Transcript
Speaker: All right.
Speaker: Good morning, everyone.
Speaker: Nice to see all of you.
Speaker: I believe you can hear me if I set this up the right way.
Speaker: So I'd like to welcome all of you to our third summit here at the Human Restoration Project to welcome Sunil Singh for joining us to humanizing mathematics.
Speaker: We'll get started here with what we'll be doing here in a minute.
Speaker: But I just want to give you a brief introduction to what this is and what we'll be doing.
Speaker: First off, this event is brought to you by our Patreon supporters.
Speaker: This is how we keep this afloat.
Speaker: It costs some money to operate our platform and things of that nature.
Speaker: So if you enjoy this, visit us on Patreon or visit us on our website at humanrestorationproject.org.
Speaker: That's highly, highly appreciated.
Speaker: And I'd like to remind you that this is an interactive discussion.
Speaker: So if at any point you want to ask a question or get involved, please type into the chat.
Speaker: Or if you'd like to appear on the screen, hit the raise hand button.
Speaker: I'll see that on my end and I can welcome you up to the stage.
Speaker: The goal is that we have an interactive discussion because we're all experts in our fields.
Speaker: We know what we're talking about.
Speaker: It's not just like a formal lecture.
Speaker: Everyone's welcome to participate and that'd be really cool.
Speaker: So some brief introductions here.
Speaker: My name is Chris McNutt.
Speaker: I'm the founder of Human Restoration Project.
Speaker: Our organization aims at providing progressive resources for free to as many people as possible.
Speaker: And this is one of our many professional development options.
Speaker: Our goal is to have one of these at least once per month.
Speaker: We also have a ton of free resources and research on our website, which again, you can check out at human restoration project.org.
Speaker: And by day I'm a public school teacher.
Speaker: I teach digital design and media to high schoolers.
Speaker: So I'll turn it over to Sunil here or to learn more about him.
Speaker: Good morning, Chris.
Speaker: Morning.
Speaker: Really excited to see where this goes.
Speaker: Um,
Speaker: going to try to give a Reader's Digest version of a little bit of background about myself.
Speaker: I was a high school math and physics teacher for an occasionally English teacher for 19 years.
Speaker: And I left teaching in 2013 for some of the reasons which are, I guess, are aligned with the Human Resurrection Project.
Speaker: And those six years after, in 2013, were quite formative in terms of everything that sort of
Speaker: happened to me personally and professionally, and you get to sort of view the large landscape of sort of life and education through your own sort of, you know, personal struggles and victories.
Speaker: And a couple of books later and working at Skoll Lab here in Montreal as a math learning specialist and being active on Twitter and seeing all the interactions that happen on a daily basis, even the micro conversations, it really,
Speaker: seems to me that we are moving or need to move towards this thing, which is going to be called humanizing mathematics.
Speaker: And what I want to do with you and all the participants is even define what that means.
Speaker: I don't want to even start from a place of we already have a definition.
Speaker: I'd like to see what that even means for each one of us and see if we can come up with some sort of amalgam roadmap of where to start.
Speaker: That's a good point.
Speaker: So as I go through kind of going through what the questions might be, if you could do me a favor, if you're in the audience and you would like to define or take a stab at what you think humanizing mathematics is, I'd love to hear your voice.
Speaker: I'll practice some wait time there, some teaching tools.
Speaker: So really quick, these are the questions that we're going to dive into once we get to that point.
Speaker: And you can just kind of read these over.
Speaker: I don't know if I'm going to read every single one.
Speaker: But the question that we'll start off with after we define humanizing mathematics is, what does it mean to have a humanized mathematics curriculum?
Speaker: And how does this differ from the predominant way mathematics is taught?
Speaker: because in order to say that we need a human centered math curriculum or we need to humanize mathematics, that must be that the current definition or predominant definition is dehumanizing.
Speaker: So we'll start there.
Speaker: And Sunil, if you want to go first, I don't have any, I don't have any raised hands yet.
Speaker: But again, I encourage, I encourage people to speak out.
Speaker: I want to hear what you have to say.
Speaker: It's not the lightest topic to start on a Sunday morning.
Speaker: So I think, you know,
Speaker: Yeah, sure.
Speaker: I'll take a stab at it.
Speaker: And I sort of say that somewhat tongue in cheek.
Speaker: Of course, I've been thinking about this for a long time.
Speaker: I guess we should start from what our current general curriculum is.
Speaker: And, you know, math education is a tiny subset of mathematics.
Speaker: I mean, it's only been around for maybe 100 years or so in a formal sense.
Speaker: And its extract came from mathematics, but it also came from, you know, what the purpose of schools were at that time, you know, post-industrial revolution, 30, 40 years on.
Speaker: So its intentions were, you know, very different from how mathematics has been explored by every person who's ever lived.
Speaker: So, you know, the final distillate, when I say final, I mean, where we are in 2019 is that
Speaker: it's really for a performance culture.
Speaker: It's really about measuring proficiency of, for me, very disconnected ideas.
Speaker: Even a simple thing, like when we have review every beginning of every school year for every grade to review what you learned, isn't the definition of learning that you haven't forgotten it?
Speaker: I mean, there's no muscle memory.
Speaker: If they're forgetting it, that means either the way that we're teaching it isn't sinking in or even
Speaker: You know, the knowledge and even I think it was offered North Whitehead, who's, you know, one of the great mathematicians of the 20th century, said something about inert knowledge, you know, being very dangerous.
Speaker: And it is.
Speaker: So I think what we have to do is first maybe define what our current sort of curriculum is doing and isn't doing.
Speaker: And then maybe just sort of spring from there.
Speaker: That's a very good point.
Speaker: We talk about this a lot on our podcast a lot, but the concept that it's not necessarily that teachers are intentionally doing something wrong or they're out to hurt students or anything of that nature.
Speaker: But instead, the curriculum is focused around efficiency because our goal is to hit a very large number of people in a very short period of time.
Speaker: And efficiency is...
Speaker: By its own definition, not very humanizing because people don't operate in that fashion.
Speaker: I actually have a raised hand.
Speaker: We'll test this out and see how it works.
Speaker: I'm going to invite Michael up here.
Speaker: Michael, I believe you can talk and we can hear you.
Speaker: Good morning, Chris.
