October 9, 2025 • 46 mins
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Today's ep ended up in a different place than Vanessa expected when she first sat down to chat with Pam Harris, founder of Math Is Figureoutable. Their first real interaction was on the DebateMath Podcast; Pam insisted that learning algorithms/shortcuts can actually hold students back from true learning, while Vanessa advocated for kids to learn however works for them.
Often, that's where it ends. Worse, especially in the "everyone yell at each other" media landscape, the conversation never begins! Which makes today's episode so refreshing - a debate that was more philosophical than ideological. Pam and Vanessa had the time to really go into depth about what they disagree on and where they see eye to eye ... spoiler alert, they're actually pretty aligned!
Links discussed:
- Math Is Figureoutable Podcast
- Free resource download: mathisfigureoutable/big
- #MathStratChat
- Vanessa & Pam debate algorithms on the DebateMath Podcast
- Outliers by Malcolm Gladwell
About Pam: (Website, LinkedIn, Instagram, Facebook)
Pam Harris is a leading math educator, author, and speaker best known for her work on making math figure-out-able. Through her books, podcast, and teaching, she helps classrooms move away from rote memorization and answer-getting, and toward math as something students can sense-make, reason through, and truly understand. She’s passionate about showing that math isn’t about tricks or steps—it’s about thinking, starting with the knowledge students already bring to the table.
Contact us:
- Vanessa Vakharia: Instagram, TikTok, Email
- Math Therapy: Text the Podcast
More Math Therapy:
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Pam Harris (00:02):
one of my favorite things to do is to ask how do
you think about this problem?
99% of the time people will go,well, you know, that's how you
think about it, but you'resupposed to do the right way.
And I'm like, what if we couldteach all math the way you just
logiced your way through thatone.
Algorithms amazing humanachievements.
They're just not very goodteaching tools because, people
like me can get trapped in themand believe that math is
(00:23):
something that it isn't.
Vanessa Vakharia (00:26):
Okay guys, it's me, Vanessa, and I could
not be more excited for you tohear today's episode Okay, I
know I say that every singleepisode is gonna change your
life, but this one is seriouslygoing to change your life.
Because the conversation I'msharing with you today is not
just about how we can improvemath education, but literally
about how we can improve the waywe all talk to each other as
people.
(00:47):
The first time I actually had aconversation with Pam Harris was
literally an hour long argumentbecause we were both guests on
the Debate Math Podcast, so wewere debating, we were actually
discussing whether studentsshould be able to use algorithms
or tricks.
See, Pam is the founder of Mathis Figureoutable, and by that
she means that students can makesense of math through reason and
(01:08):
shouldn't be taught to rely onmemorization or shortcuts.
I, on the other hand, just don'tlike believe in black and white
rules or thinking, and I believethat students should have access
to whatever tools work for thembecause everyone's different.
Now on social media, mostarguments would just end there,
right?
Like, you're wrong.
No, you're wrong.
Okay, cool.
The end.
So I wanted to have Pam on toreally dive into these big
(01:31):
questions with nuance and trulyget to the root of what we each
believe.
Spoiler, we have more in commonthan we initially thought.
This convo is a must listen foranyone passionate about teaching
and learning math.
We explore not just where wediffer, but also the shared goal
that unites us, which is helpingstudents truly think, reason,
(01:52):
and understand, rather than justmemorizing steps or like
spitting out answers.
I hope this episode inspires youto have deeper conversations
with every single person in yourlife because it certainly
inspired me.
I was trying to explain to Davidhow I knew you and I was like,
you know, I didn't really knowPam until Chris and Rob got us
(02:13):
on their Debate Math Podcast.
So our first real interactionwas a debate, which isn't like
the best way to form like a, arelationship with someone.
You would think, especiallybecause our debate was a little
heated, which if you guyshaven't listened to it, go to
the Debate Math Podcast, listento me and Pam's first
conversation via debate, aboutalgorithms, which we're
obviously gonna talk aboutlater.
(02:33):
But my point is that like youwould think after like a debate
where two people aredisagreeing, we wouldn't like
become friends afternecessarily,
Pam Harris (02:40):
Sure enough,
Vanessa Vakharia (02:41):
No, but we kind of did.
Pam Harris (02:43):
Well, I I maybe we both went into it, I think with,
the best intention, desire tohave a conversation.
We listened to each other and wespoke back to each other's
points.
And we didn't just have our, youknow, our thing that we were
gonna say, and I'm not listeningto you, whatever.
And I think it was a realconversation.
Vanessa Vakharia (03:03):
For some reason, whatever it was, I
didn't think the debate wasgoing to be as like pleasant as
it was.
Pam Harris (03:10):
Huh?
Vanessa Vakharia (03:10):
I, that's all I can say.
Like it had nothing to do withyou.
Pam Harris (03:13):
in your face or something like,
Vanessa Vakharia (03:14):
I mean, maybe just the term debate and also
just because, I don't know.
I've heard so many great thingsabout you.
I think maybe I was a bitintimidated, like maybe I was
like, I don't know if like, yourbrand Math Is Figureoutable is
really based on the idea thatalgorithms should not be used as
teaching Tools and we can figureout math, right.
Would you say
Pam Harris (03:35):
those so
Vanessa Vakharia (03:35):
Yeah.
Flip it?
Pam Harris (03:36):
emphasis is we can
Vanessa Vakharia (03:38):
Yes.
Pam Harris (03:39):
It's not rote memorizable, it's figureoutable.
And then there's a sort ofcorollary that, a thing that
follows.
If we are about figuring outmath, if, if, if it means that
we can actually teach kids tologic their way through
problems, which helps themcreate mathematical connections
and relationships, which thenhelps them logic through new
(04:01):
problems, which then helps themcreate new mathematical
relationships, the algorithmscan get in the way of that and
it can actually trap studentsinto not knowing that we can do
that, that that's, that thoseare actually the mental actions
of a mathematician.
Algorithms aren't evil.
They're amazing humanachievements.
They're just not very goodteaching tools because, I'm
(04:22):
pointing at me, people like mecan get trapped in them and
believe that math is somethingthat it isn't.
Vanessa Vakharia (04:28):
Okay.
I wanna get into this so much,and I wanna say just as to wrap
up the, the what I said before,so it doesn't seem like I
thought you were some meanperson, that's not it.
I really admire you, I thinkthere are so many cool things
about you, and I think thiswhole philosophy is something
I'd never really consideredbefore.
But more than that, I hadn'tseen it in action.
And I want people to get alittle taste of what you're
talking about.
But first I was explaining thisto David, okay.
(04:51):
And he said to me, you and yourguests keep talking about
algorithms.
So like, what is an algorithm,exactly?
Pam Harris (04:59):
These are excellent questions because we as a
mathematics education communityhave gotten muddy and we use
words to mean different things,and I don't know that we know
that.
a true algorithm means I can youany numbers, throw'em in, you
follow the steps, all the stepsevery time, and you will come
out with the correct answer.
(05:19):
It took humankind until we hadthe, uh, Roman Arabic numerals
to get to where we were in aboutseven 800 AD when Al-Khwarizmi
created both algebra and hewrote a book that then, um, he
created our, at least precursorsto our digits focused
algorithms.
(05:39):
So first we needed the, thenumer system that we have today,
and then he said, Hey, we couldactually align these numbers up
and just focus on digits.
You don't actually have to knowwhat's going on at all.
You just have to be able to dothese steps in a certain order.
Start with the smallest digits,and then the next digits, and
then the next digits.
Without even reallyunderstanding what's happening
(06:01):
or the numbers involved, you canjust do a bunch of steps, you'll
always get the correct answer.
Well, that was an amazing,historic step for mankind
because before that, the onlypeople who were able to do lots
of digit computations people whohad money.
were in the sort ofintelligentsia, they were the
upper crust that could afford tosend their kids to school to
(06:23):
learn to, to work an Abacus.
So when Al-Khwarizmi created thealgorithms, it was almost like
Gutenberg's printing press.
Like Gutenberg's printing pressis when he was able to print the
Bible and gave the word to thecommon man.
And all of a sudden the commonman could read.
And we had the Renaissance.
Well, Al-Khwarizmi's algorithmswere very similar.
(06:45):
All of a sudden you didn't haveto go to school to learn to work
an Abacus.
Could use an algorithm and allof a sudden the common man could
compute.
So hear me clearly, thealgorithms are amazing, historic
achievements.
They are amazing that we came upwith them.
We can do better.
Vanessa Vakharia (07:00):
Okay, but hold on.
I need an example of analgorithm.
Like give us an ex, like do youknow what I mean?
Like what's, give us a one thatwe all would kind of be,
Pam Harris (07:08):
99 plus 67.
The algorithm would say, linethose numbers up.
So 99 plus 67, I gotta evenpicture this in my head.
So 99 67, that means there's aseven and a nine in the
smallest.
