Intro

Mike Flynn 0:01

What Vanessa and I are saying, is it's not one or the other. We want fluency, we want automaticity, we want all of that, and we want the understanding, and they're not mutually exclusive. We can do both together. And in fact, when we do both together, it's when we actually achieve that. So it's not a, one side versus the other side, we just need to meet in the middle. The same with reading. You wanna be a fluent reader with good accuracy, but you wanna understand the story. You want to be a fluent mathematician with great accuracy and you wanna understand what you're doing.

Vanessa Vakharia 0:29

Okay guys, it's me, Vanessa, and I'm here to welcome you to a first of its kind Math Therapy episode. Last week we shared my interview with Mike Flynn, and I posted a little clip of our interview on TikTok and Instagram like I always do with every episode. Now, I don't know if this is like the algorithm blessing or cursing me, but this clip popped the fuck off. Like we are currently sitting at 57,000 views, over 200 comments. the thing has been saved by more than 350 people. It has almost 3000 likes. We're having like our 15 minutes of viral fame or like, 15 seconds or whatever. Anyway, the point is that what really stood out to both of us was not just how famous we were both getting, but the comments. There were so many that me and Mike started screenshotting and like sending them back and forth, trying to keep up with responding to them all. And finally we decided we should just have 'em back on the podcast to actually discuss some of these comments in real time. Because a lot of common themes emerged that are very hotly debated topics in math ed, and we thought it would be fun to actually like engage with them and clarify some of our points that we made in the original episode. By the way, you should check that out first if you haven't listened to it already. Before we dive in, because we threw this together literally yesterday on the fly, this will not shock anyone what I'm about to say, my producer David insists that I warn you that the, that the audio will sound a bit different than normal because it wasn't our usual recording setup. Honestly, guys, it sounds completely fine to me, but hey, that's why we love David, blah blah, he's a Taurus, we get it. Anyways. The link to view the clip that I posted on TikTok that has all the comments, that link is in the show notes, and also you can find a link there to text us, so you can text us what you think of this episode because it's like our first ever of this kind, and let us know if we should do more stuff like this. Also let us know about the title, because right now we're going with "The Comment Section", but the other title we had in mind for this type of episode was "Reply Guys". But I was like, does anyone know what that means? So text me and let me know. Okay, here we go. Let's get into the first ever episode of "The Comment Section" with Mike Flynn.

Should we read the comments?!

Vanessa Vakharia 2:40

welcome back.

Mike Flynn 2:41

Thank you. I'm glad to be here. And, um, how exciting, right. Who'd have thought?

Vanessa Vakharia 2:45

How do you feel like being a viral mathematical sensation suddenly.

Mike Flynn 2:51

Uh, yeah, it's, you know what it is. I love that it sparked conversation. It's it, I like being a little provocative, right? You want to get people debating and talking about important issues and things. And I think this is an important one. And we got, we got good opinions and, uh, we've got some interesting perspectives from all sides of the issue. So let's dig into it.

Vanessa Vakharia 3:10

Let's dig into it. Okay, so before we do, I wanna play the clip that I posted that has sparked such controversy and conversation for everyone so they can hear what it was that you said that hit such a nerve.

Mike Flynn 3:23

There's a reason why math has such a bad reputation is because, you know, imagine if we taught. Reading the same way we teach math, where it's just, just focus on saying these words really fast and don't worry about what it means. With reading we also embrace the comprehension. In fact, the comprehension's the most important thing and the speed and accuracy help us to get to that meaning faster. But in math, we just disregarded the meaning. It's like, oh, don't worry about it. Just just do this thing. I show you. Do it fast. And if you do it right, you're gonna get all the right answers. But don't worry about what it means like I was taught, yours is not to reason why just invert and multiply like that's

Vanessa Vakharia 3:57

Yours is not to reason why that's actually fucked.

Mike Flynn 4:00

Yeah, it is. But I remembered it.

Vanessa Vakharia 4:02

Like what an insane thing to say. Oh yeah. You know how to, you know how to divide fractions. Yeah. But like you're literally told like your job is not to think like, don't even, please do not.

Why last week's ep hit a nerve

Vanessa Vakharia 4:12

Before we get into the comments, I have to ask you, why do you think this comment did hit such a nerve? You know, it's not often that people on the internet want to talk about math teaching. What do you think it was?

