Math is Figure-Out-Able with Pam Harris

Ep 179: Fake Math, Not Fake People

November 21, 2023 Pam Harris Episode 179
Math is Figure-Out-Able with Pam Harris
Ep 179: Fake Math, Not Fake People
Show Notes Transcript

What does it mean when we say 'fake math' or 'less sophisticated'? Pam and Kim discuss how learning Real Math is empowering and opens a whole new world of understanding.
Talking Points:

  • Are squared numbers an important thing to own?
  • The Matrix
  • It takes experience to understand perspectives
  • Martians
  • Doing 'fake math' or using a 'less sophisticated' way of thinking does not make the person fake or unsophisticated
  • Real math is empowering and can open up a new reality!

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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

Pam  00:03

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


Kim  00:09

And I'm Kim.


Pam  00:10

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


Kim  00:39

Listen, I don't know if people recognize, or maybe have any way of knowing, how much joking around we do prior. (unclear).


Pam  00:47

Right before we hit the button? 


Kim  00:48

We're laughing about something, and Pam's like "Go!" And I was like, "Oh. I'm still laughing!"


Pam  00:53

Yeah, that's kind of why that was.


Kim  00:54

It's good fun. It's good fun. 


Pam  00:55

Yep. Yep. We actually enjoy each other, which is kind of fun.


Kim  00:58

I mean, it's super fun. 


Pam  00:59



Kim  01:01

So, listen. I'm not going to read a review every single week. But it's been super (unclear). 


Pam  01:05

Why not?! 


Kim  01:05

And well, I know. But, you know, I'll be choosy. But it is really cool to think about how people are now thinking and sharing in (unclear).


Pam  01:15

Ya'll, it makes Kim's day. So keep doing it.


Kim  01:17

It's super fun.


Pam  01:18

It makes both of our days, but especially Kim.


Kim  01:20

I mean, it's exactly what we hope for, right? 


Pam  01:22

Yeah, (unclear). Absolutely. 


Kim  01:24

I chose one from (unclear)Reviewer. And the caption at the top says "Transformative", which is cool. 


Pam  01:31



Kim  01:31

"These incredible women completely transform my teaching. I knew that what I was doing in my math class was not meaningful, but I didn't know what to do about it." That's so insightful, right? Like, that's a struggle. I was fortunate enough to learn from them almost nine years ago in their workshops, and over several years. I'm so grateful for this podcast to continue my growth. And I just love feeling like they're still with me because they're wonderful humans. Thank you, for all you do."


Pam  01:57



Kim  01:58

Super cool.


Pam  01:59

(unclear)Reviewer. That's awesome! Nice.


Kim  02:02

So, thanks for listening.


Pam  02:03



Kim  02:03

We plan to be here for a while, so don't go anywhere. 


Pam  02:06



Kim  02:07

So, Pam, the other day. I don't know if I told you this. But I was working on something for Journey.


Pam  02:13



Kim  02:13

The membership site if listeners don't know about that. And I called Sue up. You know, Sue's amazing and wonderful and (unclear).


Pam  02:20

She's on our team. Yep.


Kim  02:21

Yeah, she's or our team. And I said, "Hey, Sue? You know how I think partners of 10 and 100 and 1,000 are like super critical to all we do, and we constantly talk about that with people? Do you think it's possible that I don't see square numbers in the same way because I don't own all the relationships up to 20^2 at my fingertips?" And she was like, "Yeah." I was like... I mean, I have many of them, but I don't have them all (unclear)


Pam  02:52

(unclear) Yeah, let's define a square number. So, 16 is square because it's 4 times 4. So, like 25 is square because it's 5 times 5. 144 is square because it's 12 times 12.


Kim  03:02



Pam  03:02

Okay, cool.