Those are smallest numbers,right?
So we would add the seven andthe nine together, we know that
16.
We'd write down the, the six ofthe 16 part, carry the one or
(07:30):
the 10 depending on how well youunderstand what you're doing.
And then I would add that secondcolumn together.
and then notice I've written thesum of the smallest numbers down
and now the sum of the biggestnumbers down.
And then I would to read theanswer, I have to go the other
direction.
Vanessa Vakharia (07:43):
So let me just make sure I understand.
The algorithm part of it is the,can I call it a rule?
The rule that when we addthings, we line up the digits on
top of each other in order fromsmallest to largest.
We line up the ones, we line upby place value, and we add them
vertically.
That is an algorithm.
Pam Harris (08:02):
Yeah.
And then you have to regroup,then you have to carry
Vanessa Vakharia (08:04):
Yeah.
Like the, the whole, the wholething of it would be like, that
is
Pam Harris (08:07):
our traditional addition algorithm.
Notice I called it thetraditional addition
Vanessa Vakharia (08:11):
yep.
Pam Harris (08:13):
because people will call things standard algorithms,
and I'm gonna push on that hardbecause the way that my mom, who
grew up in Switzerland, learnedto multiply and divide, doesn't
look anything like ourtraditional multiplication and
division algorithms.
I was just in Croatia, um, lastwinter.
Their division algorithm looksnothing like our long division
algorithm.
Uh, many Latin and SouthAmerican countries, we, they use
(08:35):
a different subtractionalgorithm than we do.
So we have to be careful that wedon't assume that our
traditional algorithms arestandard.
Vanessa Vakharia (08:44):
I, It's funny 'cause David just held up a
question to me, which he veryrarely does, he said, why is she
calling that an algorithm asopposed to just doing addition?
And I think, so tell me if I'veunderstood you right.
I think it's called an algorithmbecause there's a specific rule
about how you're supposed to doit and a pattern you're supposed
to follow.
Pam Harris (09:04):
Well, it's a pattern you have to follow every time,
no, no matter what the numbersare.
So let me ask David thisquestion, the problem I used
before was 99 plus 67.
if you think the definition ofaddition is to follow that
algorithm, you line it up, youadd the numbers, and then you're
like, duh, that's what you do.
what if I were to say somethinglike 99 Do you get an urge right
(09:25):
now?
Vanessa Vakharia (09:26):
Exactly, I, because I've, because I've seen
Pam, I'd be like 99 plus 67.
It's a hundred plus 67 minusone, right?
It's 166.
I can just round that 99 up to ahundred.
Pam Harris (09:37):
face right now.
Like, what is
Vanessa Vakharia (09:38):
Oh my God,
Pam Harris (09:39):
Yeah,
Vanessa Vakharia (09:39):
I, here, David, he's like, no, he's
thinking about it.
Well, but why is that not analgorithm, but because that's,
okay.
So now he, here's his question.
Why is that not an algorithm?
Pam Harris (09:49):
Because I wouldn't want to do that strategy for
something like 32 plus 67.
I wouldn't wanna go 33 plus 67minus one.
Vanessa Vakharia (10:01):
Can I try, can I chime in here and tell me if,
well, if what I've learned fromyou is accurate, I think what
Pam might say, even though Icould just ask her, but I wanna
see if I've learned, is thepoint is if you understand what
addition is as a concept, youcan, uh, change your strategy
based on the numbers.
'cause you understand whatadding means.
So you could be like 32 plus 67,it makes more sense to do it
(10:24):
this way.
99 plus 67, oh, I'm gonna dothis because I understand the
concept of addition and I candraw on all this prior knowledge
instead of being like, no matterwhat the numbers are, I have to
line them up.
Am I right?
Pam Harris (10:36):
Yes.
And, and
Vanessa Vakharia (10:38):
You're so kind.
Pam Harris (10:40):
No, no, that was very well said.
I just wanna add in a little bitof an additional thing.
So a lot of really good peoplewould say, if we really get some
conceptual understanding down,then then good, you're, you're
good to go.
And I'm gonna say there'sactually a small set of major
relationships that lead to asmall set of major strategies
that we need kids to own.
Or when we say, well, youunderstood addition, go ahead
(11:02):
and add'em any way you want.
They're gonna be like, I don'tknow what to do.
they don't own enoughrelationships.
We need to help them own.
So the, the strategy you justused was, I'm gonna start at 99,
I'm gonna go to a hundred, addthe 67 and then back up one.
great strategy.
But another kid might say, I'mjust gonna give one from the 67
to the 99.
So now I have that a hundredthat you had, and I'm gonna add
(11:26):
what's left over the 66.
Those are slightly two differentways of thinking about the
problem that will be importantwhen the numbers get done as, as
trivial.
So 99 and 67 I use because, andwe're, we're on a, we're on a
podcast here, so we're trying tomake sure people can,
Vanessa Vakharia (11:40):
I was like, Pam, don't talk too much about
math.
It's been 10 minutes,
Pam Harris (11:45):
so, so people might hear, well, of course you can do
that.
Pam, it's 99.
Well, okay, but what about 98plus 67?
Vanessa Vakharia (11:51):
but wait, so why aren't, but now I'm kind of
with David because now you'vegone into, there's a bunch of
different, like, kind of,
Pam Harris (11:58):
a small set.
It's a, it's a very small
Vanessa Vakharia (12:00):
But how are those not algorithms?
Pam Harris (12:02):
because again, I'm gonna let the numbers influence
which of those small set ofrelationships I'm gonna use
that,
Vanessa Vakharia (12:10):
Hold on, let me, uh, let me think here.
Pam Harris (12:13):
So I have a son who would actually agree with you
right now.
He would say, all of yourstrategies are algorithms, mom.
It's just that for many theywon't work well.
Vanessa Vakharia (12:22):
Right.
Pam Harris (12:23):
One of the relationships that I would
develop in kids, I call the Overstrategy.
Um, I got this from my co-hostKim, uh, on our podcast Math is
Figureoutable podcast, where ifshe was adding something like,
and I'm gonna write this down'cause I don't hold numbers in
my head, all that great.
So I'm writing down 23 and plus49, um, 23 plus 49.
I might think about, I couldline those up and I could do the
(12:46):
thing because I can do that forany problem.
I could also think about what doI know about 23 and 49?
Well, 49 is pretty close to 50.
Well,
Vanessa Vakharia (12:55):
50.
Pam Harris (12:56):
I know what 23 and 50 are.
So 23 and 50, that's 73.
I didn't want 23 and 50, Iwanted 23 and 49.
So it's gotta be one less, it'sgotta be 72.
So that's an, that's an overstrategy that works really well
when you're adding 49.
That's, that's a, it's a goodstrategy.
What, what if you were adding89?
(13:17):
What if you were adding 149?
What if you were adding 999?
What if you're adding 3,496
Vanessa Vakharia (13:25):
we have to stop.
We have to stop.
Pam Harris (13:27):
or, or even better, 3,996.
But 3,996 is so close to 4,000.
No, hang with that one.
3,996 is so close to four.
Come on, you can do it.
Vanessa.
Vanessa Vakharia (13:41):
on.
Pam Harris (13:42):
if I had some random four digit number
Vanessa Vakharia (13:45):
I know, I'm sure.
Yeah.
Okay.
Pam Harris (13:47):
was
Vanessa Vakharia (13:47):
Okay.
Pam Harris (13:48):
it, 4,996, what if we, 4,996?
What if we
Vanessa Vakharia (13:52):
I would add four.
I would put four.
Pam Harris (13:55):
So,
Vanessa Vakharia (13:56):
then I would take four away from whatever the
answer is.
Pam Harris (13:58):
You're now thinking about, what do I know about
4,996.
Ooh, it's really close to 5,000.
I could use that.
Notice that, that, that thoughtprocess is,
Vanessa Vakharia (14:09):
Okay,
Pam Harris (14:09):
think about the numbers.
Let me actually consider thenumbers here
Vanessa Vakharia (14:13):
okay.
Okay.
Pam Harris (14:14):
I dive and choose what to do.
That's the crux of thedifference between a strategy
and an algorithm.
Vanessa Vakharia (14:22):
I think you just, I think you just,
something clicked, even thoughliterally what happened is you
threw a bunch of numbers intothe ether and that some No, it
was, it kind of worked because Ithink, I think something you
said just clicked where you saidthe difference is that you're
thinking about the numbers.
There I think is it.
Is that with a traditionalalgorithm of just line up the
(14:44):
digits by place value and add,there is zero thinking.
You are simply following.
If however, you have a boatloadof, not a boatload, but you've
got a range of strategies tochoose from that require a small
set that require your priorknowledge and thinking and you
get to be empowered to say, I'mgonna choose this because I know
this, all of a sudden thestudent is in the seat of power,
(15:06):
they're thinking and they're notjust following and now it is no
longer simply an algorithm.
