast as they could. Like... I'm not saying that very well. Sometimes teachers will say, "Well, but as long as I'm sort of naturally doing it, and I have kids that sort of naturally do it, then that's great. It's just these other people." I'm like "No, no, no." Because once you understand. Yes, you were doing some things naturally, but think how much math you could actually own If somebody knew what that Real Math was and was helping you develop as a mathematician. You can go so much further, faster on Team R, on Team Real Math. Yeah, figure-out-able math. Cool.

Kim: 22:28

Yep. So, we invite our listeners and anyone in the world to join us in this work, right, to join us in the opportunity to experience Real Math together.

Pam: 22:41

And we can do that in the Challenge tomorrow. So, if you're interested to experience what Team R looks like, feels like, grow your math, watch other people really grow in that Team R, Team Real Math perspective, watch how I interact with people who have these different perspectives, who had them as students and are now diving into a Figure-Out-Able class, the Challenge can give you a glimpse of what it means to help us all teach more and more Real Math. So, we really hope that you will consider joining us tomorrow because, ya'll, if you enjoy the Podcast. The podcast is a fantastic place to learn, but we think the best way to learn is interactive, and we can be super interactive in that Challenge. And so, a great place. You want to meet? You want to meet Kim and me? Because. yeah. Kind of fun to listen to the podcast. Well, a super place to meet us live is in the Challenge. So, join the Challenge. You can do that at mathisfigureoutable.com/change. It is not too late to sign up sometime between January 18th and the 20th. You can still register. Love to have you join us. It's going to be super fun. So, 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!