Season 2, Episode 8: Sunil Singh
Chris McNutt 0:10
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 Erin Flanagan and Matt 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 Scolab 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. What was your idea behind writing the book? And what do you want readers to take away from it?
Sunil Singh 1:37
Well, I mean, it's funny, because I'm talking to you and you're part of this thing, which I want to find more about, the Human Restoration Project. 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, a human endeavor. 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, and I didn't have to. 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. We are using mathematics the same way. I mean, I love music. 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 is to share 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 intra personal. The person who really foreshadowed this was this woman named Rachel Bussmann. She's kind of the guru of a collaborative consumption economy that she predicted 10 years ago, and she said something, which really resonated with me. She said, 25 years ago, 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 falling through and I highlighted in the introduction of my book, very briefly, I think it's something very germane to the opening question that you asked. I referenced this mathematician named Francis Sue, and he believes mathematics is for human flourishing. And this Aristotlian view of learning mathematics - beauty, truth, justice, play, and love. This is accessible for everybody. And over the years, mathematics, math education is 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 the listeners and people who read the book to see mathematics as a human endeavor,
Chris McNutt 4:09
It's very interesting, because typically the way that you're describing math is almost artsy. It's very creative. A lot of times when I think of that style of vocab, I'm thinking of humanities: English and social studies, right? Separating that very much away from the rational as what I guess they would call you, the people that are logically minded, gets "this" than "this." And I don't want to make too many overarching assumptions. But any building I've ever worked at, the math teacher tends to be the one that's very robotic, the one 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 Freakonomics.
Sunil Singh 5:00
You mentioned 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 have had, and in my teaching career. 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 all those experiences. Maybe the way they've been taught, maybe they feel that mathematics is for this logistic thinking. And it is. It's a powerful tool for that. But, and I really 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 talked about math now with people, it waxes more towards the sort of the philosophical kind of bent as you'd be sitting around a campfire at 3:30 in the morning, listening to Pink Floyd saying, "we will be talking about math." In the same very way.
Chris McNutt 6:11
This might be too big of a question. But I'm curious about then why do you think that's the case? 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 an education. But even in 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?
Sunil Singh 6:39
I only have access to my history of being a teacher, and maybe 10-15 years prior to that, because the mentors I have this domain of 50 years of math education experience textbooks, 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 we've gone backwards, but mathematics have been around for 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 for mathematics, to create what it needed for education. And this becomes now a discussion for a different day. But if you look at what's happening in schools, generally in math education, there's testing, there's lots of testing. There's a curriculum, which people have to follow. Why is that? I mean, my own gut feel beliefs is that because, one, it's an economy, textbooks and all that it's a micro economy, education, you also want to create profitability. For that reason, you want to have a teacher who's teaching in Santa Fe, teaching a certain topic to be may be aligned with someone who's teaching in New York.
I mean, all my English teachers, I remember chose their books. Why can't math teachers choose the topics they want to teach? Your brain is not partitioned into all the segmented nonsense, which the K 12 curriculum does, it just wants to think. That's what it is, it wants to think. However, you can get that thinking if there's a teacher in high school who wants to specialize and just talk about geometry, go for it. If there's a teacher who wants to have a number theory, if someone wants a type of voting theory, that's great, because it's going to spark interest in other areas. If you have a teacher who's allowed to teach topics, which sort of burn their passion with the intensive 1000 suns, as opposed to having this one size fits all. And the reason why it's one size fits all is because the goals are not to inspire kids to learn mathematics, it is just a make sure that everyone is doing the same piece of mathematics.
Chris McNutt 9:03
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 critical thought, where there are multiple correct answers. And I feel like that impacts other areas as well as a history teacher, the standardization movement has made it very much about facts and dates instead of about thematic elements and patterns and analysis.
It impacts everyone, I just feel like math specifically because of how and what we look at when it comes to math. It's lent f very easy to go ABCD, 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, the questions that are being asked are ludicrous. They don't make any sense.
Sunil Singh 10:15
Yeah. That's pretty popular. It's been turned into a meme now I think, 64 watermelons. There's a host of other questions like that. As 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... my favorite chapter 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 those questions, those applications are triggered in terms of you know, flying a kite. Forget the string is moving. So you can't say that the angle is going to always be... no kid has ever wondered, what the angle of an 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. It's just create a triangle, ask a question, if that can hold its own, great, get the green checkmark out. If that question is booed, do something else. Because, that's a 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", you know, back in grade six, or grade seven.