Kim  03:03

And so I, you know, several of them between 13 and 20 I've got. But I was thinking about it, and I said, "You know, I..." Sue has mentioned to me before that she thinks that's really important. And I called her, and I said, "I don't know that I buy it. But talk to me more." And so, then in the car one morning, I still wasn't buying it. But I asked Luke, my oldest, and I asked him the same question, and I said, "Do you think it's possible?" Like I said, "Tell me the ones that you own." And it was pretty much the same ones as me. 


Pam  03:38



Kim  03:39

I was really wondering. He and I both could find the square numbers. I mean, using relationships, we could pretty easily figure 16 by 16. But I was just very curious. In the grand scheme of all the things to own, are square numbers one of them? And I concluded that I don't know that I can make that judgment because I know that I don't fully own them. And I think I'd have to own them to be able to decide, was that worth? In all of mathematics, was that worth me owning? And (unclear) a moment for me that I had to really think about, is it possible that I didn't know them, and so I couldn't judge? And I wonder if that's how people feel about the partners have 10, 100, 1,000. You had that experience, right?


Pam  04:33

Yeah. So, let's maybe broaden the conversation because you had brought up partners of 10, 100, 1,000. You brought up square numbers. I had a similar experience where I was starting to. Early, early, when I was experimenting in my kids classrooms. I started to notice that doubles were important. 


Kim  04:50



Pam  04:50

Like, Kim, I was just doubling single digit numbers, and I was noticing how if you kind of knew the doubles of single digit numbers, you could work off of those for addition and subtraction. And in the midst of that, I was doing all this professional development for TI with graphing calculators. And I said something about, you know, doubling. And this teacher, I'll never forget. It was an Algebra 2 pre-cal workshop, where I'm teaching them about, you know, graphing calculators. And this teacher said, "Oh, yeah. Doubles are super important. Like, double 75. Double 35." And I was like, "What?" Like, those were so off my radar. 


Kim  05:24



Pam  05:25

And I said "Double 35 is important? And she goes, "Oh, yeah. It shows up everywhere." In that moment, I had to have a kind of a similar. Like I literally said, "It shows up nowhere." Like, "I have never used double 35 in my life." And she kind of looked. I don't think I said that out loud. But, you know, it was just kind of this back and forth a little bit. We were doing was pre-cal stuff, trig and whatever. And I had to dive in and double and halve. You know, like, find halves of things and mess around until, "Oh, my gosh! Double 35 shows up everywhere!" Like, doubling is a thing that mathematicians do. But I couldn't see that, until I started to play with it and own those relationships. And then, I could see where they kind of appeared in life.


Kim  06:13



Pam  06:14

So, yeah. Kim, we decided to both of us talk about those experiences a little bit because I just had. So, very recently had an experience that helped me, caused me to grapple with some of the language that I have been using because of the way it was heard by some of the participants in a workshop. And I called you up, and I was like, "Kim, I'm really grappling with what just happened because some people in the workshop really very respectfully pushed back against some of what I was saying." And we decided that we would kind of carry on that conversation here on the podcast a little bit. Actually, just a short aside. We started this podcast in part because Sue, who you mentioned earlier, would sit in the car with us when we would go to presentations and workshops. And we would come back, and you and I would beat out something that had happened at the workshop, right? And Sue said, "You know, people would want to listen to this." And you and I were like, "What?"


Kim  07:06

I was like, "No. Nobody wants to listen to us talk. 


Pam  07:09

Like, "We're just talking." She goes, "No. Like, you are creating knowledge right here between the two of you. As you're beating this around, the two of you are like figuring stuff out. You're clarifying your own understanding. And people..." She said, "I'm finding it fascinating. Other people would want to listen to this. You guys should create a podcast." And it was part of the reason that we created a podcast. So, Sue, shout out to you. Thank you for pushing us to have these conversations live.


Kim  07:34

It's all your fault.


Pam  07:35

Yeah. So, we thought that we would kind of have this conversation live. So, let me tell you a little bit about what happened, tell the listeners a little bit what happened. And Kim, I might fill in some more details than I told you the other day. 


