[00:00:00] Robert Kaplinsky:

It's really important to normalize that everyone struggles. It's normal to struggle, and actually without struggle, there's no growth. 

if you look at it with a growth mindset and realize that mistakes help you learn, and you only learn when you make mistakes, then you're encouraging kids to learn as quickly as possible.

Show intro

[00:00:17] Vanessa Vakharia: Hi, I'm Vanessa Vakharia, aka The Math Guru, and you're listening to Math Therapy, a podcast that explores the root causes of math trauma, and the empowering ways we can heal from it.

Whether you think you're a math person or not, you're about to find out that math people don't actually exist. But the scars that math class left on many of us definitely do. Oh, and don't worry, no calculators or actual math were involved in the making of this podcast. 

Vanessa Intro

[00:00:44] Vanessa Vakharia: Okay, remember when you were in math class and you were super frustrated because you would get the right answer to a question, but not in the exact same way your teacher wanted you to? And then like you'd end up getting no marks and you were like, fuck this, and then you decided you hated math, and now you're listening to this podcast because you have trauma from that exact thing I just described?

Today's guest is the antidote to that whole entire thing. His name is Robert Kalinsky and he's like the forefather of something called Open Middle Math, a problem solving method that allows kids to have autonomy over their process. In this episode, we discuss why making mistakes is crucial to learning math, why teaching algorithms is old news, and why expecting kids to use one specific method to get an answer leads to, you guessed it, math trauma.

​

What is "Open Middle"?

[00:01:28] Vanessa Vakharia: Oh my God, Robert, this is so exciting. I can't believe you're actually on the podcast I'm not just boosting you. I think you're my new like best friend in math education and I'm hoping you feel the same way. Do you? You have to say yes.

[00:01:40] Robert Kaplinsky: I absolutely do, honestly. No, but seriously, I really like the breath of fresh air that you bring. It's a different perspective that's sorely lacking. 

[00:01:48] Vanessa Vakharia: That's actually so nice. I feel the same way about you. And okay, so I actually am gonna start the interview with a confession. Obviously we've chatted a lot and you know, I know that you do this whole thing called Open Middle, and this whole time I've been like, haha, open middle, cool. But TBH, until I was like, oh, I should do some research on Robert for the podcast, I had no idea what Open Middle was, and more than that, I was talking to a friend and I was like, yeah, I'm, I'm interviewing Robert for the podcast. And she was like, oh yeah, like he invented Open Middle. And I was like, you invented it? Like did you invent what we're about to talk?

[00:02:21] Robert Kaplinsky: I, I think that would be a really generous take on that. I guess it really gets to what is an open middle problem and what does that term open middle come from? 

[00:02:28] Vanessa Vakharia: So let's start there. 

[00:02:29] Robert Kaplinsky: Okay. So like if you think of like a video game, right? And really, I first heard this term from Dan Meyer in a presentation he was doing about making math more like video games. And he was talking about like, if you think of like Super Mario Brothers, every level starts with the same beginning, and every level ends with the same ending, like you just jump on that flag. But what makes it interesting is what happens in the middle. And there's so many ways it could go, and that aspect is really interesting.

Now people say, oh, I love open-ended math problems. But the reality is that if it ends with the same answer, it wasn't open-ended, it was closed-ended. What's really interesting and, and, and almost every problem in math is closed beginning, you all start with the same problem. So what I find to be really fascinating then is that, are these problems that have open middles and closed endings where everyone got the same answer, but you can talk about like how you got there and it leads to really interesting conversations about the different strategies that worked and how they're connected.

So I co-founded the website Open Middle, and right now I'm the only one running it with a a team of volunteers, and it is absolutely like a crowdsourced community website, in terms of just teachers and educators are the ones submitting problems, there's teachers using the problems and kind of giving feedback when they work well or when they don't. But I don't know if I would, I mean, the idea of problems having open middle, I, I don't know anyone could trace who was the creator of that. But I definitely heard the term first from Dan Meyer, and then was so inspired by this kind of category of problem that it really, led to creating a website and really just exploring that. And I just really enjoy kind of diving into that kind of work. 

[00:03:52] Vanessa Vakharia: I love, oh, like, I mean, you had me at video games and I don't even play video games, but I was like, oh yeah, okay, that actually totally makes sense as a concept. And I guess, could you give an example, like here's an example of a problem just so we totally know what we're talking about. 

[00:04:04] Robert Kaplinsky: Yeah. So one of my favorite problems looks like this. So imagine a fraction that has a two digit numerator and a two digit denominator. Okay? 

Now for each of these digits, let's put a little box there. So we don't know, we know what digits gonna go there. We just don't know what digit. And you could put any digit from one to nine there, and you can't repeat a digit. So how can you make a fraction that is as close to one as possible? 

So let's just start. We put a one and a two in the numerator and make a 12, and a three and a four, in the denominator to make a 34. 