Speaker: Good morning.
Speaker: Good morning, Michael.
Speaker: So, I mean, I think of Jacob's first...
Speaker: uh, uh, textbook.
Speaker: Um, and it's actually the only textbook that I even bother using.
Speaker: Um, and it's mathematics, a human endeavor.
Speaker: And, um, as I've evolved, this is 30 years, 34, I think something like that of teaching fourth and fifth graders, mathematics.
Speaker: Um, um,
Speaker: I think first you've got to acknowledge that our students are human beings.
Speaker: They're not little machines.
Speaker: We're not trying to train them to go to a 19th century factory.
Speaker: We don't even know what they're going to be doing in the future.
Speaker: So it's really helping them love and appreciate and play together.
Speaker: with mathematics because that's what mathematicians do.
Speaker: They explore and discover and describe and shape and most of all play with it.
Speaker: It's something that mathematics is something that humans do.
Speaker: And we need to be bringing our students into that human endeavor.
Speaker: That's a great point, Michael.
Speaker: It's a very good point.
Speaker: And as well, it kind of echoes to what Barb and Liliana are saying in chat about this idea of shaping the learning environment to focus on the individual needs of students.
Speaker: And also, too, that math can be very fun, which I know, Sunil, that's a big part of your work is mathematics through play.
Speaker: I mean, it's literally basically the title of your book, Math Recess.
Speaker: Could you speak to a little bit about play in math?
Speaker: Yeah.
Speaker: And just, I know Michael, you know, he, he, he chimed in and just to sort of link Michael to the book.
Speaker: It was actually in Michael's class where the whole book started in his grade, in his fourth grade class with a student and how that whole day in terms of what was about play, playing with numbers and playing with math and,
Speaker: The amount of noise and just joy that was emanating from a simple numerical problem.
Speaker: So, again, I'm going to bring out the word subset and then I'll retire it.
Speaker: People think, OK, play is maybe some subset of math or play as a subset of learning, play as a subset of life.
Speaker: In Maslow's hierarchy of needs, I don't know where you would put play.
Speaker: I wouldn't put it necessarily in terms of at the bottom of sort of physiological needs in terms of survival, but I wouldn't put it too far up.
Speaker: Play is such an essential part of everything in terms of our socialization, of course, how we learn, how children learn.
Speaker: One of the things we do, unfortunately, when kids come into school, especially with mathematics, we wipe the slate clean.
Speaker: And we start from scratch.
Speaker: We don't even take what they might know or their misconceptions or their wonder.
Speaker: And, you know, that's why the idea of play and the first idea of play, which is important, and this is referencing Dr. Peter Gray.
Speaker: And this is the one which even myself, I wasn't terribly good at in my teaching career.
Speaker: But the first element of play is it's self-chosen, self-directed.
Speaker: Hmm.
Speaker: And that means that kids should be allowed to choose the math problems and ideas that they want to work on.
Speaker: I'm not saying every day in terms of the current infrastructure that we have, at least once a week, there should be a time out for kids to go, okay, whatever problem puzzle you've been working on, there's no deadline for it.
Speaker: In fact, they'll end up thinking like a mathematician.
Speaker: And also part of play is that you're free to quit.
Speaker: And we all we've, we've taken the word quitting to mean such a negative thing in society, but you know, quitting also allows you to do things which make you happy.
Speaker: And, uh, I think the idea of play, we're just starting to wrestle with really what it means.
Speaker: Um, for me, it's going to be the last year and a half until I even really dove, dove deeply into the idea of play.
Speaker: So I really think play is a foundation for, you know, opening the door towards, uh, uh,
Speaker: sort of more sort of human math education.
Speaker: Yeah, the, I mean, the whole concept of how do we measure achievement and success through a narrowly defined curriculum, I think that we should spend a lot more time focusing on the fact that our students are bored.
Speaker: I mean, survey after survey, the kids are just not happy in school, especially as they get older and, you know, their adolescence, the vast majority of students are not excited to be at school.
Speaker: which it doesn't have to be that way.
Speaker: There are obviously plenty of classrooms throughout the world who are engaging students through things that they find exciting and interesting and fun, and they don't lose the motivation to learn.
Speaker: That whole concept of, you know, I'm not a math person.
Speaker: And, you know, there's a very binary definition of math.
Speaker: I know when I was in high school, I was the quote-unquote not a math person.
Speaker: And I did not do well.
Speaker: And I frankly did not like it.
Speaker: I did not like being in math.
Speaker: I failed math three times in high school.
Speaker: I was ahead up until that point.
Speaker: So I came back down on track.
Speaker: Do you want to talk a little bit here?
Speaker: And I'll give some people a chance to respond.
Speaker: Again, I encourage you to raise your hand.
Speaker: So this isn't awkwardly between me and Sunil the whole time.
Speaker: But, you know, what, Sunil, could you talk a little about that concept of being a math person when we have this very narrowly defined curriculum of what math is?
Speaker: Yeah, you know, this is kind of another prickly pear for me.
Speaker: I love to use analogies and I'm going to use this one.
Speaker: My favorite sport to watch is soccer.
Speaker: Even though I played hockey, my favorite sport to watch, I'm not a very good soccer player.
Speaker: I mean, I can kick the ball around, but I can tell you every single idea aspect in terms of its beauty, its strategy, everything.
Speaker: I mean, in terms of, yeah, it is the beautiful game, the worldwide game.
Speaker: What does that mean in terms of being good at math?
Speaker: Well, somehow we have this strange, maybe not strange, but in order to like math, you have to be good at it.
Speaker: And if you're good at it, you like it.
Speaker: That itself is kind of claustrophobic.
Speaker: Like I've said this in many blogs.
Speaker: I've said it many times.
Speaker: I mean, 99.999% of the math, I don't know or understand.
Speaker: But what I do understand is how connecting and binding and beautiful and joyful math is.
Speaker: And that's the humanity part in terms of which
Speaker: I'm kind of operating under.
Speaker: So, you know, the idea of, you know, this narrow K to 12 band.
Speaker: Okay, let's, you know what, let's just fast forward the optimum situation of this current, you know, curriculum.
Speaker: And let's say everybody got the A's and the perfect papers on standardized tests.
Speaker: They got the gold stars.
Speaker: Let's make everything.