Mike Flynn 4:22

Oh, that's a great question. I think part of it is like there's, there's always that math war, right? There's the people that think we just need to go back to the basics. And then there's the people that think new math, even though there's no such thing as new math, but the narrative, right? So you get both of those sides. I think part of it is, it sparks that, but I also think the analogy of, of the way we teach reading, Uh, the way it's framed when you actually stop and think, yeah, if we only taught kids to say words really fast and not understand what they've read, they would hate reading. And I think it made sense for people why so many people don't like math, because that's exactly how they experience math. And I think it's just, it's visceral. And, and for some people, if it's like, if it validated how they felt, then they're like, they're all excited to get in there because that's, that's exactly what I experienced. But then there are other people who, for the opposite reason, it's visceral. 'cause it's like, oh, it's that other, he's pushing this agenda kind of thing. So any good topic. It's got, really strong opinions on both sides and we just lit the spark. I.

Vanessa Vakharia 5:21

Yeah, and I think it also goes to show how emotional math really is. There's this real emotional component to it where exactly like you said, it's visceral. People feel very strongly one way or another because they were made to feel very strongly one way or another when they were taught math. So let's dig in. Okay, so the first, we are, we're by the way, leaving all political comments out of this chat. Okay? We are not gonna get into the wide range of comments about the common core and the quote unquote new math. We're not gonna deal with that, but we are gonna deal with a few major themes.

1) "I didn't have the chance to understand why."

Vanessa Vakharia 5:55

The first theme that emerged surrounded this vibe, and I'm gonna read you two of the comments. Okay? So the first comment is: "My only issue I had with math was how they wanted me to do it. A 10 page essay about how you solved five plus five. Eye roll emoji. I never understood their way of doing things, but I could solve most problems in my head. They always failed me in math class because I never understood how to solve the problems their way, even though I had the right answers." Another comment I'm gonna throw in here is, someone says, "As someone with dyscalculia, I hated the not knowing why, because math is a language that I could never quite get the grasp of. Numbers don't make sense to me, but I can look at the strokes of a painting and know exactly everything the painter wanted to say with that piece." There's a ton of comments like this, and a lot of this is I knew why I was doing things, but I couldn't do it the way they wanted me to show how. That's kind of what I got from it. But I'm curious what your response is.

Mike Flynn 6:54

Yeah, I mean, that makes sense. I mean, there's this innate understanding, 'cause math can make sense also on its own. You don't need somebody to show you or someone to make sense of the math for you. Like you can start to notice, I mean any, any like that first commenter around, I could solve it, I just couldn't do it the way they wanted me to do it is, it's like they had, there was this underlining meaning that they could start to see, but they were being forced out of it to comply with like this is the only way to do that. And I think that. That is something I hear a lot when I work with teachers, and I think it's a very common frustration because it's getting, it's it's almost like they were robbed of the opportunity to make sense of it because they had intuition, but that, rather than have a teacher that was responsive and and trying to understand their perspective and how they're seeing the math and help them to build connections between the way they are seeing it and the way maybe the teacher wants the class to look at, or maybe how another peer is solving it, it's instead dismissed and validated and like, no, you gotta do it. This is the right way if you want to get a good grade in this class. And it's, it's almost like taking the meaning away from the kids. It's like going back to the literacy, right? It's like reading a book and saying, I feel like there's foreshadowing here. It's like, no, no, no, no, no, no. We're not doing that right now. I need you, we're gonna answer this other question, and I just need you to respond. What was the main character's motivation? And you're like, but I'm really curious about this foreshadowing. And it's like, no, we're not talking about that. That's, that's kind of the same thing, right?

Vanessa Vakharia 8:19

I totally get that. You know, I grouped these comments and there were a lot of other comments like this, the "I wish I'd learned this way" crew. It's all these people that really are agreeing with you and they're like, oh my God. Yes. Like there were so many people being like, yes, if I had just been taught this way, maybe I would've been given a chance. I'm like, oh my gosh, I never thought about this. But it's true. Like if. Someone had explained to me the why, then maybe I would've had a chance to, like all these people who feel exactly like you're saying, like they were robbed of something and hearing you speak, they were like, what if it had been taught that way? And it's funny, the first comment here, my only issue is they wanted me to do math the way they were doing it. And then that eye roll of, ugh, write a whole essay about how I did this problem. Like eye roll emoji. I didn't like that. I was getting it. That person interestingly, is agreeing with you. They're like, no, it's not that I wanted to just memorize stuff. I knew the why, but I was annoyed that I had to like explain it in this whole elaborate way because it wasn't good enough for them, right, like, because they're like, they have no problem with thinking. They are thinking. They're just like, why do you need me to explain it to you, to defend why I am doing this? Why is important, but also like I wanna explain to you why, because you're curious. Not because you don't believe me.