Now, is that the closest you could make to get to one? So then you start thinking like, well what, what digits should I use? Are some digits better or worse to use? And there is in fact a correct answer, but in this one singular problem, you're gonna do a lot of work. And I mean, you could just guess and check, like you could quite literally pick numbers out of a bag, put 'em there and just check it. I mean, that absolutely will work.

Uh, Your hand may fall off from, you know, writing that out. At some point you start to think, okay, there's gotta be a freaking better way to do this. And you start to realize things like, I want the value of my numerator and my denominator to be as close together as possible. And, and just if that's the only thing you realize, you've definitely made it easier.

Uh, You might also start to realize that when the denominator has a really great value, a larger value, then those missing pieces are much less significant. And so again, there's one right answer, but there are many ways to approach it. And the conversations that you use, that one singular problem could replace an entire worksheet on comparing fractions.

I think also what's really interesting is you could create a whole workshop comparing fractions and a kid could crush it, but that same child might struggle with this. And then you start to wonder like, what does it mean to deeply understand fractions if they can do a worksheet, but they can't do this. And so I really like that the nature of these kinds of problems, that it gives you better insight into what your students deeply understand about mathematics. 

[00:05:50] Vanessa Vakharia: So, okay, my first question, so the first thing I start thinking when you're talking about this, educators love resources and one thing we're always lacking is resources. So we're always like, where can we get more worksheets? Where can we get more questions? And you're kind of like, well, you actually don't need that if you have one really good problem that covers what like 50 questions in a worksheet would, right? 

[00:06:10] Robert Kaplinsky: Yeah, I would say it's not my intention to say there's never a time or place for worksheets. 

[00:06:13] Vanessa Vakharia: No.

[00:06:13] Robert Kaplinsky: But I am saying that when I first started teaching, I only used worksheets. And when I look back at that, I cringe because I had students who appeared to know what they were doing, but had no freaking clue what they were doing, but I didn't have the tools to identify that. I mean, here's a challenge about being a teacher. You're expected to teach in ways that no one ever taught you, and I don't think anyone can appreciate how challenging that is if you're not actually in education and not actually doing it.

So that's what I like about this is that, it's a resource that you can fairly easily slip into what you're already doing without making huge modifications. And it can add value in ways that, I mean, if you go on Twitter and search for the hashtag #whyopenmiddle, w h y, open middle, I retweet people just saying like, my kids didn't want to go to recess because they wanted to continue working on this problem. Or, I've never heard such great conversations, in a math class. And this is not like just elementary or just middle or just high, or just kids in this area. It's everyone all over the world sharing that these experiences are making big impacts in their classroom, and so that's super validating. 

Diversity of learners

[00:07:13] Vanessa Vakharia: So how important do you think this is for like, the variety and diversity of learners we have? Like, you know, I think we're always trying to figure out how to, make sure every single person in the classroom is engaged or feels capable of math. would you say that this is a really good way to get, you know, the weakest and the most advanced students both equally engaged in the problem?

[00:07:32] Robert Kaplinsky: Yeah, so let me, let me call myself out actually here. I used to think that there were low kids in class and high kids in class, and I understand why I thought that, and I wanna unpack why I don't think that anymore. And here's what I mean.

[00:07:42] Vanessa Vakharia: Yes. 

[00:07:43] Robert Kaplinsky: I would bring one of these kinds of problems to a class, and I'd expect that these kinds of kids are gonna thrive on this, and these kinds of kids are going to be decimated, right? The high kids would thrive and the low kids would be decimated. And what I found was often the exact opposite, where the kid who I did not anticipate doing well, crushed it, and the kids who thrived, typically, were just obliterated. 

And what I started to realize was that, for example, the kids who thrived, well they thrived in a very stereotypical definition of a math classroom where the teacher gives you a list of procedures, and you follow those blindly like a robot. So these kids were amazing robots and by that definition of being a high kid, they were amazing. But the kids who were typically low are the kids maybe who don't want to be robots, they wanna be creative thinkers. And these kinds of problems really require that creative thinking, and so they thrived in ways where they're typically disengaged. 

And it really made me question how much of what I consider to be a low or high kid is the kid, and how much of it is really the way I'm teaching mathematics. So it really made me question what it means to be high or low and, and, and to just, you know, succinctly answer your question, I have found these problems work well with all types of kids. Different kids might be at different levels of ability initially, but they all enjoy a good challenge. 

[00:09:00] Vanessa Vakharia: Well, okay. Since you're calling yourself out, I'm gonna call myself out, in that I've been doing a lot of thinking lately, just because so much of the new research and new PD and these new conversations about math are about this, it's about how we don't really teach kids to think in math class. We're teaching them to copy, we're teaching them to mimic, and like, what does that really mean? Like, I think the door is really being blown open on the like, oh my fucking god, math education has just been us teaching kids how to copy shit. Like that's all it is, and it's creating this very unequal playing field. 

