May 30, 2024 • 42 mins
Dan Finkel is an author/educator who believes that humans are wired to be curious from birth, and that play is the secret to maintaining that joy of learning throughout childhood. On today’s season 6 finale, he and Vanessa discuss how teaching kids about math can be so much more fun than we think; it can mean playing board games, counting on their fingers, anything that helps them develop an intuitive sense that there are patterns and structures in the world for them to discover. They also discuss how play-based approaches can even help grown-ups heal from math trauma!
About Dan (Website, Twitter, Facebook, LinkedIn)
Dan Finkel is the Founder and Director of Operations of Math for Love, a Seattle-based organization devoted to transforming how math is taught and learned. Dan is an author and game designer, develops curriculum, leads teacher workshops, and gives talks on mathematics and education. He contributes regularly to the New York Times Numberplay blog and hosts Seattle’s Julia Robinson Math Festival annually.
Show notes:
- Dan’s TED Talk: Five Principles of Extraordinary Math Teaching
- Martin Gardner’s “Mathematical Games” column in Scientific American
- earlyfamilymath.org
- Dan’s book: Pattern Breakers
- Upscale pattern blocks
Connect with us:
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Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Dan Finkel (00:01):
Math is basically supercharged common sense.
My perspective is we're all bornto love it Seeing young kids
naturally wanting to play withmath, none of them are like,
ugh, math, why do I have to dothis?
They just want to count, they'reinterested in shapes, they're
interested in patterns.
Kids just naturally want toplay, and they naturally learn
better from playing.
Vanessa Vakharia (00:20):
Hi, I'm Vanessa Vakharia, aka The Math
Guru, and you're listening toMath Therapy, a podcast that
explores the root causes of mathtrauma, and the empowering ways
we can heal from it.
Whether you think you're a mathperson or not, you're about to
find out that math people don'tactually exist.
But the scars that math classleft on many of us definitely
do.
Oh, and don't worry, nocalculators or actual math were
(00:43):
involved in the making of thispodcast.
Okay, I cannot believe thatSeason 6 is over.
Like, that flew by.
Over the last nine weeks, we'vecovered some of the biggest and
most pressing topics in matheducation today.
From building trust in theclassroom and giving students
real purpose, to the truemeaning of equity for literally
everyone, and today's finale,with math educator Dan Finkel
(01:06):
puts a beautiful bow on myfavorite theme for this season:
the inspiring movement towardsamplifying the joy, wonder, and
curiosity that fuels genuinelearning in our students hearts
and minds.
I don't know about you guys, butI've always been confused about
the idea of like, play in math.
I can't put my finger on it, butsometimes I get skeptical about
how those kinds of lovey doveyideas can actually help kids.
(01:29):
Which is strange if you thinkabout the fact that at my
tutoring center we make thestudents tea lattes and bedazzle
their calculator, so like, Idon't know what my problem is.
So if even I get put off bytrendy terms, I can only imagine
the average classroom teacherout there rolling their eyes at
some of the educationalcatchphrases we've been throwing
around on this podcast.
Well, Dan is here today to bringus down to earth and get
practical.
He's the founder of Math ForLove, and I have been a huge fan
(01:52):
of his forever.
We talked about the role of playin learning and therapy, and Dan
shares his belief that we areall born to like math, we just
need the right supports to stayengaged with it.
Dan, welcome to the podcast.
Thank you for your, what's thatsports term where you like put
someone in?
Dan Finkel (02:12):
Oh, the pinch hitting.
Vanessa Vakharia (02:13):
Yeah.
You're pinch hitting right now.
Dan Finkel (02:15):
Where, it's where I like to be.
That's right, just dropped in.
No prep, all improvised.
It's great.
Vanessa Vakharia (02:20):
I'm really, really glad you're here.
There's so much I want to talkto you about.
I don't know what those thingsare yet, but they're going to
come to mind.
I kind of want to start withwhat we were just talking about
when we forced David to pressrecord.
Dan Finkel (02:30):
Well, I think one of the things you said is you were
interested in, I'm alwayspromoting this idea of a play
based approach to matheducation.
And you were saying, I'm a highschool teacher.
This doesn't even make sense.
What are you talking about?
So, Yeah, so let me let me try.
So
Vanessa Vakharia (02:46):
I love that I'm getting you to ask your own
questions.
You're doing all the work.
Okay, yes, go.
Dan Finkel (02:51):
uh, so, so I started out as a high school teacher,
interestingly, and the longerI've been working, the younger
I've been working with.
So yesterday I led a session forpre K to third grade teachers.
Vanessa Vakharia (03:01):
Oh wow.
Oh my god.
Dan Finkel (03:02):
And I've been doing work with this nonprofit called
Early Family Math, it's likebirth to eight.
Because even when kids areshowing up in kindergarten,
there's like already differencesin math education, like a huge
amount of important stuffhappens.
You know, five and younger.
But part of the influence ofthat area for me, the working
with young kids is that playends up being this super
(03:26):
important part of it.
One of the things I like to sayis play is the engine of
learning for young children.
This is really well understood,in a way, and, you know, there's
been studies that have compared,like, for four year olds, you
have a play based approachversus a very didactic,
everybody sit down and staystill and then I'll tell you
what to do.
And and the kids just naturallywant to play, and they naturally
(03:47):
learn better from playing.
And my perspective is that thisis especially true when it comes
to mathematics, which I think ismore likely to be abused in the
sense that people will say,ignore your common sense.
Don't play around.
Don't experiment.
Just do what I tell you to do.
And like, if it doesn't makesense, whatever else is
happening, just ignore all thatand just repeat what I just told
(04:09):
you.
And at the same time, I thinkplaying with mathematics and
mathematical ideas ends up beingincredibly productive.
And the best workingmathematicians that I can think
of are the people who are intogames, into playing around with
things.
I used to have a professor whenI was studying math who would
(04:29):
say, like every problem he waslike, here's the game.
Because he would basicallytranslate the problem into a
game, and then you had to, like,figure out what the rules were
and play the rules to get yourending situation and translate
it back into the problem.
And so, just the idea of, like,you're always playing games,
you're always messing withpuzzles, that is somehow one of
the key skills.
(04:50):
You know, one of the greatinspirations from an earlier
generation was Martin Gardner'sScientific American columns,
which were called MathematicalGames.
That was the vision of like,
Vanessa Vakharia (05:00):
What was that?
Can you explain for us, youknow, Gen Z over here?
Dan Finkel (05:05):
Yeah, no, this was, this was like impacted a whole
generation.
He wrote probably, I'm not goingto get these dates right, but he
wrote for decades in ScientificAmerican from like the forties
to the late eighties or theearly nineties or something.
And it was the place wherepeople would go for mathematical
inspiration.
It's like, here's what's goingon at the forefront of the
(05:26):
field.
Here's magic tricks, cool newideas, here's puzzles.
It was all in one place.
He corresponded with like,everybody in the field and just
sort of was the one who waswriting for a general audience
and he inspired a generation ofmathematicians, engineers,
scientists.
But it was through a veryplayful, play based approach
Vanessa Vakharia (05:48):
Is this like an escape room situation?
Dan Finkel (05:52):
I would say not exactly in the sense that escape
rooms come in many flavors,though maybe there's a piece of
it there, but I think there issomething about the popularity
of escape rooms or, you know,Sudoku or all these things where
something in us that cravesthis.
Vanessa Vakharia (06:05):
Huh.
Dan Finkel (06:06):
And has a hard time identifying it as math and is
looking for it guises.
But anyway, so what I'm actuallyhoping is that this play based
approach, sometimes explicitlythrough playing with games,
playing with blocks,manipulatives, those kind of
things for young kids actuallystarts to influence upper
(06:26):
elementary, middle school, andhigh school, and we start to see
what is still a playful approachto mathematics, but in more and
more rigorous technicalproblems.
But, but that, for me, is one ofthe things that makes it really
fun, is when you have theseproblems that feel very playful
and very game like, puzzle like,whatever it is.
but they're still very, like,just interesting math problems
(06:48):
in their own right.
That's part of the fun of it forme.
Recreational math, I guess.
Vanessa Vakharia (06:53):
But hold on though because You're proposing,
are you?
I don't want to put words inyour mouth, are you proposing
that you're like, you're stillteaching the math concepts that
you're wanting to teach, like,don't worry, you're still going
to teach kids how to factorquadratics, we're just going to
do this in this place.
You are.
You're, Dan is nodding everyone.
This is a podcast.
Okay.
Dan Finkel (07:09):
No, no, absolutely.
Yeah.
And which is not to say, whichis not to say that you never
have to, sometimes you actuallyjust have to do a lesson and
it's like, okay, this is justkind of a little bit of a drier
topic and I need to just tellyou how this thing works.
That certainly happenssometimes.
But I think there's a hugeamount of untapped possibility
when it comes to justinteresting problems.
(07:30):
that are very playful, puzzly,interesting, have that quality
from recreational math.
And then, I think also what'sreally powerful is the skill to
take things that are dry andactually see what's interesting
and see what's fun about them.
I mean, in a way, what we reallywant students to do is not get
to the end of a problem and say,I'm done, what do I do next?
(07:50):
We want them to say, oh, Ifinished, but I was doing this,
and then I had another question.
Like, something else happened tome, and I wonder if I play
around with it like this, whatwould happen?
And those are the students who,when I see them, I'm like, Oh,
yeah, you're going placesbecause, that skill to Oh, no,
seriously, well, it's like, ifyou can ask the next question
Vanessa Vakharia (08:08):
Yeah, yeah, yeah,
Dan Finkel (08:08):
and be like, I'm not satisfied because I just did
what the teacher did, but Iactually, I'm going to play with
this myself, then they're theones who are owning it and
really gonna, I think, have asuccess in the field.
Vanessa Vakharia (08:20):
But it's interesting too, because I'm
not, I'm even thinking of itfurther of like, great, they're
going to have success, fine, butmore like, it's, it's not only
like, oh, they're, smart and I'musing air quotes, like smart
enough to ask the next question.
They actually give a fuck, likethey care enough to like, keep
going.
And like, isn't that a hugeproblem in math right now?
Is that so many kids don't seeany value or purpose in what
(08:42):
they're learning that they'relike, why would I keep asking
questions when I can just befinished?
Dan Finkel (08:47):
Totally.
Well, and this is one of thereasons I've gone down to work
with younger and youngerpopulations also, because my
perspective is young kids neverfeel that way.
They love math.
Because they're living in achaotic world, and math is this
incredible tool that's helpingthem to impose order on the
world.
(09:07):
So, so it's like, this is just,math is basically supercharged
common sense.
It's like, yeah, just what youdo to make sense of the world,
but now we're gonna help yousharpen that, and so you get
more and more control and moreand more power.
And so it's natural for peopleto feel like they own it.
The reason that so many peopleare traumatized is they go to
school and that control isessentially wrestled away from
(09:29):
them, right?
They, because, my perspective iswe're all born to love it.
Like this is meant to belong tous.
And if we go and see a teacherwho says, okay, yeah, you have
some perspective, whatever, thatdoesn't matter, ignore that,
now, just listen to what I say.
That's a fundamental perversionand inversion the natural state,
which is, no, this was my thing,and now you're telling me I
(09:50):
should ignore, like, shouldn'tmake sense, the thing that I use
to make sense of thingsshouldn't even make sense.
Like, so that is why people Ithink either love math or hate
it, and so rarely between.
We're born to love it, and ifthat's denied and that's stymied
and that's taken from us, thenwe learn to hate it, but we're
never neutral,
Vanessa Vakharia (10:08):
Oh my god, I have full body goosebumps right
now.
Well, no, because I'm reallylike what an interesting way to
look at it.
So first of all, this is apodcast about math trauma and
healing math trauma.
Dan Finkel (10:19):
Which is something I've thought about a lot, you,
as you can imagine.
Yeah.
Vanessa Vakharia (10:22):
Which is so cool.
But like, I want to go back tothis idea of like, we're born to
love math.