Mike Flynn 9:31

Right. Sometimes the interpretation that teachers would have with when we're trying to be more open and, and honoring students' ideas and things, is that, sometimes there's an overcorrection or overinterpretation, it's like, alright, you solved the problem. Now write an essay and draw a picture and build a model and solve it a separate way and, and all in one big package where it starts to feel like it's just, we're adding all these layers versus like, like what's the reason we want students to explain their thinking and or to, to show different representations of the thinking. It's the ideas to help build strong connections between these ideas. It almost goes back to that Ted Lasso, like, "be curious, not judgmental". Like if the teacher was genuinely curious versus like, I don't think she did it that way, so let me just have her prove it. 'cause I don't believe she did it versus I, it's interesting. I never would've thought it that way. Could you show me how that works? I, I wanna know more and I feel like that's the piece that might've been missing for them.

Vanessa Vakharia 10:27

I actually love that you brought this up. I'm actually gonna bring this up a bit later with another range of comments, of how you were like, I think there might be a bit of an overcorrection where we don't, you know, really understand the intention behind why we're asking why. It's because we want to know the student understands, we wanna make those connections. Just like anything, we shouldn't be asking students to do something for the sake of doing it. Like if it's clear that they understand why we don't need to be like, and now make a picture because we need to have multiple, you know what I mean? Like

Mike Flynn 10:56

Yeah.

Vanessa Vakharia 10:56

love

2) "I learned fine, so don't change anything!"

Vanessa Vakharia 10:57

that you said that. So, we're gonna move on to the next group of comments. And this I kind of framed under a group of I'm gonna call them the traditionalists, just for the purposes of this conversation. And these comments seem to be from people who were like taught math through rote memorization and mimicking, and you know the ways we've historically taught math and they vehemently disagree with you because they did great in math class and they don't see why we should change it. So I'm gonna read you a couple of those. User 1 3 2 8 5 9 1 4 1 4 5 5 9 says "it's this type of thought process that have caused sixth graders to not be able to do single digit addition. At least the old way worked. We are confusing the heck out of kids, and the results are 12% of students at grade level. Wake up." Uh, why, why don't, why don't we tackle that one right now? What are we, what are we thinking there of just, I mean, I, and again, I know we're like, kind of like giggling because this is what the internet is like, but lot of people correlate what you're saying with the fact that like students now can't add. Why is that a potentially faulty correlation causation situation?

Mike Flynn 12:02

Yeah, well, a couple things. One, when, when someone says, it, it just, it worked like math worked for me, the old way worked. It's like I always wanna just figure out, well what, what do you define as worked? Like is work that I got a good grade? is work that I passed high school? Math is work that I is is work, meaning I developed a love and joy of mathematics that, and I wanted to pursue a career in mathematics. Like, I, I doubt it's that one, it's, it's usually like I could get by. And so that's the definition of worked. And so if, and if that's the definition of worked, is that good enough? Like do we, do we want as our benchmark for students to just get by to, to pass the class or to pass the test. And I, I would hope it's not that I feel like that's, that's so limiting in what we're able to do if we say that. But then the other part is like, we'd also look at the data is like, sure, it may have worked for some people and I, I mean, I graduated with people who are literal, literal rocket scientists right now that were in my high school. And we were all taught math the same way, we were in the same classes, and they're well beyond where I am in the math world. And clearly it worked for them. But I know more students, more classmates of mine for whom the math did not work, at all. And it's like, so the, sometimes we get into that place where it worked for me, so therefore, like, don't worry about everyone else. That actually the, that more people actually didn't benefit from a system like that. So that's just one other cautionary tale that I, I bring with that. But here's the thing with this is like. The statement that like it's because of this, that kids can't add it. there's two things I'll say about this. One people say kids today don't know their facts or kids could today can't do that. But what's interesting is I started teaching in 1998 and when I started teaching teachers were saying, kids today can't do, they don't know their facts and stuff. And then my, the one my student taught with said, and it was funny, when I started student teaching, they said, kids today can't do this. And I started asking veteran teachers around like, when was the date where all kids mastered their math facts? Like, can we, can we pinpoint it? Was it 1967 where everyone had it? Because the thing is, always heard the argument that kids don't know their math facts. And that was even when math was taught in that traditional way. I think that's always been sort of problematic. I don't want to excuse it. I think it's important for students to have math facts and have that understanding, but I don't think it's this idea of we want to have sense making and somehow that's creating kids not knowing how to, to, or not mastering fact fluency. That's a whole separate argument. It's almost like there, there's two things happening here. It's the meaning is really important and we also want students to have fact fluency. But fact fluency comes from understanding. If you just memorize your facts, you, you're really good at a small set of problems. You've memorized that, but it's hard to apply it. And, and if people want proof in it, I, I remember tutoring third graders that couldn't tell me anything past nine times 12. 'cause that's all they memorized. And when I said, what's nine times 13? They're like, I don't know. Like I, we can't do it. That's the result of memorization versus like that understanding piece. So yeah, there's a lot of things to unpack with that, with that last comment.