And I'm thinking about myself, in high school I got a 98 in Grade 12 math. I remember this so distinctly cause I remember I was the math star, I mean, this is after I failed math a bunch of times, but who cares, fine. I'm in my math class, I'm getting a 98, I'm the pride and joy of the math classroom. And I remember I got asked to enter one of those math contests, and the math contest questions, none of them are algorithm based. You have to show up and like do math, like real math, like problem solving.

And I remember I showed up and I couldn't answer a single fucking question and I was, I was super sick that day, so I was like, I wasn't in the right head space. But as time goes by and I keep looking back at that day, and this is a podcast about math trauma, I actually think I got some sort of weird math trauma from that day because it was almost like an insight into like, do I really know a fucking thing or do I just know how to copy and follow algorithms and follow rules?

And like I mean, I think it's a bit of both. Like I'm not like, oh my God, like I don't know anything. But I have felt very insecure about my math ability since that day because I'm like, yeah, just like you said, we weren't given open middle problems. We weren't taught to think about stuff. We were taught to copy stuff and follow rules, and I was really, really good at that. 

So now, I think about what you're saying and I think about the fact that so many kids get left out of math and don't move on to mathematics later in life and develop math trauma and think they're bad at math just because they're not good at copying. And I'm wondering if the kind of math you're talking about welcomes more kids into the folds, and actually like welcomes kids who we need in the math community, kids who can creatively think and not just copy.

What kind of math do we actually need?

[00:11:01] Robert Kaplinsky: Yeah, I think there are, there are some dark secrets that are obvious once they're said out loud, but people don't wanna admit. The first one is that the vast majority of the math that you learn in K-12 math you never use again in your life. I, let's see, I was a math major in college, I never have ever used calculus in my life, I've never used pre-calculus in my life. I might have used some aspects of like algebra two, like exponential growth, like trying to figure out interest rates in my life.

I don't use dividing. I mean, when's the last time any one of you multiplied or divided decimals by hand, right? There's just so much of math you never use. At the same time, there's a lot of math that you actually need in life, and no one teaches that to you. Similarly, at least in the United States, they talk about how the entire goal of mathematics education is college and career readiness. So the reality then is that the mathematics that you needed to be ready for college and career in let's say 1990 and in 2015 and in 2023, are vastly different. I mean, literally the mathematics that you needed even five years ago is different than you need right now. 

But you know what hasn't changed? The standards. Like it's pretty much the same damn thing that we're learning. So if we're actually aspiring to help produce college and career ready kids, but not change anything as what you need to be successful in colleges and careers changes, then it's just bullshit. Like we're just saying these things. We're not actually trying to achieve that.

So what math do you actually need? Like especially in this era of like artificial intelligence and Chat GPT, what math is still valuable? And I think at least for the time being, the math that's really valuable is the ability to solve problems and communicate your understanding. 

And the robotic math that literally none of us use anyway, like I, again, as a math major, use a calculator for like even like two digit multiplication because why the hell would I not? And we should be focusing on more on what we should be entering into the calculator and less on the actual calculations. And I think that just we've lost our way as a society and, and it's really hard to break out of this. It's status quo bias, we keep doing it this way because that's the way we've always been doing it. 

I mean, here, here's actually an interesting thought experiment. Imagine that math standards had never been created, like ever. Tomorrow, the very first teachers are going to say, we need to make math standards, and that's what will be. What are the odds that we come up with the exact same standards that we have yesterday? Right? There's no way. 

[00:13:07] Vanessa Vakharia: Oh my God. Like zero. 

[00:13:08] Robert Kaplinsky: There's gonna be a lot of overlap, but there will absolutely be standards that we never had before that we will now have, and there'll be standards that we won't have anymore. And if that's the case, then why aren't we actually using those new standards now? If we're still teaching things that we wouldn't be teaching in that scenario, then it's because of really just this bias that that's the way we had always done. I learned it that way, so it must have been the right way to learn it. 

[00:13:30] Vanessa Vakharia: But okay. This is such an interesting thing. Cause I say this all the time, school literally was a creation of the Industrial Revolution, right? Like it was created to pump out, basically assembly line workers, cuz that's what we needed at the time, we needed people to mass produce, to rule follow, all of the things that like you're saying, were probably part of the reason for the standards we created in math. That's what we're doing in math, we're teaching rule following, we're teaching mimicking, we're teaching like order, discipline, all of this stuff that you would've needed then and that now yes, when you're thinking about career and college, that's very little of what we need. Like to solve the world's like biggest math problems like climate change or like the cure for cancer, like we don't need people to just push shit into a calculator, that's not the thing. 

So I guess my question is like, why then? if we, If so many of us know this, why aren't we changing the standards? Because if we're saying they're for career and college readiness, but the standards aren't getting anyone career or college ready, then what's going on?

