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20: Rebuilding Mathematics Education w/ Sunil Singh
21 Plays7 years ago
Sunil Singh was a high school math and physics teacher for 19 years. Before he quit teaching in the classroom in 2013, he had taught everything from basic math for junior students to IB math for honors-level students. He has worked in a socioeconomically challenging environment of an inner-city school in Toronto and at the prestigious International School of Lausanne in Switzerland. His vast experience teaching math in every setting imaginable has helped him become a leader in creative math education in North America. Since 2005, he has given over 50 workshops on kindergarten to grade 12 mathematics at various locations—math conferences, faculties of education, and even the Royal Conservatory of Music in Toronto. In addition to having been a regular contributor to the New York Times “Numberplay” section, Singh works full time as a math consultant for Scolab, a digital math resource company in Montreal, Canada. As well, he travels all over North America as a speaker and promoting Family Math Nights in local communities. He is an integral component of the Global Math Project, and his ambassador designation is helping him communicate the beauty and happiness of mathematics throughout the world. He is the author of Pi of Life: The Hidden Happiness of Mathematics, and his next book, Math Recess, a co-writing endeavor with kindred math spirit, Chris Brownell, will be out in Spring 2019.
This podcast is roughly divided into two parts - the first on current issues in mathematics, the second on what change looks like and its implementation.
Sunil and I spoke about a lot that personally resonated with me. One factor I wasn't expecting were Sunil's opinions on a shift to personal finance from Algebra I and other similar shifts in "relevant math." To me, this was a no-brainer - utilize applied math skills instead of our traditional building blocks. However, Sunil noted that not only are these concepts simple - they don't necessarily reform the issues we currently have. His analogy: instead of rearranging the room of a house, implode it. This shifted my thinking on this concept. Math is much more than I give it credit for - and a math curriculum housed (partly) around justice, love, and happiness seems otherworldly. It's hard to comprehend in a culture that's so logistically focused on math - especially in the classroom. However, I believe Sunil's argument is well-stated.
Near the end of the talk, we highlighted one of the most important notions - can real change happen? How can we make a change now? We offered starting points: "find your tribe" on social media or in your building, try new things and be open to innovation, and fight. If you know what's best practice - you know the culture of your school - and you fight for change, but nothing is done even after organizing and preaching best practice? Then perhaps you're at the wrong place. Seek out a school that embraces what's best for children - a place where your voice is heard. They're out there in increasing numbers. Change in education is more than complaining, it's about taking action.
Sunil advised that all math teachers (or educators in general) watch Dan Finkle's "Five Principles of Extraordinary Math Teaching."
Recommended
Transcript
Introduction and Gratitude
00:00:10
Speaker
Hello everyone.
00:00:11
Speaker
Welcome to Things Fall Apart.
00:00:13
Speaker
I'm Chris.
00:00:14
Speaker
I'd like to take a moment and thank our patrons that keep our show going.
00:00:19
Speaker
Two of which are Aaron Flanagan and Annette Laughlin.
00:00:23
Speaker
Thank you for your support.
00:00:25
Speaker
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.
Resources from Human Restoration Project
00:00:33
Speaker
On our website, you'll find various materials, including a ton of resources that we've released for free.
00:00:38
Speaker
Those resources range from mindfulness practice to projects for classrooms to a children's book over the history of education.
00:00:45
Speaker
Anything's on there.
00:00:47
Speaker
It's all available for free on our website at humanrestorationproject.org.
Philosophical Aspects of Mathematics
00:00:55
Speaker
Today, we're joined by Sunil Singh, who's the author of Pie 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.
00:01:12
Speaker
Thank you, Sunil, for joining us on the podcast.
00:01:15
Speaker
In Pie of Life, a major emphasis seems to be placed on the reflective and philosophical notions of math.
00:01:23
Speaker
So in your book, you talk about recognizing curiosity, gratitude, power, resilience.
00:01:27
Speaker
Most of these things, in my view, go well beyond logistic thinking, which is how we typically view traditional math.
00:01:33
Speaker
So what was your idea behind writing the book and what do you want readers to take away from it?
00:01:37
Speaker
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 is the Human Restoration Project.
00:01:46
Speaker
So
00:01:47
Speaker
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.
00:02:00
Speaker
And it's filled with human ideas.
00:02:02
Speaker
And it's filled with human questions.
00:02:04
Speaker
It's filled with human curiosities.
00:02:06
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And I'm really emphasizing the word human.
00:02:07
Speaker
I didn't have to.
00:02:09
Speaker
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.
00:02:17
Speaker
And I think that there's a new social endpoint to learning mathematics, and that is that we are using mathematics the same way.
00:02:25
Speaker
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...
00:02:36
Speaker
Really, the best part of the night is to share it with others.
00:02:39
Speaker
And mathematics is no different.
00:02:41
Speaker
And we always focus on the interpersonal aspects of learning math, which are great.
00:02:47
Speaker
But the one thing which is neglected is the intrapersonal.
00:02:51
Speaker
The person that kind of really sort of foreshadowed this was this woman named Rachel Butzman, who she's kind of the guru of the whole sort of collaborative consumption economy that she predicted 10 years ago.
00:03:04
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And she said something which I really – it sort of really resonated with me was that she said 25 years ago, you know, we met people to do new business.
00:03:15
Speaker
Now we do business to meet new people.
00:03:18
Speaker
So that same kind of lens, I think that mathematics is flowing through.
00:03:25
Speaker
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.
Math and Human Flourishing
00:03:34
Speaker
I referenced this mathematician named Francis Hsu, and he believes mathematics is for human flourishing.
00:03:41
Speaker
And sort of this Aristotelian view of learning mathematics, beauty, truth, justice, play, and love, that this is accessible for everybody.
00:03:51
Speaker
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.
00:03:59
Speaker
So really at the end, if I said a couple of words for the listeners and people who read the book to see mathematics as a human endeavor.
00:04:09
Speaker
It's very interesting because the way that you're describing math is almost artsy.
00:04:15
Speaker
It's very creative.
00:04:15
Speaker
A lot of times when I think of that style of
00:04:20
Speaker
I'm thinking of humanities.
00:04:21
Speaker
I'm not really talking in humanities, English and social studies, right?
00:04:25
Speaker
Separating that very much away from the rationals is what you, I guess they would call you the people that are, you know, like logically minded gets this, then this, then this.
00:04:34
Speaker
And I don't want to make too many overarching assumptions, but in any building I've ever worked at,
00:04:39
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The math teacher tends to be the one that's very, not robotic, but the one that's very much just like this happens and this happens and this happens.
00:04:46
Speaker
I don't typically hear about math spoken about in this philosophic, grandiose way unless I'm reading about something like behavioral economics.
Math Education: Creativity vs. Standardization
00:04:55
Speaker
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.
00:05:01
Speaker
you know, you mentioned that sort of the kind of people that we meet when we associate mathematics.
00:05:06
Speaker
And again, it's based on whatever experiences one has is how one views it.
00:05:13
Speaker
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.
00:05:22
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I mean, it's a summation of all those things.
00:05:24
Speaker
So if people who are
00:05:26
Speaker
Even in the math field don't feel that way.
00:05:29
Speaker
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 logistic thinking.
00:05:44
Speaker
And it is.
00:05:45
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It's a powerful tool for that.
00:05:46
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And it's – but – and I really say but, capital B, is that it's a little bit more than that.