Vanessa Vakharia 15:21

Yeah. But that was great. And it actually touched on a lot of, A lot of the comments were around this idea of, well, we don't need to understand the why, we need fact fluency. We need automaticity. We need kids to be able to do things faster. We need kids to know their facts. And a big question I had for you, because this is exactly what happens. These things get pitted against each other, right? You either understand or you know, your facts. And I think what you're saying is, is so important. You know, a lot of people, a lot of people were jumping to your defense in the comment saying, he's not saying you don't need automaticity or fluency. He's saying, we can have both. You know,

Mike Flynn 15:51

Yeah.

Vanessa Vakharia 15:51

I get into this argument with friends all the time who are like, well, if you understand things though, like, you know, you understand them, but how can you retrieve them quickly? Like when you memorize, you just know your facts. And I'm, I think I just wanna clarify this and ask you the expert here of, but if I understood. If I understood what multiplication was and knew how to myself, create the Times table, you know, the 12 times tables, because I understand, you know, I can add things together, I can double, this and that. That gets embedded and becomes quick to retrieve, right? Like through

Mike Flynn 16:21

Absolutely. And the difference is, I'm gonna just shout out Graham Fletcher here, 'cause he has, I love the way he says this, is that there's a difference between memorization and knowing from memory. And so when you look at, at the standards, and it doesn't matter what state you're in, every standard has, it doesn't say, students will memorize, it'll say, students will know from memory all the facts within, you know, whatever range. But knowing from memory means that you can efficiently conjure that fact and, and it could be efficiently, is like, I know that seven plus eight is 15 because I've just seen it enough. It's familiar. It almost looks like memorization, but I also know that it's 15. 'cause seven and seven is 14, and one more is 15. But I know that in an instant it's not, I had to say that. Okay. Seven and seven. Okay. That's 14. And then one more. Oh, it's that, not that, it's, it's the reasoning where they're, they're deriving the fact from taking something they know and, and then using that to understand something they don't know. That's knowing from memory. When kids can do that, where they can take a fact they know and use it to build a fact that they don't know, that numerical reasoning is the flexibility that we need. And a colleague of mine, Susan Joe Russell, had a wonderful quote saying that teaching children. To be fast doesn't help them to become flexible, but building their flexibility actually helps them to become fast. That when, because think about this. If, if I said I'd let's get away from fact fluency. Let's just do like computational fluency. If I said 3,999 plus 3,999, if that argument of like. Let's just do it the way we were taught. Do you really want someone to painstakingly get out paper and then do all that regrouping instead of saying, well, it's 4,000, 4,000 minus two. So it's not saying that there's something wrong with the algorithm. There's a time the algorithm is perfect, that's the right thing you wanna do, but it's not always.

Vanessa Vakharia 18:11

you just said there just gave me a huge aha moment. There's a difference between memorizing and knowing from memory. And then, that second part you said what, what did you say her name was? Susan Joe Russell,

Mike Flynn 18:23

Joe Russell, the, the flexibility helps kids become fast.