Speaker: Let's go to the extreme situation where this, of course, wouldn't happen.
Speaker: What's the end game of that?
Speaker: Like, what is the end game of that?
Speaker: Like, guess what?
Speaker: A lot of these students are still going to leave school less, not curious about mathematics.
Speaker: They might perform better at their jobs or whatever they're doing.
Speaker: But in terms of the kind of society we want to build, um,
Speaker: it's not going to build it.
Speaker: And when I say build it, I don't mean like terms of, you know, engineering structures and stuff.
Speaker: Just, I know I'm going to forget this point.
Speaker: So I wanted to bring it up now, right?
Speaker: We talked about K to 12 being good at math.
Speaker: And there's a research article which came out, I think last year that talked about when in the thirties and forties, the math curriculum was being constructed in the U S education.
Speaker: It had broader goals in STEM.
Speaker: It was actually for a learned,
Speaker: society for this sort of informed citizenry.
Speaker: And we've narrowed it down to STEM goals.
Speaker: And, you know, I'm all for STEM.
Speaker: I'm all for STEAM.
Speaker: I'm also for other letters too, you know, in terms of social, emotional learning.
Speaker: But that seems we've gone backwards.
Speaker: Like we had such a broader sort of initially maybe to love mathematics.
Speaker: So I think just this whole K to 12 proficiency standards, you know, it's, it's,
Speaker: it's taking a toll on all of us.
Speaker: And especially I think as educators, teachers in the classroom.
Speaker: Yeah, and I think that, you know, from a practicality standpoint too, it's up to us to try to brainstorm a way that we can approach these topics, like moving away from a very rigid and narrowly focused standard set to a more humanized system is going to require not only us banding together and talking about these things, but finding a way that we can make this work in the classroom within the current system and then working to change it.
Speaker: Because I mean, it's like, I have that daydreamer part of me that wants to just say, yeah, we're gonna go out and do it.
Speaker: But as soon as I tell them, I know if I walk into the classroom and say, there's not gonna be any standards, and we're gonna do all this crazy stuff.
Speaker: It's probably not going to end up well for me.
Speaker: It's probably not going to happen.
Speaker: So
Speaker: Is there a way then that we can redefine, moving into the second question here, is there a way that we can redefine what success looks like in mathematics where we can still at least somewhat pair it to standards, but yet lessen that math anxiety, promote wellness in the classroom, and have a class that is more self-directed, you know, without completely revolutionizing the system from day one, even though that might be the long-term goal?
Speaker: You know, that's a really good question.
Speaker: And I think it's a very practical question.
Speaker: It's philosophical, but it's very practical.
Speaker: And I'm not saying I have the answer.
Speaker: But, you know, one of the things that we can do, and it's the easiest thing we can do.
Speaker: When I graduated from Teachers College in 1992, one of the last exercises we had in our math education class, our math ed class, was we had to list all the qualities of a good teacher in groups and then present it.
Speaker: And I wrote this story in my first book, Pie of Life, because Dave Alexander, our professor, teacher, he just stared out the window the whole time.
Speaker: And I got suspicious of that as though, why is he not interested in what we're doing?
Speaker: Anyways, after all the presentations, he said, there's only two qualities which make up a good teacher.
Speaker: And he said, honesty and mutual learner.
Speaker: So I'm just going to focus on the honesty one because we need to be honest with ourselves and with our students.
Speaker: And that's not saying we're dishonest, but I mean, really be honest and be vulnerable.
Speaker: So if you have had struggles with math, if you don't know the answer, share that with your students.
Speaker: Disarm the classroom.
Speaker: Like, let them know that you've also, but not struggled in a negative way, but yeah, math has been a kind of a, you know, a puzzle for me.
Speaker: And that's why, you know, I love teaching it because it's got all these sort of, you know, locked doors and hidden passageways.
Speaker: And
Speaker: You know, you stumble and fall.
Speaker: So I wish teachers would be more.
Speaker: I mean, I started doing this too late in my teaching career where in the beginning I'd only assign the, when I taught calculus, I'd only assign the questions which I could do.
Speaker: I made sure that I could do them.
Speaker: By the end, what I was doing is assigning all the questions.
Speaker: And sure enough, kids would go, Mr. Something like that last question, 17C, questions are broken to A, B, and C, and C-Roll was the tough ones.
Speaker: could you show us how to do it?
Speaker: I go, you know the drill.
Speaker: So I go, I've looked at it.
Speaker: I'll see how far I can get.
Speaker: And it was like at least three or four times where I basically could not solve a problem in front of the whole class with the class.
Speaker: I said, okay, this is as far as, this is as much as I got.
Speaker: Anybody got anything else?
Speaker: Okay, fine.
Speaker: Let's save this.
Speaker: We'll bookmark it next week.
Speaker: Just be damn honest.
Speaker: I mean, it's one of the easiest things we do.
Speaker: And once we start to sort of
Speaker: Walk on eggshells and things like that.
Speaker: But I think if we be open with our students, especially our elementary students who really, really want to look up to us and trust us, that's a good place to start.
Speaker: That's a very good point.
Speaker: I want to invite Liana up to the stage here.
Speaker: Hello, Liana.
Speaker: Hi, can you hear me?
Speaker: Yeah, we can.
Speaker: Hi, Liana.
Speaker: Hi.
Speaker: I just kind of want to second that last point of doing the problem in front of the class and not knowing the answer.
Speaker: Or even if you do know the answer, sometimes maybe pretending that you don't know the answer, as long as it's not too fake.
Speaker: But coming to show the process that
Speaker: it's not about knowing all the time, being the teacher upfront saying, you know, kids assume that, you know, everything.
Speaker: Um, and then it's frustrating to them when they don't know, I think, um, so important to, to show the process of, of figuring it out, you know, coming at things from different angles, taking, um,
Speaker: maybe choosing an angle to approach the problem and then partway through discovering that it's wrong, that it doesn't take you where you're trying to go.
Speaker: And to see that process, like when I do a math problem myself, I will sometimes even a problem, maybe that's easy for someone else, but I didn't see it and I didn't know how to start it.
Speaker: And my whole page is full of starts, different starts.
Speaker: And I don't like to ever erase any of it.
Speaker: because sometimes maybe it comes in useful, but just to have like a whole page of starts of a problem.