Kim  07:44



Pam  07:44

So, often, in a first workshop with people, I will talk about a little bit of my history, how I kind of thought that math was about just memorizing disconnected facts and mimicking rules and procedures. I waited till the teacher showed me what to do. And I now call that fake math. Well, later on in the presentation, one of the participants said, "I have a question." And I said, "Yeah, what's your question?" And this participant said, "I'm hurt a little." These aren't quite the words the person used, but it was something... The message I got was, "I'm kind of upset. I'm sad that you're calling the math I do fake." And I was like, "Oh, no! I'm not calling you fake!" Like, the person said, "I feel like I do things my own way, and I feel like you're calling me fake that my, the way I do, the way I'm..." And I was like, "Oh, no! It's not about what you're... It's not you. It's not about you. It's this perspective that the world kind of has that in math class, 'Here's what you do,' and we're going to call that math." And what I suggest when I call things "fake math" is not in any way meant to be ugly towards a person at all. It's not me saying "You're fake" or "Your..." Kim help me. It's not about me being ugly to anybody. It really is much more about me saying, "Oh..." It's almost like The Matrix feel. Kim, did you ever see the movie The Matrix? 


Kim  09:27



Pam  09:28

So, I think I only saw parts of it. We have this rated R thing in our family, and I think was rated R when it came out, and so I saw like some TV version parts of it or whatever. But I think I understand the story well enough. That they're living their lives. And all of a sudden, something happens. They take a pill. Something about a pill. See, I didn't really see it. But all of a sudden, they realize that the life they think they're living is a computer simulation. And really, they're all in these pods hooked up to all these tubes and wires and stuff, and their minds are playing this computer simulation. So, there's this reality that they don't know about, and they think they're in reality. That's not... Like Keanu Reeves. I'm not dogging his character. I'm sure he has a name. I can't come up with his character's name right now. People are like yelling. They're like, "I can't believe you don't know this movie!" Alright, fine. I don't know it that well. I'm not dogging those characters. There's no way they could have known that the universe was sort of playing a trick on them. I'm suggesting that nobody was... I'm sure in that movie, there was some evil mastermind who created the false world. I'm not a conspiracy theorist saying that somebody is out there to fake everybody out. Not at all. I think that we somehow culturally got to a place where people said, "This is math. Math is you wait till I tell you what to do, and you mimic what I tell you to do. And now, you're doing math." And what I'm saying is, "Oh, yeah, actually not." 


Kim  09:30

Okay. Yeah.


Pam  10:57

It's actually not that way at all.


Kim  10:59

It reminds me a little bit as you were talking. Because I haven't seen the movie. But it's as if you've never been a hearing person. But for most of your life, people maybe have tried to tell you what it's like to hear. But then, if you got some sort of hearing aid, and you heard sound for the first time. It's like you have a new awareness in some way. But you couldn't have known. You couldn't have known what somebody was describing. And I feel like that's a little bit of the experience that you've had. You had no way of knowing what you now describe as Real Math was because nobody ever gave you that perspective. You had no experiences for what you describe as Real Math because people just, teachers kept telling you, "This is what math was." (unclear) Yeah.


Pam  11:49

Well, and I kept getting credit for it, right? Like, I got good grades for doing that thing. 


Kim  11:54



Pam  11:54

Because I can't say nobody tried. There were. Mrs. Newbern tried.


Kim  11:58

Oh, they did? 


Pam  11:59

I had a few instances...


Kim  12:01



Pam  12:01

...where people would say things like Mrs. Newbern. In eighth grade, we were multiplying binomials. You know, the typical x plus three times x minus 2 and whatever. And she goes, "You know, you could use that to multiply whole numbers." And I looked at her, and I was like, "Why would you..." If math to me meant,


Kim  12:18



Pam  12:19

"You have a way to get an answer. You get an answer. You get credit for that answer," why would I want another way? Like, "I get credit for the answer. I have a way. Don't give me one more thing to rote memorize." That's how I heard what she said. So, like when you have a perspective, when you're inside that matrix world, there's no way you can see out of it, until you get a chance to shift your perspective. 