Vanessa Vakharia 18:27

I think it's so incredible. It's like, we're not saying don't have it in your memory. It's how it gets there that's the important thing. And leads to flexibility versus just speed. Okay. I'm gonna read one other comment from this category. I don't even think we need to comment on, but it seriously sent me like, I was so jarred by this comment. I was like, oh my God. So somebody said, "I was taught just do it this way. I did it that way with no explanation. I excelled in math all the way through school. I would've hated common core math. I didn't need to know the why." Sorry. I said common core. I promised I wouldn't ignore the common core part. The point is this person is literally like I was to just copy shit down with no explanation and I did great and I don't need to know why. What's the problem? And somebody commented after and said, "But if you didn't need to know the why. Why did you need to even know the procedures? What use to you is being able to carry out those tasks if you don't even know what they mean?" And I was just like, ah, this is so crazy. Like there are so many people who are like, I don't see the problem with the fact that we just copy shit down for no actual reason. Who cares? What's

Mike Flynn 19:32

Yeah. Yeah.

Vanessa Vakharia 19:34

it like really sent me into like obviously out of math class and into our world where so many people just, we just follow things, everyone else is doing it, we just do it, don't think for yourself, just do the thing, you don't need to know why. And I was like, when I say math class and math therapy is not just about math class. It's about the skills you learn to use in your real life. This was like a, a real moment for me.

Mike Flynn 19:59

Yeah, it reminds me of that show Lost. I dunno if you ever watched that. Like those who haven't seen it, so there's this hatch, and then they finally get inside the hatch. And there's this dude down there, and all he's doing is entering this number and then hitting, hitting like, just like he's typing in this number, then hits enter. And he has to do that every so often, and he has no idea why. It's just like the, the guy before him said, that's what you're supposed to do. So that's, he's just doing this thing without any understanding of why means nothing, but he's doing it and it's like, it's kind of that, that's what that feels like. It's like, well, like. That's just, it feels so mundane. And again, it goes back to that like, what does it mean it worked for you? So you passed. But like, did you, did you go into a mathematics field? Did it open up a whole new. Pathway in life around programming or, creating mathematical models and doing oceanography because you just love the, the patterns around, the, the prevalence of sharks in the ocean, and you wanted to extend that model and. Or was it just that you, you complied, you got a good grade, you made the honor roll. Like I guess that's the thing is like, what, what are we actually doing this for? Are we doing it for the grade and compliance or are we, we trying to get deeper meaning?

3) "Teaching 'why' is a waste of time"

Vanessa Vakharia 21:11

Okay, let's move on to the next category. And these are those who I call the skeptics. This is a very interesting one because no one in this group mentioned how they were taught but they've decided that if we teach the why as you suggest, it must mean that we're not teaching math facts or fluency or anything else. They think that teaching the why is not only a waste of time, but that kids are not capable of thinking. Quite literally. So let me, I'm gonna read you one of these comments. Okay. Somebody here says: "Math develops differently in the brain. Not everyone is ready to even process, quote unquote, understanding in their brains. Foundational skills are essential and understanding unlocks over time." Okay, that's the first comment. But here's another one that I, I was like, oh my God, a couple of people are saying this. get to the, this is from a teacher, "To get to the why you have to be able to reason and think critically something many don't want to do. I attempted to show my 10th graders why, or, and I tried to lead them to the area of a triangle. I drew the rectangle, split it in half and everything. They couldn't see it. So it's not always, because we don't teach the why sometimes it's because reasoning is too much of a task." Oh boy.

Mike Flynn 22:25

Yeah.

Vanessa Vakharia 22:26

good.