Speaker: And then in the end, if you're lucky or the day was good, then you come to the answer of the problem from all these different ways that you tried.
Speaker: And I think that process, showing that to kids and then letting them try that and having that be what a math class is or a math experience, um,
Speaker: is that's kind of what math is.
Speaker: I mean, that's what we do.
Speaker: And maybe that's not taught so much in class.
Speaker: Yeah.
Speaker: I mean, I'm with you, but being not someone who is a math teacher, um, I did not really understand what the point of math was outside of finances until I was an adult.
Speaker: Uh, so, um, I mean, I, I definitely can relate with that point.
Speaker: Uh, just to let Liana know, I've just jotted down my first note to myself, a collection of starts, uh, that, uh,
Speaker: You know, when you said that, it kind of sent a little shiver up my spine because it really is trying to make the classroom feel like what mathematics is.
Speaker: I mean, this is what it is.
Speaker: Like, if you look back at history, and we haven't talked about that yet, mathematics is really just a collection of starts and some halfway points.
Speaker: And, yeah, the people who get to the end, those are the people we hear about.
Speaker: And, you know, those are the kind of the,
Speaker: cerebral astronauts who get out there and they land.
Speaker: But for us, it doesn't, you know, that's why this idea of productive struggle, I like the idea, but what that means really is that we will value struggle if you get it to the end.
Speaker: How about you just value struggle, period, whether you get to the end or not.
Speaker: And I know it's a tough thing for kids to see mathematics as that,
Speaker: But they won't see that if we as teachers and educators don't demonstrate that ourselves.
Speaker: If we don't show our own vulnerability and, you know, misconceptions with our students.
Speaker: Those are.
Speaker: I didn't have as many as I wanted.
Speaker: I mean, maybe it takes a lifetime to get to that point.
Speaker: But boy, those are the best moments in my class.
Speaker: I mean, this stuff is such an important concept because I think that there is a, as Skylar and Nick are talking about in the chat, there is a perceived gatekeeping or real gatekeeping element to mathematics in school because of its very, you know, one route and how it's viewed and how it's seen and what it means to be successful in those classes.
Speaker: And completely honestly, I, Sunil, I had you on the podcast on our podcast, I think it was beginning of last year, maybe earlier than that.
Speaker: It was, it was, it was a while ago.
Speaker: Um, and walking into that podcast, uh, you actually changed my mind on this.
Speaker: Uh, originally I was coming from the boat, like, well, we should just transform all math classes to be financial literacy or change them all to be very, um, quote unquote, practical skills, uh, like daily skills.
Speaker: Um,
Speaker: Because that to me is what I knew math as.
Speaker: But you brought up a very good point and it builds into our third question here, which is there's a lot of very important concepts of mathematics that build itself into really serious things that we should be focusing on in math class, for example, social justice or how it relates to huge issues in our lives.
Speaker: Um,
Speaker: And I think you also said something about, you know, you can learn about balancing a checkbook in like two days.
Speaker: These are not really that hard.
Speaker: However, you know, quantifying research on like voter discrimination, it would take a serious amount of backbone.
Speaker: And I love talking about this kind of stuff.
Speaker: And I think it does relate to how we redefine success when we redefine what it is that we're focused on or the questions that we're solving.
Speaker: So, you know, what can the substantial changes, you
Speaker: to math look like?
Speaker: Like what could that look like in the craft classroom where it could be highly engaging and cool and interesting to learn about?
Speaker: Well, I think the first thing we have to do is sort of look into our rear view mirror, which is the history of mathematics.
Speaker: And I see you've got there in terms of social justice and, you know, decolonization.
Speaker: That's been a big issue, equity in math and, you know, the whiteness of math education.
Speaker: It's been
Speaker: really a hot topic in social media and in the math education circles.
Speaker: There's been a lot of great people leading this, Rochelle Gutierrez, a whole bunch of people who really, you know, brought this to the forefront.
Speaker: And I'll give you a very simple example, you know, in terms of transforming classrooms.
Speaker: You know, kids, they need to see themselves or to see, you know, mathematics has been, you know, every civilization culture,
Speaker: has explored mathematics richly.
Speaker: And even a simple thing like zero.
Speaker: We treat it with such, it's such an important number, but we give it such an inert space, like no space.
Speaker: And we don't even, like we acknowledge authors of certain mathematics, but it's mostly Western mathematicians, like Newton and calculus, but even
Speaker: not suffer debate in terms of, you know, really in terms of where did calculus start.
Speaker: Going back to zero, I mean, the person who came up with the first axiom and the rules for zero is a Brahmagupta, Dean of Mathematician.
Speaker: Now, do we not reference Brahmagupta when kids are learning about zero because his name is funny sounding?
Speaker: Like, that's the part of decolonizing it and humanizing it when we attribute names to people who had such groundbreaking experiences
Speaker: which maybe not seem groundbreaking because we've trivialized zero in the classroom.
Speaker: You know, what is zero?
Speaker: But, you know, it came from somewhere.
Speaker: So I think going into the roots of mathematics is really important for
Speaker: educators to not only help themselves learn about mathematics, they'll learn a lot of new mathematics, but you're also going to realize that the trajectory of the Western narrative isn't true.
Speaker: And that where a lot of it came from, most of high school curriculum is ninth century Indo-Bedic mathematics, save calculus and statistics.
Speaker: It's like trigonometry quadratics, and that came from that period of time.
Speaker: So I think
Speaker: spending more time and infusing math history, the good, the bad, and the ugly.
Speaker: There's a lot of, you know, and that's what human, that's what humanizing means about the whole story.
Speaker: I mean, there's some darkness in math in terms of, you know, some of the depression that was had by some famous mathematicians who unfortunately took their lives.
Speaker: There's other obviously situations and considerations to take, but,
Speaker: Storytelling, tell the story.
Speaker: And from there, I think we're gonna pick the fruits of how to proceed forward.
Speaker: Yeah, I wanna turn this over to Eliana, who has another point.
Speaker: Oh, hi.
Speaker: Yeah, I actually had a point about this sort of side conversation going on in the chat, mostly around algebra.
Speaker: And I have noticed a lot hearing other parents.
Speaker: I'm a parent and a homeschooler as well as I do math workshops for kids.