Did I get it?
Pam Harris (15:12):
And they're using their agency.
I'd throw that in.
Yes.
Vanessa Vakharia (15:15):
Their agency.
I love it.
Pam Harris (15:16):
have agency, they get to choose, they get to,
they, they get to be
Vanessa Vakharia (15:19):
I got to choose
Pam Harris (15:20):
they get to be influenced by the numbers.
And then say, for this, for thisproblem, I think I'm actually,
how about No.
Ooh, this, I have, I have, Ihave my, my oldest son, I was
teaching high school math, knewwhat I was doing.
Vanessa, I could tell you every,give me a high school problem, I
knew the algorithm, I knew thesteps well because if I didn't,
(15:41):
I would have major impostersyndrome.
So I knew that in order to be ahigh school math teacher, I
needed to know all the things.
But what I knew was to recognizewhich algorithm to do and then
be able to do those steps.
What I didn't ever do was letthe problems influence how I
would attack the problem.
My young son was growing up andhe would logic his way through
(16:04):
problems.
I literally went to him one dayand I was, I just had a
conversation with my kids'teachers who were saying, Pam,
we're kind of concerned that ourkids don't know facts anymore
because we've been told not togive him time fact math and so
we stopped'cause we don't wannagive him math anxiety.
So we stopped giving him timefact math tests'cause we don't
wanna give him math anxiety andnow they don't know their facts
anymore.
Is that important?
(16:24):
And I was like, that'simportant.
Like kids need to know theirfacts.
I went home to my own kid, but,but just like you, I don't wanna
give kids math anxiety.
So this is,
Vanessa Vakharia (16:31):
Right.
Pam Harris (16:32):
was fussing with this.
I'm a high school math teacher.
Think I know everything.
I know it sounds so arrogant,but y'all, I had to be that
almost to be able to survive inthat, that place.
Anyway, I went home to my ownkid and I'm thinking in my head,
do you know your multiplicationfacts?
And I, what I asked him was, doyou know your fives?
I just picked one.
And he said no.
(16:52):
And I was like, I'm sorry, what?
Like, dude, thou shalt know thyfacts.
Like this is I, I, as a mathteacher, I panicked like my own
personal kid has to know his Flike he's got.
So in that panicking, he goes,mom, mom, mom, you don't have to
know your fives if you know yourtens.
And I said, what?
And he goes, you don't have toknow your fives if you know your
(17:14):
tens.
I was like, dude, I heard whatyou said.
I don't know what you mean.
Like Vanessa, at that point inmy life I could not follow.
Now maybe some of your listenersare like, duh Pam.
Well you can look down on me allyou want, but I am the product
of the current system.
Vanessa Vakharia (17:26):
Yeah.
Yeah, yeah.
Pam Harris (17:27):
I was a very successful high school math
teacher who had no idea what hemeant.
Now many, your listeners arelike, I don't either, Pam tell
me.
So I said to him, give me anexample.
said, okay, let's say that youdon't know five times nine.
Well do you know 10 times nine?
That's 95 is half of 10.
So half of 90 is 45.
To which I said, good heavens,that is nine times five.
(17:48):
Does that work every time?
Give me another example.
he said, okay, what about fivetimes 23?
Vanessa?
I'm thinking about single digitfacts and he's playing around
with a pattern withrelationships that can find five
times 23.
So in that moment I was like,wait, okay, 10 times 23 is 230
(18:09):
five is half of 10.
So half of 230 is 115.
And then I literally had to sayto myself, is that five times
23?
I did the algorithm to make
Vanessa Vakharia (18:17):
Yeah, yeah,
Pam Harris (18:18):
but then I thought if you have 10 groups of things
and you cut it in half, you'llhave five groups of things.
And times 10 is so brilliant inour Base
Vanessa Vakharia (18:26):
yeah, yeah, yeah.
Pam Harris (18:27):
that it makes it a relationship worth knowing.
Does that, does that track?
Vanessa Vakharia (18:32):
It totally tracks.
I love this story, by the way.
Pam Harris (18:35):
I'm gonna suggest that that relationship, that
five is half of 10, is one ofthe small set of major
multiplication relationshipsthat we need to build in kids.
Like I could've thought thatway, if I knew it was a thing,
if I'd had a teacher say, Hey,it's sort of important that you
know five is half of 10, andlook how you can use it,
would've used it.
Like I could have let thatinfluence how I solve things,
but nobody ever shared that withme.
(18:56):
So Vanessa, my work isinterviewing, studying naturally
math people and going, wait,wait, wait, wait.
How do you do that?
Oh,
Vanessa Vakharia (19:05):
What's a naturally mathy person?
Pam Harris (19:06):
Ok i'm gonna suggest, and I know there are
good math minds out there, matheducation, people who would
disagree with me on this, and Iwould love to have the
respectful conversation withthem.
I think we all have naturaltalents.
you're
Vanessa Vakharia (19:19):
Okay.
Pam Harris (19:20):
the video, you'll notice there's a basketball
behind me.
Vanessa Vakharia (19:23):
Yeah.
Pam Harris (19:23):
a baller.
I played semi-pro basketball inSwitzerland.
the game.
Um, I, I, I think I have somenatural talent.
To play that game.
But I gotta be honest, therewere people who were much better
than me.
One of the reasons why I was anygood is I worked blooming hard
at it.
So I had some natural talent.
I put a lot of effort into it.
I think my personal kid, thestory I just told, has some
(19:47):
natural talent to run into a lowdose of mathematical patterns
and pull them together make newrelationships in his head.
And now that he owns those, pullthose together, uh, he ran into
the same low dose of patterns weall do.
And for whatever reason, he hadboth the, the sort of talent and
the interest.
(20:07):
Like I think both of those gotogether.
If you have the talent and theinterest, I think pull out a
favorite athlete of yours.
Ooh, Alanis Morissette.
Did I get a name?
I think she has some naturaltalent.
Vanessa Vakharia (20:22):
Dying
Pam Harris (20:22):
She's
Vanessa Vakharia (20:23):
fam.
I love you an athlete,
Pam Harris (20:27):
Well, okay, because, so, so we should probably tell
everybody, you introduced me toAlanis Morissette.
You were like comparing I Ihadn't heard of her before.
Vanessa Vakharia (20:36):
but you know who she is now, right?
Do you know that song?
Pam Harris (20:38):
no, not really.
Sorry.
Vanessa Vakharia (20:40):
like rain on my wedding day.
Pam Harris (20:43):
to it.
Now I know it.
Vanessa Vakharia (20:44):
You've never heard that song?
Pam Harris (20:45):
before then.
I don't think so.
Vanessa Vakharia (20:47):
Really?
Okay.
No problem.
Go on.
Pam Harris (20:49):
me
Vanessa Vakharia (20:49):
It's fine.
Pam Harris (20:49):
ignorant.
Maybe that's probably
Vanessa Vakharia (20:51):
No, no, no, it's fine.
It's totally cool.
Yeah.
I'm not trying to shame you.
Pam Harris (20:54):
has natural talent and drive and eth work ethic
and, and when after interestshe's interest in it.
So I'm gonna suggest there arenaturally mathy people who a,
have maybe some natural talentor, or have enough natural
interest that they go for it.
And either one of those isenough for them to sort of take
interest.
Here's the rub, not the rub.
(21:15):
Here's my point.
We can all be mathy people, butwe have to know what the actual
mathy thing is.
I
Vanessa Vakharia (21:25):
Oh, boy.
Okay.
Yep.
Pam Harris (21:27):
I want, I want we, everybody can do more real math
than fake math.
I know you hate those words.
Sorry.
Vanessa Vakharia (21:34):
Oh my God.
Okay, so there's so muchhappening here.
Okay, so first of all.
Pam Harris (21:38):
take a
Vanessa Vakharia (21:38):
Let's just, let's take a drink.
We'll both take a drink.
What water?
Okay.
Decaf latte for me.
Okay.
So, mm, but electrolytes aregonna be next, so I'm gonna need
to hydrate for what's happeningnext.
Okay.
So first, I guess we probablydon't have time to go into this.
I will have to respectfullydisagree about the term
"naturally mathy", we, we likelydon't have to, and I'll only
(21:58):
say, I'm actually, I'm gonnarespectfully disagree because
that's cool.
But my actual question I don'twanna tell, I wanna ask.
No, I, I'm gonna respectfullydisagree'cause I'm wondering if
this is an opinion you have orsomething that's corroborated by
evidence.
Because all of the evidence I'veseen is that there is no.
Um, you know though, no, becauseit's such a big conversation.
(22:21):
'cause are we talking about likeat birth they pop out and
they're naturally mathy?
Or are we talking aboutculturally they become more
naturally mathy because there'sno actual scientific evidence
that there is like a mathy genein the brain.
That's all.
Something to add on is have youever read, um, Outliers by
Malcolm Gladwell?