[00:14:25] Robert Kaplinsky: It's complex. I think that in the United States, the standards that we currently have are a big response to the space race in the fifties and sixties between United States and Russia. If you start tracing it back, you see a lot more emphasis on, I dunno if you've ever saw the movie, uh, Hidden Figures. An important aspect of that was that you literally had humans doing, they were literally called calculators. They were the people doing the calculations because you did not have technology hardware to do that. You had to teach those skills because you had no alternative. Now we have devices that could do those calculations faster and more accurately than any human with infinite experience. And so we still teach it that way because we've always taught it. But like, I'll give you an example. Calculus is seen as like the end all, be all, the ultimate goal for high school students. But the reality again is, most kids will never actually use calculus in life. Most majors don't even require calculus, right? There might be other majors like statistics or some sort of data analysis that would be more actually useful and beneficial, but it's not done. 

And I think that you just keep having it this way because the political capital, say what you wanna say about Common Core, but what I think is really valuable was that in the United States, you had all the states on the same page, or you had many of the states on the same page, and it made it easier to have these conversations. When every state or every province is doing its own thing, it becomes very hard to have these conversations and there's so much bias about what it means to be good at mathematics. 

I mean, just speaking the truth it's, a lot of it's ingrained in just what white men defined as really, really good. And there's a variety of ways in terms of problem solving and just communication that is valuable. But it really became a very singular, and you see it with the math wars, right? You see procedural math versus, sort of a constructivist conceptual understanding. And it's really just hard to find consensus enough to be able to change the standards and move forward differently. 

[00:16:14] Vanessa Vakharia: Mm-hmm. I'm thinking while I'm listening to what you're saying, I don't even know how to phrase this or what my thought is, but I feel like you'll get it. I'm like, everything, you're saying sounds fucked up, for lack of a better term, right? But also I'm kind of like, this also started with us talking about open middle problems and how maybe that's the antidote to this, which I still have a lot of questions about. 

But before I even get to them, I'm thinking the way you're talking about math now, you know, my whole thing and my focus really is math therapy and math anxiety and math trauma, and I'm wondering, and I know neither of us necessarily have the answer, but I'm thinking about, imagine math, 50, 60 years ago, being taught the same way as it is now, and imagine the people, the kids who are being taught math now in the same system. Do you think being taught math in this way leads to math anxiety? Like, I don't even know what my exact question is, but you know what I mean? Like the way we're talking about math being taught in a way that is so meaningless to so many students, how do you think that would contribute to like them sort of leaving the classroom feeling like it's not for them?

[00:17:14] Robert Kaplinsky: Yeah, absolutely. I mean, again, calling myself out, I taught a lot in the style of really how I was taught when I was a student. And so when I was a student, it was about getting the correct answer as quickly as possible. Uh, you didn't really have a lot of value in terms of explaining yourself or complex problem solving, and so it leads to situations where you may not see yourself as a math person, because you think that you are not good, because it takes you longer to get correct answers. 

When in reality the vast majority, like anything that you need to use math on in real life, like measurements or things like that, speed is not a huge issue, right? But yet we, we put that out there. The actual calculations, like the computation in the multiplication, that's not important. Knowing what to multiply is what's important. So there's a big disconnect. And so you get the wrong people actually in the profession when you could have a completely different thing.

And change is so incredibly hard to do because it's such a complex system. You know, you might train all the teachers and they might all be on board, but then their curriculum is not in alignment and their curriculum may not be in alignment because their state standards are not aligned and their state standards are not aligned because the governor of the state, you know, I'm looking at you Florida, the governors of the state is like crazy. And then he decides that this is not the way it's gonna be. 

So I think that it is just such a complex system that it's really hard to really make sense of. 

[00:18:32] Vanessa Vakharia: It feels very tower card in the tarot where it's like we just need to literally start over again. Like we keep trying to like put band-aids over like a pile of rubble. Like it's like just stop, just tear it down and start again. Obviously that's way easier said than done. 

Reassessing assessment

[00:18:43] Vanessa Vakharia: What I'm also thinking of is I would assume with open middle, part of the great part of it is you can mark kids on process, right? Because I know there's so much talk about assessment and grading, and we're doing all of this trying to encourage kids and say, Hey, math is about more than getting the right answer. It's about more than speed, it's about the process, it's about creative thinking. However, then there's this big gap in assessment and we're like, yes, think creatively, la la la, but if you don't get the right answer, like fail. How does open middle challenge that? Is there an opportunity if the kid doesn't get to that final answer for them to still get marks on their creative thinking along the way?

[00:19:17] Robert Kaplinsky: Yeah, so I mean, assessment's complex. I think it's worth first just kind of calling out formative assessment versus summative assessment. I love this metaphor from Bob's Steak and he says, "when the chef tastes the soup, it's formative. When the customer tastes the soup, it's summative". 

So when that chef is tasting the soup, they're like, does it need more salt? Does it need more garlic? And they're not tasting it to consume it. They're tasting it to know I need just enough soup to then decide what adjustments to make and when it's the, the customer tastes it, it's over. Like that, it's whatever it is. And I don't use open middle a lot for summative assessments, like on a test or things like that. I use it more when I'm in class. 