Speaker: And I hear a lot from parents that algebra, do we need algebra?
Speaker: I don't remember any algebra from high school.
Speaker: So, you know, who knows?
Speaker: you know, who remembers the quadratic formula?
Speaker: That's here.
Speaker: I hear that like almost every day.
Speaker: And I think, um, in talking to people, I say, you know, like you, I don't remember the formula either, but you, um, you understand certain concepts, like people, every, I, they say, why is algebra important?
Speaker: It's,
Speaker: You use it all the time.
Speaker: You just don't even know that you're using it.
Speaker: People have a very intuitive sense of equality, like an equation and balancing an equation.
Speaker: And you actually do algebraic manipulations all the time.
Speaker: You just probably don't know how...
Speaker: that looks on paper or what the formal rules are, but the concepts are actually there.
Speaker: And I think since we're talking about humanizing, to make the point to relate what you're doing in the classroom when you're teaching the math to what people do already know to
Speaker: As kids grow up, they pick up a sense of mathematics from the world around them, and it's just not formalized yet.
Speaker: It's not connected to the language.
Speaker: But to be able to relate what you know to the formal math...
Speaker: can maybe bring people in so they can say, oh, I do know algebra.
Speaker: It's not a foreign thing.
Speaker: I actually already think like that.
Speaker: I have those skills.
Speaker: And also, I just want to say, I also love the history of math.
Speaker: Sunil, I think bringing that in to classroom is so wonderful.
Speaker: That's all.
Speaker: I'm with you.
Speaker: I mean, the concepts that we all are talking about, I think are incredibly fascinating and also very much relevant.
Speaker: I want to dive into to this, this concept of PBL.
Speaker: Now, I'm not a math teacher, but I have done a lot of co-teaching with math.
Speaker: And some of the projects that we've done together have been very enlightening to learn more about what math could look like in a very hands-on way.
Speaker: setting.
Speaker: So like, for example, last year, we built like scale model roller coasters, which is a classic, like it's a classic PBL thing, the marble roller coaster.
Speaker: But it's really interesting to do things like, well, what happens if we put like a GoPro on like a little car instead of on a marble, and then we measure the g force and figure out would this be a joyful experience to ride using mathematical formulas?
Speaker: And
Speaker: And what we found was, is that as we're going through projects like this, the teachers don't really understand, or sorry, I have to say the teachers, the students don't really understand how to apply the mathematics that they were learning until that point.
Speaker: And
Speaker: And it might not necessarily be concepts that were on the standards, but it's still useful nevertheless, because it was very interesting.
Speaker: So finding ways to use hands-on or at least applicable ideas throughout the classroom.
Speaker: One other example I'll toss out really quick.
Speaker: an English teacher and a math teacher at my school co-taught the drunkards walk which gets into the history of mathematics and talks about being a math person and kind of as we're relating to in chat here analyze that concept of the hidden curriculum of mathematics or school within a math class so dissecting what it means to be a quote-unquote math person and where that myth comes from by literally talking about it with students as opposed to just trying to fix it from the sidelines
Speaker: The idea of PBLs and project-based learning, math lends itself really well to that because it's got applications in so many different fields.
Speaker: If you want to talk about application, mathematics is a heavy hitter.
Speaker: That's historically always been its purpose in terms of school.
Speaker: That's great because it has applications everywhere, science, technology, medicine, economics.
Speaker: But
Speaker: it can do more.
Speaker: And there's a book coming out in 2020 by Francis Hsu called Mathematics for Human Flourishing.
Speaker: And it's based upon his interaction story with his friend Christopher who's serving time in a medium security prison for armed robbery who taught himself and is teaching himself mathematics.
Speaker: And in many speeches when Francis speaks, he goes, when we think of mathematics, do we think of Christopher?
Speaker: someone who's incarcerated, who's not going to have a STEM career, what does mathematics mean to him or her if they're in a situation like that?
Speaker: So humanizing means to have mathematics extend the radius of what we would traditionally think people need mathematics for.
Speaker: Going on with Francis Seuss, his view of mathematics is very sort of Aristotelian in terms of
Speaker: you know, the virtues of, you know, beauty, truth, justice, play, and love.
Speaker: I don't see those in curriculum documents.
Speaker: But in, again, 2019, where we are, especially in the state of the world we're in, and, you know, seems like the revolution is nigh, especially with someone as powerful as
Speaker: you know, Greta Thunberg in terms of climate, what can transpire in a year.
Speaker: I'm very hopeful of what we have to do.
Speaker: And part of it is simply talking about math.
Speaker: And I'm just looking around because I'm in my office downstairs and all the book titles.
Speaker: There's one, I really, it's always sitting beside me.
Speaker: It's called the mathematics devotional.
Speaker: It's a beautiful book.
Speaker: Every, every, every,
Speaker: Every page is about one day in a calendar year.
Speaker: It's got a beautiful picture of mathematics and a quote.
Speaker: And the back quote I'll read is from Sofia Kowalovskaya, the Russian mathematician.
Speaker: It's a very simple quote, but she says, it's impossible to be a mathematician without being a poet in Seoul, 1895.
Speaker: I mean, that's what mathematics does to us.
Speaker: It transcends mathematics.
Speaker: and can transcend anybody and even someone like Christopher.
Speaker: And that's why I think there's a lot of moving parts here.
Speaker: There's a lot of amazing things happening in education, people writing books, the way we communicate on social media, human restoration projects.
Speaker: No one is going to do the heavy lifting by themselves.
Speaker: And this is not going to transpire in my lifetime.
Speaker: I remember I jokingly, I said this in another podcast to my daughter, I go, if I can't change things in math education, pinky promise, will you?
Speaker: That's what I think the timelines are, but I'm okay with that.
Speaker: And what's cool is, is that because we now have access, unlike, you know, even 10 years ago, uh, to being able to easily access one another and play off each other virtually, um, it's such a powerful tool because if you're looking to collaborate and brainstorm ideas, um,
Speaker: Beyond just asking students and learning from students, there's also a huge collective of educators online who are working to do this kind of stuff.
Speaker: And it's not like it hasn't been done before.
Speaker: There are plenty of educators that are transforming mathematics or any subject area within their classrooms and making it work no matter what setting they're in, whether it be very traditional or an incredibly progressive school.