Kim  12:43

Yeah, I was going to say. If somebody's telling you to do it, I don't think you can. But that's (unclear).


Pam  12:48

You have to build relationships. 


Kim  12:49



Pam  12:50

You have to build the relationships to make it work. You know, it's funny. It reminds me of another story. I'm feeling like I'm in middle school now that I'm remembering Mrs. Newbern. I'm thinking about (unclear) Scott, Junior High when I was there. I read a Ray Bradbury short story. I don't remember the name of it. But it was a short story by Ray Bradbury, where I think he's on the Moon or Mars or something. So, it's an astronaut. And in the situation, he's in the room. I don't remember too many details. I just remember the feeling at the end. I'll get there. But he's in the room, and he's reliving the day and how he was hanging out with his brother or his dad or somebody in his family. And he lays down to go to sleep. And he's in the same room with his brother, I think. And they're astronauts. And so, you know like, he's reliving where they landed and all the things. And as he's going to sleep, something strikes him, and he's like, "Well, that's odd. That doesn't quite fit." Some sort of thing that happened in the day. He's like, "Why was... That doesn't..." And then, he kind of follows a train of thought. Well, then that would mean, and then that would mean, and then that would mean. And oh my..." And then, he realizes that actually everyone has been slaughtered. He's the only human...


Kim  13:59



Pam  13:59

...alive. And the creature in the room with him is not his brother, it's the... And he opens his eyes, and he gets eaten by the Martian or something. I mean, it was like horrible.


Kim  14:09



Pam  14:09

So, it was like this moment of like. I feel like that person had no control over. I mean the Martians basically had sort of control. They had created this environment, where he felt like he was among the people that he knew. And so, the point here isn't... I can't blame the astronaut. I can't blame the guy in The Matrix. There's no blame here. Like if anybody knows Kim and me, we're not about blaming. We're really about empowering.


Kim  14:39



Pam  14:40

It's about saying, "Man, we now know that there's this whole universe of cool math that we invite you into." And I think... I guess during this presentation I was just mentioning a minute ago, where this person pushed back. I've just been thinking about things I did differently in that presentation. Let me tell you one other thing that happened in the presentation that kind of, again, had me kind of reeling a little bit. Like, what did I say differently here? Or how was my message being heard? And so, a different participant in the virtual workshop said, "Hey, I have a question." I had just been talking about additive reasoning and multiplicative reasoning and how multiplicative reasoning is more sophisticated than additive reasoning. And I asked, "How are you thinking about something like 7 times 8. And we had talked about that if you chunk 7 times 8 into multiplicative pieces you know, then that's more sophisticated than skip counting seven 8s. Skip counting seven 8s is additive reasoning, and we want to think about something like five 8s and two more 8s. Or seven 7s and one more 7. You know like, these big chunks. That that's more multiplicative reasoning. And this person said, "We'll I have a question." And I said, "Okay." And this person said, "I'm a visual kinesthetic learner." Which I'll come back to in just a minute. "And so, I needed other ways to learn multiplication facts. I couldn't learn multiplication facts the way other kids did. And so, because I'm a visual kinesthetic learner, I needed other ways." And I said, with all sincerity, "Tell me more about those ways. What helped your visual kinesthetic-ness of you?" Which again, I want to talk about in a second, so don't let me forget. "But what do you mean? What helped you?" And this person said, "Stories." And I said, "Give me an example." This person kind of paused. And I said, "Do you mean like 6 times 8? Like, the garden gate is made of six, so it's 56?" And this person, kind of a little defensively said, "Yeah. Yeah, I needed stories like that. Stories like that helped me learn the multiplication facts." I'm taking a deep breath. In that moment... Where to even start. So, respectfully, math teachers, math educators, parents, anybody out there. Stories, like I just said, are not visual or kinesthetic. So, that's a thing. Like, it's a memory technique. So, I believe you if you say, "I'm not a good memorizer." Okay, that's a thing. Some of us have better talents in one thing than the other thing. Some of us don't have a talent for memorizing. I believe that you could say, "I'm not a good memorizer, so if I need to memorize something, then (unclear) give me stories, or give me a pneumonic, or give me rhymes, or let me sing it, or..." Absolutely. And I have no problem with that. But that comes from a perspective of saying... When this person said, "In order to learn multiplication facts, I needed stories." I'm inviting everybody into the perspective that learning multiplication facts isn't about memorizing.