00:05:55
Speaker
And I know the way I reflect about math and the way that I talk 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 at three-third in the morning listening to Pink Floyd, same way we'd be talking about math in the same very way.
00:06:11
Speaker
This might be too big of a question, but I'm curious about then, why do you think that's the case?
00:06:17
Speaker
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 the world.
00:06:30
Speaker
You have people that say, I'm not a math person, or I'm more of an English person.
00:06:35
Speaker
Why do you think that mathematics has moved so far away from that philosophical sense?
00:06:39
Speaker
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.
00:06:49
Speaker
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.
00:06:59
Speaker
And, you know, I'm going to share with you a foreword from a textbook book.
00:07:03
Speaker
from 50 years ago and you'll see how it kind of gone backwards.
00:07:06
Speaker
But, you know, mathematics has been around for thousands and thousands of years.
00:07:09
Speaker
Math education hasn't been around for probably less than a century.
00:07:13
Speaker
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.
00:07:25
Speaker
And, you know, that's this becomes now a discussion for a different day.
00:07:29
Speaker
But, you know, if you look at what's happening in schools, generally in math education, there's testing.
00:07:36
Speaker
There's I mean, there's lots of testing.
00:07:37
Speaker
There's a curriculum which people have to follow.
00:07:40
Speaker
You know, why is that?
00:07:41
Speaker
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.
00:07:51
Speaker
It's a micro economy education.
00:07:53
Speaker
You also want to create portability for that reason.
00:07:56
Speaker
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.
00:08:04
Speaker
And, you know, I find that...
00:08:07
Speaker
You know, I mean, all my English teachers, I remember, chose their books.
00:08:10
Speaker
You know, why can't math teachers choose the topics they want to teach?
00:08:14
Speaker
Your brain is not partitioned into all the segmented nonsense, which, you know, the K-12 curriculum does.
00:08:21
Speaker
It just wants to think.
00:08:23
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That's what it is.
00:08:24
Speaker
It wants to think.
00:08:24
Speaker
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.
00:08:32
Speaker
If there's a teacher who wants to talk about number theory, if someone wants to talk about voting theory,
00:08:36
Speaker
And 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.
00:08:52
Speaker
And the reason why it's one size fits all is because, you know, the goals are not to inspire kids to learn mathematics.
00:08:59
Speaker
It's just to make sure that everyone is doing the same piece of mathematics.
00:09:03
Speaker
Sure.
00:09:03
Speaker
I mean, that makes a ton of sense to me.
00:09:05
Speaker
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.
00:09:21
Speaker
If I give you a very basic math problem, there is one right answer.
00:09:25
Speaker
However, what you're talking about is way more complicated than that.
00:09:28
Speaker
It requires critical thought.
00:09:30
Speaker
where there are multiple correct answers.
00:09:32
Speaker
And I feel like that impacts other areas as well.
00:09:34
Speaker
As a history teacher, the standardization of movement has made it very much about facts and dates instead of about thematic elements and patterns and analysis.
00:09:42
Speaker
It impacts everyone.
00:09:43
Speaker
I just feel like math specifically, just because of how
00:09:47
Speaker
And what we look at when it comes to math, it's lent itself very easy to go A, B, C, D, choose one.
00:09:53
Speaker
Okay, that's right.
00:09:54
Speaker
Move on to the next segment and portion, the next topic, the next end of book questions, which is very sad.
00:10:01
Speaker
I like this quote from your book.
00:10:03
Speaker
You said mathematics is the only place where you can buy 64 watermelons and no one wonders why.
00:10:09
Speaker
It's very true.
00:10:10
Speaker
Just looking at any standardized test, just the questions that are being asked are ludicrous.
00:10:14
Speaker
They don't make any sense.
00:10:15
Speaker
Yeah.
00:10:16
Speaker
And that's part of it, too, is that once you soon as you offer up a question and that's a pretty popular question being turned into a meme now, I think 64 watermelons and there's a host of other questions like that.
00:10:28
Speaker
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 this credibility, which you don't even realize you're losing.
00:10:41
Speaker
And by the time you get to high school and those – my favorite chapter to write in the book was chapter nine, which is about laughter, because I really –
00:10:50
Speaker
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.
00:11:00
Speaker
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.
00:11:13
Speaker
And then to find such distances like the height, hypotenuse, or an angle,
00:11:19
Speaker
OK, 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.
00:11:25
Speaker
Like it's just create a triangle, ask a question.
00:11:28
Speaker
If that can hold its own.
00:11:30
Speaker
Great.
00:11:31
Speaker
Get the green checkmark out.
00:11:32
Speaker
If that question is booed, then do something else, because, you know, that's the problem I find, especially when you get to high school level is that.
00:11:39
Speaker
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.
00:11:52
Speaker
It's very draining.
00:11:53
Speaker
I wish Michael – normally I co-host this with Michael.
00:11:56
Speaker
Michael's an English teacher.
00:11:57
Speaker
And one of his –
00:11:59
Speaker
courses that he actually taught with a math teacher with mathematics appreciation.
00:12:04
Speaker
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?
00:12:13
Speaker
Why is it that there are math people?
00:12:16
Speaker
And almost deprogramming kids into thinking that math is something that it isn't.
Engagement in Math vs. Video Games
00:12:22
Speaker
I feel like it kind of sets you up for failure.
00:12:24
Speaker
If you think that math is this and you don't like it, you're not going to want to explore
00:12:29
Speaker
these philosophical concepts, at least until well until adulthood, because you're drained by it.
00:12:35
Speaker
It sucks, to put it frankly.
00:12:38
Speaker
I make sure I say this anytime I'm sort of doing a podcast or interview.
00:12:44
Speaker
I mean, it's a very short idea, a simple idea, but kids don't hate math because it's hard.
00:12:53
Speaker
Kids hate math because it's boring.
00:12:56
Speaker
Kids are playing, you know, played challenging video games.
00:13:01
Speaker
The learning curve is high.
00:13:04
Speaker
I played Minecraft with my kids a year or so back, and I didn't know how to play.
00:13:10
Speaker
I'm asking my daughter, who at the time was seven, like, what do I do next?
00:13:13
Speaker
And she's, you know, building away and doing stuff.
00:13:16
Speaker
And, you know, there's no instructions.
00:13:18
Speaker
There's no adult supervision in Minecraft.
00:13:20
Speaker
There's these, you know, Wiki links and YouTube videos that kids watch.
00:13:23
Speaker
You know, kids are learning, you know,
00:13:25
Speaker
uh, far differently than when I went to school.
00:13:27
Speaker
And if someone can ever create a math curriculum, uh, which sort of, you know, uh, maps on the way that kids explore Minecraft or things like that, then that's going to be the golden ticket.
00:13:37
Speaker
And right now, you know, kids are, kids are learning, uh, sadly, not because of their teachers, but mostly in spite of them.
00:13:44
Speaker
And that's just, I mean, I'm speaking generally and I, I mean, I have, uh, and we'll talk about this towards the end.
00:13:50
Speaker
I mean, there's still, there's a lot of positive work happening.
00:13:52
Speaker
There's a lot of
00:13:54
Speaker
really amazing math minds and teachers and communities being built.
00:14:00
Speaker
But for the most part, still, I would say, generally speaking, we're kind of in the same place that we were, you know, a couple of decades ago.
00:14:12
Speaker
Thanks in advance.
