Rebuilding Mathematics Education w/ Sunil Singh

Chris McNutt: Hello everyone, welcome to Things Fall Apart, I'm Chris, I'd like to take a moment and thank our patrons that keep our show going, two of which are Aaron Flanagan and Annette Laughlin, thank you for your support. We sincerely appreciate as we go about creating this endeavor, whether it be monetarily or just your support on social media by sharing our information. On our website you'll find various materials including a ton of resources that we've released for free. Those resources range from mindfulness practice to projects for classrooms to a children's book over the history of education, anything's on there. It's all available for free on our website at humanrestorationproject.org. Today we're joined by Sunil Singh, who's the author of Pi of Life, The Hidden Happiness of Mathematics, as well as a writer for the New York Times and math consultant for Scholab in Montreal, Canada, an organization aimed at implementing technology towards student success. Thank you Sunil for joining us on the podcast. In Pi of Life, a major emphasis seems to be placed on the reflective and philosophical notions of math. So in your book you talk about recognizing curiosity, gratitude, power, resilience. Most of these things in my view go well beyond logistic thinking, which is how we typically view traditional math. So what was your idea behind writing the book and what do you want readers to take away from it?

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Sunil Singh: Well, I mean, it's funny because I'm talking to you and you know, you're part of this thing which I want to find more about is the Human Restoration Project. So my answer is that I really wanted the book to serve as a way for people to realize, perhaps again, that mathematics is above all, it's a human endeavor and it's filled with human ideas and it's filled with human questions. It's filled with human curiosities and I'm really emphasizing the word human. I didn't have to and the key thing is that these things are to be shared with each other to find out more about mathematics but also each other and I think that there's a new social endpoint to learning mathematics and that is that we are using mathematics the same way. I mean, I love music and when I go to concerts and all that, yes, I enjoy the music on my own in terms of my own interpretation of things and songs but really the best part of the night or is to share it with others and mathematics is no different and we always focus on the interpersonal aspects of learning math which are great but the one thing which is neglected is the intrapersonal and the person that kind of really sort of foreshadowed this was this woman named Rachel Butzmann who she's kind of the guru of the whole sort of collaborative consumption economy that she predicted 10 years ago and she said something which I really sort of really resonated with me was that she said 25 years ago, you know, we met people to do new business. Now we do business to meet new people. So that same kind of lens I think that mathematics is flowing through and, you know, I highlighted in the introduction of my book very briefly but I think it's something very germane to the opening question that you asked was I referenced this mathematician named Francis Sue and, you know, he believes mathematics is for human flourishing and, you know, sort of this Aristotelian view of learning mathematics, you know, beauty, truth, justice, play and love that this is accessible for everybody and over the years and whatever, I mean, mathematics, math education has been whittled down to just really test procedures and logistic thinking as you mentioned at the top. So really at the end if I said a couple words for, you know, the listeners and people who read the book to see mathematics as a human endeavor.

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CM: It's very interesting because the way that you're describing math is almost artsy. It's very creative. Yeah. A lot of times when I think of that style of vocab, I'm thinking of humanities. I'm not really talking in humanities, English and social studies, right? Separating that very much away from the rationals is what I guess they would call you. The people that are, you know, like logically minded gets this, then this, then this. I don't want to make too many overarching assumptions, but in any building I've ever worked at, the math teacher tends to be the one that's very, not robotic, but the one that, you know, that's very much just like this happens and this happens and this happens. I don't typically hear about math spoken about in this philosophic grandiose way unless I'm reading about something like behavioral economics. The first thing that comes to mind with what you're talking about to me when it comes to envisioning cool math would be like Freakonomics.

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SS: You know, you mentioned that sort of the kind of people that we meet when we associate mathematics and again, it's based on whatever experiences one has is how one views it. I mean, my view is based on my experience in terms of whatever I've seen, the people I've met, the mentors I've had in my teaching career. I mean, it's a summation of all those things. So if people who are even in the math field don't feel that way, it's because they themselves perhaps have not had this sort of, you know, kind of, again, all those experiences, maybe the way they've been taught, maybe they feel that mathematics is for this sort of logistic thinking. And it is, it's a powerful tool for that. And it's, but, and I really, you know, say, but capital B is that it's a little bit more than that. And I know the way I reflect about math and the way that I talk to math, about math now with people, it sort of waxes more towards the sort of the philosophical kind of bent as you'd be sitting around a campfire three, three in the morning, listening to Pink Floyd same way we'd be talking about math in the same very way.

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CM: This might be too big of a question, but I'm curious about then why do you think that's the case? So there's obviously a huge binary that's in place between what you're talking about and what we typically think about math, let alone in education, but even in like the world, you have people that say, I'm not a math person or, you know, I'm more of an English person. Why do you think that mathematics has moved so far away from that philosophical sense?

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SS: Well, I mean, without knowing, I mean, I only have access to my history of being a teacher and maybe 10, 15 years prior to that because of the mentors I had. So, you know, I have kind of this domain of 50 years of math education, experience, textbooks to sort of, you know, mine in terms of information and, you know, I'm going to share with you a forward from a textbook from 50 years ago and you'll see how kind of gone backwards. But, you know, mathematics have been around for thousands and thousands of years. Math education hasn't been around for probably less than a century. And then you have to look at what was the purpose of education because really education took whatever it needed from mathematics to create what it needed for education. And, you know, this becomes now a discussion for a different day, but, you know, if you look at what's happening in schools generally in math education, there's testing, there's, I mean, there's lots of testing, there's a curriculum which people have to follow. You know, why is that? I mean, you know, my own kind of gut feel beliefs is that because, well, I mean, one, it's an economy, you know, textbooks and all that, it's a micro economy education. You also want to create portability for that reason. You want to have a teacher who's teaching in Santa Fe, teaching a certain topic to be maybe aligned with someone who's teaching in New York. And, you know, I find that, you know, I mean, all my English teachers, I remember chose their books. You know, why can't math teachers choose the topics they want to teach? Your brain is not partitioned into all the segmented nonsense, which, you know, the K-12 curriculum does. It just wants to think. That's what it is. It wants to think. So, however you can get that thinking, if there's a teacher in high school who wants to, you know, specialize and just talk about geometry, go for it. If there's a teacher who wants to talk about number theory, if someone wants to talk about voting theory, that's great because it's going to spur interest in other areas if you have a teacher who's allowed to teach topics which, you know, really, you know, sort of burn their passion with like the intensity of a thousand suns as opposed to having this one size fits all. And the reason why it's one size fits all is because, you know, the goals are not to inspire kids to learn mathematics, it's just to make sure that everyone is doing the same piece of mathematics.