Chris McNutt 11:52
I's very draining. Normally I co-host with Michael. Michael's an English teacher, and one of his courses that he had 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 methods 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 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.
Sunil Singh 12:37
I make sure I say this, anytime I'm sort of doing a podcast or interview, I mean, it's very short. idea, simple idea. 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 asked my daughter, who at the time was seven, what do I do next? And she's building away and doing stuff. And, there's no instructions, there's no adult supervision in Minecraft. There is wiki links and YouTube videos the 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.
And right now, kids are learning, sadly, not because of their teachers, but mostly in spite of them. I'm speaking generally. We'll talk about this towards the end, I mean, 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, is still I would say, generally speaking, we're kind of in the same place that we were a couple of decades ago.
Chris McNutt 14:12
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So with that in mind, let's do this, I want to break this up into two halves. So the first half, we're 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. So I have one more question that I really want 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, an argument. Should every single student be taking algebra one to begin with? 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. That's one in five people. That seems like barely anyone's using it. What are your thoughts on that?
Sunil Singh 15:41
Yeah, 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 the 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 a 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's in, I wouldn't take algebra one myself, unless I had to take it for a specific thing, which again, you can argue. Of course, you're going to engineering mathematics, or to science degree, then you would need that kind of thinking in mathematics required for University.
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 kid, my own students, would say, "when am I going to use this?" It's always with a groan, there's always 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 lots of times, I would say no, because most of the things that in terms of direct application, no. Does it create 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 asked, "When am I gonna use the periodic table?" No one asked, "When am I going to use learning about King Lear or Edward Albert Zoo story?" I mean, learning should be for these emboldening ideas of making your life better. Going back to Francis Sue, for human flourishing, to just add knowledge. So, because mathematics has become this sort of Clydesdale work horse, almost a whipping boy for, I hate using a violent metaphor, but yeah, "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 didn't proceed all the way through the curriculum.
Chris McNutt 18:23
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 Googleable questions. So it doesn't work very well. But it seems very rare that you walk into a mathematics class and let them use Wolfram Alpha, or something that solves the entire problem for you. Even using a calculator on a test is 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, do you really need to know how to use perfect spelling if there's a spell checker? Do you need to really know what a date is? What do we do in terms of that applicability when it comes to technology?
Sunil Singh 19:24
Well, we've boxed ourselves in because we create questions in which we have this debate whether we can use technology or that's the fault of the construction of the test to create this, "well, why don't you give questions which are open ended and yeah, they want to use a calculator, 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, and which all the numbers can be put into Wolfram Alpha for whatever, then that's a problem with the question. I mean, I still tutor kids, you have to memorize all these trig identities and all these things, why when 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? Again, it all goes back to selling. 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. They teach long division still, I'm not sure why. Because most kids don't understand long division algorithm and the teachers just use a calculator to do it. I mean, unless you're going to actually talk about what is happening here, and a step by step basis, where there is something of value to be shared with the students then go for it. But just to have long division is just like a Flintstones calculator. Just cut to the chase, plug it in. There's the answer. Move on.
Chris McNutt 21:04
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 is that it's they don't see why it matters, and just see 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 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 b.s. a lot of my answer and probably still do okay. I guess that's the reason why I was a history major, I could b.s. like crazy. That concept of designing math problems that have multiple answers is very interesting to me.
Sunil Singh 21:58
Back to the beginning, in terms of seeing mathematics and this 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. It's like with everything else, I tell my son about music, there's no such thing as new music is better old music. I wrote a piece on Medium about how my music collection influences my ideas, 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 every genre of music, it has good, bad and ugly. Like, there's no such thing as a bad genre of music. I mean, the same thing with mathematics. There are some bad math problems to give. Not everything you give in mathematics is that interesting.
Because you only have a finite time with your students in a math class, I think it's incumbent upon the teacher to find the best questions that are going to provoke the best kind of thinking. Because if your endgame is just you want them to cover the curriculum and get good marks, you're not going to think about that. You're just going to want them to do a 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 in an artistic lens just changes everything.
Chris McNutt 23:40
Then are you concerned about a 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? But do you feel like then something is being lost from that philosophical understanding of math?