Kim  14:46



Pam  15:36

It's like we're in The Matrix, or we're in the astronaut’s bedroom, where we're in this perspective of "Oh, if I need..." That learning multiplication facts means I'm rote memorizing multiplication facts. Well, then, yeah. Like, then do all the memory stuff. Absolutely. What we're suggesting is, that's not the universe, that that's an incorrect perspective. It's not your fault. But your teachers fed it to you. What if learning multiplication facts wasn't about that at all? What if learning multiplication facts was actually building your brain to think and reason multiplicatively, so you could use chunks, bigger and bigger chunks, to solve a problem? 


Kim  18:28



Pam  18:29

Did I say what I mean there, Kim?


Kim  18:32

Yeah. And I'm thinking about not too terribly long ago. This comment came up in a JourneyLEADER group that we have. 


Pam  18:43

Our leader support group. Mmhm.


Kim  18:44

Yeah. And so, in that, Cathy Campbell. Shout out to Cathy Campbell.


Pam  18:48

Yay, Cathy!


Kim  18:48

Was talking about how she was working with a student on rounding, and the student had some trick, if you will, for rounding tens, but then really was having difficulty with rounding hundreds because they weren't able to transfer their thinking about whatever they came up with to round tens to round to hundreds. And my comment back to her was, "Yeah." Like, that person, that child thought of rounding tens as completely different than rounding to hundreds, and there was no connection between the two. And so, it was an experience where we got to talk about, that is exactly what it means to have isolated, disconnected things to memorize. And if it's true that you don't make any connections between something...that I feel like is pretty obvious like tens to hundreds because that's my worldview...then imagine all the things that we have to think about in math as just like the stack upon stack of things to memorize. That they didn't see any connection between rounding in general and what the point of rounding is. And so, it was just a moment we talked about a little bit that I'm thinking about right now. 


Pam  20:06

Yeah, that's a good connection. 


Kim  20:08

If you think of 7 times 8 is a fact to memorize, then you're not thinking about the relationship of 70 times 8 or 7 times 80.


Pam  20:17

Yeah. So, interesting. When that person brought up, "I'm a visual kinesthetic learner, then the person next to that person. So, I often have people when I do virtual PD will have them be 2 to a device. That way I can call on them, but I can also let them have partner conversation. And the partner said, "Yeah, yeah. Like, I actually use 6 times 7 to find 7 times 8." Which I thought was interesting. I don't hear that one very often. 6 times 7 to find 7 times 8. And I said, "Great, how do you use 6 times 7?" And he said, "Yeah, for whatever reason, I just know 6 times 7 is 42, and so..." I said. "Okay, well, you know, how do you get to..." So, that was thinking about six 7s, and he's trying to find eight 7s. And he said, "So, I know I need two more 7s. And then, I would count on by ones." So, remember, I had just helped juxtapose counting strategies, additive thinking, multiplicative thinking. And so, this person was kind of like, "And then, I count by ones." And I said, "So, you're at 42. You know that one. For whatever reason, 6 times 7 sticks, and you got 42. And then, you literally go 43, 44, 45, 46..." And he's like, "Yeah." And I said, "Okay." So, I said, "So, you're adding 42 and 7. I'm kind of curious. Do you know 2 and 7?" And this person said, "No, so I've got to count on by ones." Now, I wish... I didn't at the moment. I wish I would have said, "Do you know, 7 and 2?"