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CM: Sure. I mean, that makes a ton of sense to me. I think a lot about the standardization movement and I feel like math teachers very much got the short end of the stick because when you can bring it down to its most smallest point, math is the easiest one to say that there is one right answer on specific types of problems. If I give you a very basic math problem, there is one right answer. However, what you're talking about is way more complicated than that. It requires like critical thought where there are multiple correct answers. And I feel like that impacts other areas as well. As a history teacher, the standardization of movement has made it very much about facts and dates instead about thematic elements and patterns and analysis. It impacts everyone. I just feel like math specifically, just because of how and what we look at when it comes to math, it's lent itself very easy to go, A, B, C, D, choose one. Okay, that's right. Move on to the next segment and portion, the next topic, the next end of book questions, which is very sad. I like this quote from your book. You said, mathematics is the only place where you can buy 64 watermelons and no one wonders why. It's very true. Just looking at any standardized test, just the questions that are being asked are ludicrous. They don't make any sense.

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SS: Yeah. And that's part of it too, is that as soon as you offer up a question, and that's a pretty popular instance. I've been turned into a meme now, I think, 64 watermelons, and there's a host of other questions like that. Soon as you present one question, which is completely outside the view of a student, like, okay, that doesn't even make sense. You start to lose credibility, which you don't even realize you're losing. And by the time you get to high school, and my favorite chapter to write in the book was chapter nine, which is about laughter, because trigonometry became the bane of my own existence as a teacher in terms of none of those questions, those applications of trig in terms of flying a kite. We forget the string is moving, so you can't say that the angle is going to always be who cares about, no kid has ever wondered what the angle of inclination is of a kite flying, maybe the height. And then to find such distances like the height, hypotenuse, or an angle, okay, I'm not saying those things you shouldn't find, but please don't dress it up in a false narrative, which has no reason being there. Just create a triangle, ask a question. If that can hold its own, great. Get the green check mark out. If that question is booed, then do something else, because that's the problem I find, especially when you get to high school levels, that there are some great applications to mathematics, but some of the ones that kids see, especially in high school, it just confirms that, yeah, I'm glad I checked out back in grade six or grade seven.

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CM: It's very draining. I wish Michael, normally I co-host this with Michael. Michael's an English teacher, and one of his courses that he actually taught with a math teacher was mathematics appreciation, and they did deep dives into a drunkard's walk and looked at basically why is it that we view math with such a particular lens? Why is it that there are math people? And almost deprogramming kids into thinking that math is something that it isn't. I feel like it kind of sets you up for failure. If you think that math is this and you don't like it, you're not going to want to explore these philosophical concepts, at least until well until adulthood, because you're drained by it. It sucks, to put it frankly.

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SS: I make sure I say this anytime I'm sort of doing a podcast or interview. It's very short idea, simple idea, but kids don't hate math because it's hard. Kids hate math because it's boring. Kids are playing challenging video games. The learning curve is high. I played Minecraft with my kids a year or so back, and I didn't know how to play. I'm asking my daughter, who at the time was seven, what do I do next? She's building a way and doing stuff. There's no instructions. There's no adult supervision in Minecraft. There's these Wiki links and YouTube videos that kids watch. Kids are learning far differently than when I went to school, and if someone can ever create a math curriculum which maps on the way that kids explore Minecraft or things like that, then that's going to be the golden ticket. Right now, kids are learning, sadly not because of their teachers, but mostly in spite of them. I'm speaking generally, and we'll talk about this towards the end. There's a lot of positive work happening. There's a lot of really amazing math minds and teachers and communities being built, but for the most part, still, I would say, generally speaking, we're kind of in the same place that we were a couple of decades ago.

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CM: Hey there, we hope you're enjoying the podcast. The Human Restoration Project stays alive because of generous donations by our patrons. Take a second and check out our website at humanrestorationproject.org for more podcasts, our blog, and all sorts of free resources that we've designed for educators. And if you love what we do, consider supporting us on Patreon. For as little as $1 a month, Patreon supporters receive goodies from being listed in the credits of our resources to early access to what we do. Thanks in advance. So with that in mind, let's do this. I kind of want to break this up into two halves. So the first half, we're kind of talking about the state of mathematics and the problems that exist, but I don't want to keep the entire thing negative. So after the next question, I want to move into creative applications, what can you do and that kind of stuff as well. So I have one more question that I really wanted to ask you about just the state of math and this goes beyond what most teachers can do, but it's just a logistics question because I've always been fascinated by this. There seems to be a divide, like an argument. Should every single student be taking, first off, should they even be taking algebra one to begin with? So like starting right there, should they even get to that level? Because there's a survey that's been done. It was done by the Atlantic and it's been replicated where they showed that roughly 20% of people don't use math at their jobs beyond algebra one, which seems like that's one in five people. That seems like barely anyone's using it. What are your thoughts on that?