00:14:38
Speaker
So with that in mind, let's do this.
00:14:39
Speaker
I kind of want to break this up into two halves.
00:14:41
Speaker
So the first half, we're kind of talking about the state of mathematics and the problems that exist.
00:14:48
Speaker
But I don't want to keep the entire thing negative.
00:14:50
Speaker
So after the next question, I want to move into creative applications.
00:14:55
Speaker
What can you do?
00:14:56
Speaker
And that kind of stuff as well.
00:14:57
Speaker
So I have one more question that I really wanted to ask you about.
00:15:01
Speaker
just the state of math.
00:15:02
Speaker
And this goes beyond what most teachers can do, but it's just a logistics question because I've always been fascinated by this.
00:15:08
Speaker
There seems to be a divide, like an argument.
00:15:11
Speaker
Should every single student be taking, first off, should they even be taking Algebra 1 to begin with?
00:15:17
Speaker
So like starting right there, should they even get to that level?
00:15:20
Speaker
Because there's a survey that's been done
00:15:24
Speaker
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 1, which seems like that's one in five people.
00:15:38
Speaker
That seems like barely anyone's using it.
00:15:40
Speaker
What are your thoughts on that?
00:15:41
Speaker
Yeah, I have quite a bit on that.
00:15:44
Speaker
I'm just going to go to, because we don't have Algebra 1 up here in Canada.
00:15:50
Speaker
And I've had this conversation with U.S. teachers.
00:15:54
Speaker
The fact that there's even a course called Algebra 1 to me really makes no sense.
00:15:59
Speaker
Because...
00:16:00
Speaker
Algebra is not an appendage of mathematics.
00:16:02
Speaker
It's its circulatory system.
00:16:05
Speaker
And the algebraic thinking is something which can be installed as even as early as grade one.
00:16:09
Speaker
And to have this sort of formal thing waiting for you in high school called Algebra 1 –
00:16:16
Speaker
really does a disservice to mathematics and to the kids learning algebra.
00:16:20
Speaker
So yes to your question, should everyone take algebra one?
00:16:24
Speaker
I would say, heck no.
00:16:25
Speaker
In the current state it is, I wouldn't take algebra one myself unless I had to take it for a specific thing, which, you know, again, you can argue.
00:16:33
Speaker
I mean, if of course you're going to engineering, mathematics or, you know, pure science degree, then you would need that kind of thinking and mathematics require university.
00:16:43
Speaker
But, you know, you brought up something very subtle, which comes up quite a bit in terms of the usefulness of mathematics.
00:16:50
Speaker
And, you know, I remember as a high school teacher, my own students would, you know,
00:16:56
Speaker
When am I going to use this?
00:16:57
Speaker
It's always with a groan.
00:16:58
Speaker
There's always like a deflating body language.
00:17:00
Speaker
And I'd be very honest with him.
00:17:03
Speaker
I'd say whether you would use it or you would not, I'd say no.
00:17:06
Speaker
And most of the times I would say no because most of the things that in terms of direct application, no.
00:17:11
Speaker
Does it create sort of better problem-solving thinking?
00:17:15
Speaker
Absolutely.
00:17:16
Speaker
But
00:17:17
Speaker
There's much better things to induce problem-solving thinking capabilities with far more rigor and depth than Algebra 1.
00:17:26
Speaker
And so at this point, back to your question, would I say everyone has to take Algebra 1?
00:17:31
Speaker
Absolutely not.
00:17:33
Speaker
You know, no other subject gets asked for its usefulness.
00:17:35
Speaker
No one asks, when am I going to use the periodic table?
00:17:37
Speaker
No one asks, when am I going to use, you know, learning about, you know, King Lear or, you know, Edward Albee's zoo story?
00:17:45
Speaker
You know, when am I going to use this?
00:17:46
Speaker
I mean, learning should be for, you know, these emboldening ideas of, you know, making your life better, going back to Francis Zoo, you know, for human flourishing to just add knowledge.
00:17:57
Speaker
So, you
00:17:58
Speaker
Because mathematics has become this sort of Clyde Dill workhorse, almost a whipping boy for, you know, so I hate using that violent metaphor, but to, yeah, when are you going to help me out?
00:18:12
Speaker
When can I use you?
00:18:13
Speaker
And if we don't answer or can answer that question correctly, kids get snarky and rightfully so because that's the way mathematics has been perceived all the way through the curriculum.
00:18:22
Speaker
Sure.
00:18:22
Speaker
So kind of with that being said, with technological advancement,
00:18:27
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I feel like mathematics in particular also has been disparaged against because, again, it's not that philosophical notion.
Technology and Testing in Math Education
00:18:36
Speaker
So, for example, in history class, we let kids now look up answers on Google.
00:18:41
Speaker
They're intentionally not Google-able questions, so it doesn't work very well.
00:18:45
Speaker
But –
00:18:47
Speaker
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.
00:18:55
Speaker
Even using a calculator on a test is still kind of not always the case, which I think is kind of odd.
00:19:02
Speaker
And this is coming from someone who's not mathematically oriented.
00:19:05
Speaker
But if I have a tool that does all this work for me, I understand that there's a step-by-step process.
00:19:10
Speaker
But do you actually need to know it?
00:19:11
Speaker
I mean, the argument could also be like, do you really need to know how to use perfect spelling skills?
00:19:17
Speaker
If there's a spell check or do you need to really know what a date is?
00:19:21
Speaker
What do we do in terms of that applicability when it comes to technology?
00:19:24
Speaker
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,
00:19:33
Speaker
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 open-ended and that, yeah, if they want to use a calculator, go for it.
00:19:48
Speaker
It's not going to help you here, but if you want it as a tool, use it the way you want.
00:19:52
Speaker
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,
00:20:02
Speaker
That's a problem with the question itself.
00:20:03
Speaker
And yeah, I mean, why are you making students?
00:20:05
Speaker
I mean, I still tutor kids who have to memorize, you know, all these trigger identities and all these things.
00:20:11
Speaker
Why?
00:20:11
Speaker
You can look it up.
00:20:12
Speaker
When did anyone have to ever memorize a formula or something?
00:20:17
Speaker
especially in this day and age where you can look it up.
00:20:20
Speaker
And if you, again, it's all goes back to selling.
00:20:22
Speaker
I mean, when you ask kids to do things, guess what?
00:20:25
Speaker
You got one or two customers short who are not going to be appreciating mathematics because of things like this.
00:20:30
Speaker
So it's, if you, if something can be used as like, you know, they teach long division still.
00:20:36
Speaker
I'm not sure why, because most kids don't understand long division algorithm and neither the teachers just use a calculator to do it.
00:20:44
Speaker
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.
00:20:55
Speaker
But just to have long division is like a Flintstones calculator.
00:21:00
Speaker
It's like, just cut to the chase, plug it in, there's the answer, move on.
00:21:04
Speaker
Yeah, something that you keep bringing up that I think a lot about when it comes to math is that
00:21:08
Speaker
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
00:21:36
Speaker
is not going to be the correct answer.
00:21:37
Speaker
And it doesn't feel good to get something wrong.
00:21:40
Speaker
Whereas in English or social studies or even science, I can BS a lot of my answer and probably still do okay.
00:21:46
Speaker
And I guess the reason why I was a history major, I could BS like crazy.
00:21:49
Speaker
That concept of designing math problems that have multiple answers is very interesting to me.