Gosh, it's been countless times where I thought, these kids really understand this. Right? And you can see where I'm going with this. I, I give 'em an open middle problem and I'm like, oh, crap, they really have so many misconceptions, I had no idea. So in that moment, if I don't have an open middle problem, I'm like, yay, me, kids are great, let's move on. An open middle problem gives me real time information I can use to adjust my curriculum or, or my instruction to make better decisions.

And that's really what I love about it. I'm not huge on, on grading. For example, I, I used to let my students take their tests unlimited number of times. And the reason why was the test should measure what you know in that moment, as opposed to what you got in that time. 

So if, for example, if the whole point of education is to help kids learn, and maybe a kid wasn't in a mental place, for whatever reason wasn't able to pass the test. But if you've got unlimited test revis, you know, if you could take it a million times, and you have this motivation, now go back and learn that thing. Like, isn't it the whole fucking point of education? 

[00:20:53] Vanessa Vakharia: But is it the same question every time? I always wonder this about this philosophy. 

[00:20:57] Robert Kaplinsky: No, I, so I had a way to generate similar but different versions.

[00:21:00] Vanessa Vakharia: Okay. So new, new questions. So they're not just memorizing the answer to a question. 

[00:21:04] Robert Kaplinsky: Correct. 

So my point though is, just open middle problems. If your point is to really just know where kids are at, they're great for that. They can be used as a, as a summative assessment. I have something on the open middle website called the Open Middle Worksheet that gives points for each attempt and for each explanation. So if you get it wrong, many times you're gonna get more points for more attempts and more explanations. And I tell kids like, I hope you don't get it right on the first time because you know you're not gonna get as many points.

Again, the whole point is not, in my opinion, it's really just to help kids learn. It's not to mark them where they were in that moment. So again, I don't use open middle problems very much summatively, I use it mostly formatively, and I don't necessarily even grade them because I just need the information I need, I don't necessarily need to give them a grade for it. 

[00:21:46] Vanessa Vakharia: That's really cool. So you're using it to inform your teaching where you need to adjust like the chef in the situation, but also I think it's like a really great way to get kids to interact with the material. Like again, as opposed to just sitting singularly and doing a worksheet, like when you're talking about it and when you're doing the problem, you can actually have that conversation and communicate. And I find like a lot of time I mean we assign kids marks or grades for communication, but we don't teach them how to communicate in math.

So we're like, you know, do this, write out your answer and then communicate how you got this. And they've never actually done that in real life and in real time, so they don't know how to do it. Whereas I would assume open middle like gets them used to being like, yes, conversations and communication are something that happen when you're doing math.

[00:22:26] Robert Kaplinsky: Yeah. And, and I think the context matters. So let's go back to that open middle problem. We said, let's say that I pick three seven over four nine, 37 over 49, and then you pick 53 over 86. Who the hell is right? mean, I, I literally have no idea right now. 

[00:22:42] Vanessa Vakharia: I would just do it on a calculator.

[00:22:44] Robert Kaplinsky: Okay. And I might use a different strategy. And my point then is that, again, using that idea of there's one right answer, but the way you think about it is different. And I think that it allows for these kinds of conversations in ways that maybe you don't typically see. And the context provides something where kids want to communicate their reasoning and they want to explain their thinking. Versus just doing a worksheet, there's nothing worth communicating, nothing interesting. 

[00:23:08] Vanessa Vakharia: No. 

The benefits of struggle

[00:23:09] Vanessa Vakharia: You know what I'm thinking? So I'm thinking like a lot, a big thing, um, especially with new teaching methods, is that teachers who already are sort of anxious around math are very, like, hesitant to try them. Right? They're scared to make a mistake in front of the class. I kind of feel like this would be such a great thing for a math anxious teacher. What do you think? Because like, so, none of it is really about being right and none of it's about doing it a certain way.

[00:23:30] Robert Kaplinsky: So first off, I don't think there's anyone that these kinds of problems are not good for. And, it is about being right, there are right answers, but there are many ways to get there. There's not a right way necessarily to do it. You absolutely could guess and check. I'll be honest, when I start an open middle problem, sometimes I have no freaking clue where to start. So I just pick some four random numbers and see what happens. And I pick more random numbers and I, eventually I'm like, okay, this is definitely not gonna be efficient here, there's gotta be a better way with the pattern. And so it, it has a very low floor and makes it accessible, and it's got a high ceiling. And in that way, I think yes, if you're feeling anxious about your own mathematical ability, this could be a really good way to do it. 

And I tell kids this was really hard for me too, and it makes, it sort of normalizes, I think a lot of times people think that you have to get it right on the first try. And I tell them, I got this problem wrong so many times I lost track. This is a challenging one, I want you to give it a shot.

[00:24:18] Vanessa Vakharia: Yeah, you're right, fine, there is a right answer. But I think a lot of teachers who are math anxious to begin with feel like they need to like know how to start a problem. And I really like the fact that this is like, I guess what I meant, it's not that there's no right answer, there's no right way to start. And I think that's the key here is that it's like, there is no right way to start. You could literally start any way. 