We're born to love math.
And this reminds me of all thenature versus nurture arguments
that are out there consistentlyof this idea, well, can anyone
do math?
Can anyone be good at math?
Like, is there a math gene?
When you say we're born to lovemath and then that's taken away
(10:44):
from us, that is such a powerfulsentiment.
But I guess my first questionis, what do you mean by we're,
all born to love math?
Dan Finkel (10:53):
Yeah, I mean, again, like, seeing young kids
naturally wanting to play withmath, like, none of them are
like, ugh, math, why do I haveto do this?
They're like, they just want tocount, they're interested in
shapes, they're interested inpatterns, because it's helping
them make sense of things andfeel more in control of the
world.
So it's just like, that's justthere from the
Vanessa Vakharia (11:11):
Wait, stop, say that, like, let's talk about
that though.
Like, it's funny because I, Ihated math for a long time, I
failed grade 11 math twice, andthen when I, you know, things
changed for me, one of thethings I found so, like I found
math really meditative.
There was this sense of orderand this sense of like poetry
and this sense of like,everything has its place and
when you can reduce a giantalgebraic expression down to
(11:33):
like one number, like it waslike, so like complexly simple.
But there's two things, like,you're kind of saying, like,
kids use math as a way tocontrol and make order of the
world, or math is used as a wayto control them.
Dan Finkel (11:47):
That's exactly right like it's something we have to
learn, but there is an instincttowards it, like there's an
instinct to want to make senseof the world, to want to find
patterns that will help usunderstand how the world works.
So the problem that you see inhigh school, I think, of kids
being like, why do I have to dothis?
Can I just be done with this?
I'm saying that's not a problemfor first graders.
(12:08):
They're, they're justinterested.
And even younger, the more,like, the younger, essentially
that is a special type ofignorance that is learned in
school.
Vanessa Vakharia (12:14):
Yeah.
Oh my God.
I love that.
I love that.
Well, yeah, because it's almostlike once you label something,
it's like when you like arereally enjoying hanging out with
someone and then they call youyour, their girlfriend and
you're like, Ooh, wait, what?
That's what we're doing?
Dan Finkel (12:28):
Yeah, maybe I have to think about that metaphor.
Uh, yeah.
Vanessa Vakharia (12:33):
Cause you're like, Oh, like you're having
fun.
And then someone's like, you'redoing math.
And then all of the connotationsthat come with math and your
inability to do it and what itmeans, do you
Dan Finkel (12:43):
My experience, like when I worked with high
schoolers, I feel like I wouldget kids who were in this
category of like, oh, just tellme when I'm done with this.
It was possible of almost all ofthem to show them some beautiful
result in mathematics and havethem still say like, wow, you
know what I mean?
And I just felt like, wow, itseems like it's so universal
(13:03):
that there's something in usthat responds to the beauty of
the subject and to the power ofthe subject.
And it would be so much nicer tonot have to try to undo all the
damage happens, in school, likewhen kids are in high school or
adults, and instead just kind ofdo it right in the first place.
(13:25):
And I think play for me is thecentral ingredient of this,
because play has a lot to dowith owning things.
It has a lot to do with makingyour own choices.
The things that you can't playwith are the things that aren't
yours, and the things that areyours are the things you can
play with, and the things youcan kind of break and mess
around with.
And there's just a deepconnection between play and
ownership, and some big part, Ithink, of liking math and also
(13:49):
success in math has to do withfeeling ownership over it,
feeling like it's yours, feelinglike, you know, you're on board
with this project.
So it's true, there are allthese hypotheticals of like,
well, what if this way leads tosuccess, but this way leads to
people feeling better about it.
I think most of the time, thesame approach can give you both
of those things.
usually not a fundamentaltension there, fortunately.
(14:10):
If kids didn't come in alreadyliking math, it would be a lot
harder.
But the kids do arrive at schoolready to just like math.
So,
Vanessa Vakharia (14:19):
Well, I guess like at certain ages, yes.
But as you were saying, evenlike in kindergarten, like, I
run a tutoring center, like,that's what I've done for,
almost 20 years.
And I actually find that, Ithink this is for a variety of
reasons, but like more and morelately, do I get kids who are
like, parents are like wanting atutor for their three year old.
And like, the reason is becausethey're already anxious about
(14:41):
math or they're already sayingthe words, I hate math.
And they're three.
Dan Finkel (14:45):
Gosh, I haven't seen three year olds saying they hate
math, that's tough, that ishard.
But, There certainly are hugedifferences when kids are
arriving at school that I'maware of, and I think that's
zero to five.
Vanessa Vakharia (14:57):
Like what?
Dan Finkel (14:58):
I mean, kindergarten readiness is just a huge issue,
and there's kids who show up.
Vanessa Vakharia (15:02):
It is?
Dan Finkel (15:02):
Oh, yeah.
Oh, yeah.
Vanessa Vakharia (15:05):
Like, what are you, aren't they three?
How old are you in
Dan Finkel (15:07):
Kindergarten starts at five.
Yeah, this is in the U.
S., yeah,
Vanessa Vakharia (15:11):
So what needs to happen?
Dan Finkel (15:12):
Well, there's some kids who show up knowing their
numbers to 20 or beyond, who arejust comfortable playing around
with numbers, who have like,played with blocks a lot, and
kind of have a sense of howshapes fit together.
Often, like, number lines, likethe proto number line skill is
like, have you played Sorry oryou know, Shoots and Ladders.
(15:33):
Can you advance a piece on aboard in a
Vanessa Vakharia (15:35):
What?
Dan Finkel (15:35):
line?
Parcheesi.
Kindergarten teachers will tellme, like, Oh, I know the kids
who've been playing board gamesat home where you have to move a
pawn on a board, and those whocan't.
Because some of them intuitivelyget number lines or related
types of things, and some ofthem don't.
And, so, again, this is likethis play based approach.
If you've been playing aroundwith things.
(15:56):
a lot of the early math topicsare really natural and feel
straightforward.
if you haven't, then you'rebasically already kind of behind
in kindergarten in the sensethat you've got some kids who
are just ready to start thinkingabout numbers and, Oh, what if
you put them together?
What if you take them apart?
Sort of addition, subtraction,counting up higher.
(16:17):
And then you have others who arestill trying to grasp like
numbers within 10, just basiccounting and cardinality.
Vanessa Vakharia (16:24):
That's so crazy to think that at that
young of an age, that there'salready, like, this difference
building, and so much of it hasto do with, what's happening in
the home, because I can imaginethat must be so stressful for
parents.
Like, I actually need you togive my friend parental advice
right now, I didn't think ofthis, but she was, she was
saying her daughter, she's like,well, we try to do math games
with her and stuff, but she justdoesn't like to do them, like,
(16:46):
she'd rather do, like, roleplaying games more like story
based games.
But it's interesting because myfriend hates math and is like so
anxious around her own math.
So I'm kind of like, is this athing where it's like your
daughter's just picking up onthat?
Is it a thing where like shelegitimately doesn't want to do
it?
Like, what do you do in thatsituation?
Dan Finkel (17:03):
Research seems to suggest that kids do pick up on
it at very young age.
And yeah, and usually by likearound second to fifth grade,
girls have a sense of like, mathis a boy's subject.
That is, and often the parents,it's like very powerful, the
signaling.
Um, however, so I've beenworking with this organization,
Early Family Math,EarlyFamilyMath.org, if anyone
wants to go, there's like tonsof free materials there.
(17:24):
The goal being like, how can wehelp people have a good time
with their kids around math froma young age?
And the line that is the mostwidely known thing that I've
ever said is what books are toreading, play is to mathematics.
Vanessa Vakharia (17:37):
What books are to reading, play is to
mathematics.
Dan Finkel (17:41):
The point being that we all know we're supposed to
read at home with our youngchildren.
There's this campaign of like,what do you do?
Hey, you want your kids to read,read to them, get a book.
From the moment they're born,right, so then it's like, okay,
well, what do you do for math?
And the answer is you've got tobe playing with kids, but it's a
type of playing that has to dowith counting and organizing,
(18:05):
but also like patterns.
In a way, jokes are kind ofmathematical in the sense that
you,
Vanessa Vakharia (18:12):
Like the formula of a joke?
Dan Finkel (18:14):
Yeah, you set up a pattern and then you break it.
You know, it's always like thefirst person does this, the
second person does this.
But the third person, you knowwhat I mean?
It's always like, um, And I hada really interesting experience
with this because I have nowwritten a children's book, which
is called Pattern Breakers.
And I read it in my kidspreschool class.
And the game is there's a littlegirl who is looking for these
(18:36):
monsters called the patternbreakers and they're hiding
behind different colored dots.
But they always break thepattern when they hide.
So it goes purple, yellow,purple, yellow, purple, yellow,
purple, yellow, blue.
And she's like, wait, what doesthat blue one doing there?
And then there's a littlemonster behind them.
And that's, and so it's sosimple, you know, very, but what
happened when I read it is whenwe're doing this, the kids were
(18:57):
erupting in laughter and theyweren't erupting in laughter
because the monster was there.
It was just that there was apattern that set up an
expectation that then switched.
And that was all they, yeah, andso it was like, that was so
funny to them.
I was like, that is reallysurprising
Vanessa Vakharia (19:12):
This is insane.
Dan Finkel (19:14):
Yeah,
Vanessa Vakharia (19:15):
I love this because people always ask me
what should you do with yourkids and you're always like well
do math with them in the kitchenlike do, but you're right,
you're just like, play games.
Dan Finkel (19:23):
Playing games is huge.
Anything with dice, anythingwith cards, anything where
you're moving pieces on a board.
It's like, anything where you'rekeeping score, like all of that
is like involving numbers in aplace where just kids want to do
it.
But then even more basicallylike, when I had, you know, a
kid under one year old, I feellike I was always doing little
fun, like, pick up and kiss kindof games, but you do it on the
(19:45):
count of three, right?
Like, one, two, three.
Then maybe you go to foursometime, and it's a surprise.
I have videos of, like, my ninemonth old, and I literally, you
say, one, and like, they justjerk to attention because they
know something fun is about tohappen.
Then two, and they're just likewaiting for what's going next.
And it's just to have that builtin where it's like, this is part
(20:05):
of what organizes time,organizes our, our time
together.
So we, while we play, because ifI hadn't done that, then it
would be less fun.
There'd be less anticipation ifthey didn't know there's this
regular sequence that always hassomething fun happen at this
point.
Vanessa Vakharia (20:21):
Yeah I just interviewed Francis Su and he
was saying similar, like totallydifferent, but he was talking
about how he does somethingsimilar where he uses his
fingers and he goes, so I'mholding up one finger right now
and I'm up another, and he'llsay, you know, well, how many
fingers do I have on this onehand?
And the kid will look and sayone.
And on the other hand, one, andthen like doing this and the,
and his little kid will be ableto say two.
(20:43):
Okay.
We delete this because thismakes no sense.
Okay.
Anyways, go listen to Francis.
Go.
Dan Finkel (20:48):
All visual, yeah.
Vanessa Vakharia (20:49):
Anyways, the point is that like, I think it's
really cool because these areall, I don't want to say like
easy, such a bad word, but Ithink these are accessible
things that basically any parentcould do.
Even if you hate math and arethe most anxious, you're
probably doing it anyway, it'smore about like, right?
Dan Finkel (21:03):
Yeah, this is one of the main things is math is in
all our lives in these small,these small ways and just to
identify it as like, oh, I'mactually doing it in this little
way and it's helping me.
And even like with young kids,just even talking about over
under, positional stuff ends upbeing very important for math
development.
There's a lot of littletechnical things that are like,
(21:23):
Oh, if they count something, youlike, say how much they count at
the end.
It's like 1 2 3 4 5.
And you say, Oh, yeah, there's 5Cheerios or whatever, that sort
of emphasizes that, like, that'sa technical point about like,
Oh, the number at the end sort
Vanessa Vakharia (21:37):
means
Dan Finkel (21:37):
the amount of the whole thing.