00:21:56
Speaker
And if you go to, if you, you know, take the breadcrumbs back of this conversation back to the beginning in terms of, you know, seeing mathematics and that sort of philosophical, artistic, creative lens, then naturally, you know, it's going to go to what kind of questions do you ask your kids?
00:22:13
Speaker
It all stems from the kind of math questions that
00:22:16
Speaker
that you ask, it creates the culture, the environment of learning.
00:22:22
Speaker
It's like with everything else, I tell my son about music, I go, there's no such thing as like, new music is better, old music.
00:22:34
Speaker
I wrote a piece in Medium about how my music collection influences my ideas of math education.
00:22:39
Speaker
I have over 50 genres of music in my iPod.
00:22:43
Speaker
There's every genre of music I will be open to and listen to, but every genre of music also has its good, bad, and ugly.
00:22:50
Speaker
There's no such thing as a bad genre of music.
00:22:53
Speaker
And the same thing with mathematics.
00:22:56
Speaker
There are some bad math problems to give.
00:22:58
Speaker
Not everything that you give in mathematics is that interesting.
00:23:02
Speaker
And because you only have a finite time...
00:23:05
Speaker
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.
00:23:15
Speaker
And because if your end game is just to see what kind of, you want them to cover the curriculum, get good marks,
00:23:21
Speaker
You're not going to think about that.
00:23:22
Speaker
You're just going to want them to ape procedures they've done many, many times, and hopefully, fingers crossed, everything lined up on that Tuesday afternoon, and they got it right.
00:23:30
Speaker
So it depends.
00:23:32
Speaker
It all goes back to what are the goals of math education, but I think going and seeing mathematics through an artistic lens just changes everything.
00:23:40
Speaker
Then are you concerned about...
00:23:43
Speaker
of movement towards particularly applied mathematics.
00:23:47
Speaker
So you're talking a lot about this philosophic artistic approach.
00:23:52
Speaker
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
00:24:04
Speaker
I would argue most kids need those things, but do you feel like then something is being lost from that philosophical understanding of math?
00:24:11
Speaker
Yeah, it's almost like you're not really fixing the problem.
00:24:16
Speaker
I mean, it's like you're maybe, if I'm using a house analogy, okay, you bought some new furniture and you painted the room and it looks nice and looks different, but
00:24:28
Speaker
And really, if we're going to go to that sort of house or building metaphor, do what they do in Las Vegas with hotels.
00:24:37
Speaker
They implode them.
00:24:37
Speaker
They get rid of them.
00:24:39
Speaker
I mean, those are still structurally sound hotels.
00:24:43
Speaker
It's just they don't work for the time anymore.
00:24:45
Speaker
And I'm sure there's more to this than that sort of simple metaphor I'm trying to go to, which I just kind of made up on the spot.
00:24:51
Speaker
But, you know, I've the tweaking as earnest as it is and all that.
00:25:00
Speaker
Yeah, I'm not for that.
00:25:02
Speaker
And now I'd be applied mathematics.
00:25:04
Speaker
I would love to see things like.
00:25:06
Speaker
You know, voting theory, you know, I know some teachers do it kind of, you know, subversively, and that's odd because mathematics is a subversive, you know, has a lot of subversiveness to it.
00:25:17
Speaker
I would love to see voting theory, Eros paradox, you know, I mean, you know, the man won a, I think, Nobel Prize, Memorial Prize in economics in 1972 for more or less coming to the conclusion that every form of voting, democratic voting,
00:25:34
Speaker
has some flaws and some contradictions.
00:25:37
Speaker
And, you know, this would be very interesting because we always talk about voting, gerrymandering, all these things.
00:25:44
Speaker
Why isn't that in the curriculum?
00:25:45
Speaker
Why isn't, you know, game theory in the curriculum?
00:25:48
Speaker
Why isn't there a more analysis of
00:25:51
Speaker
how skewed lotteries are in terms of your expectation of winning.
00:25:57
Speaker
We're talking about finances and mortgages.
00:25:59
Speaker
To me, that seems like, okay, well, most kids wouldn't even understand.
00:26:03
Speaker
The only thing you need to know about mortgages is that you're going to be paying a lot of interest.
Relevance of Finance in Math Curriculum
00:26:08
Speaker
Really, that's all you need to know.
00:26:09
Speaker
I don't think you need to know the complicated formula because that's not going to really help you.
00:26:12
Speaker
You just have to know that the banks are going to be getting rich and you're going to be paying a lot of interest.
00:26:17
Speaker
And, you know, then it leads into, okay, for me, I mean, school is about equity.
00:26:22
Speaker
And guess what?
00:26:22
Speaker
Not all those kids who are in finance courses are probably going to see a house in their lifetime.
00:26:26
Speaker
So be very careful, you know, where you tread here because as soon as you talk about finance, how it's money, and if you survey the kids in your classroom, there's quite a disparity of class
00:26:38
Speaker
And so I'm all for having applied math and things which are every day because those are very – even filling out an income tax form, those are great.
00:26:50
Speaker
But I don't want mathematics defined by that.
00:26:53
Speaker
I mean it's just one thing in the whole buffet of mathematics.
00:26:57
Speaker
So yeah, I'd rather just scrap the whole thing and start from scratch.
00:27:01
Speaker
That actually makes a lot of sense.
00:27:03
Speaker
I'm recalling back to my personal finance class in high school.
00:27:07
Speaker
And predominantly, it was a math course, and it was focused on the stock market.
00:27:12
Speaker
And I learned later in life, you have to have a pretty decent amount of money to be investing into a stock market.
00:27:18
Speaker
That's not like a retirement account.
00:27:19
Speaker
I mean, I don't personally have any stocks.
00:27:22
Speaker
And if I did, it was like play money.
00:27:23
Speaker
It was just like a joke.
00:27:25
Speaker
I wasn't doing it to actually think that I was going to make a lot of money.
00:27:28
Speaker
Yeah, that makes a lot of sense to me.
00:27:31
Speaker
I think a lot of what
00:27:32
Speaker
you're advocating for with gerrymandering and things of that nature almost gets to be in the realm of social justice.
00:27:39
Speaker
So like I think about calculating payday loans and how that impacts low income communities, especially, which is something that we actually talk about in my class in social studies, but
00:27:50
Speaker
It obviously lends itself to math very well.
00:27:52
Speaker
Like, how do you design a building that takes people's money?
00:27:55
Speaker
That sounds very deceptive, but it's true.
00:27:57
Speaker
I mean, that's the whole industry.
00:27:59
Speaker
It's banned in many states.
00:28:01
Speaker
And I'm not sure what it's like in Canada, but there's a lot of these major mathematical problems.
00:28:06
Speaker
Well, and this is, I mean, this kind of idea has spiraled in our conversation.
00:28:12
Speaker
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.
00:28:22
Speaker
And, you know, I know that education and schools, they want, you know, all these goals for math education.
00:28:31
Speaker
But really, and this is the only time I'm going to do the conspiracy route, but
00:28:36
Speaker
It wouldn't really benefit society for it to have 100% of the 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 things.
00:28:56
Speaker
You know, anything you throw at them mathematically, they're going to go, that's not sound.
00:29:00
Speaker
I'm going to analyze this.
00:29:01
Speaker
But in order to get to that level, you have to get to at least high school mathematics and be introduced to the right topic.