Kim  21:38

I think that's what you just said. So...


Pam  21:40

Oh, I didn't say 2 and 7? 


Kim  21:41

Oh, yeah, you did. I thought you asked (unclear).


Pam  21:43

Well, so I wanted to switch it. I wanted to flip the order a little bit.


Kim  21:45



Pam  21:45

So, this person said, "42, 43, 44..." and literally counted up to 49. And then, I decided to kind of let it go at that point. I said, "Okay, so now you're 49. You're going to add another 7? He's like, "Yeah." And I was like, "How would you do that?" "Well, I would count by ones." And I said, "So, I'm curious. So, 49... Do it for me." And he said, "50." And I said, "Okay, so you just added 1 to 49, and you got to 50. How much more do you have to add?" And he said, "6." And I said, "So, I know you can count by ones from there." And he's like, "Yeah, that's what I would do. I would count my ones." And I said, "I'm just super curious. Now, that you're at 50, and you know you have 6 more. Do you know 50, and 6?" And I'm writing right now because when I present, I have my iPad. I'm sharing my iPad. And so, on the paper, I had written 50 and a jump of 6. And I said, "Do you know 50 and 6?" And he looked up, and he goes, "Oh. That's just 56." So, what I didn't say in that moment, because I'll be honest, emotions were kind of hot. We were actually at the end of the time. I tried to spend a minute to say, "I'm not saying you're fake. I'm not saying that you're unsophisticated. I'm not saying..." You know, all of the words I had just used to describe the kinds of thinking wasn't me trying to be ugly towards people at all! It's really more me trying to say, "Oh, that's the way you're thinking? Do you know you can grow from there? There are other ways you could actually like be empowered to think more sophisticatedly. If you're interested. If you're interested. Like, once you added that 49 to 50, bam, you could just think about the rest of that. We could grow your additive reasoning. And once you’re reasoning additively more, we could grow your multiplicative reasoning." And I think actually relatively quickly. Once you know it's a thing. Like, it's opening the universe. It's realizing you're on Mars with the Martians. That's maybe not the best one. It's realizing you're in... Because you don't want the Martian to eat you. But you're in The Matrix, realizing what reality actually is. When you realize what reality actually is, now you have choices. Now, you can choose. Like, I'm just going to submit. If you were the person who thought, "The only way I can do this is sort of less than. I need these things. Everybody else somehow was able to get it differently than me, and I needed these other things." If that was the universe. But what if the universe is actually different? What if the universe is actually where you actually can reason like a mathematician?


Kim  24:08



Pam  24:08

That's the world that we're trying to invite you into. I hope I'm saying this well.


Kim  24:14

Well, I think I'm hearing that the perspective isn't... I don't want to say "correct". The perspective is not complete. There's more to the story maybe that this participant wasn't able to see based on what they have been taught. 


Pam  24:34

Well, it's like you said earlier. You don't know if square numbers are important because you don't own them, so they don't appear for you. I didn't think doubles were all that important because I didn't own them, and so they didn't show up for me places. The day you said to me, "Pam, I don't think you understand how important partners of 10, partners of 100 are." And I was like, "Yeah, yeah, yeah." And you go, "No, you don't know. No, clearly you don't because there are opportunities where you could be using those relationships" that you saw, Kim. That as we were doing workshops together, you saw that I was missing. That wasn't you looking at me. You weren't looking down on me. I don't think so.


Kim  25:07

No, no, no.


Pam  25:07

You weren't like shaking your finger at me going, "You idiot. You're such a dork. You're fake. You're..."


Kim  25:13

No, it was an opportunity, right? I love that you said that because it was an opportunity to use something that was within your grasp. You just didn't know it was a thing at that point.


Pam  25:21

I just didn't know it was a thing.


Kim  25:22



Pam  25:22

You opened the universe to go, "No, no, no. Like, this is a thing." And I was like, "That's a thing? Well, now that I know that's a thing, I can do that thing." Ya'll, now that you know it's a thing, you could do that thing.