But playing is really the keyelement.
Vanessa Vakharia (21:41):
So, okay.
So I think it's reallyinteresting because like, I got
into like a lot of internettrouble, a lot of hot water,
shall we say,
Dan Finkel (21:47):
ok
Vanessa Vakharia (21:47):
a few weeks ago, because I was talking about
the times tables on TV and Isaid, I believe kids need to
know the times tables.
I don't believe they need tomemorize them.
And what I meant was like, yes,you should have math facts
stored in your brain, but likerote memorization is not
necessarily the way to getthere.
And then what I said, you candisagree with me by the way, but
what I said was, I said, it'slike when you learn not to touch
(22:09):
a hot stove, it's not becauseyou've memorized that rule in
your head, it's because, youfigured it out or you've
actually done it and it's beenhot and you've learned a lesson
or like dah, dah, dah, dah, dah.
You hate it.
You hate that.
Dan Finkel (22:20):
Well, no, no, I know exactly, I think I know exactly
what you're saying and whatyou're, where you're coming
from.
This is a tricky communicationpoint because I think it has to
do with the word memorize.
So in math, there's this bigquestion, like, what things do
you need to have memorized andwhat things do you not?
And I think people can disagreeon that, and people do.
I personally believe thatmultiplication facts are
something that you definitelyneed to have in your, like that
(22:43):
needs to be automatic at somepoint because it just slows you
down too much later, it's toohard to not have that.
And how do you get there?
And I think what you're saying,when you're saying don't
memorize them is you don't wantit to be like disconnected
facts.
You want it to be like, Oh,here's just like 6 times 8, 48,
that's just like I learned thislittle rhyme.
Vanessa Vakharia (23:02):
Exactly.
You don't even know it's sixgroups of eight.
Like you don't know what it is.
Dan Finkel (23:06):
Exactly.
like, we have this with squarenumbers for people like, Oh,
know, 6 squared is 36.
But like, Oh, it's actually asquare and like connecting that
to the area of a square.
Like, Oh, I never thought thatthat was connected.
Um, so what we want is theautomaticity to be growing, not
just out of rote practice, butout of a sort of a connected,
contextualized understandingwhere you're actually learning
what the things mean and have adifferent representations for
(23:29):
them in different ways tounderstand them, but then also
get them in your memory at somepoint and have them down cold.
That's where I fall on that.
Vanessa Vakharia (23:37):
But so fine.
Yes.
I agree.
But this isn't even, so that wasone argument.
But the thing that I wanted tobring up is what people kept
commenting, one of the comments,like other than calling me like
an idiot and saying that Ishould get off the internet and
girls with sparkly eyeshadowshouldn't comment on math.
Other than those comments,People kept saying, this idea of
like.
(23:58):
it's in our genetics or likeit's in our biology to, to not
want to touch something hot.
But that math is not somethingthat's like in our genetic code.
And you, you, I'm still on thispoint of your, you being like,
as babies, like we are all, bornwith this, I
Dan Finkel (24:17):
Well, it's an instinct towards math
Vanessa Vakharia (24:19):
Yes, yes, that's
Dan Finkel (24:21):
it's true, and now suddenly I want to be careful
because it is true that thedeeper you go in mathematics the
less natural it does feel and
Vanessa Vakharia (24:30):
Sure, but we were talking about, like,
patterns in the just Like, we'retalking about math.
Dan Finkel (24:35):
I think there is something fundamentally
appealing about that and we arefundamentally drawn towards like
the symmetries, the patterns,the sort of sense of like
simplicity and beauty that comesout of those things.
I do think that is that has aninherent appeal.
Yeah,
Vanessa Vakharia (24:51):
And this isn't a science podcast, for everyone,
not like we're like, oh, there'sresearch, just talking about
what we know, and what we, whowe've talked about, and like,
whatever, and just ponderingthis, so no one cancel us and
everyone chill.
Dan Finkel (25:02):
I mean, partly, I'm also aware of how easy it is to
be misunderstood, I think, whenyou, like, put something
forward.
Vanessa Vakharia (25:09):
But we've always counted, like, there's
always been, like, a need tofind pattern, order.
Dan Finkel (25:15):
But this is an interesting point also because,
you know, there are somecultures which don't have, like,
number words that go beyondthree, say.
Vanessa Vakharia (25:22):
Ok.
Dan Finkel (25:22):
It's like one, two, many.
And this is going really deep inthe weeds now, but there's like,
there seems to be a hardwiredunderstanding of number that
goes up to maybe, three or four,and then there seems to be
another sort of hardwired sortof estimational ability of like
more or less in larger groups,but that's not connected to like
the actual literal number.
(25:43):
But then I think we develop thetool.
So so how do you say this?
I think there is a fundamentalinstinct towards mathematics
that has to do with the draw topatterns, and being able to make
sense of the world throughsimplifying and through finding
underlying order.
And then there is also thisinstinct towards the beauty of
(26:05):
it and towards the power of itand just what it gives us in
that sense.
But then a lot actually doeshave to be developed.
And the development doesn'tnecessarily happen on its own.
I don't know what this tells usabout the arguments you are
having with people online aboutthe times tables.
Vanessa Vakharia (26:20):
That I'm right about everything.
Dan Finkel (26:22):
I don't, Yeah, I don't, I don't have enough
background to even totally getwhat are saying there.
But, um,
Vanessa Vakharia (26:27):
Okay, what you need to know is the internet a
cesspool and we're moving on.
Dan Finkel (26:29):
That I agree with.
That I think is clear, yeah.
Vanessa Vakharia (26:33):
So I, do, do people ever say to you like, Oh
my god, Dan Finkel and his mathplay.
Like, are people ever like, wedon't have time to be playing
around.
Dan Finkel (26:42):
Yeah, I get that less than you would think.
I actually would almost expectto get it more.
But I think, this is again acommunication thing.
I never want people to hear"play", that just means, oh, we
just mess around and we don'tcare.
What I'm trying to say is, Iactually feel like math, as it
is often taught, the math, Iguess, that traumatizes people,
(27:03):
right?
The math that people needtherapy for, uh, is the math
that because it's so notplayful, but it's actually a
much more superficial kind ofmath also.
The math is much less deep, it'smuch less interesting.
The understanding that comesfrom it is much more fragile.
It's the kind of thing whereit's like we spent so long
(27:23):
saying, here's exactly how to dothis kind of problem.
And then the test has one worddifferent and everyone misses it
on the test and the teacher'slike, why did they change that
one word?
Like I've been teaching themthat every time they see the
word difference it means this
Vanessa Vakharia (27:35):
Yes.
Dan Finkel (27:35):
But they use it this way.
The test is doing that onpurpose because they're trying
to see how fragile the studentsknowledge is.
And we want a robust knowledgewhere, you know, you change the
word and kids like, well, Istill get it because I've like,
I don't just have one path.
I've been like exploring all thewoods, you know, and like, if I
get a little off, I can comeback in another way.
That's what we want.
And you get that from playing.
Vanessa Vakharia (27:57):
I'm realizing I had my back up whenever people
are like, math play, it liketurns me off so much.
And I'm, and I'm wondering,like, now, hearing you talk
about it, I'm like, Oh, my God,yes.
But I guess, to me, it seemedalmost like a trite, silly word.
Like Oh, he just wants me tolike, play with like toys or
manipulatives.
But that's not at all whatyou're saying.
Dan Finkel (28:17):
What I'm saying is that the invitation to play is
what will help get into muchdeeper
Vanessa Vakharia (28:22):
What is my problem with the, why did the
word play throw me off so much?
Dan Finkel (28:25):
In fairness, a lot of people have that, I think,
and maybe I should expect moreof a backlash.
Maybe if I get a little morepopular, I'll get more of a
backlash.
Vanessa Vakharia (28:33):
No, no, no.
Well after this podcast, watchout.
Well, I get the same thing maththerapy though, right?
People are like, therapy.
And you're like, well, hold on.
Dan Finkel (28:41):
Though I will say, you're also, you're doing high
school, that's where I started,but it's less and less my focus
these days.
Vanessa Vakharia (28:46):
Sure.
but it's almost like even moreimportant, like the way you're
talking about it.
I'm like, Oh my God, like, thinkabout gaming, it's like
teenagers love playing.
They just, they wouldn't want tosit around and play with a toy,
they would think that waschildlike, but like, they're all
playing video games, they're alllike making TikToks.
Like they are engaged.
And I like the way you put itbefore.
What did you say?
It wasn't extracurricular math,was it?
(29:08):
Uh, recreational math.
this idea of recreational,they're doing sudoku, they're
doing their wordle, like,
Dan Finkel (29:13):
Yeah, thing that I do that, like, gets the most,
online views of anything is Iauthor these TED Ed riddles
sometimes.
Vanessa Vakharia (29:20):
Ooh.
Yeah, people love riddles.
People love a riddle.
Dan Finkel (29:23):
The internet loves riddles.
It's funny, literally, it's likea side project and I just do it
because sometimes I have a goodidea for a riddle and so I've
written a few of these and it'slike, 2 million views, 5 million
views and it's
Vanessa Vakharia (29:33):
You're so famous.
Dan Finkel (29:35):
Well nobody knows, they're animated also, like,
that's the whole, that's TEDreally
Vanessa Vakharia (29:39):
Sure, we should put your face in there
though, if you want to startgetting some haters.
Dan Finkel (29:42):
I keep telling them, I'm like, just like slap my face
on there!
Vanessa Vakharia (29:45):
Oh my god.
Okay.
Listen, I have to like wrap upsoon which is sad because this
has gone by so fast.
Um, What do we think of play orrecreational math or what you're
talking about as a part of maththerapy.
Like math therapy to me has fivesteps and like those steps
involve you know, learning aboutgrowth mindset, rewriting your
story, unpacking trauma, likefinding motivation.
(30:06):
I feel like, this idea ofincorporating play as a means
for students to get to knowthemselves and how they think
and develop this curious, like,I don't know, like there's
something there for me.
What do you think?
Like, does play have the powerto heal?
Dan Finkel (30:19):
I think yes.
I think definitely.
I mean, there is, for youngkids, there is a thing called
play therapy, right?
It's a tricky question.
Play requires a kind of safety.
Like, if you feel like you'rebeing judged, feel like the
stakes are really high, it'svery hard to play, unless you're
like a professional and this islike you've prepared.
Um,
Vanessa Vakharia (30:37):
Oh my god, sports are playing!
Dan Finkel (30:39):
Yeah.
We do it everywhere, right?
Yeah.
Vanessa Vakharia (30:42):
We play in a band! Oh!
Dan Finkel (30:44):
Yeah, music, theater, right?
You are in a play.
Vanessa Vakharia (30:48):
Oh my god.
Dan Finkel (30:49):
Yeah, there is a kind of frame which defines the
space, you know, the rules ofthe sport or the rules of the
game or the lines of the play,whatever, but then there's
within that frame, there isspace for you to put yourself in
there also, and kind of say,okay, how am I going to
contribute to this?
What of this would only be thisway because I'm the one doing
(31:10):
it.
That's something very powerfuland I think, I think it can heal
in some cases, but it definitelycan help grow and help you learn
about yourself.
Um, and I think it just feelsvery positive to do that.
Like we all want to feel likewe're important enough that like
the thing would not be exactlythe same if somebody else did
it.
Vanessa Vakharia (31:26):
Oh my god, yeah, we're all so self
obsessed.
We all want to be the maincharacter of our math question.
Dan Finkel (31:31):
Yeah, sure.
Someone gave me this advice oncethey said, someday you'll have
kids and you'll be sending themto kindergarten.
Here's how you pick akindergarten.
Go to the school, look at theart on the wall, and if it all
looks the same, don't send yourkid to that school.
The idea being like, that's allframe.
We're like, here's the rules,first make this, then do this,
and they're like, yeah, we wouldnever do that with art.
(31:53):
Like, we would know that that'snot gonna be good for kids to
control every movement they makewith art because part of art is
to put yourself into it, youknow, express yourself, all
those things.