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CM: Yeah, I have quite a bit on that. I'm just going to go to, because we don't have algebra one up here in Canada, I've had this conversation with US teachers. The fact that there's even a course called algebra one to me really makes no sense because algebra is not an appendage of mathematics, it's its circulatory system and the algebraic thinking is something which can be installed as even as early as grade one and to have this formal thing waiting for you in high school called algebra one really does a disservice to mathematics and to the kids learning algebra. So yes to your question, should everyone take algebra one? I would say heck no. In the current state it is, I wouldn't take algebra one myself unless I had to take it for a specific thing, which again, you can argue, I mean, if of course you're going to engineering mathematics or a pure science degree, then you would need that kind of thinking and mathematics required university, but you brought up something very subtle, which comes up quite a bit in terms of the usefulness of mathematics and I remember as a high school teacher, my own students would, when am I going to use this? It's always with a groan, there's always like a deflating body language and I'd be very honest with them. I'd say whether you would use it or you would not, I'd say no and most of the times I would say no because most of the things that in terms of direct application, no. Does it create sort of better problem solving thinking? Absolutely, but there's much better things to induce problem solving thinking capabilities with far more rigor and depth in algebra one and so at this point, back to your question, would I say everyone has to take algebra one? Absolutely not, but no other subject gets asked for its usefulness. No one asks, when am I going to use the periodic table? No one asks, when am I going to use learning about King Lear or Edward Albee's zoo story. When am I going to use this? Learning should be for these emboldening ideas of making your life better, going back to Francis for human flourishing to just add knowledge. Because mathematics has become this sort of Clyde to the workhorse, almost a whipping boy for, so I hate using that violent metaphor, but to yeah, when are you going to help me out? When can I use you? And if we don't answer or can answer that question correctly, kids get snarky and rightfully so because that's the way mathematics had been perceived all the way through the curriculum. 

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CM: Sure. So kind of with that being said, with technological advancement, I feel like mathematics in particular also has been disparaged against because again, it's not that philosophical notion. So for example, in history class, we let kids now look up answers on Google. They're intentionally not Google-able questions, so it doesn't work very well, but it seems very rare that you walk into a mathematics class and then use Wolfram Alpha or something that solves the entire problem for you. And using a calculator on a test is so kind of not always the case, which I think is kind of odd. And this is coming from someone who's not mathematically oriented, but if I have a tool that does all this work for me, I understand that there's a step-by-step process, but do you actually need to know it? I mean, the argument could also be like, do you really need to know how to use perfect spelling if there's a spell check or do you need to really know what a date is? What do we do in terms of that applicability when it comes to technology?

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SS: Well, we kind of box ourselves in because we create questions in which we have this kind of debate, whether we can use technology or, you know, that's the fault of the construction of the test to create this kind of, okay, well, why don't you give questions which are more sort of have, you know, open-ended and that, yeah, if they want to use a calculator, you know, go for it. It's not going to help you here, but if you want it as a tool, use it the way you want. But if you are creating questions in which basically it's a computational question in which all the numbers can be put into Wolfram Alpha or whatever, then that's a problem with the question itself. And yeah, I mean, why are you making students? I mean, I still tutor kids who have to memorize, you know, all these trig identities and all these things. Why? You can look it up. When did anyone have to ever memorize a formula or something, especially in this day and age where you can look it up? And if you, again, it all goes back to selling. I mean, when you ask kids to do things, guess what? You got one or two customers short who are not going to be appreciating mathematics because of things like this. So it's, if you, if something can be used as like, you know, they teach long division still, I'm not sure why, because most kids don't understand long division algorithm and other the teachers just use a calculator to do it. I mean, unless you're going to actually talk about what is happening here in a step-by-step basis and where it has some sort of like, you know, that there is something of value to be shared with the students, then go for it. But just to have long, long division is just a, it's like a Flintstones calculator. It's like, just go, just cut to the chase, plug it in. There's the answer. Move on.

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CM: Yeah. Something that you keep bringing up that I think a lot about when it comes to math is that concept of only having one right answer. And you keep saying, well, there has to be multiple answers to the problem. In my opinion, the reason why many kids don't grow up liking math, one reason is that it's, they don't see why it matters. It's just kind of like numbers on a page. But the other reason is it's very easy to get something wrong because there's only one way that it's right. So, you know, if I mess up at any stage during this entire process, there's a pretty high likelihood that the answer that I get at the end is not going to be the correct answer and it doesn't feel good to get something wrong. Whereas in English or social studies or even science, I can BS a lot of my answer and probably still do okay. I guess the reason why I was a history major, I could BS like crazy. That concept of designing math problems that have multiple answers is very interesting to me.

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SS: And if you take the breadcrumbs back of this conversation back to the beginning in terms of seeing mathematics and that sort of philosophical artistic creative lens, then naturally, it's going to go to what kind of questions do you ask your kids? It all stems from the kind of math questions that you ask. It creates the culture, the environment of learning. You know, it's like with everything else, you know, I tell my son about music. I go, you know, there's no such thing as like, you know, new music is better or old music. You know, every show, I wrote a piece in Medium about how my music collection influences my ideas of math education. I have over 50 genres of music in my iPod. There's every genre of music I will be open to and listen to. But every genre of music also has good, bad and ugly. Like there's no such thing as a bad genre of music. I mean, the same thing with mathematics. I mean, there are some bad math problems to give. Not everything that you give in mathematics is that interesting. And because you only have a finite time with your students in a math class, you know, I think it is incumbent upon the teacher to find the best questions that you know is going to provoke the best kind of thinking. And because if your end game is just to see what kind of you want them to cover the curriculum, get good marks, you're not going to think about that. You're just going to want them to eight procedures they've done many, many times and hopefully fingers crossed everything lined up on that Tuesday afternoon and they got it right. So it depends. It all goes back to what are the goals of math education. But I think going and seeing mathematics and artistic lens just changes everything.