00:29:08
Speaker
So when kids are turning off of math and all that, 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.
00:29:17
Speaker
Yeah, I mean, a lot of this is very much political.
00:29:20
Speaker
I question that.
00:29:21
Speaker
heavily.
00:29:23
Speaker
There's many people that say, well, you have to constantly remain neutral in everything that you do.
00:29:27
Speaker
And I actually disagree with that.
00:29:28
Speaker
If there are things that are going wrong in society, it should be your job as a teacher to try to correct those
Addressing Societal Issues in Education
00:29:34
Speaker
problems.
00:29:34
Speaker
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.
00:29:44
Speaker
The case in point example to me is racism.
00:29:46
Speaker
There is nothing currently defined in standards that say that you should adamantly
00:29:51
Speaker
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.
00:30:02
Speaker
And it's very odd that.
00:30:04
Speaker
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.
00:30:13
Speaker
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.
00:30:24
Speaker
And I feel like if mathematics move towards the style that you're talking about, it would get into that category.
00:30:31
Speaker
You're fighting for people using math or fighting for your own rights using math.
00:30:34
Speaker
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.
00:30:44
Speaker
You know what?
00:30:45
Speaker
We have to.
00:30:45
Speaker
I mean, because right now a lot of those subjects are pink elephants.
00:30:48
Speaker
Nobody talks about them or they talk about them politely.
00:30:50
Speaker
So, you know, wherever we had to go, we had to go.
00:30:54
Speaker
But ironically, well, maybe not so much, but there's a big movement now in mathematics to move towards some of the things I was talking about, especially in terms of
00:31:06
Speaker
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
00:31:34
Speaker
You know, there's kids in the classroom who come from, you know, various backgrounds and various cultures who are subjective to both conscious and subconscious bias.
00:31:45
Speaker
And then, you know, once they start to not take certain courses, math courses, then, you know, careers and such.
00:31:53
Speaker
So, you know, I'm very happy to know that, you know, there's
00:31:58
Speaker
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.
00:32:14
Speaker
So yeah, mathematics and justice are being tied much strongly now.
00:32:20
Speaker
That is very reassuring.
00:32:22
Speaker
I'm glad that there are people thinking about this.
00:32:24
Speaker
Sometimes,
00:32:26
Speaker
especially when you're isolated in the teaching world, it can become very scary to feel like it's just you versus the world.
00:32:32
Speaker
Oh, yeah, I know.
00:32:33
Speaker
And maybe 10 years ago, I would have probably said, yeah, it feels like that as well.
00:32:37
Speaker
But having been to numerous math conferences and having Twitter conversations and just meeting people,
00:32:46
Speaker
There's the way that I use, I use a lot of metaphors.
00:32:52
Speaker
I mean, I taught English, I mean, I taught math, physics and English.
00:32:55
Speaker
I taught English for two years.
00:32:56
Speaker
But the sort of the metaphor analogy I came up with in terms of what's happening now in 2018 in math education is,
00:33:03
Speaker
is like, it's like the gases which are swirling to make a new sort of, you know, planetary system, that there's a lot of swirling gases.
00:33:11
Speaker
And now we're in this sort of, you know, contraction phase of where things are starting to form.
Reforms and Philosophical Teaching in Math
00:33:19
Speaker
They're not just sort of these ideas in the ether, they're coming to form solid ideas.
00:33:24
Speaker
And we're still a couple of years away from this sort of new solar system of mathematics.
00:33:30
Speaker
But it's,
00:33:31
Speaker
The gases and all the different conditions for it are definitely set up right now.
00:33:36
Speaker
That's definitely good news.
00:33:38
Speaker
I wish education moved faster, but I'll take what we can get at this point.
00:33:42
Speaker
Exactly.
00:33:43
Speaker
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?
00:34:02
Speaker
My gut answer is no.
00:34:05
Speaker
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 that the standardized testing in 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.
00:34:29
Speaker
And
00:34:30
Speaker
That doesn't mean that it's imminent, the death of grades and assessment and numbers and things.
00:34:36
Speaker
It could be another generation or so.
00:34:37
Speaker
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.
00:34:48
Speaker
They want to see what you've done.
00:34:49
Speaker
They want to see, you know, what you've created.
00:34:53
Speaker
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.
00:35:01
Speaker
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.
00:35:10
Speaker
So right now, no, you can't square that circle.
00:35:13
Speaker
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.
00:35:22
Speaker
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.
00:35:29
Speaker
So I'm not going to say yes, because if you can, that's wonderful.
00:35:35
Speaker
Then you're a bigger man than I am, Charlie Brown.
00:35:37
Speaker
But right now, I would say no.
00:35:40
Speaker
They're pretty binary positions.
00:35:43
Speaker
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.
Critique of Standardized Testing
00:35:53
Speaker
It's a false positive.
00:35:54
Speaker
You can do amazing at the SAT in math and go on to do absolutely nothing in math.
00:35:59
Speaker
I really have no idea what you're doing.
00:36:01
Speaker
That indicator that the SAT gives you is just a snapshot first off, but it's also not even
00:36:07
Speaker
It doesn't matter.
00:36:09
Speaker
It's so irrelevant.
00:36:10
Speaker
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.
00:36:25
Speaker
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.
00:36:33
Speaker
It's on the test.
00:36:35
Speaker
And it just kind of stops there.
00:36:37
Speaker
And I worry sometimes that we're raising a generation of non-critical thinkers.
00:36:42
Speaker
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.
00:36:50
Speaker
A lot of math teachers that are decrying against these math practices are like you.
00:36:55
Speaker
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.
00:37:03
Speaker
in order to see the bigger picture.
00:37:04
Speaker
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.
00:37:14
Speaker
And the, you know, the ironic part of is math education.
00:37:18
Speaker
It's sort of, you know, champions this practicality, which is kind of, it's here or there or miss.
00:37:25
Speaker
It's not
00:37:26
Speaker
I mean, you know, you could create a much better curriculum for application, as we spoke earlier.
00:37:31
Speaker
But I mean, what's ironic is that they do champion this application part.
00:37:36
Speaker
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
00:37:44
Speaker
Two lottery tickets, not one, but two.
00:37:47
Speaker
They've just nullified their entire mathematical thinking because the lottery is a negative expectation.
00:37:54
Speaker
I always tell students buying one ticket is great because it's a cheap kind of –
00:38:00
Speaker
leisure kind of amusement in terms of whatever you pay to fantasize what you would do.
00:38:05
Speaker
There was millions.
00:38:05
Speaker
You'd buy some sort of island or take all your friends.
00:38:08
Speaker
That's cheap entertainment.
00:38:09
Speaker
And if you don't buy any tickets, you can't dream that.
00:38:12
Speaker
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 –
00:38:23
Speaker
If you buy two tickets, now it's two and 14 million.
00:38:26
Speaker
You've spent an extra $2.
00:38:27
Speaker
And let's say if you buy 100 tickets, right?
00:38:33
Speaker
So that's now one in 140,000.
00:38:35
Speaker
You've just given up a great steak dinner for two for changing the probability in the seventh decimal place.
00:38:44
Speaker
They don't teach that.
00:38:45
Speaker
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.
00:38:55
Speaker
So I'm generalizing here.
00:38:56
Speaker
I've got to be very careful.
00:38:56
Speaker
But again, in the whole sort of general scheme of things, if you're going to.