And yet math, how many mathexperiences would rise to that
level, right?
Mostly you're like, if you didit right, it should look exactly
everyone's else.
And I could take you out and putsomeone else in and it doesn't
(32:15):
matter.
Right?
So
Vanessa Vakharia (32:18):
This is blowing my mind! You're speaking
to like the ego in me.
Like yeah, what the fuck?
Why am I not, why is this notcentered around me?
Dan Finkel (32:26):
Well who would want?
I mean, nobody wants to be like,Oh, I could just do something
else and you could do it.
Right.
And I think that's why there'salways this question, like, why
do we have to do this?
I finished, can I like go now?
Like, is this what they want meto do?
You know, it's just like, whenam I ever going to use this is
the classic, which isn't sayinglike, Oh, in 20 years, like
you're going to need to groutyour floor, and so this is like,
you'll know how much grout tobuy.
(32:47):
It's like right now you'reasking me to do something really
weird, cause like.
I don't even need to be here forthis.
And so I think that theperspective of like, we need to
be framing experiences wherethere are really clear, rigorous
technical rules, like in a sportor a game or in music or a
theater or whatever, but there'sstill space inside where you can
(33:09):
actually put something ofyourself.
And so you made something andmaybe you make something and it
still has to like satisfy therules, but it, it wouldn't be
the same if somebody else didit.
I do think that that can behealing to experience especially
if you haven't before.
Vanessa Vakharia (33:23):
And just that sense of belonging, finally
feeling like there's a reasonfor you to be, I love that you
said that, there's a reason foryou to be there.
You.
Dan Finkel (33:30):
And I'll tell you, I, so I gave a session yesterday
at, it was pre-K through thirdgrade, but we were doing some
things with pattern blocks,using actually our upscale
pattern blocks developed byCanadian Nat Banting, who's,
they're super cool.
Anyway, we were talking about,like, there's these different
sizes of pattern blocks, andwe're talking about how many of
the little triangles would taketo cover the big one.
And someone was like, well, Isort of see, once I see them in
(33:51):
the little triangles insidethem, I see how I could fill
them up and do this.
And I was like, oh, that's areally great observation of how
it works.
And they were blown away thatsome idea they had was like,
somebody thought it was a goodidea.
You know what I mean?
And she had this very sort ofheartbreaking line, which was,
she actually commented later tothe group, she was like,"I've
(34:12):
never really loved math until Iguess until today".
Vanessa Vakharia (34:16):
But how cool is that for you?
Like it's never too late.
Dan Finkel (34:19):
Well, this is why I think your perspective of math
therapy, I have said this for along time, but I feel like my
first interaction with teachers,especially elementary school
teachers is often therapy.
Like that's what the firstsession is, but it is also a
session that is play based andis very non judgmental and is
something where they can feellike whatever they do, it's
like, oh, there's something tolearn in whatever you did.
(34:41):
And like, you're contributing.
If you participate, you'recontributing.
Vanessa Vakharia (34:45):
Okay.
I have to ask you this becauseI've been dying to unpack this
with you and I, I literallyquoted you saying this in my
book, but I never dreamed Icould ask you in person what you
meant.
So do you know what I'm talkingabout?
You have this quote basicallywhere you're like, it's bullshit
to tell everyone that there aremath people.
Dan Finkel (35:01):
Yeah.
Vanessa Vakharia (35:02):
Can you just tell me what you mean?
Because, and I say this everytime I'm like, for me, the goal
of math therapy is to help everystudent build a better
relationship with math, even ifit's like the teeniest better
relationship with math.
And whenever people are like,what if like, they really can't
do it?
Or like, you can't tell kidsthat they can all do math.
I'm like, I'm not saying thatI'm saying they can all build a
better relationship with maththan they have right now.
(35:24):
But we do want to be sayinglike, you know, there's a lot of
discourse being like, we shouldtell everyone they're math
people, everyone can do math.
Dan Finkel (35:30):
Yeah.
I am very nervous whenever themessaging is like, let's all
just tell everybody this thingand that'll solve the problem.
Talk is very cheap, uh, ineducation, and fads are endemic
and it's very easy to be like,you just say the right thing,
and I just feel like thatdoesn't address what the real
problem is.
And it leads to a place whereit's almost harder because the
(35:51):
kids are smart, they know if theteachers are BSing them, know,
you know, if the teacher says,like, you're all math people,
but like, you got it right, youdidn't, you're smart, you're
dumb.
I mean, they infer all of that.
So when it comes to saying,like, are you a math person or
not?
Where I want people to be is Iam not afraid of math.
I can use it as much as I needto and that's not going to scare
(36:14):
me.
I'm not going to, like, give upon my dream of being an
architect or a veterinarian or anurse because I can't pass the
requisite math courses, and Isee why someone else would
really love this subject.
I remember I think my youngerbrother at one point like
visited France and he had neverlearned another language and
he's like, Oh, I see how I couldlearn French, but I'm not going
to.
Vanessa Vakharia (36:33):
Yes, that's empowering.
That's what I think too.
It's like just changing yournarrative to be like, I guess I
could do this if I want to, butI'm going to choose not to.
Dan Finkel (36:42):
Yeah.
And which is fine.
Like, not everybody needs tolike, go into the deep recesses
of mathematical research.
Like it's fine.
Vanessa Vakharia (36:48):
Do something else.
Dan Finkel (36:49):
But, but, but I had something really similar with
art.
Actually, I was always afraid ofart.
I was always really bad at art.
I think I used to say, like, Iwas so bad that I would like
make people worse at drawingjust by like drawing next to
them.
Vanessa Vakharia (37:01):
That's ridiculous.
Dan Finkel (37:02):
Well, no, I mean, but at some point in college, I
was like, this is ridiculous.
I'm going to take an artfoundations class.
This just seems dumb.
I learned the basics.
I was like, I'm never going tobe a great artist, but I could
learn this and get decent at it.
And it was a nice thing to justfeel like, yeah, that's totally
in me if I want to pursue it.
So, yeah, I think we could allbe decent in mathematics if we
(37:25):
wanted to.
Um, not everyone can be aresearch mathematician.
That's very hard.
Vanessa Vakharia (37:29):
I think it's actually a really important
message because you're right.
If you're saying to someonelike, no, everyone can, fly to
the moon, people are gonna belike, okay, that's ridiculous.
Like,
Dan Finkel (37:39):
you know, this is, there is a part of me that even
if things are right and true, Iget nervous once everybody
starts, once it becomes kind oflike the common wisdom, like
growth mindset is a little bitlike that for me, where I'm
like, yeah, seems totally legit,totally right.
And yet, there's something in methat when, like, we're preaching
growth mindset to kids all thetime, just like, I start getting
(38:00):
a little nervous.
Vanessa Vakharia (38:00):
Why?
Dan Finkel (38:01):
Well, it's too easy to say it, I think, and harder
to do it, and I just feel like,and, yeah, and what I really
want is for teachers to maybetalk about it less to kids, but
maybe work on it morethemselves.
Vanessa Vakharia (38:16):
100%.
Oh my god there's a wholechapter in my book about this
that's coming out.
Because the whole thing too withgrowth mindset is, this is like
being like, I believe I can getjacked, I believe I can be
ripped, but I'm not going tochange any of my behavior.
I'm just going believe it canhappen.
It's like, no, I need to believeI can get ripped and then I need
to go to the actual gym.
Like, you know, it's like wenever get to the behavior part.
(38:37):
You can't just tell kids likeyou can do anything.
You've got to prove it to themand give them opportunities to
discover that within themselves.
Dan Finkel (38:43):
Yeah.
Yeah.
So I think that's where I getnervous.
Vanessa Vakharia (38:45):
Yeah, the just saying it, like the poster on
the wall aspect of it.
Dan Finkel (38:49):
Right.
And education is so susceptibleto fads, kind of, easy answers.
There's a great line, uh, aboutthis, which is that school
change is measured, not inyears, but in generations.
For me, the thing it's like,okay, you could just got to be
in it for the long haul and youcan't just be like, Oh, what's
going to fix this quickly.
It's
Vanessa Vakharia (39:06):
Right now, yeah.
Dan Finkel (39:07):
Settle in, get ready for this to be like a lifetime
project.
Vanessa Vakharia (39:11):
Okay, final two questions.
You have to answer them inliterally 30 seconds.
We can't do this anymore.
Okay.
Dan Finkel (39:15):
But it's so fun to talk to you, Vanessa!
Vanessa Vakharia (39:17):
I know I'm having so much fun, but like
actually David's gonna kill me.
Okay, number one.
What is the one thing you'd liketo see change about the way math
is taught in schools?
Dan Finkel (39:27):
Jeez
Vanessa Vakharia (39:28):
Your face is so good.
Dan Finkel (39:29):
That's like a huge question! The number one thing,
um
Vanessa Vakharia (39:34):
This isn't like picking your favorite
album, like just say something
Dan Finkel (39:36):
Yeah, no, no, I mean, I, coming from a sense of
sense making for students, Imean, and we've been talking
about play based approach.
Maybe I'll say like, have moreplayfulness in it as a, as a
short answer.
But there's, I, that's like abook in itself.
Vanessa Vakharia (39:51):
You look stressed.
Dan Finkel (39:52):
That's a stressful question.
Because I'm like anything I sayis incomplete.
Vanessa Vakharia (39:56):
Yeah this is like timed Exactly.
Okay.
Final question.
And you kind of already answeredthis, but whatever.
What do you say to someone who'slike, Dan, this is such a great
talk, but like, I'm just not amath person.
Dan Finkel (40:09):
Yeah, what I usually say is, that's a very reasonable
thing to feel, based on theexperiences you've probably had
around math.
Uh, however, there, you know,that, you know, that's, that's
reasonable and there may be somethings in math that, you know,
you would have a differentexperience with, like school
math is not the same as whatmath actually is.
(40:32):
But I think just being toldlike, Oh, you actually are a
math person.
That doesn't actually, yeah,people, people are like, you're
telling me to not like trust myown eyes.
Vanessa Vakharia (40:40):
Right.
Right.
Okay.
Okay.
We're done.
I have to say goodbye to you.
Like, if you could see David'sface right now, he's like, I
gave you the ten minute warningfive times.
Dan Finkel (40:50):
What a pleasure.
This was so fun.
Vanessa Vakharia (40:52):
I'm so glad that's your reaction, especially
because I felt like I kind ofstalked you to come on the
podcast.
Dan Finkel (40:57):
Not at all.
This was great.
Vanessa Vakharia (40:58):
This was amazing.
I'll talk to you later.
Dan Finkel (41:00):
Ok, bye bye!
Vanessa Vakharia (41:00):
Bye! I loved every second of that.
And honestly, I mean, you guysprobably hear it in my
interviews, obviously I lovemath and sometimes I get so
excited about learning somelittle trick or finding some
curious little discovery, butrarely would I think of
associating that stuff with theword play.
But that's what it is.
Who cares if it sounds cheesy?
Say it with me.
(41:20):
Learning can be fun.
I am all in on this playconcept.
I love the idea that learningcan be a joyful discovery and
not just cramming some numbersand facts into your brain so you
can get a good mark on a test.
Well, season six in the can orin the bag or whatever people
say when something's done.
Thank you as always forlistening.
It means so much to me to knowthat these conversations aren't
(41:41):
just helping me but they'rereaching students and teachers
and parents who just want thebest for our education system
and our future.
I would love to hear what youthought of this season and who
you'd like me to interview forthe next one.
So hit me up.
If something in this episodeinspired you, please tweet us
@maththerapy, and you can alsofollow me personally@themathguru
on Instagram, Twitter, andTikTok.
(42:04):
Math Therapy is hosted by me,Vanessa Vakharia, it was created
by me and Sabina Wex, and it'sproduced and edited by David
Kochberg.
Our theme music is by GoodnightSunrise.