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CM: Then are you concerned about of movement towards particularly applied mathematics? So you're talking a lot about this philosophic artistic approach. Are you concerned then about movements that are aiming towards replacing, let's say, algebra one with personal finance or replacing geometry with health and wellness, things that I would argue most kids need those things. But do you feel like then something is being lost from that philosophical understanding of math?

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SS: Yeah, it's it's it's almost it's like a you know, you're not really fixing the problem. I mean, you're you're it's like you're maybe, you know, if I'm using a house analogy, OK, you bought some new furniture and you painted the room and looks nice and looks different. But really, if we're going to go to that sort of house, we're building metaphor to what they do in Las Vegas with hotels. They implode them. They get rid of them. They just I mean, those are still structurally sound hotels. It's just they don't work for the time anymore. And I'm sure there's more to this than that than that sort of simple metaphor I'm trying to go to, which I just kind of made up on the spot. But, you know, I've the tweaking as earnest as it is and all that. Yeah, I'm not for that. And now I'd be applied mathematics. I would love to see things like, you know, voting theory. You know, I know some teachers do it kind of, you know, subversively. And that's odd because mathematics is subversive, you know, has a lot of subversiveness to it. I would love to see voting theory, Arrow's paradox. You know, I mean, you know, the man won a Nobel Prize Memorial Prize in economics in 1972 for more or less coming to the conclusion that every form of voting democratic voting has some flaws and some contradictions. And, you know, this would be very interesting because we always talk about voting, gerrymandering, all these things. Why isn't that in the curriculum? Why isn't, you know, game theory in the curriculum? Why isn't there more analysis of how skewed lotteries are in terms of, you know, your expectation of winning? We're talking about finances and mortgages. To me, that seems like, OK, well, most kids wouldn't even understand. The only thing you didn't know about mortgages that you're going to be paying a lot of interest. Really, that's all you need to know. I don't think you need to know the complicated formula because that's not going to really help. You just have to know the banks are going to be getting rich and you're going to be paying a lot of interest. And, you know, then it leads into, OK, for me, I mean, schools about equity and guess what, not all those kids who are in finance courses are probably going to see a house in their lifetime. So be very careful, you know, where you tread here, because as soon as you talk about finance, you talk about money. And if you survey the kids in your classroom, there's quite a disparity of class. And so I'm all for having, you know, applied math and things which are every day because those are very, you know, even filling out an income tax form. Those are great, but I don't want mathematics defined by that. I mean, it's just it's just one thing in the whole buffet of mathematics. So, yeah, I'd rather just scrap the whole thing and start from scratch.

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CM: That actually makes a lot of sense. I'm recalling back to my personal finance class in high school and predominantly it was a math course and it was focused on the stock market. And I learned later in life you have to have a pretty decent amount of money to be investing into a stock market. That's not like a retirement account. I mean, I don't personally have any stocks that if I did, it was like play money. It was just like a joke. I wasn't doing it to actually think that I was going to make a lot of money. Yeah, that makes a lot of sense to me. I think a lot of what you're advocating for, the gerrymandering and things of that nature almost gets to be in the realm of social justice. So like I think about calculating payday loans and how that impacts low income communities especially, which is something that we actually talked about in my class in social studies. But it obviously lends itself to math very well. Like how do you design a building that takes people's money? That's not very deceptive, but it's true. I mean, that's the whole industry. It's banned in many states. And I'm not sure what it's like in Canada, but there's a lot of these major mathematical problems.

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CM: Well, and this is I mean, this kind of ideas is spiraled in our in our conversation. But the you know, one of the things which, you know, mathematics allows you to do, you know, it gives you power and it gives you another lens to see the world. And, you know, I know that education and schools, they want, you know, all these goals for math education. But really, this is the only time I'm going to do the conspiracy route. It wouldn't really benefit society for to have, you know, 100 percent of the people to be mathematically literate, because now you're going to, you know, severely, you know, cut into the profits of those things like payday loans and, you know, warranty providers, insurance and all that, because you're going to have people who are going to be able to like, you know, dissect in a second, you know, anything you throw at them mathematically, they're going to go, that's not that's not sound. I'm going to analyze this. But in order to get to that level, you know, you have to get to, you know, at least high school mathematics and be introduced to the right topic. So when kids are turning off of math and all that, you know, you're not going to hear a lot of booing from insurance companies and that because they know they can keep going and doing what they're doing.

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CM: Yeah, I mean, a lot of this is very much political. I question that heavily. Like there's many people that say, well, you have to constantly remain neutral in everything that you do. And I actually disagree with that. If there are things that are going wrong in society, it should be your job as a teacher to try to correct those problems. If your goal is to raise someone for the future, you don't necessarily have to have a liberal or conservative bias, but there are certain things that are just wrong and have to be brought up. The case in point example to me is like racism. There is nothing currently defined in standards that say that you should adamantly preach against racism. It says you could talk about the civil rights movement or something of that nature. But there's nothing that says like have a curriculum that focuses on tolerance and just fighting for advocacy. And it's very odd that if we're trying to change things in society through education, the constant preaching is remain neutral, don't offend anyone, stay true to your word. I think of, for example, Howard Zinn, who is a historian who is famous or infamous, depending on how you view him, for saying teachers should preach social justice. And I feel like if mathematics move towards the style that you're talking about, it would get into that category. You're fighting for people using math or fighting for your own rights using math.