00:39:01
Speaker
uh go all raw about application then go in all in for application like start doing some heavy-duty analysis of all the things in which kids uh you know can be should be looking out for especially from the monetary sense let's do some heavy-duty applications 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
00:39:28
Speaker
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.
00:39:40
Speaker
It doesn't even have resale value.
00:39:43
Speaker
So it's really bizarre to me.
00:39:45
Speaker
especially young children, 10, maybe even younger now, playing games like Fortnite that offer those services.
00:39:53
Speaker
And really, they're just fun ways to gamble in the same exact way that I think of trading cards or the same exact concept.
00:40:01
Speaker
You're buying a randomized thing.
00:40:03
Speaker
Your chances of getting what you want are quite slim, but you're getting that dopamine rush.
00:40:06
Speaker
It is.
00:40:06
Speaker
It's a dopamine rush.
00:40:08
Speaker
And, you know, I mean, we just have I mean, I promised myself I was going to write about this even like a year or two ago.
00:40:16
Speaker
We have this lottery in Ontario.
00:40:18
Speaker
It's called Lotto Max.
00:40:20
Speaker
And the last four or five weeks, the prize, the Lotto Max prize, $50 million, no one's won it.
00:40:28
Speaker
That's not a big surprise to me because there's two things happening here with Lotto Max.
00:40:32
Speaker
I mean, to win the actual Lotto Max, I think the probability is one in 26 million.
00:40:38
Speaker
But they've done something very ingenious and kind of nefarious is that they've made the cost of the ticket $5.00.
00:40:45
Speaker
So that's kind of prohibitive.
00:40:46
Speaker
So let's say, you know, you know, if it's one in 26 million, the probability of winning it, I think.
00:40:52
Speaker
And let's say that particular week, you know, there's 13 million tickets purchased, you know, 13 million times five.
00:41:00
Speaker
There's just still scooped $65 million, the government.
00:41:04
Speaker
But there's still a 50 percent chance no one's going to win the big prize.
00:41:06
Speaker
That's why it gets rolled over.
00:41:09
Speaker
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.
00:41:16
Speaker
Like, I mean, they, they, they just, because they were never kind of inspired to, to look at mathematics with that eye.
00:41:23
Speaker
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
Play and Creativity in Math Education
00:41:30
Speaker
should do math.
00:41:30
Speaker
He says, do more math, cause more destruction.
00:41:34
Speaker
You know, it's, it's, it's more from a punk point of view in terms of,
00:41:38
Speaker
I used to tell my kids, you know what, do as much math as you can.
00:41:42
Speaker
And I use the punk angle.
00:41:43
Speaker
I mean, I had to kind of know my audience, some of these kids who are, you know, they had some challenging backgrounds and stuff.
00:41:49
Speaker
So they liked when I sort of took that route.
00:41:50
Speaker
I said, you know what?
00:41:51
Speaker
do the math to sort of, you know, get back to the system.
00:41:54
Speaker
If everyone knew the math, that what you're talking about, there's no denying that things would change in society.
00:42:00
Speaker
Hopefully, hopefully.
00:42:04
Speaker
So let's, let's move into then, because we're already kind of talking about it.
00:42:09
Speaker
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?
00:42:19
Speaker
So like actual math practice with this, I guess new would be the word of saying it, new form of mathematics, even though it's already existed.
00:42:27
Speaker
Let's talk about gaming for a second, because we were just talking about like Fortnite and the lottery is technically a game.
00:42:34
Speaker
You talk a lot about play as an important theme in math.
00:42:37
Speaker
Specifically, you talk a lot about Sudoku.
00:42:39
Speaker
I know your Twitter is kind of filled with math gaming type stuff.
00:42:42
Speaker
I think about Fortnite and
00:42:44
Speaker
During my era, I think about the beginnings of World of Warcraft and player economies.
00:42:48
Speaker
I think of tycoon games, which were my favorite when I was a kid.
00:42:51
Speaker
And how much math is involved in those games.
00:42:53
Speaker
It's insane.
00:42:54
Speaker
I mean, the amount of what you have to know about economics...
00:42:57
Speaker
And understanding profit margins and just math in general is pretty insane.
00:43:01
Speaker
As well as sports.
00:43:03
Speaker
Sports, obviously, there's a lot of math.
00:43:04
Speaker
There's careers built on sports analytics and gambling as well.
00:43:09
Speaker
That's fun.
00:43:09
Speaker
That's math.
00:43:11
Speaker
Where is that place for play in math?
00:43:15
Speaker
Well, where is the place for play and learning?
00:43:18
Speaker
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,
00:43:32
Speaker
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 begins with play
00:44:00
Speaker
And there's a false demarcation in education that, okay, play is sort of Montessori-esque or it's an elementary school.
00:44:08
Speaker
Maybe stops at grade five or six.
00:44:10
Speaker
Now we have to get serious.
00:44:12
Speaker
If you knew anything about play in terms of what play is and especially mathematics, play is serious business.
00:44:19
Speaker
And I wrote an article many months ago where I referenced Wayne Gretzky, the hockey player, which is arguably the greatest hockey player
00:44:29
Speaker
And he lamented about the current state of the game, the NHL.
00:44:34
Speaker
And I mean, the analogy was set up for me because he said, you know, these kids are overcoached.
00:44:39
Speaker
And the same way with mathematics.
00:44:40
Speaker
I mean, it's all about procedures and things like that.
00:44:43
Speaker
And sure, they're doing well in these procedures.
00:44:46
Speaker
He says there's no room for creativity.
00:44:47
Speaker
When I was a kid, I mean, you just threw some pucks to the rink or the frozen lake or whatever.
00:44:52
Speaker
You played and you tried different things.
00:44:54
Speaker
How did Gretzky do that famous bank pass off the boards at a 110 degree angle?
00:45:01
Speaker
Because he practiced that.
00:45:02
Speaker
He played with all the different angles on boards and tried things with the sticks.
00:45:06
Speaker
That's what he got.
00:45:07
Speaker
And that's what we should try to create.
00:45:09
Speaker
I mean, not everyone is going to be the Wayne Gretzky of hockey.
00:45:12
Speaker
But, you know, we should be trying to create these creative thinkers like that.
00:45:17
Speaker
And it all begins with play.
00:45:18
Speaker
I mean, you have to give problems where there's ample room for play.
00:45:22
Speaker
And I'll give you a perfect example of that in terms of ties in a lot of things, talks about this will tie in the current state of math education, textbooks.
00:45:31
Speaker
So this is from a course that I taught in Ontario back in the early 2000s.
00:45:37
Speaker
Sadly, this course no longer is available.
00:45:40
Speaker
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.
00:45:52
Speaker
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.
00:46:02
Speaker
So it says, the problems in this section offer you the opportunity to solve some significant problems related to the topics you have studied throughout the course.
00:46:09
Speaker
Several problems can be solved in more than one way.
00:46:11
Speaker
Back to alluding to what you spoke about earlier in our interview.
00:46:14
Speaker
Some of the problems are challenging.
00:46:16
Speaker
Considerable ingenuity may be needed.
00:46:18
Speaker
There's ingenuity meaning creativity.
00:46:20
Speaker
May be needed to solve them.
00:46:21
Speaker
You may be unable to complete a solution in the first attempt.
00:46:24
Speaker
That's very important because mathematics has mostly been about failure in the first attempt, not about success.
00:46:31
Speaker
And you may find it helpful to work with others.