And guys, if you know someonewho needs math therapy or just
needs to hear someone elsegetting math therapy, please,
please, please share thispodcast, and rate or review it
on whatever podcast app you use.
(42:25):
Those things actually make sucha big difference for us.
I'm determined to change theculture surrounding math and I
need your help, so spread theword.
Until next time, peace, love,and pi.
Math is basically supercharged common sense.
My perspective is we're all bornto love it Seeing young kids
naturally wanting to play withmath, none of them are like,
ugh, math, why do I have to dothis?
They just want to count, they'reinterested in shapes, they're
interested in patterns.
Kids just naturally want toplay, and they naturally learn
better from playing.
Vanessa Vakharia (00:20):
Hi, I'm Vanessa Vakharia, aka The Math
Guru, and you're listening toMath Therapy, a podcast that
explores the root causes of mathtrauma, and the empowering ways
we can heal from it.
Whether you think you're a mathperson or not, you're about to
find out that math people don'tactually exist.
But the scars that math classleft on many of us definitely
do.
Oh, and don't worry, nocalculators or actual math were
(00:43):
involved in the making of thispodcast.
Okay, I cannot believe thatSeason 6 is over.
Like, that flew by.
Over the last nine weeks, we'vecovered some of the biggest and
most pressing topics in matheducation today.
From building trust in theclassroom and giving students
real purpose, to the truemeaning of equity for literally
everyone, and today's finale,with math educator Dan Finkel
(01:06):
puts a beautiful bow on myfavorite theme for this season:
the inspiring movement towardsamplifying the joy, wonder, and
curiosity that fuels genuinelearning in our students hearts
and minds.
I don't know about you guys, butI've always been confused about
the idea of like, play in math.
I can't put my finger on it, butsometimes I get skeptical about
how those kinds of lovey doveyideas can actually help kids.
(01:29):
Which is strange if you thinkabout the fact that at my
tutoring center we make thestudents tea lattes and bedazzle
their calculator, so like, Idon't know what my problem is.
So if even I get put off bytrendy terms, I can only imagine
the average classroom teacherout there rolling their eyes at
some of the educationalcatchphrases we've been throwing
around on this podcast.
Well, Dan is here today to bringus down to earth and get
practical.
He's the founder of Math ForLove, and I have been a huge fan
(01:52):
of his forever.
We talked about the role of playin learning and therapy, and Dan
shares his belief that we areall born to like math, we just
need the right supports to stayengaged with it.
Dan, welcome to the podcast.
Thank you for your, what's thatsports term where you like put
someone in?
Dan Finkel (02:12):
Oh, the pinch hitting.
Vanessa Vakharia (02:13):
Yeah.
You're pinch hitting right now.
Dan Finkel (02:15):
Where, it's where I like to be.
That's right, just dropped in.
No prep, all improvised.
It's great.
Vanessa Vakharia (02:20):
I'm really, really glad you're here.
There's so much I want to talkto you about.
I don't know what those thingsare yet, but they're going to
come to mind.
I kind of want to start withwhat we were just talking about
when we forced David to pressrecord.
Dan Finkel (02:30):
Well, I think one of the things you said is you were
interested in, I'm alwayspromoting this idea of a play
based approach to matheducation.
And you were saying, I'm a highschool teacher.
This doesn't even make sense.
What are you talking about?
So, Yeah, so let me let me try.
So
Vanessa Vakharia (02:46):
I love that I'm getting you to ask your own
questions.
You're doing all the work.
Okay, yes, go.
Dan Finkel (02:51):
uh, so, so I started out as a high school teacher,
interestingly, and the longerI've been working, the younger
I've been working with.
So yesterday I led a session forpre K to third grade teachers.
Vanessa Vakharia (03:01):
Oh wow.
Oh my god.
Dan Finkel (03:02):
And I've been doing work with this nonprofit called
Early Family Math, it's likebirth to eight.
Because even when kids areshowing up in kindergarten,
there's like already differencesin math education, like a huge
amount of important stuffhappens.
You know, five and younger.
But part of the influence ofthat area for me, the working
with young kids is that playends up being this super
(03:26):
important part of it.
One of the things I like to sayis play is the engine of
learning for young children.
This is really well understood,in a way, and, you know, there's
been studies that have compared,like, for four year olds, you
have a play based approachversus a very didactic,
everybody sit down and staystill and then I'll tell you
what to do.
And and the kids just naturallywant to play, and they naturally
(03:47):
learn better from playing.
And my perspective is that thisis especially true when it comes
to mathematics, which I think ismore likely to be abused in the
sense that people will say,ignore your common sense.
Don't play around.
Don't experiment.
Just do what I tell you to do.
And like, if it doesn't makesense, whatever else is
happening, just ignore all thatand just repeat what I just told
(04:09):
you.
And at the same time, I thinkplaying with mathematics and
mathematical ideas ends up beingincredibly productive.
And the best workingmathematicians that I can think
of are the people who are intogames, into playing around with
things.
I used to have a professor whenI was studying math who would
(04:29):
say, like every problem he waslike, here's the game.
Because he would basicallytranslate the problem into a
game, and then you had to, like,figure out what the rules were
and play the rules to get yourending situation and translate
it back into the problem.
And so, just the idea of, like,you're always playing games,
you're always messing withpuzzles, that is somehow one of
the key skills.
(04:50):
You know, one of the greatinspirations from an earlier
generation was Martin Gardner'sScientific American columns,
which were called MathematicalGames.
That was the vision of like,
Vanessa Vakharia (05:00):
What was that?
Can you explain for us, youknow, Gen Z over here?
Dan Finkel (05:05):
Yeah, no, this was, this was like impacted a whole
generation.
He wrote probably, I'm not goingto get these dates right, but he
wrote for decades in ScientificAmerican from like the forties
to the late eighties or theearly nineties or something.
And it was the place wherepeople would go for mathematical
inspiration.
It's like, here's what's goingon at the forefront of the
(05:26):
field.
Here's magic tricks, cool newideas, here's puzzles.
It was all in one place.
He corresponded with like,everybody in the field and just
sort of was the one who waswriting for a general audience
and he inspired a generation ofmathematicians, engineers,
scientists.
But it was through a veryplayful, play based approach
Vanessa Vakharia (05:48):
Is this like an escape room situation?
Dan Finkel (05:52):
I would say not exactly in the sense that escape
rooms come in many flavors,though maybe there's a piece of
it there, but I think there issomething about the popularity
of escape rooms or, you know,Sudoku or all these things where
something in us that cravesthis.
Vanessa Vakharia (06:05):
Huh.
Dan Finkel (06:06):
And has a hard time identifying it as math and is
looking for it guises.
But anyway, so what I'm actuallyhoping is that this play based
approach, sometimes explicitlythrough playing with games,
playing with blocks,manipulatives, those kind of
things for young kids actuallystarts to influence upper
(06:26):
elementary, middle school, andhigh school, and we start to see
what is still a playful approachto mathematics, but in more and
more rigorous technicalproblems.
But, but that, for me, is one ofthe things that makes it really
fun, is when you have theseproblems that feel very playful
and very game like, puzzle like,whatever it is.
but they're still very, like,just interesting math problems
(06:48):
in their own right.
That's part of the fun of it forme.
Recreational math, I guess.
Vanessa Vakharia (06:53):
But hold on though because You're proposing,
are you?
I don't want to put words inyour mouth, are you proposing
that you're like, you're stillteaching the math concepts that
you're wanting to teach, like,don't worry, you're still going
to teach kids how to factorquadratics, we're just going to
do this in this place.
You are.
You're, Dan is nodding everyone.
This is a podcast.
Okay.
Dan Finkel (07:09):
No, no, absolutely.
Yeah.
And which is not to say, whichis not to say that you never
have to, sometimes you actuallyjust have to do a lesson and
it's like, okay, this is justkind of a little bit of a drier
topic and I need to just tellyou how this thing works.
That certainly happenssometimes.
But I think there's a hugeamount of untapped possibility
when it comes to justinteresting problems.
(07:30):
that are very playful, puzzly,interesting, have that quality
from recreational math.
And then, I think also what'sreally powerful is the skill to
take things that are dry andactually see what's interesting
and see what's fun about them.
I mean, in a way, what we reallywant students to do is not get
to the end of a problem and say,I'm done, what do I do next?
(07:50):
We want them to say, oh, Ifinished, but I was doing this,
and then I had another question.
Like, something else happened tome, and I wonder if I play
around with it like this, whatwould happen?
And those are the students who,when I see them, I'm like, Oh,
yeah, you're going placesbecause, that skill to Oh, no,
seriously, well, it's like, ifyou can ask the next question
Vanessa Vakharia (08:08):
Yeah, yeah, yeah,
Dan Finkel (08:08):
and be like, I'm not satisfied because I just did
what the teacher did, but Iactually, I'm going to play with
this myself, then they're theones who are owning it and
really gonna, I think, have asuccess in the field.
Vanessa Vakharia (08:20):
But it's interesting too, because I'm
not, I'm even thinking of itfurther of like, great, they're
going to have success, fine, butmore like, it's, it's not only
like, oh, they're, smart and I'musing air quotes, like smart
enough to ask the next question.
They actually give a fuck, likethey care enough to like, keep
going.
And like, isn't that a hugeproblem in math right now?
Is that so many kids don't seeany value or purpose in what
(08:42):
they're learning that they'relike, why would I keep asking
questions when I can just befinished?
Dan Finkel (08:47):
Totally.
Well, and this is one of thereasons I've gone down to work
with younger and youngerpopulations also, because my
perspective is young kids neverfeel that way.
They love math.
Because they're living in achaotic world, and math is this
incredible tool that's helpingthem to impose order on the
world.
(09:07):
So, so it's like, this is just,math is basically supercharged
common sense.
It's like, yeah, just what youdo to make sense of the world,
but now we're gonna help yousharpen that, and so you get
more and more control and moreand more power.
And so it's natural for peopleto feel like they own it.
The reason that so many peopleare traumatized is they go to
school and that control isessentially wrestled away from
(09:29):
them, right?
They, because, my perspective iswe're all born to love it.
Like this is meant to belong tous.
And if we go and see a teacherwho says, okay, yeah, you have
some perspective, whatever, thatdoesn't matter, ignore that,
now, just listen to what I say.
That's a fundamental perversionand inversion the natural state,
which is, no, this was my thing,and now you're telling me I
(09:50):
should ignore, like, shouldn'tmake sense, the thing that I use
to make sense of thingsshouldn't even make sense.
Like, so that is why people Ithink either love math or hate
it, and so rarely between.
We're born to love it, and ifthat's denied and that's stymied
and that's taken from us, thenwe learn to hate it, but we're
never neutral,
Vanessa Vakharia (10:08):
Oh my god, I have full body goosebumps right
now.
Well, no, because I'm reallylike what an interesting way to
look at it.
So first of all, this is apodcast about math trauma and
healing math trauma.
Dan Finkel (10:19):
Which is something I've thought about a lot, you,
as you can imagine.
Yeah.
Vanessa Vakharia (10:22):
Which is so cool.
But like, I want to go back tothis idea of like, we're born to
love math.
We're born to love math.
And this reminds me of all thenature versus nurture arguments
that are out there consistentlyof this idea, well, can anyone
do math?
Can anyone be good at math?
Like, is there a math gene?
When you say we're born to lovemath and then that's taken away
(10:44):
from us, that is such a powerfulsentiment.
But I guess my first questionis, what do you mean by we're,
all born to love math?
Dan Finkel (10:53):
Yeah, I mean, again, like, seeing young kids
naturally wanting to play withmath, like, none of them are
like, ugh, math, why do I haveto do this?
They're like, they just want tocount, they're interested in
shapes, they're interested inpatterns, because it's helping
them make sense of things andfeel more in control of the
world.
So it's just like, that's justthere from the
Vanessa Vakharia (11:11):
Wait, stop, say that, like, let's talk about
that though.
Like, it's funny because I, Ihated math for a long time, I
failed grade 11 math twice, andthen when I, you know, things
changed for me, one of thethings I found so, like I found
math really meditative.