Mike Flynn 22:28

Well, here's two things I'm gonna actually like, play nice for a moment. Is that there's, I, I understand that frustration, right? It's like there's, I don't want to invalidate that the, because I could say, I, I teach preschool through high school and college and stuff, so I've, I've done all levels of math and I work primarily with adults 'cause I work with teachers and coaches and caregivers and, but here's the thing that we see is that kids early on if taught math in a way where it is just passive and I'm just following the, the rules and the script and just doing the steps and mimicking. I'm not really understanding you can get become complacent pretty quickly and realize that it's, someone's gonna show you how to do it. And there's a quick, easy way to do it where you don't have to think too hard. And then whenever, let's say let's three years, you have that and then you get a teacher that wants to try to open it up a little bit to build some meaning it. The cognitive demand on that is so much higher for kids. And it's almost like being on a treadmill and then the teachers just raise the incline on it and it's like, oh, this is hard work. And kids, like kids or people working out, when you raise the the treadmill, it's like you almost don't like it at first 'cause it's so much harder when it could be just so much easier if we just drop the treadmill down. But the thing is, if our goal was to get better at running, raising the incline. Is really helpful to build that. And the same is true if we want kids to get used to being good thinkers in math. And so the first few times we do that, yeah, it's gonna be tiring. So maybe you do it for small chunks and get them acclimated to it a little bit, build up their stamina. But once students start to see the meaning, it changes everything. And I'll just name, I'll cite a couple of in instances. So the first, and I think I might have mentioned this at at the other time, the other podcast is When I was 26-year-old, 26 years old in a professional learning experience, and I first made this connection in math, I remember turning to someone saying, if I could have learned it this way, it would've made such a difference. It was so powerful for me. But in the work that I did at, when I worked at the college, I taught in a class that had that mixed classroom teachers in undergraduates, and some of them were math majors. And I remember a lot of times students telling me who were excelled in math, I mean, they're coming over to a prestigious. College in Massachusetts, they, they have amazing grades, everything. And they were, were saying how much it meant to them to finally understand it. It's really important for people to make some of those connections. But to go back at that, that thought of like, our brains don't work this way or not like that kids can't learn that way, they can't think this way. So I study learning. I mean, I, I study how long-term learning works. and this is what my field is, is the way learning works is that we, our long-term memory is all based on schemas, it's all categories. And schemas are connected ideas that form some kind of category. And those connections are new knowledge connected to prior knowledge, and so that's where meaning making comes in. And so one of the things that, like starting with a five-year-old if we want, or a 4-year-old, a 3-year-old, I've worked in preschool, I can say that if you can help kids to connect a new idea with something they've already understood, that's all meaning making is. But to say that kids can't think that way, like that's the only way we think. That's how humans make connections. it's slightly slower to go a lot faster later on. Going back to that flexibility, right, you build in that understanding builds their flexibility. But we just slow down a little bit in the beginning so that they can understand it, versus, I just remember it 'cause Mr. Flynn showed me this thing and now that's what I'm gonna rely on for the rest of my life.

Vanessa Vakharia 26:14

As I'm listening to you, I'm thinking I was literally one of math students and teachers. Like remember, I, you know, I was getting a 96% in calculus. Like I was like the star math student after I failed it a few times, and I remember I, my teacher was like, oh my God, like, you're, you're so bright. I'm gonna pick you to do one of those like crazy math contests. So, you know what I mean? Like, you're so smart. I could not answer one question, not a single question on this math contest, because none of them were about following any of the procedures I learned. They were all about like thinking. And it's not that I was incapable of thinking, but I had never had to, I had not had to think mathematically, truly mathematically for my entirety of high school. And I was getting a 96%. And I remember feeling so dismayed. I was like, I can't answer a single question. I was like, oh, what question is this like, I was trying to compare like what is this like that I've done before? What formula can I use? None of them even required formulas, right? But like that was so how I was used to doing math and, another thing that stood out to me as I was reading these comments, 'cause again, there were a lot of these comments, this is idea of, oh my God, this is all bullshit. Like, no one needs to know the why and kids can't even process this stuff. A lot of people, I think. misunderstanding what you mean by the why. Like they almost, they're like, what, what? You want us to sit and tell kids how we derive the quadratic formula? Like no one cares. And I'm like, but that's not what that, and, and actually I've been a victim to this. I've often thought, you know, I previously, probably a few years ago, I was like, what do you mean the why? Like literally like why a triangle exists? Like I think we conflate the idea with, explaining why something works and number sense, and having kids truly understand math, we conflate that with, we need to teach them like mathematical philosophy or like, do you know what I mean? Like etymology, like we, I think there's a confusion there, like it's like the why feels like a very nebulous territory that like it could mean something really big or it could mean something as basic as we just need to teach them like why it works.