Sunil Singh 24:14
You're not really fixing the problem. I mean, if I'm using a house analogy, okay, you bought some new furniture, and you painted the room, it looks nice and looks different. But really, if we're going to go to that sort of house rebuilding metaphor, do what they do in Las Vegas with hotels, they implode them, they get rid of them. Those are still structurally sound hotels, it just didn't work for the time anymore. And I'm sure there's more to this than that. The tweaking as earnest as it is, yeah, I'm not for that. And now applied mathematics, I would love to see things like, you know, voting theory. I know some teachers do it subversively. And that's odd, because mathematics has a lot of subversiveness to it. I would love to see voting theory, arrow's paradox. A man won a Memorial Prize in economics in 1972, for more or less coming to the conclusion that every form of democratic voting has some flaws and some contradictions.
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 game theory in the curriculum? Why isn't there more analysis of how skewed lotteries are in terms of your expectation of winning? Talking about finances and mortgages? To me, that seems like okay, well, most kids wouldn't even understand that. The only thing they know about mortgages is they're going to 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 beginning to getting rich, and you're gonna be paying a lot of interest.
And you know, then it leads into, schools are about equity. And guess what, not all those kids who were 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, of money, and if you survey the kids in your classroom, there's a quite a disparity of class. And so I I'm all for having applied math and things which are every day, even filling out an income tax form, those are great. But I don't want mathematics defined by that. 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.
Chris McNutt 27:01
That actually makes a lot of sense. I'm recalling back to my personal finance class in high school. And predominantly, it wasn't a math course. And it was focused on the stock market. I learned later in life, you have to have a pretty decent amount of money to be investing into a stock market. That it's not like a retirement account. I don't personally have any stock. But if I did, it was like play money. It was just a joke. I wasn't doing it to actually think that I was going to make a lot of money. Yeah, that that makes a lot of sense.
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. I think about calculating payday loans, and how that impacts low low income communities especially, which is something that we actually talked about in my class and social studies, but it obviously lends itself to math very well. Like, how do you design a building that takes people's money? It's not very deceptive, but it's true. I mean, that's the whole industry and 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.
Sunil Singh 28:06
These kind of ideas as spiraled in our in our conversation. One of the things which mathematics allows you to do, is it gives you power, and it gives you another lens to see the world. I know that education in schools, they want all these goals for math education, but really, and this is the only time I'm going to the conspiracy route, it wouldn't really benefit society for 100% of people to be mathematically literate, because now you're going to severely cut into the profits of those things like payday loans, and warranty providers insurance and all that. Because you're going to have people who are going to be able to dissect in a second anything you throw out there mathematically. They're going to go, "that's not sound. I'm going to analyze this." But in order in order to get to that level, you have to get to these high school mathematics and be introduced the right topics. 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, because they know they can keep going and doing what they're doing.
Chris McNutt 29:17
Yeah, I mean, a lot of this is very much political. I question that heavily. There's many people that say, well, you have to constantly remain neutral in everything that you do, and I actively 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 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, have a curriculum that focuses on tolerance and just fighting for advocacy.
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 and stay true to your word. I think of, for example, Howard Zinn, who was a historian who was famous, or infamous, depending on how you view him for saying teachers should preach social justice. And if mathematics moved 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.
Sunil Singh 30:35
It's funny you said that because we've talked about the first half hour in terms of some of the negative and what we have to. I mean, because right now a lot of subjects are pink elephants, nobody talks about them when they talk about them politely. We were wherever we had to go, we had to go. There's a big moving out of 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 the theme of that particular conference or whatever, these have been building, and they're now really being spoken as like mandates that we have to address the equity, race issue in mathematics before we can do anything else.
There's kids in the classroom who come from various backgrounds and various cultures who are subjective to both the conscious and subconscious bias, and then once they start to not take certain courses, math courses, then certain careers and such. I'm very happy to know that there's movements to really be make sure that mathematics is not just for... Yeah, it can help you become like a rocket scientist, and things like that. And going back to the flourishing for human life. I did mention justice is one of those five sort of markers. So yeah, mathematics and justice, are being tied much stronger now.
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.