There was this sense of orderand this sense of like poetry
and this sense of like,everything has its place and
when you can reduce a giantalgebraic expression down to
(11:33):
like one number, like it waslike, so like complexly simple.
But there's two things, like,you're kind of saying, like,
kids use math as a way tocontrol and make order of the
world, or math is used as a wayto control them.
Dan Finkel (11:47):
That's exactly right like it's something we have to
learn, but there is an instincttowards it, like there's an
instinct to want to make senseof the world, to want to find
patterns that will help usunderstand how the world works.
So the problem that you see inhigh school, I think, of kids
being like, why do I have to dothis?
Can I just be done with this?
I'm saying that's not a problemfor first graders.
(12:08):
They're, they're justinterested.
And even younger, the more,like, the younger, essentially
that is a special type ofignorance that is learned in
school.
Vanessa Vakharia (12:14):
Yeah.
Oh my God.
I love that.
I love that.
Well, yeah, because it's almostlike once you label something,
it's like when you like arereally enjoying hanging out with
someone and then they call youyour, their girlfriend and
you're like, Ooh, wait, what?
That's what we're doing?
Dan Finkel (12:28):
Yeah, maybe I have to think about that metaphor.
Uh, yeah.
Vanessa Vakharia (12:33):
Cause you're like, Oh, like you're having
fun.
And then someone's like, you'redoing math.
And then all of the connotationsthat come with math and your
inability to do it and what itmeans, do you
Dan Finkel (12:43):
My experience, like when I worked with high
schoolers, I feel like I wouldget kids who were in this
category of like, oh, just tellme when I'm done with this.
It was possible of almost all ofthem to show them some beautiful
result in mathematics and havethem still say like, wow, you
know what I mean?
And I just felt like, wow, itseems like it's so universal
(13:03):
that there's something in usthat responds to the beauty of
the subject and to the power ofthe subject.
And it would be so much nicer tonot have to try to undo all the
damage happens, in school, likewhen kids are in high school or
adults, and instead just kind ofdo it right in the first place.
(13:25):
And I think play for me is thecentral ingredient of this,
because play has a lot to dowith owning things.
It has a lot to do with makingyour own choices.
The things that you can't playwith are the things that aren't
yours, and the things that areyours are the things you can
play with, and the things youcan kind of break and mess
around with.
And there's just a deepconnection between play and
ownership, and some big part, Ithink, of liking math and also
(13:49):
success in math has to do withfeeling ownership over it,
feeling like it's yours, feelinglike, you know, you're on board
with this project.
So it's true, there are allthese hypotheticals of like,
well, what if this way leads tosuccess, but this way leads to
people feeling better about it.
I think most of the time, thesame approach can give you both
of those things.
usually not a fundamentaltension there, fortunately.
(14:10):
If kids didn't come in alreadyliking math, it would be a lot
harder.
But the kids do arrive at schoolready to just like math.
So,
Vanessa Vakharia (14:19):
Well, I guess like at certain ages, yes.
But as you were saying, evenlike in kindergarten, like, I
run a tutoring center, like,that's what I've done for,
almost 20 years.
And I actually find that, Ithink this is for a variety of
reasons, but like more and morelately, do I get kids who are
like, parents are like wanting atutor for their three year old.
And like, the reason is becausethey're already anxious about
(14:41):
math or they're already sayingthe words, I hate math.
And they're three.
Dan Finkel (14:45):
Gosh, I haven't seen three year olds saying they hate
math, that's tough, that ishard.
But, There certainly are hugedifferences when kids are
arriving at school that I'maware of, and I think that's
zero to five.
Vanessa Vakharia (14:57):
Like what?
Dan Finkel (14:58):
I mean, kindergarten readiness is just a huge issue,
and there's kids who show up.
Vanessa Vakharia (15:02):
It is?
Dan Finkel (15:02):
Oh, yeah.
Oh, yeah.
Vanessa Vakharia (15:05):
Like, what are you, aren't they three?
How old are you in
Dan Finkel (15:07):
Kindergarten starts at five.
Yeah, this is in the U.
S., yeah,
Vanessa Vakharia (15:11):
So what needs to happen?
Dan Finkel (15:12):
Well, there's some kids who show up knowing their
numbers to 20 or beyond, who arejust comfortable playing around
with numbers, who have like,played with blocks a lot, and
kind of have a sense of howshapes fit together.
Often, like, number lines, likethe proto number line skill is
like, have you played Sorry oryou know, Shoots and Ladders.
(15:33):
Can you advance a piece on aboard in a
Vanessa Vakharia (15:35):
What?
Dan Finkel (15:35):
line?
Parcheesi.
Kindergarten teachers will tellme, like, Oh, I know the kids
who've been playing board gamesat home where you have to move a
pawn on a board, and those whocan't.
Because some of them intuitivelyget number lines or related
types of things, and some ofthem don't.
And, so, again, this is likethis play based approach.
If you've been playing aroundwith things.
(15:56):
a lot of the early math topicsare really natural and feel
straightforward.
if you haven't, then you'rebasically already kind of behind
in kindergarten in the sensethat you've got some kids who
are just ready to start thinkingabout numbers and, Oh, what if
you put them together?
What if you take them apart?
Sort of addition, subtraction,counting up higher.
(16:17):
And then you have others who arestill trying to grasp like
numbers within 10, just basiccounting and cardinality.
Vanessa Vakharia (16:24):
That's so crazy to think that at that
young of an age, that there'salready, like, this difference
building, and so much of it hasto do with, what's happening in
the home, because I can imaginethat must be so stressful for
parents.
Like, I actually need you togive my friend parental advice
right now, I didn't think ofthis, but she was, she was
saying her daughter, she's like,well, we try to do math games
with her and stuff, but she justdoesn't like to do them, like,
(16:46):
she'd rather do, like, roleplaying games more like story
based games.
But it's interesting because myfriend hates math and is like so
anxious around her own math.
So I'm kind of like, is this athing where it's like your
daughter's just picking up onthat?
Is it a thing where like shelegitimately doesn't want to do
it?
Like, what do you do in thatsituation?
Dan Finkel (17:03):
Research seems to suggest that kids do pick up on
it at very young age.
And yeah, and usually by likearound second to fifth grade,
girls have a sense of like, mathis a boy's subject.
That is, and often the parents,it's like very powerful, the
signaling.
Um, however, so I've beenworking with this organization,
Early Family Math,EarlyFamilyMath.org, if anyone
wants to go, there's like tonsof free materials there.
(17:24):
The goal being like, how can wehelp people have a good time
with their kids around math froma young age?
And the line that is the mostwidely known thing that I've
ever said is what books are toreading, play is to mathematics.
Vanessa Vakharia (17:37):
What books are to reading, play is to
mathematics.
Dan Finkel (17:41):
The point being that we all know we're supposed to
read at home with our youngchildren.
There's this campaign of like,what do you do?
Hey, you want your kids to read,read to them, get a book.
From the moment they're born,right, so then it's like, okay,
well, what do you do for math?
And the answer is you've got tobe playing with kids, but it's a
type of playing that has to dowith counting and organizing,
(18:05):
but also like patterns.
In a way, jokes are kind ofmathematical in the sense that
you,
Vanessa Vakharia (18:12):
Like the formula of a joke?
Dan Finkel (18:14):
Yeah, you set up a pattern and then you break it.
You know, it's always like thefirst person does this, the
second person does this.
But the third person, you knowwhat I mean?
It's always like, um, And I hada really interesting experience
with this because I have nowwritten a children's book, which
is called Pattern Breakers.
And I read it in my kidspreschool class.
And the game is there's a littlegirl who is looking for these
(18:36):
monsters called the patternbreakers and they're hiding
behind different colored dots.
But they always break thepattern when they hide.
So it goes purple, yellow,purple, yellow, purple, yellow,
purple, yellow, blue.
And she's like, wait, what doesthat blue one doing there?
And then there's a littlemonster behind them.
And that's, and so it's sosimple, you know, very, but what
happened when I read it is whenwe're doing this, the kids were
(18:57):
erupting in laughter and theyweren't erupting in laughter
because the monster was there.
It was just that there was apattern that set up an
expectation that then switched.
And that was all they, yeah, andso it was like, that was so
funny to them.
I was like, that is reallysurprising
Vanessa Vakharia (19:12):
This is insane.
Dan Finkel (19:14):
Yeah,
Vanessa Vakharia (19:15):
I love this because people always ask me
what should you do with yourkids and you're always like well
do math with them in the kitchenlike do, but you're right,
you're just like, play games.
Dan Finkel (19:23):
Playing games is huge.
Anything with dice, anythingwith cards, anything where
you're moving pieces on a board.
It's like, anything where you'rekeeping score, like all of that
is like involving numbers in aplace where just kids want to do
it.
But then even more basicallylike, when I had, you know, a
kid under one year old, I feellike I was always doing little
fun, like, pick up and kiss kindof games, but you do it on the
(19:45):
count of three, right?
Like, one, two, three.
Then maybe you go to foursometime, and it's a surprise.
I have videos of, like, my ninemonth old, and I literally, you
say, one, and like, they justjerk to attention because they
know something fun is about tohappen.
Then two, and they're just likewaiting for what's going next.
And it's just to have that builtin where it's like, this is part
(20:05):
of what organizes time,organizes our, our time
together.
So we, while we play, because ifI hadn't done that, then it
would be less fun.
There'd be less anticipation ifthey didn't know there's this
regular sequence that always hassomething fun happen at this
point.
Vanessa Vakharia (20:21):
Yeah I just interviewed Francis Su and he
was saying similar, like totallydifferent, but he was talking
about how he does somethingsimilar where he uses his
fingers and he goes, so I'mholding up one finger right now
and I'm up another, and he'llsay, you know, well, how many
fingers do I have on this onehand?
And the kid will look and sayone.
And on the other hand, one, andthen like doing this and the,
and his little kid will be ableto say two.
(20:43):
Okay.
We delete this because thismakes no sense.
Okay.
Anyways, go listen to Francis.
Go.
Dan Finkel (20:48):
All visual, yeah.
Vanessa Vakharia (20:49):
Anyways, the point is that like, I think it's
really cool because these areall, I don't want to say like
easy, such a bad word, but Ithink these are accessible
things that basically any parentcould do.
Even if you hate math and arethe most anxious, you're
probably doing it anyway, it'smore about like, right?
Dan Finkel (21:03):
Yeah, this is one of the main things is math is in
all our lives in these small,these small ways and just to
identify it as like, oh, I'mactually doing it in this little
way and it's helping me.
And even like with young kids,just even talking about over
under, positional stuff ends upbeing very important for math
development.
There's a lot of littletechnical things that are like,
(21:23):
Oh, if they count something, youlike, say how much they count at
the end.
It's like 1 2 3 4 5.
And you say, Oh, yeah, there's 5Cheerios or whatever, that sort
of emphasizes that, like, that'sa technical point about like,
Oh, the number at the end sort
Vanessa Vakharia (21:37):
means
Dan Finkel (21:37):
the amount of the whole thing.
But playing is really the keyelement.
Vanessa Vakharia (21:41):
So, okay.
So I think it's reallyinteresting because like, I got
into like a lot of internettrouble, a lot of hot water,
shall we say,
Dan Finkel (21:47):
ok
Vanessa Vakharia (21:47):
a few weeks ago, because I was talking about
the times tables on TV and Isaid, I believe kids need to
know the times tables.
I don't believe they need tomemorize them.
And what I meant was like, yes,you should have math facts
stored in your brain, but likerote memorization is not
necessarily the way to getthere.
And then what I said, you candisagree with me by the way, but
what I said was, I said, it'slike when you learn not to touch
(22:09):
a hot stove, it's not becauseyou've memorized that rule in
your head, it's because, youfigured it out or you've
actually done it and it's beenhot and you've learned a lesson
or like dah, dah, dah, dah, dah.
You hate it.
You hate that.