And part of the joy is actually saying to a student, oh my God, I never would've thought of, like, it's almost like a bonus to be like, I never would've done what you were doing. That wasn't even my, in my brain. And you're proving two things. Number one, you're proving like, there's no one way to approach a problem, there's no one way to be good at math, there's no better way necessarily. And you're also showing that even you as a teacher, will always and forever have learning to do, which is just, I think like, I feel like with growth mindset sometimes, not that we're gonna go into a whole thing about growth mindset, but it's like we say it out loud and we say it to the kids, but as teachers, sometimes we're too scared to model it because that would mean showing someone that you're not the be all and end all of math. So it's such a good way to hit all those things.

[00:25:15] Robert Kaplinsky: I think it's really important as society to call out our struggles. I was telling you earlier that I, I'm teaching lessons and I go in there. I'm like, I've never tried this kind of problem before. I want to see how it goes. And if it goes well, I'll learn from that. And if it doesn't go well, we'll talk about what you didn't like what you liked.

And I think that normalizing the growth and the struggle is really important because what we see is on social media that only anything that's being shared are, are successes. 

[00:25:39] Vanessa Vakharia: Oh my God. I always say this, Robert. I like literally say this all the time. I have a whole slide on it. Okay, go on. I also say TikTok is ruining our lives. Okay, fine. Back to you. 

[00:25:47] Robert Kaplinsky: I, think it just, it, it can screw with your mental health because it will make, your successes still look small in comparison to other people's successes, and not enough people share their struggles. So I think it's really important to normalize that everyone struggles. It's normal to struggle, and actually without struggle, there's no growth. 

Normalizing mistakes

[00:26:04] Vanessa Vakharia: Okay. Oh my God, that is so beautifully said. And now I'm gonna have to draw you into my drama because I know you just saw me tweet this. So, as you know, I talk about failure and making mistakes all the time. And my whole thing is that we should actually encourage kids to make mistakes. Okay. So like, I want to, because you know, on Twitter you only have a certain amount of characters, I want to say exactly what happened. 

So I'm talking about how we need to encourage kids to literally go out there and actively make mistakes so they build that muscle of, mistakes happen, it's normal, we can learn from them, that kind of thing. And an educator recently told me that he does not believe in that philosophy. And he was like, no, I mean, I think it's actually kind of damaging to just be telling kids to make mistakes when in the real world you would get fired from making a mistake or like mistakes aren't encouraged. 

And he said, and this was the part I want your take on, he was like, fine, there's a difference between accepting that mistakes happen, like mistakes are going to happen, and actually encouraging kids to make mistakes. I just, how, what do you feel about this? 

[00:26:57] Robert Kaplinsky: I, I have a lot of thoughts, but I'll, I'll say one thing that just came to mind was that a saying in the tech industry is, "fail fast, fail often". And I mean, 

[00:27:05] Vanessa Vakharia: Mm-hmm. Mm-hmm. Okay. 

[00:27:06] Robert Kaplinsky: How do you process that without the idea, I mean, that's literally the idea of encouraging mistakes, right? Because if you wanna test ideas and, and so I think that's one part of it. I think at the very least you want students to realize that mistakes are acceptable. It reminds me of, Peter Liljedahl's work with Building Thinking Classrooms and the idea that vertical, non-permanent surfaces like whiteboards had a different effect than chart paper. 

They're just vertical things you can write on, but the chart paper, if you make a mistake, it stays there, it's memorialized on that paper. With whiteboard type surface, you can erase it. And just this idea that mistakes are okay, it's normalized and okay, move on. I think that part's fine.

I think this person's taking things a little bit too literally. I think encourage doesn't mean like, everyone make a mistake now. It's more just like mistakes are totally ok. And I think that that I, if I'm being honest, I'm trying to remember, before I read Carol Dweck's Growth Mindset book, where I was at, it's very hard to remember, but if you've got a fixed mindset and you think that mistakes mean failure, then I guess that person would assume that you're saying I'm encouraging kids to fail. But if you look at it with a growth mindset and realize that mistakes help you learn, and you only learn when you make mistakes, then you're encouraging kids to learn as quickly as possible.

So, I don't know, I, I just have to imagine this person's coming from a very fragile place and is thinking that, you know, mistakes are not beneficial. 

[00:28:27] Vanessa Vakharia: Yeah. And I guess, I mean, you're right, is it just the literal idea of being like, we shouldn't be telling kids to go up and like fuck shit up, like fine. But I also think it's like, when we literally look at the idea of risk or what you said in the tech industry, right, what we're saying is, this is how I interpret it, if you are taking a risk or trying something new, and let's just translate that into math, like you have an open middle problem in front of you. Okay, let's just say in the context of this thing. And you have no fucking idea how to start and you have to start, it means that you are likely going to make a mistake.