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SS: Well, it's funny you said that because, you know, in terms of, you know, we've talked about the first half hour in terms of some of the negative. And, you know, we have to because right now a lot of those subjects are pink elephants. Nobody talks about them or they talk about them politely. So, you know, we wherever we had to go, we had to go. But ironically, well, maybe not so much. But there's a there's a big movement now in mathematics to move towards some of the things I was talking about, especially in terms of race and equity. And that's being championed by large math organizations like NCTM. And they're just not like, you know, the theme of the that particular conference or whatever these have been building and they're now like really being spoken as like these are like mandates that we have to address the equity race issue in mathematics before we can do anything else, because, you know, there's there's kids in the classroom who come from, you know, various backgrounds and various cultures who are subjective to both the conscious and subconscious bias. And then, you know, once they start to not take certain courses, math courses, then, you know, careers and such. So, you know, I'm very happy to know that, you know, there's movements to really make sure that mathematics is not just for, yeah, it can help you become like a rocket scientist or in the past and things like that, that the things you speak about and going back to the flourishing for human life, I did mention justice as one of those five sort of markers. So, yeah, mathematics and justice are being tied much strongly now.

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CM: That is very reassuring. I'm glad that there are people thinking about this sometimes, especially when you're isolated in the teaching world. It can become very scary to feel like it's just you versus the world.

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SS: Oh, yeah, I know. And maybe 10 years ago, I would have probably said, yeah, it feels like that as well. But having been to numerous math conferences and having Twitter conversations and just meeting people, there's the way that I use I use a lot of metaphors. I mean, I taught English. I mean, I taught math, physics and English. I taught English for two years. But the sort of the metaphor analogy I came up with in terms of what's happening now in 2018 and math education is like it's like the gases which are swirling to make a new sort of planetary system that there's a lot of swirling gases. And now we're in this sort of contraction phase of where things are starting to form. They're not just sort of these ideas in the ether. They're coming to form solid ideas. And we're still a couple of years away from this sort of new solar system of mathematics. But it's that the gases and all the different conditions for it are definitely set up right now.

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CM: That's definitely good news. I wish education grew faster, but I'll take what we can get at this point. Exactly. I do have one more critical question before we move into what math teachers could do now, because I feel like it would be the one caveat if I were a math teacher listening to this, the thing that I would say, is it possible to teach math in this philosophical way and still have students do well on standardized tests?

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SS: My gut answer is no. I didn't think too much about what I just said there, but my gut answer was no, only because part of the philosophical way of doing this is, you know, that the standardized testing in itself. And luckily, one of the things that I began through conversations, I think we're in the death rattle stage of formal grading assessment for standardized testing. And that doesn't mean that it's imminent, the death of grades and assessment and numbers and things, it could be another generation or so. But, you know, when you go to interview for, let's say, if you're going to for art, architecture, or even if you're a computer programmer, they want to see your portfolio, they want to see what you've done, they want to see, you know, what you've created. They don't want to see necessarily your GPA or things like that, which is like this statistically invalid distillate of, you know, your years of testing. That's the other ironic part, is if people actually understood statistics, they would understand that most of the numbers which get reported are statistically invalid. So right now, no, you can't square that circle. The philosophical things that I'm sort of, you know, pining for, yeah, you can sort of, you know, talk about them here and there in the classroom. But for them to have the impact that they're going to have to, they're going to have to be part of a new curriculum, which doesn't involve standardized testing. So I'm not going to say yes, because if you can, that's wonderful. Then you're a bigger man than I am, Charlie Brown. But right now, I would say no, it's either they're pretty binary sort of positions.

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CM: We are raising kids to meet the needs of the SAT, ACT, which are so math focused, so reading focused, but actually not teaching kids math at all. It's a false positive. You can do amazing at the SAT and math and go on to do absolutely nothing in math. They really have no idea what you're doing. That indicator that the SAT gives you is just a snapshot first off, but it's also not even, it doesn't matter. It's so irrelevant. And teaching someone that that does matter their entire lives has raised a generation and now generations of students who aspire their entire life goal to being really good at something that's obviously not that relevant. And if you tell someone now, parents included, this doesn't really matter that much. They're going to respond in kind with, no, it does matter. It's on the test. And it just kind of stops there. And I worry sometimes that we're raising a generation of non-critical thinkers. It seems like most of the people that are out crying about these things are those that are either multispecialized or didn't do well in school. A lot of math teachers that are decrying against these math practices are like you. They have a dual major in English or they have a major in philosophy or they're going beyond just this one thing that they were really good at in order to see the bigger picture. It's a very wide spectrum of different things going on that goes beyond just, it's going beyond standardized testing and seeping into our culture.

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SS: And the, you know, the ironic part of is math education, it's sort of, you know, champions this practicality, which is kind of it's here or there. Miss, it's not I mean, you know, you could create a much better curriculum for application as we spoke earlier. But I mean, what's ironic is that they do champion this application part. So even if, let's say, a student graduates with 100 percent or perfect SATs, if that student walks into a convenience store and purchases a two lottery tickets, not one, but two, they've just nullified their entire mathematical thinking because the lottery is a negative expectation. I always tell students buying one ticket is great because it's a cheap kind of leisure kind of amusement in terms of whatever you pay to fantasize what you would do. There was millions you'd buy some sort of island or take all your friends. That's cheap entertainment. And if you don't buy any tickets, you can't dream that. But as soon as you buy the second ticket and let's say the probability of winning a particular, you know, draw is like one in 14 million. If you buy two tickets now, it's two in 14 million. You spent an extra two dollars. And let's say if you buy 100 tickets. Right. So that's now one in 140,000. You've just given up a great stake dinner for two for changing the probability in the seventh decimal place. They don't they don't teach that, so I'm not really impressed by people graduating with, you know, unless they really love math and they're doing a peer and their teacher and their curriculum. So I'm generalizing here. I've got to be very careful. But again, in the whole sort of general scheme of things, if you're going to go all rah rah about application, then go in all in for application, like start doing some heavy duty analysis of all the things in which kids, you know, can be should be looking out for, especially from the monetary sense. Let's do some heavy duty applications.