Pam Harris (22:39):
And, do I think that some people have a math gene and
some people don't?
Absolutely not.
We all have the math gene.
Do I think some people paybasketball better than others?
Yes.
Is that because they were in thegym a lot with their dad, who
was the coach?
Vanessa Vakharia (22:53):
Yeah.
Pam Harris (22:53):
so as from a young kid, they had a ball in their
hands.
Like, so my high school coach,we, we called his kids gym rats.
Like he, his
Vanessa Vakharia (23:00):
Yeah.
Pam Harris (23:01):
in the gym.
Were they?
And, and then they grew up tobe, uh, basketball coaches as
well.
that because they were naturallybasketball players or is it
because they grew up in the gymwith a
Vanessa Vakharia (23:10):
Yeah.
Yeah, yeah,
Pam Harris (23:11):
So I think nature, nurture, there's a lot of, um,
I, when I meet people who say,Ooh, I've always thought about
numbers that way, and I justassumed everybody else did too.
Are you
Vanessa Vakharia (23:22):
yeah.
Pam Harris (23:22):
that you didn't?
And I'll smile and I go, Ididn't.
And
Vanessa Vakharia (23:24):
Mm-hmm.
Pam Harris (23:25):
at me like, really?
if I ask that person, did youhave some, so I would call that
person kind of naturally mathfor
Vanessa Vakharia (23:33):
Okay.
Pam Harris (23:34):
As they were growing up, they played with
relationships.
I did not,
Vanessa Vakharia (23:39):
Yeah.
Okay.
Pam Harris (23:39):
thought about using relationships and they assumed
the rest of us did too, or theyweren't sure why the rest of us
weren't.
did not.
Many people that I meet, themajority of the math teachers I
work with will say to me, I waslike, you, Pam, believed that
math was wrote, memorizing andmimicking.
And that's what I did.
I did not, I never played withnumbers.
Now, I, I don't know if thereason some people kind of did
(24:03):
that on their own was because.
They had a natural inclination,more talent, or it was because
they had more interest or it wasbecause they had a mom, a dad,
an uncle, an aunt a a, someother significant person in
their life who played withnumbers with them.
So often when I meet that personI'll say, did anybody play with
numbers with you when you were akid and they'd say oh my gosh,
(24:23):
my granddad would put me on hisknee and we played cards and we
always had to figure out ourscore.
And like often, often, so thiswas research I would love to do
when I have a minute, be tolike, like they have some
influential person who early intheir life helped them do the
mental actions of math then thatset them on the course of math.
(24:47):
And sure, that could be, thatcould absolutely be true.
Vanessa Vakharia (24:51):
Okay, so then we're kind of fine.
Then.
You know what, actually, I thinkyou and I are so funny in this
way because I am, so, like, Ithink it's, for us, most of our
like quote unquote disagreementsare simply in language.
Pam Harris (25:03):
Yeah.
Vanessa Vakharia (25:04):
I actually think we're saying the same
thing.
'cause when you say"naturallymathy", it sounds like you're
like, some people are just kindof born with this, like abil.
But you're not saying that atall.
You're you're not saying that atall.
And that's exactly, and you knowwhat, all the research actually
corroborates what you aresaying, which is what outliers
is all about.
Which is when we look at thesepeople that are like the most
skilled mathematicians orathletes or whatever it is
(25:24):
usually nothing genetic.
It is about this 10,000 hours ofpractice.
Right.
And whether you get that
Pam Harris (25:28):
born.
Glad.
We'll also talk about right whenthe, when the hockey players in
Canada were born,
Vanessa Vakharia (25:33):
at different times of the year.
Yeah,
Pam Harris (25:35):
year.
So if they were born so thatthey were the oldest kids in
their
Vanessa Vakharia (25:38):
exactly.
Pam Harris (25:39):
magically they looked like they had more
talent.
So Yeah, absolutely.
I, I completely can.
I think you are right.
I think often where you and Iare have to, where we dive in to
have a longer conversation iswhen there's some vocabulary
that we're like,
Vanessa Vakharia (25:52):
It is a vocab.
Pam Harris (25:53):
do, what do we mean.
Vanessa, I just wanna encourageanybody listening to this
podcast, we in math education,need to have more conversations
like this where we don't justnod at each other and
Vanessa Vakharia (26:04):
Mm-hmm.
Pam Harris (26:04):
yeah, you're good.
So sure, I'm gonna agree.
Like, we need to parse out whatwe're talking about because too
many people think we're all onthe same page when I don't know
that we are
Vanessa Vakharia (26:14):
Yes.
Pam Harris (26:15):
the same page, when in fact we are.
Vanessa Vakharia (26:18):
Which is actually, you know what's so
ironic about this?
Which by the way, AlanisMorissette's, uh, key song was
called, isn't it Ironic?
Um, what's ironic is that so farthis whole podcast has actually,
this whole interview has justbeen about language.
What is an algorithm?
What do we mean when we'resaying algorithm?
You know, it's funny, it's likewhen we use the term common
sense, it bugs me'cause I'mlike, my common sense is not the
(26:38):
same as someone else's commonsense, right?
So it's like there's nodefinition of common sense that
we're all gonna be like, wellit's common sense that blah,
blah, blah.
Because depending what you grewup, depending what your values
are, it's not common.
It's actually not common.
And like when we use the termalgorithm, we don't all mean the
same thing.
So we're having thisconversation and we're actually
saying completely differentthings because we have a
different definition than we'regoing on.
(26:59):
And actually as mathematiciansisn't the number one rule to
define our terms, isn't thatliterally what we're supposed to
do before we get into anyproblem?
Pam Harris (27:07):
It
Vanessa Vakharia (27:07):
Okay.
So,
Pam Harris (27:08):
would be a good idea.
Yeah.
This is, this is tricky andsuper subtle and so let me
Vanessa Vakharia (27:11):
Okay.
Pam Harris (27:12):
what
Vanessa Vakharia (27:13):
Hmm.
Pam Harris (27:13):
You and I, which I love by the way.
Thank you.
We are not.
these terms so that everybodyhas to use our definitions.
We're defining these terms sothat you and I can have a
conversation
Vanessa Vakharia (27:25):
Yes.
Pam Harris (27:26):
we can understand what each other means.
We're not commanding everybodynow take on our definitions.
Vanessa Vakharia (27:32):
Yeah.
This isn't like going in thedictionary of Pam and Vanessa.
Pam Harris (27:35):
Uh,
Vanessa Vakharia (27:35):
No,
Pam Harris (27:36):
uh, me trying to be arrogant to say I know best of
what the
Vanessa Vakharia (27:39):
no.
Pam Harris (27:40):
and everybody
Vanessa Vakharia (27:40):
Love it.
Pam Harris (27:41):
I wanted to
Vanessa Vakharia (27:41):
Thank you for clarifying that.
Actually, no, I really, reallyliked that.
Pam Harris (27:44):
Yeah.
Vanessa Vakharia (27:45):
We're making sure we're speaking the same
language so that we're actually,
Pam Harris (27:48):
we can't have a
Vanessa Vakharia (27:48):
or we can't have a conversation.
Yeah, exactly.
This is just, I mean, there's somuch here.
You know what I wanna ask younow?
Pam Harris (27:55):
Yes.
Vanessa Vakharia (27:56):
Just to, to bring it all together.
You at one point said, ourstudents deserve, to, learn
these reasoning skills.
You know, we don't need them tojust pump out an answers
anymore.
They, we, they deserve this, andwe are robbing them for that.
If we don't um, facilitate that.
How do you think learning in theway that you're proposing versus
learning the standard algorithmactually shapes math identity?
(28:18):
you know, obviously this is apodcast about math, trauma and
math, anxiety.
How do you think teaching oneway versus the other plays into
that?
Pam Harris (28:25):
Huge, so if I'm in a math class and the teacher says,
here is math.
I'm gonna give you a problem.
I'm gonna work it out.
Now we're gonna do it together.
Now you go mimic exactly what Ijust told you to do.
Then the student has no agencyand this, the math becomes this
thing that I'm, uh, uh, I, what,what I do is, is mimic what you
(28:48):
have told me to do.
And then if I like that, if I'm,if I'm rewarded for that now,
I've created, uh, an identityof, ooh, I'm good at, and, and
it was exactly the identity Icreated.
Like I, I was, I was a nerd.
I didn't have friends, whatever,but hey, I, I won round the
world, Arlene Wheeler.
I wonder if she would everlisten to this.
Vanessa Vakharia (29:08):
Who's that?
Pam Harris (29:09):
she was my third grade nemesis.
Well, third grade she won theaward in middle
Vanessa Vakharia (29:13):
Should we find her?
Pam Harris (29:14):
two.
Oh, I love that.
We, it was the two of us thatwere, we were always like, like
we were the quickest we aroundthe world.
It was the two of us that werealways at the end.