Dan Finkel (22:20):
Well, no, no, I know exactly, I think I know exactly
what you're saying and whatyou're, where you're coming
from.
This is a tricky communicationpoint because I think it has to
do with the word memorize.
So in math, there's this bigquestion, like, what things do
you need to have memorized andwhat things do you not?
And I think people can disagreeon that, and people do.
I personally believe thatmultiplication facts are
something that you definitelyneed to have in your, like that
(22:43):
needs to be automatic at somepoint because it just slows you
down too much later, it's toohard to not have that.
And how do you get there?
And I think what you're saying,when you're saying don't
memorize them is you don't wantit to be like disconnected
facts.
You want it to be like, Oh,here's just like 6 times 8, 48,
that's just like I learned thislittle rhyme.
Vanessa Vakharia (23:02):
Exactly.
You don't even know it's sixgroups of eight.
Like you don't know what it is.
Dan Finkel (23:06):
Exactly.
like, we have this with squarenumbers for people like, Oh,
know, 6 squared is 36.
But like, Oh, it's actually asquare and like connecting that
to the area of a square.
Like, Oh, I never thought thatthat was connected.
Um, so what we want is theautomaticity to be growing, not
just out of rote practice, butout of a sort of a connected,
contextualized understandingwhere you're actually learning
what the things mean and have adifferent representations for
(23:29):
them in different ways tounderstand them, but then also
get them in your memory at somepoint and have them down cold.
That's where I fall on that.
Vanessa Vakharia (23:37):
But so fine.
Yes.
I agree.
But this isn't even, so that wasone argument.
But the thing that I wanted tobring up is what people kept
commenting, one of the comments,like other than calling me like
an idiot and saying that Ishould get off the internet and
girls with sparkly eyeshadowshouldn't comment on math.
Other than those comments,People kept saying, this idea of
like.
(23:58):
it's in our genetics or likeit's in our biology to, to not
want to touch something hot.
But that math is not somethingthat's like in our genetic code.
And you, you, I'm still on thispoint of your, you being like,
as babies, like we are all, bornwith this, I
Dan Finkel (24:17):
Well, it's an instinct towards math
Vanessa Vakharia (24:19):
Yes, yes, that's
Dan Finkel (24:21):
it's true, and now suddenly I want to be careful
because it is true that thedeeper you go in mathematics the
less natural it does feel and
Vanessa Vakharia (24:30):
Sure, but we were talking about, like,
patterns in the just Like, we'retalking about math.
Dan Finkel (24:35):
I think there is something fundamentally
appealing about that and we arefundamentally drawn towards like
the symmetries, the patterns,the sort of sense of like
simplicity and beauty that comesout of those things.
I do think that is that has aninherent appeal.
Yeah,
Vanessa Vakharia (24:51):
And this isn't a science podcast, for everyone,
not like we're like, oh, there'sresearch, just talking about
what we know, and what we, whowe've talked about, and like,
whatever, and just ponderingthis, so no one cancel us and
everyone chill.
Dan Finkel (25:02):
I mean, partly, I'm also aware of how easy it is to
be misunderstood, I think, whenyou, like, put something
forward.
Vanessa Vakharia (25:09):
But we've always counted, like, there's
always been, like, a need tofind pattern, order.
Dan Finkel (25:15):
But this is an interesting point also because,
you know, there are somecultures which don't have, like,
number words that go beyondthree, say.
Vanessa Vakharia (25:22):
Ok.
Dan Finkel (25:22):
It's like one, two, many.
And this is going really deep inthe weeds now, but there's like,
there seems to be a hardwiredunderstanding of number that
goes up to maybe, three or four,and then there seems to be
another sort of hardwired sortof estimational ability of like
more or less in larger groups,but that's not connected to like
the actual literal number.
(25:43):
But then I think we develop thetool.
So so how do you say this?
I think there is a fundamentalinstinct towards mathematics
that has to do with the draw topatterns, and being able to make
sense of the world throughsimplifying and through finding
underlying order.
And then there is also thisinstinct towards the beauty of
(26:05):
it and towards the power of itand just what it gives us in
that sense.
But then a lot actually doeshave to be developed.
And the development doesn'tnecessarily happen on its own.
I don't know what this tells usabout the arguments you are
having with people online aboutthe times tables.
Vanessa Vakharia (26:20):
That I'm right about everything.
Dan Finkel (26:22):
I don't, Yeah, I don't, I don't have enough
background to even totally getwhat are saying there.
But, um,
Vanessa Vakharia (26:27):
Okay, what you need to know is the internet a
cesspool and we're moving on.
Dan Finkel (26:29):
That I agree with.
That I think is clear, yeah.
Vanessa Vakharia (26:33):
So I, do, do people ever say to you like, Oh
my god, Dan Finkel and his mathplay.
Like, are people ever like, wedon't have time to be playing
around.
Dan Finkel (26:42):
Yeah, I get that less than you would think.
I actually would almost expectto get it more.
But I think, this is again acommunication thing.
I never want people to hear"play", that just means, oh, we
just mess around and we don'tcare.
What I'm trying to say is, Iactually feel like math, as it
is often taught, the math, Iguess, that traumatizes people,
(27:03):
right?
The math that people needtherapy for, uh, is the math
that because it's so notplayful, but it's actually a
much more superficial kind ofmath also.
The math is much less deep, it'smuch less interesting.
The understanding that comesfrom it is much more fragile.
It's the kind of thing whereit's like we spent so long
(27:23):
saying, here's exactly how to dothis kind of problem.
And then the test has one worddifferent and everyone misses it
on the test and the teacher'slike, why did they change that
one word?
Like I've been teaching themthat every time they see the
word difference it means this
Vanessa Vakharia (27:35):
Yes.
Dan Finkel (27:35):
But they use it this way.
The test is doing that onpurpose because they're trying
to see how fragile the studentsknowledge is.
And we want a robust knowledgewhere, you know, you change the
word and kids like, well, Istill get it because I've like,
I don't just have one path.
I've been like exploring all thewoods, you know, and like, if I
get a little off, I can comeback in another way.
That's what we want.
And you get that from playing.
Vanessa Vakharia (27:57):
I'm realizing I had my back up whenever people
are like, math play, it liketurns me off so much.
And I'm, and I'm wondering,like, now, hearing you talk
about it, I'm like, Oh, my God,yes.
But I guess, to me, it seemedalmost like a trite, silly word.
Like Oh, he just wants me tolike, play with like toys or
manipulatives.
But that's not at all whatyou're saying.
Dan Finkel (28:17):
What I'm saying is that the invitation to play is
what will help get into muchdeeper
Vanessa Vakharia (28:22):
What is my problem with the, why did the
word play throw me off so much?
Dan Finkel (28:25):
In fairness, a lot of people have that, I think,
and maybe I should expect moreof a backlash.
Maybe if I get a little morepopular, I'll get more of a
backlash.
Vanessa Vakharia (28:33):
No, no, no.
Well after this podcast, watchout.
Well, I get the same thing maththerapy though, right?
People are like, therapy.
And you're like, well, hold on.
Dan Finkel (28:41):
Though I will say, you're also, you're doing high
school, that's where I started,but it's less and less my focus
these days.
Vanessa Vakharia (28:46):
Sure.
but it's almost like even moreimportant, like the way you're
talking about it.
I'm like, Oh my God, like, thinkabout gaming, it's like
teenagers love playing.
They just, they wouldn't want tosit around and play with a toy,
they would think that waschildlike, but like, they're all
playing video games, they're alllike making TikToks.
Like they are engaged.
And I like the way you put itbefore.
What did you say?
It wasn't extracurricular math,was it?
(29:08):
Uh, recreational math.
this idea of recreational,they're doing sudoku, they're
doing their wordle, like,
Dan Finkel (29:13):
Yeah, thing that I do that, like, gets the most,
online views of anything is Iauthor these TED Ed riddles
sometimes.
Vanessa Vakharia (29:20):
Ooh.
Yeah, people love riddles.
People love a riddle.
Dan Finkel (29:23):
The internet loves riddles.
It's funny, literally, it's likea side project and I just do it
because sometimes I have a goodidea for a riddle and so I've
written a few of these and it'slike, 2 million views, 5 million
views and it's
Vanessa Vakharia (29:33):
You're so famous.
Dan Finkel (29:35):
Well nobody knows, they're animated also, like,
that's the whole, that's TEDreally
Vanessa Vakharia (29:39):
Sure, we should put your face in there
though, if you want to startgetting some haters.
Dan Finkel (29:42):
I keep telling them, I'm like, just like slap my face
on there!
Vanessa Vakharia (29:45):
Oh my god.
Okay.
Listen, I have to like wrap upsoon which is sad because this
has gone by so fast.
Um, What do we think of play orrecreational math or what you're
talking about as a part of maththerapy.
Like math therapy to me has fivesteps and like those steps
involve you know, learning aboutgrowth mindset, rewriting your
story, unpacking trauma, likefinding motivation.
(30:06):
I feel like, this idea ofincorporating play as a means
for students to get to knowthemselves and how they think
and develop this curious, like,I don't know, like there's
something there for me.
What do you think?
Like, does play have the powerto heal?
Dan Finkel (30:19):
I think yes.
I think definitely.
I mean, there is, for youngkids, there is a thing called
play therapy, right?
It's a tricky question.
Play requires a kind of safety.
Like, if you feel like you'rebeing judged, feel like the
stakes are really high, it'svery hard to play, unless you're
like a professional and this islike you've prepared.
Um,
Vanessa Vakharia (30:37):
Oh my god, sports are playing!
Dan Finkel (30:39):
Yeah.
We do it everywhere, right?
Yeah.
Vanessa Vakharia (30:42):
We play in a band! Oh!
Dan Finkel (30:44):
Yeah, music, theater, right?
You are in a play.
Vanessa Vakharia (30:48):
Oh my god.
Dan Finkel (30:49):
Yeah, there is a kind of frame which defines the
space, you know, the rules ofthe sport or the rules of the
game or the lines of the play,whatever, but then there's
within that frame, there isspace for you to put yourself in
there also, and kind of say,okay, how am I going to
contribute to this?
What of this would only be thisway because I'm the one doing
(31:10):
it.
That's something very powerfuland I think, I think it can heal
in some cases, but it definitelycan help grow and help you learn
about yourself.
Um, and I think it just feelsvery positive to do that.
Like we all want to feel likewe're important enough that like
the thing would not be exactlythe same if somebody else did
it.
Vanessa Vakharia (31:26):
Oh my god, yeah, we're all so self
obsessed.
We all want to be the maincharacter of our math question.
Dan Finkel (31:31):
Yeah, sure.
Someone gave me this advice oncethey said, someday you'll have
kids and you'll be sending themto kindergarten.
Here's how you pick akindergarten.
Go to the school, look at theart on the wall, and if it all
looks the same, don't send yourkid to that school.
The idea being like, that's allframe.
We're like, here's the rules,first make this, then do this,
and they're like, yeah, we wouldnever do that with art.
(31:53):
Like, we would know that that'snot gonna be good for kids to
control every movement they makewith art because part of art is
to put yourself into it, youknow, express yourself, all
those things.
And yet math, how many mathexperiences would rise to that
level, right?
Mostly you're like, if you didit right, it should look exactly
everyone's else.
And I could take you out and putsomeone else in and it doesn't
(32:15):
matter.
Right?
So
Vanessa Vakharia (32:18):
This is blowing my mind! You're speaking
to like the ego in me.
Like yeah, what the fuck?
Why am I not, why is this notcentered around me?
Dan Finkel (32:26):
Well who would want?
I mean, nobody wants to be like,Oh, I could just do something
else and you could do it.
Right.
And I think that's why there'salways this question, like, why
do we have to do this?
I finished, can I like go now?
Like, is this what they want meto do?
You know, it's just like, whenam I ever going to use this is
the classic, which isn't sayinglike, Oh, in 20 years, like
you're going to need to groutyour floor, and so this is like,
you'll know how much grout tobuy.