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CM: Yeah, the lottery application makes me think a lot about in today's world loot boxes, which you'll find, you know, in like online video games, the chances of you getting what you want in terms of cost investment. There's a reason why game makers call those people, quote unquote, whales, the people that put thousands of dollars into a game without actually receiving really anything in return doesn't even have a resale value. So it's really bizarre to me, especially young children, 10, maybe even younger now playing games like Fortnite that offer those services. And really, they're just fun ways to gamble. In the same way that like, I think of like trading cards are the same as that concept. You're buying a randomized thing. Your chances of getting what you want are quite slim, but you're getting that dopamine rush.

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SS: It is a dopamine rush. And, you know, I mean, we just have I mean, I've promised myself I was going to write about this even like a year or two ago. We have this lottery in Ontario. It's called LottoMax. And the last four or five weeks, the prize, the LottoMax prize, 50 million dollars. No one's won it. That's not a big surprise to me because there's two things happening here with LottoMax. I mean, to win the actual LottoMax, I think that probably is one in twenty six million. But they've done something very ingenious and kind of nefarious is that they've made the cost of the ticket five dollars. So that's kind of prohibitive. So let's say, you know, you know, if it's one in twenty six million, the probability of winning it, I think. And let's say that particular week, you know, there's 13 million tickets purchased, you know, 13 million times five, they just still scooped sixty five million dollars the government. But there's a 50 percent chance no one's going to win the big prize. That's why it gets rolled over. So, I mean, it's I mean, the analysis has to be much deeper than that. But I mean, no one's no one's questioning things like I mean, they they they just because they were never kind of inspired to to look at mathematics with that eye. And I forget the person who came up with this quote, but it's one of my favorite math quotes in terms of why you should do math. He says, do more math, cause more destruction. You know, it's it's more from a punk point of view in terms of I used to tell my kids, you know what, do as much math as you can. And I use the punk angle. I mean, I had to kind of know my audience. Some of these kids were, you know, they had some challenging backgrounds and stuff. So they like when I sort of took that route. I said, you know what, do the math to sort of, you know, get back to the system.

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CM: If everyone knew the math, that what you're talking about, there's no denying that things would change in society. Hopefully, hopefully. So let's let's move into then because we're already kind of talking about it. What can math teachers do now or possibly in the near future to either try to circumvent current practice or just throw it all out the window and fix it to something new? So like actual math practice with this with this, I guess new would be the word of saying it and new form of mathematics, even though it's already existed. Let's talk about gaming for a second, because we were just talking about like Fortnite and the lottery is technically a game. You talk a lot about play as an important theme in math. Specifically, you talk a lot about Sudoku. I know your Twitter is kind of filled with math gaming type stuff. I think about Fortnite during my era. I think about like the beginnings of World of Warcraft and like player economies. I think of tycoon games were my favorite when I was a kid and how much math is involved in those games. It's insane. I mean, the amount of you have to know about economics and understanding profit margins and just math in general is pretty insane, as well as sports. Sports, obviously, there's a lot of math. There's careers built on sports analytics and gambling as well. That's fun. That's math. Where is that place for play in math?

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SS: Well, where is the place for play and learning? I'll preface my answer with Francis Sue again, who gave the closing keynote at this year's NCTM National Conference, a teacher of mathematics annual conference in Washington in April. And he gave it to a full house. And rightfully so, because he's an amazing speaker. And when he was opening his keynote, you know, we talked about, again, the idea of mathematics for human flourishing. And if you go back to get into our conversation, I did mention play in that mix, beauty, truth, justice, play and love. But when he started speaking, his first bullet point was play. Everything's everything begins with play. And, you know, there's a false demarcation in education that, OK, play is sort of Montessori-esque or it's an elementary school, maybe stops at grade five or six. Now we have to get serious. If you knew anything about play in terms of what play is and especially mathematics, play is serious business. And I wrote an article many months ago where I referenced Wayne Gretzky, the hockey player, you know, which is arguably the greatest hockey player. And he lamented about the current state of the game, the NHL. And I mean, the analogy was set up for me because he said, you know, these kids are overcoached. In the same way with mathematics. I mean, it's all about procedures and things like that. And sure, they're doing well in these procedures. But he says there's no room for creativity. When I was a kid, I mean, he just threw some pucks the rink or the, you know, the frozen lake or whatever. He just played and he tried different things. He tried to how did Gretzky do that famous bank pass off the boards at a, you know, hundred and ten degree angle because he practised that he played with all the different angles on boards and tried things with sticks. That's what he got. And, you know, that's what we should be trying to create. I mean, not everyone is going to be the Wayne Gretzky of hockey, but, you know, we should be trying to create these creative thinkers like that. It all begins with play. I mean, you have to give problems where there's ample room for play. And I'll give you a perfect example of that in terms of its ties in a lot of things talks about this will tie in the current state of math, education, textbooks. So this is from a course that I taught in Ontario back in the early 2000s. Sadly, this course no longer is available. And one of the reasons it was taken away because it was it proved to be really demanding and difficult. But there is this little paragraph at the back for these performance problems. And if after you listen to this, you're going to realize that we don't have this kind of culture, generally speaking, in our math education. But we did have it at some point back 15, 20 years ago. So it says the problems in this section offer you the opportunity to solve some significant problems related to the topics you studied throughout the course. Several problems can be solved in more than one way. Back to alluding to what you spoke about earlier in our interview. Some of the problems are challenging. Considerable ingenuity may be needed. There's ingenuity and creativity may be needed to solve them. You may be unable to complete a solution in the first attempt. That's very important because mathematics has mostly been about failure in the first attempt, not about success. And you might you may find it helpful to work with others. There's a social component and share ideas and strategies. Be persistent. Try a problem. Set it aside. Try it again later or try another strategy. And here to me is the kicker. It may take several days or even longer to solve some of these problems. Kids need time and space to do that. Time and space to play.