Vanessa Vakharia (29:23):
Mm-hmm.
Pam Harris (29:23):
division first, like all the things.
I got this identity that I wassmart and I,
Vanessa Vakharia (29:29):
Okay.
Pam Harris (29:29):
math.
I've heard you kinda talk abouthow, I like your take on that by
the way, that we have thiscultural sort of assumption that
if you're good at math, you'resmart.
Vanessa Vakharia (29:38):
Yeah, it's gross.
Pam Harris (29:39):
I'm just gonna say if you're quick at math.
even good, but if
Vanessa Vakharia (29:44):
Mm.
Mm-hmm.
Yeah.
Pam Harris (29:45):
cause you gotta define good, right?
Vanessa Vakharia (29:47):
Totally.
Totally.
Pam Harris (29:48):
my identity was based on the fact that I was
quick.
And then I became a high schoolmath teacher, and I thought I
was the god of math.
Imagine my dismay when Irealized wasn't doing the mental
actions that other people weredoing it all.
I was memorizing and mimicking,and there was this whole other
world.
Now imagine my joy when Irealized I could do that too.
(30:09):
I just needed to know it was athing.
I bought into the myth and it,it sh completely shaped my
identity.
Now I realize I, I can do thattoo.
I can be in that club and maybebetter, because this is my life
mission, I can invite everyoneelse into that club, like the
real club.
Vanessa Vakharia (30:30):
Okay.
Okay.
I was asking about, you know,how does, uh, teaching
algorithmically and throughmimicking affect, you know,
one's math identity?
And there's kind of two partshere.
On the one hand, you and yourpal, Arlene Wheeler, which if
anyone knows where she is,please do locate her.
You actually formed a verystrong, confident math identity
as a result of this procedure,uh, sorry, as, as a result of
(30:52):
being taught this way becauseyou were, for a while, because
you were able to nail this.
Okay.
So on the one hand, we've gottwo kids here who form a very
strong math identity.
They're quote unquote good atit.
They're quick at it.
They can follow the steps.
However, later in life, whenthat becomes challenged in a
sense because they are presentedwith math in a different way,
all of a sudden that identitykind of collapses.
(31:14):
There's a bit of an identitycrisis, and then there's this
beautiful plot twist romcomending where you discover math
in a whole new light and you'relike, I can do it to like
beautiful, cool, some ups anddowns.
Now forget you and Arlene.
Let's think about the rest ofthe class who are watching you
and Arlene just kill it.
And they're like, oh my God, wesuck.
Pam Harris (31:33):
Yeah.
Vanessa Vakharia (31:34):
So now not only like, you know, we have
this like kind of partialsuccess story with you two, you
and Arlene, that then later endsup in a bit of an existential
crisis, but the rest of theclass is not quote unquote good
at math in this way, and theydon't feel good.
They aren't presented with anyother options.
They just leave the classthinking, well I guess I'm not a
math person and I'm not good atit.
Pam Harris (31:55):
Uh yes.
And what a tragedy.
Because
Vanessa Vakharia (31:57):
and what a tragedy.
Pam Harris (31:59):
in reality, they are a math person and they
Vanessa Vakharia (32:01):
Mm-hmm.
Pam Harris (32:01):
can math if they just need to know it's a thing,
and, and
Vanessa Vakharia (32:05):
Well, yeah,
Pam Harris (32:06):
get experiences to help them build their brain to
be able to math more and more.
Vanessa Vakharia (32:12):
Well, and the crazy thing is everyone is at a
disadvantage in this situation,including the two of you or
whoever it was that formed apositive math identity.
Because like my mind is nowgoing somewhere else here where
I have never thought about it inthis way of thinking like.
You know how there's all thesedis, this, you know, hoop law
now about people being like,well, why can't we just teach it
(32:33):
this way?
There are people who are good atit and those are the people who
are good at math, whatever.
You're kind of living proof ofbeing like, well, hold on.
And now this doesn't, this isnot a general statement, this
doesn't apply to everyone, but alot of people who get through
this system and feel good aboutit, it's not even happening for
the reason that I think we'd alllike, which is like we'd all,
like everyone to deeplyunderstand mathematics and
(32:55):
numbers.
I'm not saying that peopledon't, I really believe that a
lot of people who are, who havebeen taught through this, uh,
mimicking an algorithmic way, Ibeing included, and many of us
being included still have, youknow, number sense and deep
reasoning skills and all of thisstuff.
They've just gained it in adifferent way because they
certainly didn't learn it atschool kind of thing.
Pam Harris (33:15):
Yeah.
Yeah,
Vanessa Vakharia (33:16):
Sorry, I'm saying a million things at once,
but I guess I'm kind of like,where I'm, I'm kind of trying to
get to is like, it's kind ofcrazy to think that we're trying
so deeply to protect this way ofteaching that actually didn't
service most people.
Even those who felt good at mathwere actually being robbed.
Pam Harris (33:37):
Yeah.
Agreed.
Agreed.
And can I add a third
Vanessa Vakharia (33:40):
Oh, say that again.
I liked it.
Pam Harris (33:42):
agree with you.
Vanessa Vakharia (33:42):
Okay.
Yes.
A third group.
Pam Harris (33:45):
add a third group because
Vanessa Vakharia (33:46):
Yeah.
Pam Harris (33:47):
people listening who while they were being taught
algorithmic mimicking, throughit kinda like my kid and said,
Ooh, I could logic my waythrough that.
And they use relationships andconnections and think that the
way they were able to do thesereal math mental actions is
because they were shownalgorithms.
Vanessa Vakharia (34:08):
Mm-hmm.
Pam Harris (34:08):
Like they almost can't, they almost can't
separate it out.
Vanessa Vakharia (34:11):
Yep.
Yep.
Pam Harris (34:12):
this is the way we should teach because it worked
for me.
So does that make sense?
In other words, there's me who,
Vanessa Vakharia (34:17):
I wanna talk about this.
Pam Harris (34:18):
it didn't actually work for me.
And I'm clear on that.
But there are people who aresuccessfully math, they're doing
the mental
Vanessa Vakharia (34:24):
Yep.
Pam Harris (34:24):
and they think it's because of the way they were
taught.
And I'm gonna respectfullyinvite the, that if you're
listening, I respectfully inviteyou to consider if your teacher
hadn't given you things tomimic?
What if your teacher hadactually helped you, knew, knew
the things you were developingon your own, helped you do that
intentionally.
What if they had set upexperiences for you so you could
(34:47):
have developed those things youkind of did on your own,
quicker, faster, better, becausethe teacher knew what they were
and helped you intentionallybuild it.
Think of how far and fast youcould have gone if you hadn't
had to do it on your own.
Does that make sense?
I don't think
Vanessa Vakharia (35:03):
it makes, it makes so much sense.
Pam Harris (35:05):
to try to parse out.
How
Vanessa Vakharia (35:07):
No, I.
Pam Harris (35:07):
how did you become the person you are?
Well, of course it was theexperiences that that created
me.
I respectfully submit that whenyou were shown an algorithm for
whatever reason, I don't knowwhy you were able to see things
through that the rest of us werenot, if we were taught
differently, all of us couldhave done what you did in spite
of the way you were taught.
Vanessa Vakharia (35:27):
Uh, you know what I think is, I think it's
just a really hard ask.
I, I don't think it'simpossible.
I think it's actually, this iswhat like, you know, most
therapy is, is this idea oflike, let's try and deeply
reflect on what, um, you know,we weren't just quote unquote
born this way or, you know,these things all played a role,
but I actually think it's reallyhard to be like, okay, so
(35:47):
imagine you were taughtcompletely differently because
like, it is so hard to parsethose two things apart.
Like even I'm trying to do itbecause obviously I've kind of
fall into this camp of beinglike, yeah, I was taught the
algorithm, but I still havethese deep reasoning skills and
I was able to buildrelationships.
And I imagine, and I think thismight be only because I've sat
through a couple of your lessonsand been like, oh my gosh.
(36:09):
You know, like, I think, I thinkpeople need to experience it in
order to, you know, there's thisthing I read.
Okay, I think you're gonna likethis actually.
So my a, a lot of my work isbased around this phrase by Joe
Dispenza, who's like.
Let's call him a pseudoscientist.
Um, he's like spiritual science,but I love what he says.
(36:29):
He says, uh, his whole phraseis, believe, behave, become.
It's like you have a belief.
So maybe I believe that whatyou're saying could be true.
You know, I believe that maybewhat you're saying is could be
true.
If I was taught in thisdifferent way, I'd have a
different relationship withmath.
I changed my behavior.
So I go to one of your sessions,I actually see it in action and
I'm like, oh my God, thisactually has changed the way I
(36:50):
think.
And now I've become a personwho's like, yep, you know what?
I really believe that this canwork and now I'm gonna teach
this way.