(32:47):
It's like right now you'reasking me to do something really
weird, cause like.
I don't even need to be here forthis.
And so I think that theperspective of like, we need to
be framing experiences wherethere are really clear, rigorous
technical rules, like in a sportor a game or in music or a
theater or whatever, but there'sstill space inside where you can
(33:09):
actually put something ofyourself.
And so you made something andmaybe you make something and it
still has to like satisfy therules, but it, it wouldn't be
the same if somebody else didit.
I do think that that can behealing to experience especially
if you haven't before.
Vanessa Vakharia (33:23):
And just that sense of belonging, finally
feeling like there's a reasonfor you to be, I love that you
said that, there's a reason foryou to be there.
You.
Dan Finkel (33:30):
And I'll tell you, I, so I gave a session yesterday
at, it was pre-K through thirdgrade, but we were doing some
things with pattern blocks,using actually our upscale
pattern blocks developed byCanadian Nat Banting, who's,
they're super cool.
Anyway, we were talking about,like, there's these different
sizes of pattern blocks, andwe're talking about how many of
the little triangles would taketo cover the big one.
And someone was like, well, Isort of see, once I see them in
(33:51):
the little triangles insidethem, I see how I could fill
them up and do this.
And I was like, oh, that's areally great observation of how
it works.
And they were blown away thatsome idea they had was like,
somebody thought it was a goodidea.
You know what I mean?
And she had this very sort ofheartbreaking line, which was,
she actually commented later tothe group, she was like,"I've
(34:12):
never really loved math until Iguess until today".
Vanessa Vakharia (34:16):
But how cool is that for you?
Like it's never too late.
Dan Finkel (34:19):
Well, this is why I think your perspective of math
therapy, I have said this for along time, but I feel like my
first interaction with teachers,especially elementary school
teachers is often therapy.
Like that's what the firstsession is, but it is also a
session that is play based andis very non judgmental and is
something where they can feellike whatever they do, it's
like, oh, there's something tolearn in whatever you did.
(34:41):
And like, you're contributing.
If you participate, you'recontributing.
Vanessa Vakharia (34:45):
Okay.
I have to ask you this becauseI've been dying to unpack this
with you and I, I literallyquoted you saying this in my
book, but I never dreamed Icould ask you in person what you
meant.
So do you know what I'm talkingabout?
You have this quote basicallywhere you're like, it's bullshit
to tell everyone that there aremath people.
Dan Finkel (35:01):
Yeah.
Vanessa Vakharia (35:02):
Can you just tell me what you mean?
Because, and I say this everytime I'm like, for me, the goal
of math therapy is to help everystudent build a better
relationship with math, even ifit's like the teeniest better
relationship with math.
And whenever people are like,what if like, they really can't
do it?
Or like, you can't tell kidsthat they can all do math.
I'm like, I'm not saying thatI'm saying they can all build a
better relationship with maththan they have right now.
(35:24):
But we do want to be sayinglike, you know, there's a lot of
discourse being like, we shouldtell everyone they're math
people, everyone can do math.
Dan Finkel (35:30):
Yeah.
I am very nervous whenever themessaging is like, let's all
just tell everybody this thingand that'll solve the problem.
Talk is very cheap, uh, ineducation, and fads are endemic
and it's very easy to be like,you just say the right thing,
and I just feel like thatdoesn't address what the real
problem is.
And it leads to a place whereit's almost harder because the
(35:51):
kids are smart, they know if theteachers are BSing them, know,
you know, if the teacher says,like, you're all math people,
but like, you got it right, youdidn't, you're smart, you're
dumb.
I mean, they infer all of that.
So when it comes to saying,like, are you a math person or
not?
Where I want people to be is Iam not afraid of math.
I can use it as much as I needto and that's not going to scare
(36:14):
me.
I'm not going to, like, give upon my dream of being an
architect or a veterinarian or anurse because I can't pass the
requisite math courses, and Isee why someone else would
really love this subject.
I remember I think my youngerbrother at one point like
visited France and he had neverlearned another language and
he's like, Oh, I see how I couldlearn French, but I'm not going
to.
Vanessa Vakharia (36:33):
Yes, that's empowering.
That's what I think too.
It's like just changing yournarrative to be like, I guess I
could do this if I want to, butI'm going to choose not to.
Dan Finkel (36:42):
Yeah.
And which is fine.
Like, not everybody needs tolike, go into the deep recesses
of mathematical research.
Like it's fine.
Vanessa Vakharia (36:48):
Do something else.
Dan Finkel (36:49):
But, but, but I had something really similar with
art.
Actually, I was always afraid ofart.
I was always really bad at art.
I think I used to say, like, Iwas so bad that I would like
make people worse at drawingjust by like drawing next to
them.
Vanessa Vakharia (37:01):
That's ridiculous.
Dan Finkel (37:02):
Well, no, I mean, but at some point in college, I
was like, this is ridiculous.
I'm going to take an artfoundations class.
This just seems dumb.
I learned the basics.
I was like, I'm never going tobe a great artist, but I could
learn this and get decent at it.
And it was a nice thing to justfeel like, yeah, that's totally
in me if I want to pursue it.
So, yeah, I think we could allbe decent in mathematics if we
(37:25):
wanted to.
Um, not everyone can be aresearch mathematician.
That's very hard.
Vanessa Vakharia (37:29):
I think it's actually a really important
message because you're right.
If you're saying to someonelike, no, everyone can, fly to
the moon, people are gonna belike, okay, that's ridiculous.
Like,
Dan Finkel (37:39):
you know, this is, there is a part of me that even
if things are right and true, Iget nervous once everybody
starts, once it becomes kind oflike the common wisdom, like
growth mindset is a little bitlike that for me, where I'm
like, yeah, seems totally legit,totally right.
And yet, there's something in methat when, like, we're preaching
growth mindset to kids all thetime, just like, I start getting
(38:00):
a little nervous.
Vanessa Vakharia (38:00):
Why?
Dan Finkel (38:01):
Well, it's too easy to say it, I think, and harder
to do it, and I just feel like,and, yeah, and what I really
want is for teachers to maybetalk about it less to kids, but
maybe work on it morethemselves.
Vanessa Vakharia (38:16):
100%.
Oh my god there's a wholechapter in my book about this
that's coming out.
Because the whole thing too withgrowth mindset is, this is like
being like, I believe I can getjacked, I believe I can be
ripped, but I'm not going tochange any of my behavior.
I'm just going believe it canhappen.
It's like, no, I need to believeI can get ripped and then I need
to go to the actual gym.
Like, you know, it's like wenever get to the behavior part.
(38:37):
You can't just tell kids likeyou can do anything.
You've got to prove it to themand give them opportunities to
discover that within themselves.
Dan Finkel (38:43):
Yeah.
Yeah.
So I think that's where I getnervous.
Vanessa Vakharia (38:45):
Yeah, the just saying it, like the poster on
the wall aspect of it.
Dan Finkel (38:49):
Right.
And education is so susceptibleto fads, kind of, easy answers.
There's a great line, uh, aboutthis, which is that school
change is measured, not inyears, but in generations.
For me, the thing it's like,okay, you could just got to be
in it for the long haul and youcan't just be like, Oh, what's
going to fix this quickly.
It's
Vanessa Vakharia (39:06):
Right now, yeah.
Dan Finkel (39:07):
Settle in, get ready for this to be like a lifetime
project.
Vanessa Vakharia (39:11):
Okay, final two questions.
You have to answer them inliterally 30 seconds.
We can't do this anymore.
Okay.
Dan Finkel (39:15):
But it's so fun to talk to you, Vanessa!
Vanessa Vakharia (39:17):
I know I'm having so much fun, but like
actually David's gonna kill me.
Okay, number one.
What is the one thing you'd liketo see change about the way math
is taught in schools?
Dan Finkel (39:27):
Jeez
Vanessa Vakharia (39:28):
Your face is so good.
Dan Finkel (39:29):
That's like a huge question! The number one thing,
um
Vanessa Vakharia (39:34):
This isn't like picking your favorite
album, like just say something
Dan Finkel (39:36):
Yeah, no, no, I mean, I, coming from a sense of
sense making for students, Imean, and we've been talking
about play based approach.
Maybe I'll say like, have moreplayfulness in it as a, as a
short answer.
But there's, I, that's like abook in itself.
Vanessa Vakharia (39:51):
You look stressed.
Dan Finkel (39:52):
That's a stressful question.
Because I'm like anything I sayis incomplete.
Vanessa Vakharia (39:56):
Yeah this is like timed Exactly.
Okay.
Final question.
And you kind of already answeredthis, but whatever.
What do you say to someone who'slike, Dan, this is such a great
talk, but like, I'm just not amath person.
Dan Finkel (40:09):
Yeah, what I usually say is, that's a very reasonable
thing to feel, based on theexperiences you've probably had
around math.
Uh, however, there, you know,that, you know, that's, that's
reasonable and there may be somethings in math that, you know,
you would have a differentexperience with, like school
math is not the same as whatmath actually is.
(40:32):
But I think just being toldlike, Oh, you actually are a
math person.
That doesn't actually, yeah,people, people are like, you're
telling me to not like trust myown eyes.
Vanessa Vakharia (40:40):
Right.
Right.
Okay.
Okay.
We're done.
I have to say goodbye to you.
Like, if you could see David'sface right now, he's like, I
gave you the ten minute warningfive times.
Dan Finkel (40:50):
What a pleasure.
This was so fun.
Vanessa Vakharia (40:52):
I'm so glad that's your reaction, especially
because I felt like I kind ofstalked you to come on the
podcast.
Dan Finkel (40:57):
Not at all.
This was great.
Vanessa Vakharia (40:58):
This was amazing.
I'll talk to you later.
Dan Finkel (41:00):
Ok, bye bye!
Vanessa Vakharia (41:00):
Bye! I loved every second of that.
And honestly, I mean, you guysprobably hear it in my
interviews, obviously I lovemath and sometimes I get so
excited about learning somelittle trick or finding some
curious little discovery, butrarely would I think of
associating that stuff with theword play.
But that's what it is.
Who cares if it sounds cheesy?
Say it with me.
(41:20):
Learning can be fun.
I am all in on this playconcept.
I love the idea that learningcan be a joyful discovery and
not just cramming some numbersand facts into your brain so you
can get a good mark on a test.
Well, season six in the can orin the bag or whatever people
say when something's done.
Thank you as always forlistening.
It means so much to me to knowthat these conversations aren't
(41:41):
just helping me but they'rereaching students and teachers
and parents who just want thebest for our education system
and our future.
I would love to hear what youthought of this season and who
you'd like me to interview forthe next one.
So hit me up.
If something in this episodeinspired you, please tweet us
@maththerapy, and you can alsofollow me personally@themathguru
on Instagram, Twitter, andTikTok.
(42:04):
Math Therapy is hosted by me,Vanessa Vakharia, it was created
by me and Sabina Wex, and it'sproduced and edited by David
Kochberg.
Our theme music is by GoodnightSunrise.
And guys, if you know someonewho needs math therapy or just
needs to hear someone elsegetting math therapy, please,
please, please share thispodcast, and rate or review it
on whatever podcast app you use.
(42:25):
Those things actually make sucha big difference for us.
I'm determined to change theculture surrounding math and I
need your help, so spread theword.
Until next time, peace, love,and pi.
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I’m Jay Shetty host of On Purpose the worlds #1 Mental Health podcast and I’m so grateful you found us. I started this podcast 5 years ago to invite you into conversations and workshops that are designed to help make you happier, healthier and more healed. I believe that when you (yes you) feel seen, heard and understood you’re able to deal with relationship struggles, work challenges and life’s ups and downs with more ease and grace. I interview experts, celebrities, thought leaders and athletes so that we can grow our mindset, build better habits and uncover a side of them we’ve never seen before. New episodes every Monday and Friday. Your support means the world to me and I don’t take it for granted — click the follow button and leave a review to help us spread the love with On Purpose. I can’t wait for you to listen to your first or 500th episode!
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com