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 a Twitter conversations and just meeting people. I use a lot of metaphors. I taught math, physics, and English. The metaphor analogy I came up with an terms of what's happening now in 2018: math education, it's like the gases which are swirling to make a new planetary system, that there's a lot of swirling gases. And now we're in this contraction phase of where things are starting to form. They're not just 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 the gases, and all the different conditions for it are definitely set up right now.
Chris McNutt 33:36
That's definitely good news. I wish education grew faster. But I'll take what we can get this point. 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?
Sunil Singh 34:02
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 the standardized testing and itself. And luckily, one of the things that I've again, 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 can be either generation or so but when you go to interview for, let's say, 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 what you've created. They don't want to see necessarily your GPA or things like that, which is this statistically invalid distillate, 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 were reported are statistically invalid. So right now, no, you can't square that circle, the philosophical things that I'm pining for? Yeah, you can talk about them here and there in the classroom. But for them to have the impact that they're going to have, 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, they're pretty binary positions.
Chris McNutt 35:43
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 in math and go on to do absolutely nothing in math - you can really have no idea what you're doing. That indicator that the SAT gives you is just a snapshot, first off - but it also doesn't matter. It's so irrelevant, and teaching someone that it does matter their entire lives, raising 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 that matter that much. They're going to respond in kind with, "no, it does matter, it's on the test." And they 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 multi specialized or didn't do well in school. A lot of math teachers that are decrying against these math practices either 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, it's going beyond standardized testing and seeping into our culture.
Sunil Singh 37:14
The ironic part of math education is it champions practicality. 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%, are perfect on their SATs... If that student walks into a convenience store and purchases two lottery tickets, not one, but two, they've just nullify 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 a leisure, a kind of amusement in terms of whatever you pay to fantasize, what you would do if there was millions, you'd buy some sort of island and take all your friends, that's cheap entertainment. And if you if you don't buy 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 draw is like one in 14 million... if you buy two tickets, now it's two and 14 million, you spent an extra $2.
And let's say you can even buy 100 tickets, right? So that's now 140,000, you've just given up a great steak dinner for two for changing the probability in the seventh decimal place. They don't teach that. So I'm not really impressed by people graduating unless they really love math. So I'm generalizing. I 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 on application, then go all in for application, like start doing some heavy duty analysis of all the things in which kids can be should be looking out for, especially from the monetary sense. Let's do some heavy duty applications.
Chris McNutt 39:18
Yeah, the lottery application makes me think a lot about in today's world - loot boxes, what you'll find in 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 "whales", the people that put thousands of dollars into a game, without actually receiving really anything in return - it doesn't even have a resale value. 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 a fun place the gamble. Trading cards are the same concept, you're buying a randomized thing, your chances of getting what you want are quite slim, but you're getting that dopamine rush, it is that dopamine rush.
Sunil Singh 40:07
I promised myself I was going to write about this, even like a year or two ago, we have this law lottery. In Ontario, it's called Lotto Max. And the last four or five weeks, the prize, the Lotto Max is $50 million. And no one's want it. That's not a big surprise to me. Because there's two things happening here with the Lotto Max. To win the actual lotto Max, I think is one in 26 million, but they're done something very ingenious and kind of nefarious is that they've made the cost of the ticket $5. So that's kind of prohibitive. So let's say, you know, if it's one in 26 million, the probability of winning it, I think, and let's say that particular week, there's 13 million tickets purchased, 13 million times five, there's $65 million for the government, but there's a 50% chance no one's going to win the big prize. That's where it gets rolled over. The analysis has been much deeper than that.
if everyone knew the that you're talking about, there's no denying that things would change in society. Also, let's move into then, 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? I guess new would be the word, a new way for mathematics, even though it's already existed.
But I mean, no one's no one's questioning things because they were never inspired to look at mathematics with that. And I forget the person who came up with this quote, but it's one of my favorite math quotes in terms of why should do math, he says, "Do more math, cause more destruction." You know, it's more from a punk point of view in terms of, I used to tell my kids, "do as much math as you can", and I use the punk angle. I had to know my audience, some of these kids who had some challenging backgrounds and stuff. So they like when I took that route. Do the math to sort of get back with the system.
Chris McNutt 42:27
Let's talk about gaming for a second because we were just talking about 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 filled with math, gaming type stuff, I think about Fortnite. During my era, I think about the beginnings of World of Warcraft and player economies. Tycoon games are my favorite, and as a kid, how much math is involved in those games? It's insane. I mean, the amount of you need to know about economics and understanding profit margins, and just math in general is pretty insane. As well as 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?