Kim  25:33



Pam  25:33

And it would just empower all of us more and more. Please remember, I was the ultimate mimicker! Like, when I dove into the research and dove into my kids’ classrooms, I kind of kid a little bit that it was a midlife crisis. But I mean, it kind of wasn't. Like, I had built my self-identity on the fact that I was the god of high school math. I knew all the math. And I had to admit to myself maybe there's this other universe of stuff that I don't know, but I can. 


Kim  26:03



Pam  26:03

Like, that was my saving grace. My saving grace was, "If there is this other worldview that. But I have access to it. And it's kind of fun!" 


Kim  26:13



Pam  26:13

Like, "This is... I'm super intrigued!" And it's okay for me to dive in now, and open up my worldview. And wow, now I can open up everybody else's. Hey, Kim, this reminds me when we filmed our Building Powerful Proportional Reasoning workshop. So, you know we have these online workshops, and we film them in a two-day live workshop, and then we cut it up in this really creative way, and make these online workshops. When we filmed the proportional reasoning workshop, it's a little different than some of the others because the audience... How do I say this? They didn't know. They were going to a mandatory PD day in their district. And so, it was kind of a communication mix up between me and the district. I thought the district had told the people they were coming to be filmed, so they would know. The people showed up. They didn't know. A couple of people were kind of... Yeah, it was a little uncomfortable. But in a way, it's one of the best ones we've done because boy those people pushed back. You know, if I'm doing a workshop with only people who want to be there, then they're not going to. I mean, they still push back. And everyone, anyone who's seen any of our other workshops are like, "Oh, they were pushing back." It's just in this particular one, there was a set of teachers who just would not let me get away with anything. They're like, "Well, what about these students?" There was especially group of Special Education teachers who are like, "Well, our students..." What was fascinating to me was for all the times in that first day and a half. It was a two-day. In the first day and a half that they would go, "Well, Pam. For our students." "Well, these students." By the end of that workshop, those teachers started to say, "Oh. Oh." Like, this is maybe what our students can do." And I will never forget the gal right in the middle, just off to the left, who all of a sudden had this look on her face, and she started to, "I did that. I did... I just..." Like, she was just like breathing and she goes, "I just... I..." And I was like, "And you can to." And she goes, "If I can do it, my students can do it! Like, this is..." Oh, I get what you mean!" It like opened up her universe. And all of a sudden, a person who had been pushing back, "Well, my students can't." And, you know, "They struggle with..." And, "They need these different things." And, "Don't tell them..." You know, "Don't be mean to them." All of a sudden, she opened up her worldview to like she could, and if that's what mathing meant. Well, good heavens. She could do it. They could do it. "Oh, that's what you mean!" Like, it's an amazing moment of that's what we're trying to do. So, ya'll, if you've ever listened to any of our podcasts, where you've come away like feeling less than like we're calling you fake or calling you less sophisticated? No, no, no. Please don't ever hear that that's what we're doing. We just now have a perspective of what's possible, and we just invite you into that world. We just invite you. We want to empower you.


Kim  29:05



Pam  29:06



Kim  29:07

Yeah, I think if your perspective is, "Well, that's just the way I am. That's just the way it is. That's it. Can't do anything about it." You might be right because it does take some willingness and some desire to see things different and to learn and grow. But it doesn't have to be that way, right?


Pam  29:28



Kim  29:28

We can all learn and grow. And different paces. Which is perfectly fine.


Pam  29:34

Yes. Yes. Because for sure even Kim and I have different paces. And there are times where I'm like, "Kim, Kim, Kim. Hang on. Hang on. Back that up. Slow that down."


Kim  29:45

And the opposite is true. Depending on the conversation that we're having, right? (unclear)


Pam  29:49

For sure. For sure. Yeah. Alright, so everybody leave this podcast feeling empowered. And 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 Let's keep spreading the word that Math is Figure-Out-Able!