So embracing that and being like, okay, like I am so not scared of that, I'm so not scared of putting my hand up or trying to just solve this problem that I have no idea how to solve, that's a risk you're taking. But with risks, I feel like risks and mistakes are almost like interchangeable. 

[00:29:15] Robert Kaplinsky: Yeah, I mean, I, I'm reminded of, of 

[00:29:16] Vanessa Vakharia: Is that too much?

[00:29:18] Robert Kaplinsky: No, I don't think so at all, but I, I'm reminded of this Thomas Edison quote, and I'm butchering it, but it was something like, he tried to make a light bulb and, you know, 10,000 experiments that didn't go right, it didn't work. And they were asking about what that felt like, and he's like, I just found 10,000 ways that don't work yet. You know, there's nothing 

[00:29:33] Vanessa Vakharia: I like that.

[00:29:34] Robert Kaplinsky: I mean, just anything worth figuring out at this point, like all the easy problems have been solved. Whatever's left in the world right now, whether it's climate change or whether it's, you know, pandemic stuff, these are hard problems that require countless mistakes on the way to getting that correct answer. And I just think that, if you're an employer and you tell a researcher, you know, if you, if this vaccine doesn't work, you're fired, what the fuck results are you expecting? Like you need to provide safe environment where they realize that this is a normal problem.

I mean, encouraging mistakes in that context means try out your ideas and don't worry we wasted some money. Like you need, that's what you want. So I, I just, I take exception to the way he's interpreting that. 

[00:30:15] Vanessa Vakharia: Yeah, same. And I also think like, I'm thinking about my own math classroom experience and we were not encouraged to make mistakes. Math has traditionally been focused on like get the right answer and that's all you're getting rewarded for, you're not getting rewarded on process, you're not getting a compliment because you worked hard unless you get the right answer. 

And like you can see the generation upon generations of math anxious people that environment has produced. Right? You're just getting people who, like, whenever students come to me for tutoring, some of them come for the actual math, but most of them are coming for a lack of confidence. And the whole lack of confidence is, I'm scared I'm gonna make a mistake and I'm too scared to try. Like, that's what a lack of confidence in, in math is, is you're so scared of not being right. That's all it is. You're scared of not being right. 

[00:30:56] Robert Kaplinsky: You know what's a really weird question that ties back into math therapy that I think is funny? If you knew what to do, what would you do? So I have kids where they're not sure what to do, when you ask them, if you knew what to do, what would you do? And then they say, well, I would think about maybe multiplying these numbers together. And what you find is that, they always knew what to do, but they were afraid that they would look dumb or that it wouldn't work. And so it helps you access what they're thinking without that trauma in the way. 

And again, that question sounds like the only response is, well, if I fucking knew what to do, I wouldn't be asking you right now. But the reality is that we come with this trauma and this fear of being wrong, that it prevents us from even walking down that thing. So again, going back to encouraging mistakes, if that phrase allows you to break through that wall, then I'm a hundred percent for it. 

[00:31:44] Vanessa Vakharia: I love it. Okay. What was it again? If you knew what to do, what

[00:31:46] Robert Kaplinsky: If you knew what to do, what would you do? 

[00:31:48] Vanessa Vakharia: Oh my god, that kind of sounds like a cute crop top. 

[00:31:54] Robert Kaplinsky: Yeah.

Rethinking professional development

[00:31:57] Vanessa Vakharia: Okay, Robert, we have to wrap up somehow. We're at the end, we're at the end of our rope here and our time. But I have to, I wanna talk about your Grassroots Workshop thing, because I think this is one of the coolest things. we actually met through professional development stuff, and I mean, I'm not, I don't know that we have time to get so into it, even though I kind of wanna hear your hot juicy takes. You're kind of a believer that professional development has to change and you're doing something about it. Can you give us a little snip.

[00:32:22] Robert Kaplinsky: Yeah. Grassroots Workshops provides online workshops from education leaders that teachers know, like, and trust. Right? How many times you've been to PD where you're like, I could be the one freaking doing this, or I've learned nothing from this, or, you know, you're outta your classroom and now you're even farther behind with your students.

Having flexible online workshops you can do whenever you want, from the people that you chose, right? Where you're like, I love this person's work and I would love to learn from this person, in an extended experience. You know, conferences are great, but what do you really learn in like that 60 to 90 minutes? You need that somewhat extended experience to really learn something. So that's what it's about. It's really giving educators back control of their own professional learning. 

[00:32:57] Vanessa Vakharia: And it's like very masterclass vibes. I will say from having watched a bunch of them. 

[00:33:01] Robert Kaplinsky: I would definitely say that we aspire to be the masterclass of education, where it's people that you admire and now you get to learn from them.

Q1

[00:33:08] Vanessa Vakharia: Alright. So we're at the point in the podcast where I have to ask you the final two questions. Are you ready? Let's do it. Okay. 

What is the one thing you'd like to see change about the way math is taught in schools? Let's hear it.