'Cause when I sat in yourproblem strings lesson, like
I've heard of it, I've read thebook, whatever.
I get it.
I was like, this sounds cool,but I, my entire body was on
fire.
Like, I was like, oh mygoodness.
It's that.
Aha.
That's when we know something tobe true.
Pam Harris (37:12):
I love that.
And, and you're not people willsay to me, that's what you mean?
Like, they'll sit in a sessionwith their ma with their jaw
open.
Vanessa Vakharia (37:21):
Yeah.
Pam Harris (37:22):
Yeah.
And, and I'll be honest, I, Idid too when I ran into Kathy
Fasno, so she's an elementarymath researcher.
When I watched her, when Iwatched kids, it wasn't really
watching the teacher at first.
It was, it was like me watchinglearning happening live.
I was like, I want that, I wantthat.
I want, I want to.
And I had to experience it.
(37:43):
And then now my goal is to helpus all experience it.
Yeah.
Vanessa Vakharia (37:47):
Well, and if you think about it when you're
teaching a lesson, what you do,this is actually gonna be
interesting'cause we're gonnapresent together soon.
I, I notice this, you guide usthrough the experience and then
you explain what you did, right?
So you're not intellectualizingit first.
You're giving us the experiencefirst, and then you're unpacking
it anyways, k.
Fine, fine.
We really do have to wrap thisup.
But my point is, the whole thingis
Pam Harris (38:09):
You have a point?
Vanessa Vakharia (38:10):
well, I, I, I know it's, I don't have a point,
but there is one thing I wannasay.
I,
Pam Harris (38:13):
Okay.
Vanessa Vakharia (38:14):
I wanna make clear, I think, at least from my
end, but you can definitelyobviously chime in that if
you're listening to this andyou're a teacher who teaches
through algorithms, okay.
I personally wanna make it very,very clear,
Pam Harris (38:25):
right?
We're not
Vanessa Vakharia (38:26):
which we're not, not only are we not blaming
because like, you know, yeah.
Pam Harris (38:32):
right.
We're not.
We're not.
We're
Vanessa Vakharia (38:33):
There's nothing bad happening.
Pam Harris (38:35):
we're?
Vanessa Vakharia (38:36):
I wanna make it so clear.
I wanna make it so clear thatit's like, Hey, first of all, we
all learn to teach this way, sowhatever you're up to.
Totally cool.
We all have the same mission.
We all want kids to developreasoning skills.
if you are doing that, you arenot doing something wrong.
And this whole episode is meantto be like, oh my God, we're
robbing kids like you are notrobbing kids.
Everything's cool.
I'm sure they're learning,they're, you know, you're
(38:57):
helping them feel confident.
You're helping them build theiridentity.
That is the most importantthing.
And if you're interested inperhaps shifting a little and
exploring how you might teach ina different way, maybe you'll
like it, there's an opportunity.
Would you agree?
Pam Harris (39:12):
Absolutely.
Yes.
Yes.
Very positive.
we know better, we can dobetter.
I'm suggesting there might besomething worth investigating,
worth experiencing
Vanessa Vakharia (39:21):
Yeah.
Pam Harris (39:22):
that you might find, um, will help you shift you're
teaching to reach more studentsin less time.
Vanessa Vakharia (39:30):
Yeah, in less time, that's who doesn't wanna
do that?
And also, I also would imaginethat there are some teachers
that are like, but I don'tunderstand the math fully enough
to be doing all this stuff.
Like I learned throughalgorithms, just so everyone
knows that is me.
Like I'm a trained high schoolmath teacher.
That's Pam.
She's pointing at herself.
(39:50):
That's her.
So.
I would personally invite youtwo to be like, just see what
happens.
Like, take one of theseworkshops, like put, you know,
whatever, if you can see Pampresent, like go do it.
Um, explore it just for your, Iactually think for you, the
listener, and I'm talking tomyself too, it's gonna build
your confidence.
Because what happened is I satin one of these sessions with
Pam and I was like, oh my God,by the way, there's nothing that
(40:11):
intimidates me more thanelementary school math.
Okay.
Like the worst.
Like, I'm just like, oh God.
So I was very intimidated andyeah, right.
I found myself having so manyahas, like sitting quietly in
the back being like, oh my, ohmy God, oh my God.
And I was like, oh my God, Ifeel like I understand more than
I gave myself credit for.
So even if you just go as anexplor, uh, exploratory, session
(40:32):
for yourself, just, I want allteachers to have the confidence
themselves.
And you know, I think so manyteachers have walked away with
so much math trauma from the waywe were taught, I just want you
to have a good experience.
You know, because yeah, just tosee that there's hope.
We can all be learning andgrowing and changing and there's
magic in math and we candiscover that every day.
(40:53):
Tell people where to go before Iwrap up with the final two
questions.
Pam Harris (40:56):
Excellent.
So the first thing I would dois, uh, suggest, wait.
I have a free ebook.
That would be a great place foryou to start.
So you can go tomathisfigureoutable.com/big B.
'cause I think it's big, it's abig, it's a big add to the
world.
That would be a great place foryou to start.
We have the math isFigureoutable podcast where Kim,
we've talked about a little bit,uh, where she And I talk about
(41:17):
all things, Math isFigureoutable from super young
all the way through high school.
Um, another thing that you coulddo is join me on social media at
the hashtag Math Strat Chatwhere I threw out a problem on
Wednesday evenings to peoplefrom around the world chat about
their strategies and comment oneach other's, uh, thinking.
So that's totally fun.
Those would be some super goodways to sort of kick off.
(41:37):
Uh, joining me to make math morefigureoutable.
Vanessa Vakharia (41:41):
Oh my God.
I can't believe we have to endthis.
We didn't even talk about thefake math thing, but I mean,
whatever.
Pam Harris (41:45):
We could send'em to the Debate Math Podcast if they
wanted to hear a little bit
Vanessa Vakharia (41:48):
You can, but I feel like both of us have
changed since then.
Pam Harris (41:51):
well, okay.
Vanessa Vakharia (41:52):
You know, it's not important.
Um, it's not important because Ifeel like it's old news and I
feel like we actually covered itin a way by talking about all
these other things.
Pam Harris (42:00):
Well, it's
Vanessa Vakharia (42:01):
Do you?
Pam Harris (42:01):
mean.
Everything we talked about todayIs the important stuff.
Vanessa Vakharia (42:04):
Is what I mean.
David's doing this, by the way.
He is doing the wrap up.
I love telling people that.
It's so fun.
Okay, so final two questions.
Quick fire.
I ask every guest.
Pam Harris (42:13):
I'm ready.
Vanessa Vakharia (42:13):
Number one, if there's one thing you could
change about the way math istaught in school is, what would
it be?
Pam Harris (42:21):
Holy.
I would help teachers experiencewhat it means to do the mental
actions of math thing, becausethat would shift everything they
do.
Vanessa Vakharia (42:31):
I love it.
Okay.
So what if a teacher's listeningto this and they're like, you
know, this is so awesome.
It sounds really great, but Ijust, I'm not a math person and
that's just it.
I'm just not a math person.
What would you say?
Pam Harris (42:42):
I would say you're, you're not a math person yet, or
you actually are a math person.
Um, and, and one of my favoritethings to do is to ask them, how
do you think about this problem?
And, and then, and 99% of thetime people will go, well, you
know, that's how you think aboutit, but you're supposed to do
the right way.
And I'm like, what if we couldteach all math the way you just
logiced your way through thatone.
Vanessa Vakharia (43:03):
Oh, I love that.
Well, that's all she wrote.
I mean, it's not, I have like 20more questions, but that's all.
That's all we have time for iton today's segment of Pam and
Vanessa, figure out what wordsand math mean and truly
understand each other.
Thank you so much.
(43:23):
This was so much fun.
Pam Harris (43:25):
You're a gift.
Vanessa Vakharia (43:26):
Oh my God, you're a gift.
This is so sweet.
We should tell Chris and Robthat you know they really were
the start of our love story.
Thanks guys.
The matchmaker, the matchmakers.
Okay, until next time.
Pam Harris (43:37):
Woo.
Vanessa Vakharia (43:39):
Okay, guys, be honest.
When we started that convo, didyou think we'd be besties by the
end of it?
I loved this talk with Pam.
In a world where our differencesand disagreements are amplified.
I just found it so refreshing tohave time for actually nuanced
debate about some math questionsthat people seem to lose their
minds about online, but thatreally shouldn't be so
(44:00):
controversial.
Especially when we all have thesame goal, which is just helping
kids learn and feel confident.
So, I have some homework for youthis week.
Maybe my biggest challenge foryou yet.
I want you to find someone youdisagree with about math or like
anything, and sit down for anhour, okay, that's, that's a
long time.
But like, sit down for like 20minutes and really talk about
(44:21):
it.
See each other's side and trulytry to understand where they're
coming from and where youactually might share common
ground, one piece of commonground.