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CM: I actually just wrote something yesterday about gamification and how gamification really isn't the same thing as play. Gamification is a mask of something that you're doing to make it more fun. Playing a game is actually supposed to be fun. It's not meant to be. Yeah, it's not meant to like be deceptive in any way. It's meant to just make you enjoy it. And let alone math education. We'll come back to that in a second. But just letting kids play games, I feel like is very valuable. We've collectively as a society associated game playing or talking or whatever with wasting time, which that verbiage implies that it's not time well used, which to me doesn't make any sense. That play, first off, is foundational learning. It's the first way that you ever learn how to do anything. Animals do it, too. And two, that's kind of what makes you a human being. Socializing with other people, playing around, having fun, being happy. These are things that every human should aspire to do. It has nothing to do with a wasting of time. So it saddens me that many places, many administrations, many teachers see, oh, like I can't spend 15 minutes, 30 minutes, an hour playing a random game in my class or letting kids talk to each other because they're not going to be learning then. I think that's a very narrow definition of learning. I feel like kids actually learn a ton from just being given multiple days to solve a problem or just playing a game or doing whatever. It doesn't really matter what you do. You're going to take something away from it. As long as you're reflecting on that knowledge gained, you should be doing OK. I mean, that's the whole basis of experiential education. It's John Dewey's whole idea is you just reflect on what you've done and you learn from your experiences. And that's kind of like what you're getting at. If we could supply math classrooms with multiple day projects or multiple day questions or multiple day games where some kids move ahead, some of them stay behind. But as long as they're all enjoying it, they'll take a lot away.

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SS: Well, and you're so right. And there's many reasons for play. And you already outlined all on the social component, the learning. You know, it's just foundational to what play is and just really sort of narrowing it down to mathematics. In order for kids to, there's a quote by Paul Lockhart, which I'm going to read right now. He says, you know, mathematics is the art of explanation. If you deny students the opportunity to engage in this activity, to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, to cobble together explanations and proofs, you deny the mathematics itself. And we cannot get our kids there if they don't have the space and time to play. Because mathematics, I mean, in fact, what's happening in our classrooms today is completely, it's not the thematic history narrative of mathematics. I mean, you know, people who explored all the mathematicians that were known or even this, you know, even, you know, our recreational mathematicians throughout the ages, you know, they spent days, weeks, months, the best mathematicians spent their entire careers on one problem. They might not even have made any sort of, you know, headway into it. That is the, that's the narrative of mathematics. And to make it seem like that the kids have to solve multiple problems in one day over and over and over again, that's not mathematics. That's more computational based. And they're completely missing the whole larger vista of what mathematics is. And as soon as, and this will get, I guess, into the following questions, what can we do? Soon as you start introducing the history of mathematics into the curriculum and how mathematics was developed thematically through various cultures and civilizations, then you're going to get to those wide open spaces and time for the problems that kids need to do.

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CM: Sure. You just, just a side note, you just opened up a compartment in my brain that I think I was repressing, which was proofs in mathematics. But kind of getting into what you were just saying, which is what can we do? You've mentioned gerrymandering, you've mentioned voting, you've mentioned the lottery, gambling, play, all these things that are great uses of mathematics. They're philosophical, they're applicable, they're relevant, most especially. They're things that kids will enjoy doing. Without sounding too, without sounding like too over the top, what are things we could do?

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SS: Well, there's a lot of small, simple things that we need to do. First of all, you know, it's important to create math communities. And that's already being built. And, you know, use social media, use Twitter for that, you know, find your tribe, find your tribes. Find, even if you've never been on social media, you know, start, set up a Twitter account, follow people, get to see their, you know, it's free flowing everyday professional development. And that's the thing which I would say first and foremost is forget about trying to be a master teacher, try to be a master learner. You know, most, you know, I mentioned this book and I've said it many times quite proudly. I possess 0.00, keep throwing as many zeros as you want, 1% of the mathematical knowledge in the universe. I'm not going to live long enough to move that decimal place. You know, what gets me up in there every morning is that there's something new for me to learn. It could be a micro idea, it could be a macro idea. But I know that I could be, you know, wowed every single day, but I knew math concept. So I would tell teachers, especially new teachers, even reluctant teachers, that, you know, find time when you can. I know teaching, I was a teacher for 20 years, it's a demanding profession. But, you know, try to find, you know, little spaces to be inspired by mathematics. There's a couple places, you know, there's a website called Math for Love written by Dan, that's hosted by Dan Finkel. Who, you know, he has his TED talk, Five Extraordinary, I think, lessons for math teachers. It has close to 400,000 views. Now, I would even start there because it's really about, you know, what is mathematics and what can be done. And just start with small, just creating a community of discussions like this. Just to start discussions and to see that there's other people like you or to bounce ideas off. Because you can't do it as an individual or a solo. You have to, any change is going to come because of community. So I would definitely start there, start as a, you know, a community. The other thing which I would definitely sort of, and this is also happening now. This is great because there are things happening is that, you know, as a teacher, try to do something. There's more things called family math nights. I do them, I've done them for many years now. And to me, I've found these to be probably one of the greatest things to enact some sort of change. Because what you're getting is you're getting all the stakeholders in one place after school. You're getting usually the principal, an administrator. You're getting teacher volunteers. You're getting students, kids. You're getting parents who might think initially they're just bringing their kids out to a play date. They're going to sit against the wall with a coffee and talk to their other, you know, parent friends about something else. But these family math nights, if they're done really well, you have whole families sitting at tables doing math after hours. And they're laughing. They're smiling. And you're this intersection of all these people. So that's usually parents, they're confused too. Like, oh my God, my daughter or son learning this new math. So I feel for parents too. And so I find that hosting math nights or organizing math nights in your schools can really be this sort of like a science fair or this sort of micro exposition, poor man's museum of mathematics, just to make mathematics like really fun and exciting.