Mike Flynn 28:16

Yeah. Yeah. I mean that's, that's, I'm so glad you brought that up. It's so true that it, like, it's almost like this gross overgeneralization of it. It's like, it's one of the reasons I hate the word discovery math, because the, it gets so interpreted of like, oh, well, we teach this way. We just hope we're just let the kids meander around and we hope they discover it and it's like. That's not at all how it works. So discovery math is that we want them to make the meaningful connections. And so we orchestrate these experiences where they have the right tools, they've got different representations, and then we ask really intentional questions to draw their attention to like, where do I see the distributive property in Vanessa's representation? Where do I see it in David's formula or his algorithm? And, and how are these two similar? And that's the, that's all it is. That's what meaning making is. It's just building connections so that you tap into something they already know so that this new thing makes more sense. It doesn't require this Ted Talk lecture or like this, uh, they've gotta read this like giant book to understand the theory of, of number. It's not that at all. But it's, it can get, um, it makes for good social media posts, those kind of jokes and memes. And stuff like that. But at the end of the day, it's like, it's, it's quite simple for the, the meaning making and it's just one additional step. It's like, we just don't want students to just like, do something. It's like, well, I, I, the only reason I know is 'cause Miss so-and-so showed me this. So that's, that's the answer. That's, that's not good enough anymore. But if just ask 'em to understand it at just a tiny bit, goes a long way. And that's all we're trying to do here.

Vanessa Vakharia 29:53

Yeah. I love it. Okay.

4) "You're SO right."

Vanessa Vakharia 29:55

We're, you know, we've done I think the, the bulk of what people are saying, but I do wanna say that there are a ton of people online that are agreeing with you and not just agreeing with you, but agreeing with you in a very moving way. I think because they, they, they're touching on what you just said, kind of. Earlier about how, this idea of we don't think kids are capable of thinking and yes, it is a lot trickier for them to, take on the extra cognitive work of really digging into something when they've never had to. But a lot of these comments show not only can kids do it, not only can it be done, kids are hungry for it. They want it, and when they get it, something opens up. So somebody said here, "I hated the just do it memorization math. I fell behind one year and I stayed behind for the rest of my life. I even asked a teacher who knew I was struggling to help me catch up. She told me she didn't have time. It wasn't until my last year of high school when I took remedial math that I finally had an environment where I could stop my teacher mid lesson and go, wait, why did you do that?" And I have like goosebumps saying this because I'm like, how the fuck, why the fuck do we have to get to remedial math? Well, I hear this a lot from students. Oh, in remedial math, you know, in the, in the quote unquote lower math. That's where I get to ask why. That's where we learn relevant math. I hear it all the time and, and that really upsets me. It's like, why? that kind of crazy? That in, and it's also crazy because this is actually what we were talking about in our, our last interview, is asking the why and learning. The why is is, you know, kind of potentially even harder than just copying and memorizing. Yet in these remedial classes, kids are technically doing the tougher work of digging into the why. Like, isn't that bizarre?

Mike Flynn 31:37

it makes me happy to hear that though, that, because I see sometimes the opposite, whereas the belief that students who have, have any learning challenges, any needs at all, just need to be shown how to do that. I hear that argument so much, so that actually brings me hope that in some remedial math classes, that we're actually seeing more meaningful connections.

Vanessa Vakharia 31:56

Well, but you know why though? It's because in many of those, in most I would say remedial math classes, the curriculum is so much smaller because they don't think kids can learn that much. So they literally, they have more time

Mike Flynn 32:06

Hmm.

Vanessa Vakharia 32:06

there's less of an emphasis on just getting the highest score. Because most of those kids have already been trained to think they can't do that. And the teacher is like, whatever, we're not all getting A's here. Like yeah, but like what a crazy thing that happens when you stop focusing so much on marks and results, you actually get to the interesting stuff of the math and the kids build higher math confidence. So it's like

Mike Flynn 32:25

Yeah.

Vanessa Vakharia 32:26

know, it kind of like is a little oomph to that argument that like, yeah, that's what happens when we stop thinking about speed and getting the highest grade after. Real understanding happens.

Mike Flynn 32:36

Yeah. And then you empower the kids, right? Because then they're like, then they believe they can do it. Yeah.