Sunil Singh 43:15
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 NCUTM national conference of teaching 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, we talked about again, the idea of mathematics for human for flourishing. And if you go back to get into our conversation, I did mention play and that next beauty, truth, justice, playing love. But when he started speaking, his first bullet point was play. Everything begins with play. There's a false demarcation in education that play is sort of Montessori esque, or it's for elementary school, maybe stops or 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. I wrote an article many months ago where I referenced Wayne Gretzky, the hockey player, who is arguably the greatest hockey player. And he lamented about the current state of the game, the NHL. The analogy was set up for me because he said, "You know, these kids are over coached." And 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, they just threw some pucks on the rink, or the frozen lake or whatever. You just played and you tried different things." How did Gretzky do that famous bank pass off the boards that is a 110 degree angle? Because he practiced that. He played with all the different angles on boards and the sticks, that's what he got. That's what we should be trying to create.
I mean, not everyone is going to be the Wayne Gretzky of hockey. But, we should be trying to create these creative thinkers like that. It all begins with play. You have to give problems where there's ample room for playing, I'll give you a perfect example of that . This will tie in the current state of math education textbooks. This is from a course that I taught in Ontario back in the early 2000s, sadly this course is no longer is available. And one of the reasons it was taken away because it proved to be really demanding and difficult. But there is this little paragraph at the back for these performance problems. And 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 that you studied throughout the course. Several problems can be solved in more than one way.", alluding to what you spoke about earlier in our interview. "Some of the problems are challenging, considerable ingenuity may be needed." Here's ingenuity and creativity. "Maybe you need to solve them, you may be unable to complete a solution in the first attempt. That's very important because mathematics is 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 their 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 space to play.
Chris McNutt 46:53
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 like be deceptive in any way. It's meant to just make you enjoy it. Let alone math education, we'll come back to that in a second, but just letting kids play games, I feel 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. 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 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 wasting of time. So it saddens me that many places, many administrations, many teachers, say "I can't spend 15 minutes, 30 minutes, an hour, playing a random game with my class or letting kids talk to each other, because they're not going to be learning", I think that's a very narrow definition of learning. I feel like kids actually learned 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 gain then you should be doing okay, that's the whole basis of experiential education. That's John Dewey's whole idea is you just reflect on what you've done, and you learn from your experiences. That's 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 stay behind, but as long as they're all enjoying it they'll take a lot of way.
Sunil Singh 48:59
You're so right. There's many reasons for play, and you already outlined on the social component, the learning, you know, that's foundational to what play is. There's a quote by Pollock I was going to read right now, he says, "mathematics is the art of explanation, if you deny students the opportunity to engage in this activity, to oppose their own problems, to make their own conjectures and discoveries to be wrong, to be creatively frustrated, to have an inspiration to cobble together long explanations improves, you deny the mathematics itself." And we cannot get our kids there if they don't have the space and time to play.
What's happening in our classrooms today, is not the thematic history, narrative and mathematics. People who explored all the mathematicians that were known or even our recreational mathematicians, throughout the ages, they spent days, weeks, months. The best mathematician has spent their entire careers on one problem, they might not even have made any sort of headway into it. That's the narrative of mathematics. It seemed like 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. They're completely missing the whole, larger vista with what mathematics is. What can we do to start introducing the history of mathematics into the curriculum? And how mathematics was developed mathematically through various cultures and civilizations, then you're going to get to those wide open spaces for the problems that kids need to do.
Chris McNutt 50:51
Sure and just as a side note, you just opened up a compartment of my brain that I think I was repressing, which was proofs in mathematics. But 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 are things that kids will enjoy doing. without sounding too over the top, what are things we could do?
Sunil Singh 51:29
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. Use social media, use Twitter for that, find your tribe. Even if you've never been on social media, set up a Twitter account, follow people, it's free flowing every day 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. I mentioned this book, and I've said it many times, quite proudly, I possess .00 keep throwing as many zeros as you want .000001% of the mathematical knowledge of the universe, I'm not gonna live long enough to move that decimal place.