Speaker: There are ways that we can adapt these ideas and make them work.
Speaker: So, Neil, I don't know, before we move into this, like more of like a Q&A or just answering questions, is there anything else that, I know a lot of your writing recently has been on equity in math education.
Speaker: And I know you briefly hit it, but is there anything else that you would want to add to how teachers can ensure that they have an equitable math class, not just in terms of the curriculum, but also in terms of, you know, the students and how it reflects in the classroom?
Speaker: Yeah.
Speaker: Well, one of the things which I'd like to see, and this is sort of touching upon Liliana's point when she said a collection of starts, you know, one of the things which we do, and again, it's all with good intention, especially on social media, Twitter, is that we show the kind of the climax of the story.
Speaker: Here are the five strategies to solve the problem.
Speaker: That's great.
Speaker: That is obviously wonderful, all the multiple representation and solutions.
Speaker: What I'm interested in is the whole journey.
Speaker: You know, it's almost like the hero's journey.
Speaker: When the student first sees a math problem, what's your initial response?
Speaker: I hate this.
Speaker: Like, or, okay, I'll try it.
Speaker: Like, document the whole story.
Speaker: Like, that's where I think is important because then that's what it feels like to be a mathematician.
Speaker: And if we are, if that's our goal, and I think it is, maybe we just have to adjust our rudder here.
Speaker: Like just, if we're trying to capture the whole story, I think that's part of it.
Speaker: And maybe that's part of journaling or something that students and teachers can do.
Speaker: But I want, I want everything.
Speaker: I want the, you know, throwing the kitchen sink, everything that you feel about mathematics, the good, the bad, the ugly.
Speaker: I've said that already previously 20 minutes ago, but,
Speaker: That's what humanity means, being honest.
Speaker: Just give it everything to.
Speaker: And from there, I think the seeds of disruption will, something will come.
Speaker: But I think going back and cycling back, being honest and just letting students tell their stories about doing mathematics.
Speaker: That's a really good point.
Speaker: I mean, sometimes the simplest solutions can happen as of tomorrow, like the concept of just redoing an assignment.
Speaker: Like the grade does not count right away or finding ways to purposefully ungrade and just have conversations or maybe the journal itself is the documentation that you're looking for.
Speaker: Let me turn this over to Michael.
Speaker: Michael, welcome back.
Speaker: You know what, I got so wrapped in what Sunil was talking about with equity, I'm not positive I even remember what the point was I wanted to share.
Speaker: But I think where I was thinking was the problems have to start with the student.
Speaker: The mathematics has to start with the student.
Speaker: You know, yes, I do remember what I was saying.
Speaker: We don't expect our music students to know how to build the instrument when they start.
Speaker: They, you know, we don't...
Speaker: We don't demand that they only play scales until they have some level of basic proficiency.
Speaker: We don't do that in the visual arts.
Speaker: We don't do that in the humanities.
Speaker: We don't even do that.
Speaker: I mean, some science curriculum, unfortunately, do start there.
Speaker: But
Speaker: Why is it the mathematics gets relegated to just the basic tools that they were built?
Speaker: You know, algebra was Al-Khwarizmi's solution to these ridiculously complex Islamic rules of inheritance.
Speaker: And, you know, they would take years to figure out who got what.
Speaker: he made it efficient so that you didn't have to understand all of those complex ratios and proportions.
Speaker: Anybody could solve it.
Speaker: So how algebra becomes a gatekeeper when it's nothing more than a toolbox.
Speaker: Um, that's always been a great puzzle to me.
Speaker: The, the mathematics of that's been done.
Speaker: Um, it's how you use that in creative ways.
Speaker: That is the mathematics.
Speaker: I'll get off my soapbox now.
Speaker: There's, um,
Speaker: Michael said a word which I had on my nose to make sure I don't think I get everything in but he said gatekeeper there's a film coming out by director Vicky Abliss who also made the films Raised to Nowhere and Beyond Measure and it's called Gatekeeper Math in America and it's literally talking about really what
Speaker: current math education is doing it.
Speaker: It is a gatekeeper and we have sub gatekeeping within the curriculum, whether it be algebra later on, I think fractions is a gatekeeper.
Speaker: Absolutely.
Speaker: You know, like we move on from whole numbers, which is the complete fascinating idea of number theory and is, and is transfixed and mesmerized millions of people and has a branch in mathematics.
Speaker: And then we move on to fractions and give more time to fractions.
Speaker: To me, that's asinine.
Speaker: Like it is really like, I understand like a fraction is a number on the number line.
Speaker: And, you know, we need to know some conversion percentage and decimals and some common fractions and how they apply to practicality.
Speaker: But when we start getting at the multiply and dividing fractions with denominators past seven, eight or nine, I'm checking out.
Speaker: My daughter's already checked out.
Speaker: And so let's call for what it is as we're sort of, you know, getting to the sort of,
Speaker: tail end of this sort of a discussion, you know, it's gatekeeping.
Speaker: It's bookkeeping.
Speaker: That's what it is.
Speaker: No one's being inspired.
Speaker: No one's leaving the classroom more curious.
Speaker: No one leaves mathematics, generally speaking, more curious.
Speaker: And that's how we should measure what we're doing in our schools.
Speaker: Are kids still curious after they leave your classroom every day?
Speaker: They should be.
Speaker: That's not a tall order.
Speaker: Yeah, I mean, I think that we have the mindset now and we're thinking about it in these ideas.
Speaker: And I think that, at least in my experience, the best part of PD is always the questions, the troubleshooting at the end and figuring out specifics here.
Speaker: Let me see.
Speaker: this well I but the Q&A is this kind of works it kind of doesn't work so feel free to ask questions in the in the chat here for for anyone that that could answer it because we all have you know these backgrounds we could talk about these things but we've left a pretty substantial amount of time open like about 15 minutes here at a quarter of the time just answer questions briefly while you're writing those down I think it's a really important point to note that we can
Speaker: We can technically measure motivation and curiosity and things of that nature.
Speaker: I'm not saying that it should turn into a standardized thing necessarily, but having students reflect and give feedback on whether or not what you're teaching is interesting to them or whether they are motivated to learn more math after a certain thing is great data.
Speaker: And I am the complete opposite of a data guy.