00:46:35
Speaker
There's a social component.
00:46:37
Speaker
and share ideas and strategies.
00:46:39
Speaker
Be persistent.
00:46:40
Speaker
Try a problem.
00:46:41
Speaker
Set it aside.
00:46:41
Speaker
Try it again later or try another strategy.
00:46:43
Speaker
And here, to me, is the kicker.
00:46:45
Speaker
It may take several days or even longer to solve some of these problems.
00:46:49
Speaker
Kids need time and space to do that, time and space to play.
00:46:53
Speaker
I actually just wrote something yesterday about gamification and how gamification really isn't the same thing as play.
00:47:02
Speaker
Gamification is a mask of something that you're doing to make it more fun.
00:47:06
Speaker
playing a game is actually supposed to be fun.
00:47:08
Speaker
It's not meant to be, yeah, it's not meant to like be deceptive in any way.
00:47:13
Speaker
It's meant to just make you enjoy it.
00:47:17
Speaker
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.
00:47:26
Speaker
We've collectively as a society associated game playing or talking or whatever with wasting time,
00:47:34
Speaker
which that verbiage implies that it's not time well used, which to me doesn't make any sense.
00:47:40
Speaker
Play, first off, is foundational learning.
00:47:42
Speaker
It's the first way that you ever learn how to do anything.
00:47:44
Speaker
Animals do it too.
00:47:45
Speaker
And two, that's kind of what makes you a human being, socializing with other people, playing around, having fun, being happy.
00:47:54
Speaker
These are things that every human should aspire to do.
00:47:57
Speaker
It has nothing to do with a wasting of time.
00:48:01
Speaker
So it saddens me that many places, many administration, 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.
00:48:19
Speaker
I think that's a very narrow definition of learning.
00:48:21
Speaker
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.
00:48:29
Speaker
It doesn't really matter what you do.
00:48:30
Speaker
You're going to take something away from it.
00:48:32
Speaker
As long as you're reflecting on that knowledge gained, you should be doing okay.
00:48:36
Speaker
I mean, that's the whole basis of experiential education.
00:48:38
Speaker
It's John Dewey's whole idea is you just reflect on what you've done and you learn from your experiences.
00:48:44
Speaker
And that's kind of like what you're getting at.
00:48:46
Speaker
If we could supply math classrooms with multiple day projects or multiple day questions or multiple day games where, you know, some kids move ahead, some of them stay behind.
00:48:55
Speaker
But as long as they're all enjoying it, they'll take a lot away.
00:48:58
Speaker
Well, and one of the – and, you know, you're so right.
00:49:00
Speaker
And, you know, there's many reasons for play, and you already outlined all of them, the social component, the learning.
00:49:06
Speaker
You know, that's – it's just foundational to what play is and just really sort of narrowing it down to mathematics.
00:49:15
Speaker
In order for kids to – there's a quote by Paul Lockhart, which I'm going to read right now.
00:49:20
Speaker
He says, you know, mathematics is the art of explanation.
00:49:22
Speaker
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 their own explanations and proofs, you deny the mathematics itself.
00:49:37
Speaker
And we cannot get our kids there if they don't have the space and time to play.
00:49:41
Speaker
Because mathematics, I mean, in fact, what's happening in our classrooms today is completely, is not the thematic history narrative of mathematics.
00:49:51
Speaker
I mean, you know, people who explored all the mathematicians that were known or even this, you know, even, you know, recreational mathematicians throughout the ages, you know, they spent
00:50:02
Speaker
For days, weeks, months, the best mathematicians spent their entire careers on one problem.
00:50:06
Speaker
They might not even have made any sort of headway into it.
00:50:10
Speaker
That's the narrative of mathematics.
00:50:14
Speaker
And to make it seem like the kids have to solve multiple problems in one day over and over and over again—
00:50:20
Speaker
That's not mathematics.
00:50:22
Speaker
That's more computational based.
00:50:24
Speaker
And they're completely missing the whole larger vista of what mathematics is.
00:50:30
Speaker
And as soon as you, as soon as, and this will get, I guess, into the follow-up questions, what can we do?
00:50:35
Speaker
As soon as you start introducing the history of mathematics into the curriculum and how mathematics was developed thematically through various cultures and civilizations,
00:50:44
Speaker
then you're going to get to those wide open spaces for the problems that kids need to do.
00:50:51
Speaker
Sure.
00:50:51
Speaker
Just a side note, you just opened up a compartment in my brain that I think I was repressing, which was proofs in mathematics.
00:50:59
Speaker
But kind of getting into what you were just saying, which is, what can we do?
00:51:04
Speaker
You've mentioned gerrymandering, you've mentioned voting, you've mentioned the lottery, gambling, play, all these things that are
00:51:13
Speaker
Great uses of mathematics.
00:51:15
Speaker
They're philosophical.
00:51:16
Speaker
They're applicable.
00:51:17
Speaker
They're relevant, most especially.
00:51:19
Speaker
They're things that kids will enjoy doing.
00:51:22
Speaker
Without sounding too over the top, what are things we could do?
00:51:29
Speaker
Well, there's a lot of small, simple things that we need to do.
00:51:33
Speaker
First of all, it's important to create math communities.
00:51:37
Speaker
And that's already being built.
00:51:41
Speaker
And use social media, use Twitter for that.
00:51:43
Speaker
Find your tribe, find your tribes.
00:51:46
Speaker
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.
00:52:01
Speaker
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.
00:52:10
Speaker
You know, I mentioned this book and I've said it many times quite proudly.
00:52:17
Speaker
I possess.00, keep throwing as many zeros as you want.
00:52:20
Speaker
one percent of the mathematical knowledge of the universe i'm not going to live long enough to move that decimal place you know what gets me up in every morning is that there's something new for me to learn um 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 a new math concept so i would tell teachers especially new teachers uh even reluctant teachers
00:52:45
Speaker
Find time when you can.
00:52:46
Speaker
I know teaching, I was a teacher for 20 years.
00:52:48
Speaker
It's a demanding profession.
00:52:50
Speaker
But try to find little spaces to be inspired by mathematics.
00:52:58
Speaker
There's a couple places.
00:53:00
Speaker
There's a website called Math for Love that's hosted by Dan Finkel.
00:53:08
Speaker
He has his TED Talk, Five Extraordinary, I think, Lessons for Math Teachers, as it has close to 400,000 views.
00:53:16
Speaker
Now, I would even start there because it's really about what is mathematics and what can be done and just –
00:53:24
Speaker
Start with small – just creating 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.
00:53:36
Speaker
You have to –
00:53:39
Speaker
Any change is going to come because of community.
00:53:41
Speaker
So I would definitely start there, start as a community.
00:53:47
Speaker
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 as a teacher, try to do something.
00:53:57
Speaker
There's more things called family math nights.
00:54:00
Speaker
I do them.
00:54:01
Speaker
I've done them for many years now.
00:54:02
Speaker
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.
00:54:13
Speaker
You're getting usually the principal and administrator.
00:54:17
Speaker
You're getting teacher volunteers.
00:54:18
Speaker
You're getting students, kids.
00:54:20
Speaker
You're getting parents who might think initially they're just bringing their kids out to a play day and they're going to sit against the wall with a coffee and talk to their other parent friends about something else.
00:54:29
Speaker
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 at this intersection of all these people.