Vanessa Vakharia 32:40

Okay, here's another comment. I'm just gonna read this. "I wish we had number sense when I was coming up. I would not have struggled so much. My ninth grade algebra one teacher took the time to help me, quote unquote get it, and man, I took off with math after that." So this is someone just to your point, who was just taught the just do it, wait all the way up until grade nine. And then when somebody helped her understand it and understand the why she took off, it's not like she was like, oh my God, now this is making it even worse. 'Cause now I have to think this actually helped her. And somebody else said, I struggled in math, now I'm teaching and I wish I had learned the different strategies I'm teaching to students. It would've helped me so much." So I think that's also a little extra like bonus for teachers out there. Who might feel like how I did or how a lot of teachers do, where they're like, oh, I, I just understand how to do it. My math confidence isn't super strong. I don't wanna now get into all this. Why stuff? Because it's gonna screw me over. This is proof that no, it'll actually help you even more. And now you get you for the first time, really dig into learning and understanding the math and you can do it, and it's gonna make you a richer teacher, a more excited teacher, you know, a happier teacher, all of those things.

Mike Flynn 33:48

I, I a hundred percent agree. And it's like, and once you start to make, you get that meaning making, once that happens for you as an adult or a kid, you can't shut that part of your brain off. You start to realize, oh, all of this is supposed to make sense. You're a musician, right? So I, I remember when I first started learning guitar, I just would cheat. I used to get these guitar magazines and they would have tablets in the back. So you would just match your fingers to the numbers and I could play like, Stairway to Heaven or you know, welcome to the jungle, whatever. But I didn't understand actually the, the mechanics of the guitar. I could just match my fingers to the numbers. And I remember when I eventually started to get away from the tablet shirt and started to understand like the notes and like it made sense. Like, this is a G oh, and this is a G and this is another way to make a G. And I realize it's, the guitar's not about matching your fingers and numbers, there's this whole structure here and once I understood that, like my playing took off and it was way more fun, it was like it was enjoyable. So it's the same in math as it is with music or any other things that we're learning.

Vanessa Vakharia 34:47

Yeah, I love

5) "YOU'RE SO WRONG"

Vanessa Vakharia 34:48

it. Okay, we're gonna wrap up, but I do wanna say there is one more category that we haven't talked about, and I call those the, reflex rejectors. And they're people who think you're wrong with no actual reason as to why you're wrong, because the internet, so

Mike Flynn 35:03

Fair enough. Yeah.

Vanessa Vakharia 35:04

the comments, the comments include, one of the comments is, "you're wrong, pal." Do anything

Mike Flynn 35:10

Yep.

Vanessa Vakharia 35:11

than

Mike Flynn 35:11

Hey. Can't argue with that. That was a very sound, uh, argument. Good justification. Good reasoning. Yeah, absolutely. Alright,

Final thoughts

Vanessa Vakharia 35:19

I'm so glad we did this and honestly, as I'm literally opening TikTok right now, 'cause this is the funniest thing is as we've been recording, 15 more comments have rolled in, um, 5,000 more views. So who knows where this is gonna go. But I'm really, really, I'm really glad we did this because I actually think it's really what you said at the beginning is, is the truest and most important part, discussions are so important to engage in. You know, it's through this discourse, it's through talking about it, it's through going back and forth that we actually all start understanding with what one another is saying. And I'm really glad you took the time, so thank you, to actually respond to a lot of these people who had questions and had concerns. user 1, 2 1 4 5 5 9 x 3 5 0 2.

Mike Flynn 36:01

Yeah. And if I could just put a period on the whole thing here, which is

Vanessa Vakharia 36:04

Yeah.

Mike Flynn 36:04

what Vanessa and I are saying, and what a lot of us in the math world are saying is it's not one or the other. It's both. We want, we want fluency, we want automaticity, we want all of that, and we want the understanding and they're not mutually exclusive. We can do both together. And in fact, when we do both together, it's when we actually achieve that. And that's what we're arguing. So it's not a, a. One side versus the other side. We just need to meet in the middle there and recognize that we need both of those things happening. The same with reading. You wanna be a fluent reader with good accuracy, but you wanna understand the story. You want to be a fluent mathematician with, great accuracy and you wanna understand what you're doing. That's, that's not a huge ask.

Vanessa Vakharia 36:40

That was perfect. Thank you so much for coming on the podcast. you're listening to this, you can now text the podcast so you can chime in on the discussion, to the description of the episode, there's a link there, you can text us. You can DM me @themathguru. You can find us both on TikTok @mikeflynn55 I believe. Look, I memorized your handle 'cause you're so viral. themathguru for me. You can chime in on TikTok. Go find the clip of that we've been talking about, comment on it and uh, Okay, we're done. Cut. bye.