Speaker: But being able to present that information
Speaker: to an administrator or to a co-worker where it's like, yeah, I missed, you know, 20% of the standards, but my students love this class and they're taking a lot more away from it.
Speaker: Chances are, if they understand that content really well and they're motivated to learn that content, when it comes to the brass tacks, which is really sad, but the brass tacks of standardized testing, they'll probably actually do better.
Speaker: Because they're motivated and they care about the thing that you're talking about even if they didn't necessarily check all the boxes off on the giant list of standards that may or may not exist Yeah, I guess you just mentioned standardized testing so here in Ontario we have standardized testing in grades three six and nine for math I
Speaker: I'm going to pull my, my daughter's in grade six, so I'm going to pull her out that day of testing.
Speaker: Not because she can't do the math.
Speaker: I don't want her to think that that's what math is.
Speaker: I don't want her to be poisoned by, okay, that's what the final distillate of math is, is circling in bubbles and doing these sort of, you know, generally inert questions and you did well on them.
Speaker: That's, I just don't want her exposed to that.
Speaker: I don't even if she got perfect for whatever that means, I don't even don't even get me started on, you know, assessment because the mathematics assessment is is completely, you know, crazy.
Speaker: But yeah, I just I don't want my kids and they've already been, you know, from well-intentioned teachers because they have to deliver the curriculum.
Speaker: But both my kids have checked out of math in terms of school math.
Speaker: Like they I used to ask them when they were early on.
Speaker: They were excited to tell me what they were doing.
Speaker: I don't even bother.
Speaker: I ask now just in terms of how their day is, tell me the best part of your day, and it never includes math.
Speaker: Yeah, so I'm gonna take Liana here, and then there's actually a question that we can answer.
Speaker: So Liana, you are on.
Speaker: wanted to go back just a tiny bit to something else that Neil said about when you ask, when you pose a problem to the students to find out how they feel about the problem, to start the problem.
Speaker: And
Speaker: I just maybe wanted to emphasize how important that is and also just take a piece of life experience as well to say that I loved math all growing up.
Speaker: I always loved math and I had a lot of excellent experiences in classroom and with teachers, but I still lacked a lot of confidence in
Speaker: I was always afraid to speak out in class and to think that I might get the wrong answer, that the right answer was so important.
Speaker: It was important to know.
Speaker: And I had the most fun doing math, usually on my own by myself.
Speaker: And then I went through engineering school and I
Speaker: I got out of engineering school the idea that you can solve any problem.
Speaker: Anyone can solve any problem just if you have enough time and enough resources.
Speaker: It's not always practical for you to solve any problem.
Speaker: But I think that that confidence and then going forward to the rest of my life and combine that with the math.
Speaker: It's something I never got from the math classroom that, whoa, here's a problem.
Speaker: You can solve this.
Speaker: It's just about being allowed to make mistakes and to fail and to go through this problem-solving process, which seems to be okay for engineers to do or in other departments.
Speaker: I would love to see students come out of a math class feeling uncomfortable
Speaker: confident that they can approach problems and then possibly solve them.
Speaker: I think that's a really good point and it relates to that concept, Sunil, that you were talking about with the hero's journey or about that process.
Speaker: Perhaps part of the way that we humanize mathematics is by placing more emphasis on the reflection and the questions that we ask as opposed to getting the one correct answer at the end.
Speaker: I just...
Speaker: I pulled those looking at some of my books and this one is by Theoni Pappas.
Speaker: This, and it's called the magic of mathematics, discovering the spell of mathematics.
Speaker: I'll just hold it up like that.
Speaker: But for me, if you just look at the title, like wouldn't that be like curriculum goals, the magic of mathematics, discovering the spell of mathematics for all students.
Speaker: Like this has already been cataloged and documented.
Speaker: And this is what,
Speaker: Like if you go into a bookstore, like you're going to see all these titles like this about math.
Speaker: Who's buying these books?
Speaker: Like all these people went through our system.
Speaker: So it's almost like they're trying to find, well, where is the light of mathematics?
Speaker: I didn't find it in school.
Speaker: Okay, that's where it is.
Speaker: And I, you know, for me, what is, I don't know, maybe frightening is the wrong word.
Speaker: It's too dramatic.
Speaker: But education is an institution.
Speaker: Right now, we're in this age of disruption where there's a lot of loss of institutional trust all across the board, government, journalism, education, et cetera.
Speaker: And that trust, it's like the law of thermodynamics.
Speaker: It's not being lost.
Speaker: It's being redistributed.
Speaker: So trust, which used to move up in terms of vertical, is moving horizontal among all of us.
Speaker: Look, we're here today.
Speaker: This wouldn't have existed maybe 10, 15 years ago.
Speaker: So there's a more democratized way of how we're sharing information.
Speaker: And once you start to share information, the truth of mathematics, i.e.
Speaker: the book titled Theone Pappas, The Magic of Mathematics, that's where our new vector is going to be.
Speaker: And institutions like education, they may be around for their half century, but their relevance is almost bordering obsolescence by the end of the century.
Speaker: And speaking to that point too about equity, I think it's important that we realize that those that have the most access to resources are the ones that are benefiting the most from wanting more creative fields.
Speaker: Like there is this false perception that we have to double down on a very regimented standardized test heavy math or any subject with the students that quote unquote need it most.
Speaker: So those that have the least access to resources, but
Speaker: There's a reason why someone like Elon Musk, for example, sends his three kids or two kids to a school that is entirely hands on that does work like this that he funded.
Speaker: People that have the most access to resources realize that this rote memorization is not the most important thing.
Speaker: So therefore, it's imperative for those of us that are working with students from all backgrounds that they also have access to the means of the few.
Speaker: And I think that we should also, if you want to address, Sunil, there was a question.
Speaker: You started typing the answer from, I believe it's Leitra.
Speaker: I could be pronouncing that wrong.
Speaker: I'm sorry.
Speaker: about the challenges and success in social justice and mathematics.
Speaker: We've spoken before about general scenarios, but just to kind of weigh in really quick, something that I find fascinating, someone who has a background in humanities, is not only looking at, for example, voter registration records and analyzing who
Speaker: is waiting in longer lines versus those who aren't, but then tracing that back through history through a mathematical lens.
Speaker: So for example, redlining and analyzing redlining maps and where these things are located and then tracing that even back to like slave codes or black codes.