00:54:42
Speaker
So that's usually parents, they're confused too, like, oh my God, my daughter or son learning this new math.
00:54:49
Speaker
So I feel for parents, too.
00:54:50
Speaker
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 mathematics, just to make mathematics like really fun and exciting.
00:55:05
Speaker
Yeah, I agree with you 100%.
00:55:07
Speaker
One thing I would add personally, I think about this, maybe it's my more 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.
00:55:17
Speaker
I mean, one only knows the culture of their school, not everyone's going to be able to do this.
00:55:22
Speaker
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, and
00:55:34
Speaker
That supports these concepts.
00:55:36
Speaker
And you go to your administrator who hopefully you have a positive relationship with and you say, hey, here's what's going on.
00:55:42
Speaker
This is what I want to do.
00:55:43
Speaker
Can we beta test this?
00:55:44
Speaker
Can we do this one day a week?
00:55:45
Speaker
Can we throw out the math curriculum?
00:55:48
Speaker
Push for whatever you can.
00:55:49
Speaker
And if they say no, to me, that's a point where it almost becomes, well, why am I working here?
00:55:56
Speaker
Why are you going to limit me from doing what I think is right?
00:56:00
Speaker
If you're presented with all this information and you're that beholden,
00:56:03
Speaker
to something that is very corporately minded, something that's very malicious in nature.
00:56:10
Speaker
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
00:56:19
Speaker
another outlet for me to express what I think is real math education or just education in general.
00:56:25
Speaker
I think that goes without being said.
00:56:27
Speaker
I think that people are being too mouse-like.
00:56:31
Speaker
Teachers have power.
00:56:32
Speaker
You made a really good point there.
00:56:36
Speaker
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.
00:56:46
Speaker
And
00:56:47
Speaker
I think we need teachers to find their boundaries and to work at those boundaries.
00:56:57
Speaker
You know, everyone should be at least working at them.
00:57:01
Speaker
You know, your comfort zone to me is your death zone.
00:57:04
Speaker
And I say death zone, maybe not for you, but it's –
00:57:10
Speaker
indirectly becomes a death zone for the students learning because they're not getting, you know, the best.
00:57:16
Speaker
And you should be an advocate for your kids.
00:57:18
Speaker
And, you know, you should do as much as you can for your kids and you should find where those, you know, tipping points are.
00:57:25
Speaker
Like I said, you know, asking your administrator and things like that.
00:57:28
Speaker
And, you know, again, I come from, you know, yes, part of the kind of music I listen to is punk.
00:57:34
Speaker
And that's where it has influence in terms of
00:57:38
Speaker
My math education and I'm completely I'm at that stage where, you know, I'm 54 years old.
00:57:43
Speaker
I mean, I've had a teaching career.
00:57:45
Speaker
I'm sort of working outside the system.
00:57:47
Speaker
And that's a difference between outside, inside.
00:57:51
Speaker
Inside, you can innovate.
00:57:53
Speaker
But disruption occurs in the outside.
00:57:55
Speaker
Disruption rarely occurs in the inside.
00:57:57
Speaker
I mean, it can occur in 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.
00:58:08
Speaker
But, you know, as someone who's...
00:58:11
Speaker
has had 20 years of teaching experiences now on the outside, I can outside looking in.
00:58:15
Speaker
I'm going to tell you right now, because just the advances in, we're in second generation of social media, everything which is really cool in mathematics is happening outside the system.
00:58:27
Speaker
And that's unfortunately doesn't have to be like, you know, you've got this video channel called Numberphile.
00:58:32
Speaker
You have a museum of mathematics where they're talking about mathematics the exact same way they've been talking about for the last hour.
00:58:39
Speaker
There's a lot of anachronisms in mathematics, math education, which are still the pink elephant stage.
00:58:46
Speaker
And we have to make sure that all the elephants in the room first.
00:58:49
Speaker
you know, stop becoming pink and that we can, we can talk about that.
00:58:53
Speaker
And, you know, speaking, I'm going to end this in a positive way.
00:58:59
Speaker
I definitely have seen a lot of changes in the last couple of years that we are moving in the direction that
00:59:04
Speaker
It's still somewhat incremental, but we are moving towards the, yeah, mathematics for human flourishing.
00:59:11
Speaker
Mathematics is for justice.
00:59:12
Speaker
It is for equity.
00:59:14
Speaker
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.
00:59:21
Speaker
And then we have, we're turning education and teaching back to the human profession.
00:59:27
Speaker
We're not going to become the robots that Asimov predicted 60 years ago.
00:59:31
Speaker
That cultural shift.
00:59:33
Speaker
I mean, it's not only happening in academic sense, it's literally happening in schools themselves.
00:59:39
Speaker
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.
00:59:51
Speaker
And it's not to say that all these schools are doing the right thing, but they're at least trying to change something.
00:59:56
Speaker
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
01:00:04
Speaker
Your job will even last, honestly.
01:00:05
Speaker
I mean, a lot of those schools go under.
01:00:08
Speaker
But I feel like that risk is needed to keep that passion alive.
01:00:14
Speaker
I feel like if I were just to sit there inside a history class from the same school for 20 years –
01:00:20
Speaker
and just keep trying to push for this change, I would get burned out so quickly.
01:00:25
Speaker
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.
01:00:33
Speaker
I still have to be careful, and I could probably push way harder.
01:00:36
Speaker
But there's that open dialogue between us and administration.
01:00:41
Speaker
We can change things.
01:00:42
Speaker
And those schools exist everywhere.
01:00:45
Speaker
It doesn't matter where you are.
01:00:46
Speaker
There are schools like that.
01:00:48
Speaker
So I sometimes worry that teachers feel like they're complacent just because they have nowhere to turn to.
01:00:55
Speaker
It's one thing to try to change the system from the inside, which is great.
01:00:58
Speaker
I feel like everyone should start there, change with their current kids, change your classroom, find your tribe, do all that kind of stuff.
01:01:04
Speaker
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.
01:01:12
Speaker
Fight your hardest to get that job because you're just going to be miserable if you're constantly weighed down with extension protocols that force you to do what you don't want to do, which is the case for
01:01:25
Speaker
a sizable amount of people 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 um the idea that there's a philosophy mindset to um to have this kind of change which is okay sometimes it's veering towards something called punk um there's a photographer of my generation glenn friedman um he's like one of the most amazing photographers and he was asked many years ago his definition of punk and
01:01:54
Speaker
He said in very simple terms, if you didn't know who he was, everyone would go, this is like an amazing quote.
01:02:00
Speaker
He says, it's an intense obligation to your most innermost feelings.
01:02:05
Speaker
And, you know, that's where it goes all back to is my accountability is first with myself.
01:02:11
Speaker
I have to check, am I being accountable to who I am as a person and what I believe in?
01:02:16
Speaker
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.
01:02:25
Speaker
And I think teachers have to ask themselves, so when I go into mathematics, what's my goal as a math educator is to inspire other people to be inspired by mathematics.
01:02:35
Speaker
So whatever it takes to do that, yeah, I'm willing to do that.
01:02:42
Speaker
Hope you enjoyed this podcast.
01:02:43
Speaker
We want to connect with you and hear your thoughts.
01:02:45
Speaker
Follow us on Twitter, YouTube, Medium, and other social media, and be sure to check us out on our website at humanrestorationproject.org.
01:02:52
Speaker
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01:02:59
Speaker
Thanks again.