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CM: Yeah, I agree with you 100%. One thing I would add personally, I think about this, maybe it's my rebellious nature or maybe it's just maybe I'm more of a punk person. But I think back of like fighting for what you believe in. I mean, one only knows the culture of their school. Not everyone's going to be able to do this. But I feel like if you gather up a group of teachers, math teachers or not math teachers, and you present to them all this evidence of what's going on and here's all the research that supports it because there's a ton of research that supports these concepts. And you go to your administrator who hopefully you have a positive relationship with and you say, hey, here's what's going on. This is what I want to do. Can we beta test this? Can we do this one day a week? Can we throw out the math curriculum, you know, push for whatever you can? And if they say no, to me, that's a point where it almost becomes, well, why am I working here? Why are you going to limit me from doing what I think is right? If you're presented with all this information and you're that beholden to something that is very corporately minded, something that's very malicious in nature, and you aren't willing to budge one bit, even though you're presenting with research that shows what's best for students, then maybe I should go somewhere else or start looking into another outlet for me to express what I think is real math education or just education in general. I think that goes without being said. I think that people are being too mouselike. Teachers have power.

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SS: You made a really good point there. I'm not sure if you're aware of in terms of I don't know what I have shared with you in terms of any sort of bio information, but I quit teaching in 2013 for exactly the same reasons. And I think we need teachers to find their boundaries and to work at those boundaries. You know, everyone should be least working at them. You know, your comfort zone to me is your death zone. And I say death zone, maybe not for you, but it indirectly becomes a death zone for the students learning because they're not getting the best. And you should be an advocate for your kids. And you should do as much as you can for your kids. And you should find where those tipping points are. Like I said, you know, asking your administrator and things like that. And, you know, again, I come from, you know, yes, part of the kind of music I listen to is punk. And that's where it has influence in terms of my math education. And I'm completely I'm at that stage where, you know, I'm 54 years old. I mean, I've had a teaching career. I'm sort of working outside the system. And that's the difference between outside, inside. Inside, you can innovate, but disruption occurs in the outside. Disruption rarely occurs from the inside. I mean, it can occur from the inside because the pressure forces, just like how you make a diamond, is under so much pressure and duress that something really amazing can sort of emanate. But, you know, as someone who has had 20 years of teaching experiences now on the outside, I can outside looking in. I'm going to tell you right now, because just the advances and we're in second generation of social media. Everything which is really cool in mathematics is happening outside the system. And that's unfortunately doesn't have to be like, you know, you've got this video channel called Numberphile. You have Museum of Mathematics where they're talking about mathematics the exact same way that we've been talking about for the last hour. There's a lot of anachronisms in mathematics, math education, which are still the pink elephant stage. And we have to make sure that all the elephants in the room first, you know, stop becoming pink and that we can we can talk about that. And, you know, speaking and going to end this in a positive way, I definitely have seen a lot of changes in the last couple of years that we are moving in the direction. It's still somewhat incremental, but we are moving towards the, yeah, mathematics for human flourishing. Mathematics is for justice. It is for equity. It is to make sure that every student in the classroom has access to the best mathematical ideas and concepts so that they can be happy. And that we're turning education and teaching back to the human profession. We're not going to become the robots that Asimov predicted 60 years ago.

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CM: That cultural shift is, I mean, it's not only happening in an academic sense, it's literally happening in schools themselves. The number of progressive alternative schools that have opened up where you're allowed to do things a lot more against the system are almost a dime a dozen in most areas. And it's not to say that all these schools are doing the right thing, but they're at least trying to change something. And it's not that necessarily that, you know, if you go to one of those schools, you can do whatever you want or you're going to be happy or your job will even last. Honestly, I mean, a lot of those schools go under, but, you know, I feel like that risk is needed to keep that passion alive. I feel like if I were just to sit there inside a history class from the same school for 20 years and just keep trying to push for this change, I would get burned out so quickly. I'm fortunate that I found a progressive school where I can essentially do most of what I want and face a little criticism for it. I still have to be careful and I could probably push way harder, but there's that open dialogue between, you know, us and administration. We can change things and those schools exist everywhere. It doesn't matter where you are, there are schools like that. So I sometimes worry that teachers feel like they're complacent just because they have nowhere to turn to. It's one thing to try to change the system from the inside, which is great. I feel like everyone should start there, change with their current kids, change your classroom, find your tribe, do all that kind of stuff. But if push comes to shove and you're not happy and you need to expand out further, find those other schools and go there. Fight your hardest to get that job because, I mean, you're just going to be miserable if you're constantly weighed down with existential protocols that force you to do what you don't want to do, which is the case for a sizable amount of people. 

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SS: Yeah. And, you know, one of the themes which is sort of, you know, bobbed up and down, you know, in terms of just, I guess, the idea that there's a philosophy mindset to have this kind of change, which is, OK, sometimes it's veering towards something called punk. There's a photographer of my generation, Glenn Friedman, who's like one of the most amazing photographers, and he was asked many years ago his definition of punk. And he said in very simple terms, if you didn't know who he was, everyone would go, this is like an amazing quote. He says, it's an intense obligation to your most innermost feelings. And, you know, that's where it goes all back to is my accountability is first with myself. I have to check, am I being accountable to who I am as a person and what I believe in? And if I am, then I know that whatever direction I take, even if I don't make it, I can at least make sure that, yeah, I was square with myself. And I think teachers have to ask themselves, so we're going to go into mathematics. What's my goal as a math educator is to inspire other people to be inspired by mathematics. So whatever it takes to do that, yeah, I'm willing to do that.

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CM: Hope you enjoyed this podcast. We want to connect with you and hear your thoughts. Follow us on Twitter, YouTube, Medium, and other social media, and be sure to check us out on our website at humanrestorationproject.org. If you want to support us in our endeavor of starting a movement towards progressive ed through high quality resources, consider supporting us on Patreon. Thanks again!

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