Speaker: It's amazing what you can learn from mathematics inside the humanities, whether it be through English, a book or history or really anything.
Speaker: It's very, very interesting to me because I, you know, I just wasn't exposed to that growing up.
Speaker: So as a teacher, I had to learn about those things again.
Speaker: And it's been fascinating to see what can come out of it.
Speaker: The social justice lens, I mean, it opens up, you know, it gets into obviously the heart of equity and
Speaker: you know, access bias and barriers to success, all the things which are still currently embedded in our institutions.
Speaker: So, you know, when you start talking about social justice and math, you know, you're going to get the reactionary from people, you know, well, math is math, you know, and that's generally coming from, you know, communities which, you know, hold the power.
Speaker: You know, we're, why can't we just teach calculus and the quadratic formula and trigonometry and things like that?
Speaker: which is ironic because trigonometry is, you know, again, founded sort of Indo-Vedic mathematics, but none of the names are ever referenced to trigonometry from those people.
Speaker: But when we get into calculus, of course, and there's something that comes up in statistics, which came later on.
Speaker: So social justice is going to be, it's no longer going to be a niche kind of
Speaker: area of topic where one or two math educators spoke about it and spoke about it strongly.
Speaker: There is some amazing people.
Speaker: Dr. Chris Charles, who I am good friends with,
Speaker: He's one of the strongest advocates for social justice equity in terms of all across math education in the classroom, in publishing companies.
Speaker: You know, he's definitely an advocate for making sure there's representation in terms of who is seen doing mathematics.
Speaker: So he's.
Speaker: We're gonna go through some sort of bumps and bruises because it's gonna be pushed back from the entrenched community of power.
Speaker: But these are necessary battles to go through if we're gonna get to that humanizing end.
Speaker: It's not gonna be an easy road.
Speaker: And I don't want it to be an easy road.
Speaker: I want it to be fraught with some difficulties and challenges because that's what doesn't end us.
Speaker: Well, cliche, make us stronger.
Speaker: Yeah.
Speaker: And two, I think that sometimes when we look at things like this, it can feel very overwhelming because we feel like we need to make like an activity every single day that relates to one of these things and we have to reinvent the wheel.
Speaker: You know, a big part of progressive education and humanizing education is, you
Speaker: just coming up with topics or things that you think students might be interested in, or you just ask them, and then you figure it out together in the class, as in you have a lot of time for research where students are the ones coming up with the questions and they're the ones coming up with the answers.
Speaker: And the class might not always feel like a, you know, might not feel like a math class or like a history class or anything like that.
Speaker: It might just feel like,
Speaker: you know, people talking to one another about things, which means that yes, the content is going to be covered much slower.
Speaker: It's not going to necessarily have standardized assessment.
Speaker: It's not necessarily going to have a traditional test at the end with just a list of questions.
Speaker: But it will just be very interesting and everyone will be moving at different paces.
Speaker: The goal of progressive education and humanizing mathematics is not that the teacher spends four or five hours after school every day doing some research so that their class is cutting edge or innovative.
Speaker: Instead, it's you literally are, you know, getting rid of that power differential between teacher and student and just having a conversation together about things that matter to you and your community or things that are just interesting and then walking that path together.
Speaker: Well, the it wasn't a fluke.
Speaker: The last chapter of our book, Math Resist, I wrote with Dr. Chris Burnell, who's also a good friend of mine.
Speaker: That friendship comes up early in the book.
Speaker: And that's why the last chapter of our presentation.
Speaker: book is called, you know, mathematics is for friendship.
Speaker: That's its goal that, you know, because if you look at what friendship means, you know, friendship in terms of other things, like you need bond over a good meal or travel stories or music.
Speaker: Well, why can't we have mathematics be a conduit vessel to knowing each other to form friendships?
Speaker: And
Speaker: The deeper the mathematical exploration, freely, openly, candidly, the deeper the friendships.
Speaker: So there's a whole kind of, we're in this sort of, it's a galaxy formations.
Speaker: You know, we're a lot of swirling gases and we're going to eventually get to the contraction of these gases to form these old planets of this sort of new solar system of education.
Speaker: But right now we're in a swirling gas phase and it's very exciting.
Speaker: There's a lot of great discussions happening and even something like this is all part of going a long way to get us where we need to go.
Speaker: So I think that that kind of builds into our last part here.
Speaker: So I, again, want to thank you all for joining us and talking about this topic.
Speaker: It makes me very hopeful when a bunch of people show up to talk about, you know, humanizing education, because that if someone who's willing to give up their Sunday morning, uh, having a, uh, you know, pretty deep discussion on math philosophy and humanizing ed, I mean, that's, that's amazing and really cool.
Speaker: Um,
Speaker: And I encourage all of you to connect with each other on social media and talk about these things and ask questions.
Speaker: I know that, you know, one of my greatest joys as a teacher or as just a human being is to help people find connections and talk about these things and extending my reach beyond my four walls.
Speaker: And I'm sure it is for you all as well.
Speaker: I encourage you to check out Sunil's book, quick book promo there.
Speaker: Mathree says it's pretty cool.
Speaker: As well as visit our website at human restoration project org and again if you want to see more stuff like this our goal is to have at least one Special guest in every month for some free PD because why not?
Speaker: But it helps us kind of extrapolate our costs by visiting our patreon page which you can find a link right through human restoration project org Sunil any any final thoughts?
Speaker: Yeah, I mean, final for our session, but of course not final for anything.
Speaker: I'm just looking at some points that I was hoping to make.
Speaker: And there's one which I used in my TED Talk, which is Madame Curie's quote, you know, nothing is to be feared, it's only to be understood.
Speaker: There's a second part of that quote, which is never really shared.
Speaker: The first part is great on its own, but it goes on to say is, now is the time for more understanding so that we may fear less.
Speaker: And mathematics shouldn't be feared.
Speaker: And we shouldn't be teaching it as, okay, you should overcome your fear of mathematics.
Speaker: That's like giving into the idea that mathematics is to be feared.
Speaker: So
Speaker: I really want to get into hopefully what humanizing means is to, yeah, mathematics wasn't to be feared and really honing on Madame Curie's quote, which applies to so many things and definitely applies to where we need to go with math education.