And, ahem, a good way to breakthe ice with this person might
just be to send them thisepisode.
And whether you try thischallenge out or just wanna
share your thoughts on theepisode, please text the
podcast, DM me on Instagram atthe Math Guru, or email me at
(44:44):
vanessa@themathguru.ca.
Links to do all of those thingsare in the show notes.
Also, my audio book isofficially out and I cannot
believe how many of you guyshave already bought a copy and
are listening to me narrate MathTherapy in my voice, in your
ears, that's actually wild.
You can grab it wherever you buyyour audio books, including
Audible and actually Spotifywhere it just got added like
(45:06):
today.
Finally, my Math Therapy merchline has dropped and I'm dying
for the cute pics you guys aresending me with you in your MT
swag, please keep sending methose, and you can shop the drop
at maththerapy.com/merch.
Math Therapy is hosted by me,Vanessa Vakharia.
It's produced and edited byDavid Kochberg, and our theme
music is by our band, GoodnightSunrise.
(45:28):
Okay, that's it.
Go forth.
Trust yourself.
And remember, your innermathematician is already in
there.
You just have to give them themic.
Pam Harris (45:41):
They're logical relationships, but we're not
logicing our, see, I've made itmy own word.
They're logicing.
We're
Vanessa Vakharia (45:46):
I like it.
Pam Harris (45:46):
logicing our way.
What is on your shirt?
Vanessa Vakharia (45:50):
Brittany Spears, do you know who that is?
Pam Harris (45:51):
do, but I, there's two people on your shirt that,
so they can't be.
Vanessa Vakharia (45:57):
They're, they're both just Brittany.
It's like both, just twodifferent,
Pam Harris (45:59):
right now.
There's
Vanessa Vakharia (46:00):
no,
Pam Harris (46:01):
on your shirt.
Sorry.
Okay.
Pop, pop culture ignorant here.
Vanessa Vakharia (46:07):
I mean, no, you're not ignorant.
You're, you know who BritneySpears is.
Pam Harris (46:10):
mean, ish.
Vanessa Vakharia (46:11):
Yeah, it's just a very poorly designed
shirt.
Pam Harris (46:15):
We won't tell anyone that you said that.
Vanessa Vakharia (46:18):
Okay.
Pam Harris (46:18):
We won't put that out publicly or anything.
Vanessa Vakharia (46:22):
Oh my God.
Okay.
one of my favorite things to do is to ask how do
you think about this problem?
99% of the time people will go,well, you know, that's how you
think about it, but you'resupposed to do the right way.
And I'm like, what if we couldteach all math the way you just
logiced your way through thatone.
Algorithms amazing humanachievements.
They're just not very goodteaching tools because, people
like me can get trapped in themand believe that math is
(00:23):
something that it isn't.
Vanessa Vakharia (00:26):
Okay guys, it's me, Vanessa, and I could
not be more excited for you tohear today's episode Okay, I
know I say that every singleepisode is gonna change your
life, but this one is seriouslygoing to change your life.
Because the conversation I'msharing with you today is not
just about how we can improvemath education, but literally
about how we can improve the waywe all talk to each other as
people.
(00:47):
The first time I actually had aconversation with Pam Harris was
literally an hour long argumentbecause we were both guests on
the Debate Math Podcast, so wewere debating, we were actually
discussing whether studentsshould be able to use algorithms
or tricks.
See, Pam is the founder of Mathis Figureoutable, and by that
she means that students can makesense of math through reason and
(01:08):
shouldn't be taught to rely onmemorization or shortcuts.
I, on the other hand, just don'tlike believe in black and white
rules or thinking, and I believethat students should have access
to whatever tools work for thembecause everyone's different.
Now on social media, mostarguments would just end there,
right?
Like, you're wrong.
No, you're wrong.
Okay, cool.
The end.
So I wanted to have Pam on toreally dive into these big
(01:31):
questions with nuance and trulyget to the root of what we each
believe.
Spoiler, we have more in commonthan we initially thought.
This convo is a must listen foranyone passionate about teaching
and learning math.
We explore not just where wediffer, but also the shared goal
that unites us, which is helpingstudents truly think, reason,
(01:52):
and understand, rather than justmemorizing steps or like
spitting out answers.
I hope this episode inspires youto have deeper conversations
with every single person in yourlife because it certainly
inspired me.
I was trying to explain to Davidhow I knew you and I was like,
you know, I didn't really knowPam until Chris and Rob got us
(02:13):
on their Debate Math Podcast.
So our first real interactionwas a debate, which isn't like
the best way to form like a, arelationship with someone.
You would think, especiallybecause our debate was a little
heated, which if you guyshaven't listened to it, go to
the Debate Math Podcast, listento me and Pam's first
conversation via debate, aboutalgorithms, which we're
obviously gonna talk aboutlater.
(02:33):
But my point is that like youwould think after like a debate
where two people aredisagreeing, we wouldn't like
become friends afternecessarily,
Pam Harris (02:40):
Sure enough,
Vanessa Vakharia (02:41):
No, but we kind of did.
Pam Harris (02:43):
Well, I I maybe we both went into it, I think with,
the best intention, desire tohave a conversation.
We listened to each other and wespoke back to each other's
points.
And we didn't just have our, youknow, our thing that we were
gonna say, and I'm not listeningto you, whatever.
And I think it was a realconversation.
Vanessa Vakharia (03:03):
For some reason, whatever it was, I
didn't think the debate wasgoing to be as like pleasant as
it was.
Pam Harris (03:10):
Huh?
Vanessa Vakharia (03:10):
I, that's all I can say.
Like it had nothing to do withyou.
Pam Harris (03:13):
in your face or something like,
Vanessa Vakharia (03:14):
I mean, maybe just the term debate and also
just because, I don't know.
I've heard so many great thingsabout you.
I think maybe I was a bitintimidated, like maybe I was
like, I don't know if like, yourbrand Math Is Figureoutable is
really based on the idea thatalgorithms should not be used as
teaching Tools and we can figureout math, right.
Would you say
Pam Harris (03:35):
those so
Vanessa Vakharia (03:35):
Yeah.
Flip it?
Pam Harris (03:36):
emphasis is we can
Vanessa Vakharia (03:38):
Yes.
Pam Harris (03:39):
It's not rote memorizable, it's figureoutable.
And then there's a sort ofcorollary that, a thing that
follows.
If we are about figuring outmath, if, if, if it means that
we can actually teach kids tologic their way through
problems, which helps themcreate mathematical connections
and relationships, which thenhelps them logic through new
(04:01):
problems, which then helps themcreate new mathematical
relationships, the algorithmscan get in the way of that and
it can actually trap studentsinto not knowing that we can do
that, that that's, that thoseare actually the mental actions
of a mathematician.
Algorithms aren't evil.
They're amazing humanachievements.
They're just not very goodteaching tools because, I'm
(04:22):
pointing at me, people like mecan get trapped in them and
believe that math is somethingthat it isn't.
Vanessa Vakharia (04:28):
Okay.
I wanna get into this so much,and I wanna say just as to wrap
up the, the what I said before,so it doesn't seem like I
thought you were some meanperson, that's not it.
I really admire you, I thinkthere are so many cool things
about you, and I think thiswhole philosophy is something
I'd never really consideredbefore.
But more than that, I hadn'tseen it in action.
And I want people to get alittle taste of what you're
talking about.
But first I was explaining thisto David, okay.
(04:51):
And he said to me, you and yourguests keep talking about
algorithms.
So like, what is an algorithm,exactly?
Pam Harris (04:59):
These are excellent questions because we as a
mathematics education communityhave gotten muddy and we use
words to mean different things,and I don't know that we know
that.
a true algorithm means I can youany numbers, throw'em in, you
follow the steps, all the stepsevery time, and you will come
out with the correct answer.
(05:19):
It took humankind until we hadthe, uh, Roman Arabic numerals
to get to where we were in aboutseven 800 AD when Al-Khwarizmi
created both algebra and hewrote a book that then, um, he
created our, at least precursorsto our digits focused
algorithms.
(05:39):
So first we needed the, thenumer system that we have today,
and then he said, Hey, we couldactually align these numbers up
and just focus on digits.
You don't actually have to knowwhat's going on at all.
You just have to be able to dothese steps in a certain order.
Start with the smallest digits,and then the next digits, and
then the next digits.
Without even reallyunderstanding what's happening
(06:01):
or the numbers involved, you canjust do a bunch of steps, you'll
always get the correct answer.
Well, that was an amazing,historic step for mankind
because before that, the onlypeople who were able to do lots
of digit computations people whohad money.
were in the sort ofintelligentsia, they were the
upper crust that could afford tosend their kids to school to
(06:23):
learn to, to work an Abacus.
So when Al-Khwarizmi created thealgorithms, it was almost like
Gutenberg's printing press.