[00:33:20] Robert Kaplinsky: So this is sort of ancillary to that, but I fucking hate acceleration. And what I mean by that is in Science and English, there's no one like, "my kids only in biology, why are they not in chemistry yet?" No one says that. "My kids only in seventh grade English, why are they're not in eighth grade English?" Like no one says that. But if your kid, is in 

[00:33:37] Vanessa Vakharia: That's so true! 

[00:33:38] Robert Kaplinsky: Eighth grade math, and not in algebra, something's traumatically wrong with your kid? And the reality is that the whole purpose of acceleration, I surveyed teachers and asked, do you have enough time to teach one year of math in one year? And 83% of teachers said there was not enough time to teach one year in one year.

So when you're doing one and half years, two years, I've literally seen a school that had to do three years, sixth, seventh, and eighth grade math all in sixth grade. What the fuck are you expecting? I'm not joking at all. What the hell are you expecting? And so the challenge there is that, besides the fact that you don't really even use high school math in life as much, you're racing to get to this class that is called calculus.

And what the data overwhelmingly shows is that kids who even take calculus in high school, wind up retaking it again when they get to college and may not even pass it. So this creates math trauma. If you struggle to learn one year of math in one year, imagine how much you're gonna struggle in one and a half years in a year or two years in a year.

And so it puts you, this is a, I'll, I'll say this really heavy thing. Whether or not you're in favor of the death penalty, this is heavy, whether or not you're in favor of the death penalty, you have to accept the fact that innocent people have been put to death. You could be in favor or not, but absolutely innocent people die.

If you're in favor of acceleration, you have to accept that there will be kids who would've been amazing at mathematics, but because you forced two years of math down their throat in one year, they're gonna hate math, and all the STEM field jobs are just cut off. So you have to accept that when you accelerate kids, you are killing kids from the whole math career, and I freaking hate it. 

[00:35:09] Vanessa Vakharia: Okay. We have to pause, I wanna drop a mic, but it's on a stand. But like, that was like, wow, okay, wow, wow. I have, I'm sweating. Okay. 

Q2

[00:35:17] Vanessa Vakharia: Final question. Oh my God, this is so amazing, given your shirt. Everyone, Robert is wearing a shirt that says "you are a math person". And my question, I'm not even making this up, is what do you say to someone who doesn't think they're a math person?

[00:35:31] Robert Kaplinsky: Basically, I say it was the way you were taught math, it's not you. Everyone uses math, but we narrowly define math to be, you are a math person if you can be a good robot who gets correct answers quickly. And as we all see that doesn't actually matter in real life. And so people have really just kind of absorbed traumas that are not really theirs to have.

[00:35:53] Vanessa Vakharia: That was so sweet at the end how you said that. That was nice. Okay. Oh my God, you're looking so bashful. I wish everyone could see you. 

Outro

[00:36:01] Vanessa Vakharia: Okay, it's, we're done! We're finished. This is the end. I don't, this has been so much fun. I feel like, oh my God. Like we talked about so much stuff. Things got really intense there, but like in a really good way. I had a great time. Did you?

[00:36:12] Robert Kaplinsky: Yeah, I loved having a chance to talk with you. 

[00:36:14] Vanessa Vakharia: Okay. Tell people where to find you and like what things to look you up at.

[00:36:18] Robert Kaplinsky: Yeah. So my website is robertkaplinsky.com. K a p l i n s k y. You can find me on all the social media platforms with the same name. And I would love to connect with you. Openmiddle.com, openmiddle on social media as well. If you're interested, hit me up.

[00:36:32] Vanessa Vakharia: Okay, now we have to say goodbye. Bye 

[00:36:37] Robert Kaplinsky: Bye Vanessa. 

[00:36:38] Vanessa Vakharia: Bye 

Vanessa outro

Okay, so is it just me or does Robert swear almost as much as I do? Like I think I've met my match and I love it. 

I have to say that since this interview, I have been trying open middle problems with my own students and it's actually so cool to watch their eyes widen with excitement when I'm like, no, I actually don't care about the answer, I care about finding the most wack way to get there you can possibly think of. PS, I know that's not exactly what Robert said we were supposed to do, but hey, we're all bringing our own unique spin to teaching math. So this is just me putting my personal je ne sais quoi into open middle math. 

If you've tried open middle, or have any favorite open middle problems of your own, send them to Robert and me, we would love to see them. And until next week, you get out there and solve something in your own wack way. Do it. And of course, pics or it didn't happen. 

 If something in this episode inspired you, please tweet us @maththerapy, and you can also follow me personally @themathguru on Instagram, Twitter, and TikTok. 

Math Therapy is hosted by me, Vanessa Vakharia, it was created by me and Sabina Wex, and it's produced and edited by David Kochberg. Our theme music is by Goodnight Sunrise.

And guys, if you know someone who needs math therapy or just needs to hear someone else getting math therapy, please, please, please share this podcast, and rate or review it on whatever podcast app you use. Those things actually make such a big difference for us. I'm determined to change the culture surrounding math and I need your help, so spread the word. Until next time, peace, love, and pi.