What gets me up in every morning is that there's something new for me to learn. It could be a micro idea could be a macro idea. But I know that I could be wowed every single day by a new math concept. So I would tell teachers, especially new teachers, even reluctant teachers, find time when you can. I know teaching as a teacher for 20 years, it's a demanding, demanding profession, but try to find little spaces to be inspired by mathematics. There's a couple places. There's a website called math for love, that's hosted by Dan Finkel, he has his TED Talk, Five Extraordinary Lessons for Math Teachers, and it has close to 400,000 views now. I would even start there, because it's really about what is mathematics and what can be done?
Just creating a community of discussions like this, just to start discussions and to see that there's other people like you, and bounce ideas off because you can't do it. Any change is going to come because of community. So I would definitely start there. Start as a community. As a teacher try to do something, there's things called family math nights, I do them I've done them for many years now. And to me, I found these to be probably one of the greatest things to enact some sort of change, because you're getting all the stakeholders in one place after school, you're getting usually the principal or 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 play day, they're gonna sit against the wall with a coffee and talk to their other parent friends about something else. But these family math nights, 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 the central section of all these people. So that's usually parents, they're confused to like, "Oh, my God, my daughter, son is learning this new math." So I feel for parents too and so I find that hosting math nights, organizing math nights in your schools can really be this sort of like a science fair, this sort of micro exposition, poor man's museum mathematics, just to make mathematics really fun and exciting.
Chris McNutt 55:05
Yeah, I agree with you 100%. One thing I would add, personally, maybe it's my rebellious nature. And maybe I'm more of a punk person. But I think that can be 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 that, because there's a ton of research that supports this, 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 that's a point where it, it almost becomes, "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 presented 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 people are being too mouse like. Teachers have power.
Sunil Singh 56:30
You made a really good point there, I'm not sure if you're aware of, but I quit teaching in 2013 for exactly the same reasons. And I think we need teachers to find their boundaries. To work at those boundaries. You know, everyone should be least working at....your comfort zone, to me is your dead zone. And it's also it's not a dead zone, maybe not for you, because but it's it's it indirectly becomes a dead zone for the students learning because they're not getting, he best, and you should be an advocate for your kids. You should do as much as you can for your kids. And you should find where those tipping points are, like I said, asking your administrator and things like that.
I come from, the kind of music I listen to is punk. And that's where it has influenced in terms of my math education. I'm at that stage where, you know, I'm 54 years old, I mean, I've had a teaching career, sort of working outside the system. And that's a difference between outside, inside, and us. Inside, you can innovate, but disruption occurs and the outside disruption rarely occurs to me inside. I've encouraged the inside because the pressure of forces just like how you make a diamond is under so much pressure. And duress is something really amazing can sort of emanate. But, you know, as someone who's had 20 years of teaching experiences, now the outside I can look outside looking in, I need to tell you right now, because just the advances and we're in second children's sub generation, social media, everything, which is really cool in mathematics is happening outside the system.
We've got this video channel called Numberphile, Museum Mathematics, where they're talking about mathematics the exact same way they'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 stop becoming pink. We can talk about that. I'm going to end this in a positive way. I definitely have seen a lot of changes last couple of years, that we are moving in the direction, it's still somewhat incremental, but we are moving towards 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 then we're turning education and teaching back to a human profession, we're not going to become the robots that Asimov predicted 60 years ago.
Chris McNutt 59:31
That cultural shift, 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 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 the 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 a sit there inside a history class in the same school for 20 years, and just keep trying to push for this change, I would get burnout.
I'm fortunate that I found a progressive school where I can essentially do most of what I want, and face little criticism for it, I still to be careful, and I could probably push way harder. But there's that open dialogue between us and administration, we can change things. And those schools exist, everywhere, doesn't matter where you are, there are schools like that. 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 their 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 you're just gonna be miserable if you're constantly weighed down with essential protocols that that force you to do what you don't want to do. Which is the case for a sizable amount of people.
Sunil Singh 1:01:30
One of the themes, which is bobbed up and down, the idea that there's a philosophy mindset, sometimes it's veering towards something called punk. There's a photographer from my generation, Glenn Friedman, is 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, "it's an intense obligation to your most innermost feelings." And, that's where it goes all back to, 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 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 going to mathematics, what's my goal as a math educator? It's to inspire other people to be inspired by mathematics. So whatever it takes to do that, yeah, we'll do that.
Chris McNutt 1:02:42
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Transcribed by https://otter.ai