Like Gutenberg's printing pressis when he was able to print the
Bible and gave the word to thecommon man.
And all of a sudden the commonman could read.
And we had the Renaissance.
Well, Al-Khwarizmi's algorithmswere very similar.
(06:45):
All of a sudden you didn't haveto go to school to learn to work
an Abacus.
Could use an algorithm and allof a sudden the common man could
compute.
So hear me clearly, thealgorithms are amazing, historic
achievements.
They are amazing that we came upwith them.
We can do better.
Vanessa Vakharia (07:00):
Okay, but hold on.
I need an example of analgorithm.
Like give us an ex, like do youknow what I mean?
Like what's, give us a one thatwe all would kind of be,
Pam Harris (07:08):
99 plus 67.
The algorithm would say, linethose numbers up.
So 99 plus 67, I gotta evenpicture this in my head.
So 99 67, that means there's aseven and a nine in the
smallest.
Those are smallest numbers,right?
So we would add the seven andthe nine together, we know that
16.
We'd write down the, the six ofthe 16 part, carry the one or
(07:30):
the 10 depending on how well youunderstand what you're doing.
And then I would add that secondcolumn together.
and then notice I've written thesum of the smallest numbers down
and now the sum of the biggestnumbers down.
And then I would to read theanswer, I have to go the other
direction.
Vanessa Vakharia (07:43):
So let me just make sure I understand.
The algorithm part of it is the,can I call it a rule?
The rule that when we addthings, we line up the digits on
top of each other in order fromsmallest to largest.
We line up the ones, we line upby place value, and we add them
vertically.
That is an algorithm.
Pam Harris (08:02):
Yeah.
And then you have to regroup,then you have to carry
Vanessa Vakharia (08:04):
Yeah.
Like the, the whole, the wholething of it would be like, that
is
Pam Harris (08:07):
our traditional addition algorithm.
Notice I called it thetraditional addition
Vanessa Vakharia (08:11):
yep.
Pam Harris (08:13):
because people will call things standard algorithms,
and I'm gonna push on that hardbecause the way that my mom, who
grew up in Switzerland, learnedto multiply and divide, doesn't
look anything like ourtraditional multiplication and
division algorithms.
I was just in Croatia, um, lastwinter.
Their division algorithm looksnothing like our long division
algorithm.
Uh, many Latin and SouthAmerican countries, we, they use
(08:35):
a different subtractionalgorithm than we do.
So we have to be careful that wedon't assume that our
traditional algorithms arestandard.
Vanessa Vakharia (08:44):
I, It's funny 'cause David just held up a
question to me, which he veryrarely does, he said, why is she
calling that an algorithm asopposed to just doing addition?
And I think, so tell me if I'veunderstood you right.
I think it's called an algorithmbecause there's a specific rule
about how you're supposed to doit and a pattern you're supposed
to follow.
Pam Harris (09:04):
Well, it's a pattern you have to follow every time,
no, no matter what the numbersare.
So let me ask David thisquestion, the problem I used
before was 99 plus 67.
if you think the definition ofaddition is to follow that
algorithm, you line it up, youadd the numbers, and then you're
like, duh, that's what you do.
what if I were to say somethinglike 99 Do you get an urge right
(09:25):
now?
Vanessa Vakharia (09:26):
Exactly, I, because I've, because I've seen
Pam, I'd be like 99 plus 67.
It's a hundred plus 67 minusone, right?
It's 166.
I can just round that 99 up to ahundred.
Pam Harris (09:37):
face right now.
Like, what is
Vanessa Vakharia (09:38):
Oh my God,
Pam Harris (09:39):
Yeah,
Vanessa Vakharia (09:39):
I, here, David, he's like, no, he's
thinking about it.
Well, but why is that not analgorithm, but because that's,
okay.
So now he, here's his question.
Why is that not an algorithm?
Pam Harris (09:49):
Because I wouldn't want to do that strategy for
something like 32 plus 67.
I wouldn't wanna go 33 plus 67minus one.
Vanessa Vakharia (10:01):
Can I try, can I chime in here and tell me if,
well, if what I've learned fromyou is accurate, I think what
Pam might say, even though Icould just ask her, but I wanna
see if I've learned, is thepoint is if you understand what
addition is as a concept, youcan, uh, change your strategy
based on the numbers.
'cause you understand whatadding means.
So you could be like 32 plus 67,it makes more sense to do it
(10:24):
this way.
99 plus 67, oh, I'm gonna dothis because I understand the
concept of addition and I candraw on all this prior knowledge
instead of being like, no matterwhat the numbers are, I have to
line them up.
Am I right?
Pam Harris (10:36):
Yes.
And, and
Vanessa Vakharia (10:38):
You're so kind.
Pam Harris (10:40):
No, no, that was very well said.
I just wanna add in a little bitof an additional thing.
So a lot of really good peoplewould say, if we really get some
conceptual understanding down,then then good, you're, you're
good to go.
And I'm gonna say there'sactually a small set of major
relationships that lead to asmall set of major strategies
that we need kids to own.
Or when we say, well, youunderstood addition, go ahead
(11:02):
and add'em any way you want.
They're gonna be like, I don'tknow what to do.
they don't own enoughrelationships.
We need to help them own.
So the, the strategy you justused was, I'm gonna start at 99,
I'm gonna go to a hundred, addthe 67 and then back up one.
great strategy.
But another kid might say, I'mjust gonna give one from the 67
to the 99.
So now I have that a hundredthat you had, and I'm gonna add
(11:26):
what's left over the 66.
Those are slightly two differentways of thinking about the
problem that will be importantwhen the numbers get done as, as
trivial.
So 99 and 67 I use because, andwe're, we're on a, we're on a
podcast here, so we're trying tomake sure people can,
Vanessa Vakharia (11:40):
I was like, Pam, don't talk too much about
math.
It's been 10 minutes,
Pam Harris (11:45):
so, so people might hear, well, of course you can do
that.
Pam, it's 99.
Well, okay, but what about 98plus 67?
Vanessa Vakharia (11:51):
but wait, so why aren't, but now I'm kind of
with David because now you'vegone into, there's a bunch of
different, like, kind of,
Pam Harris (11:58):
a small set.
It's a, it's a very small
Vanessa Vakharia (12:00):
But how are those not algorithms?
Pam Harris (12:02):
because again, I'm gonna let the numbers influence
which of those small set ofrelationships I'm gonna use
that,
Vanessa Vakharia (12:10):
Hold on, let me, uh, let me think here.
Pam Harris (12:13):
So I have a son who would actually agree with you
right now.
He would say, all of yourstrategies are algorithms, mom.
It's just that for many theywon't work well.
Vanessa Vakharia (12:22):
Right.
Pam Harris (12:23):
One of the relationships that I would
develop in kids, I call the Overstrategy.
Um, I got this from my co-hostKim, uh, on our podcast Math is
Figureoutable podcast, where ifshe was adding something like,
and I'm gonna write this down'cause I don't hold numbers in
my head, all that great.
So I'm writing down 23 and plus49, um, 23 plus 49.
I might think about, I couldline those up and I could do the
(12:46):
thing because I can do that forany problem.
I could also think about what doI know about 23 and 49?
Well, 49 is pretty close to 50.
Well,
Vanessa Vakharia (12:55):
50.
Pam Harris (12:56):
I know what 23 and 50 are.
So 23 and 50, that's 73.
I didn't want 23 and 50, Iwanted 23 and 49.
So it's gotta be one less, it'sgotta be 72.
So that's an, that's an overstrategy that works really well
when you're adding 49.
That's, that's a, it's a goodstrategy.
What, what if you were adding89?
(13:17):
What if you were adding 149?
What if you were adding 999?
What if you're adding 3,496
Vanessa Vakharia (13:25):
we have to stop.
We have to stop.
Pam Harris (13:27):
or, or even better, 3,996.
But 3,996 is so close to 4,000.
No, hang with that one.
3,996 is so close to four.
Come on, you can do it.
Vanessa.
Vanessa Vakharia (13:41):
on.
Pam Harris (13:42):
if I had some random four digit number
Vanessa Vakharia (13:45):
I know, I'm sure.
Yeah.
Okay.
Pam Harris (13:47):
was
Vanessa Vakharia (13:47):
Okay.
Pam Harris (13:48):
it, 4,996, what if we, 4,996?
What if we
Vanessa Vakharia (13:52):
I would add four.
I would put four.
Pam Harris (13:55):
So,
Vanessa Vakharia (13:56):
then I would take four away from whatever the
answer is.
Pam Harris (13:58):
You're now thinking about, what do I know about
4,996.
Ooh, it's really close to 5,000.
I could use that.
Notice that, that, that thoughtprocess is,
Vanessa Vakharia (14:09):
Okay,
Pam Harris (14:09):
think about the numbers.
Let me actually consider thenumbers here
Vanessa Vakharia (14:13):
okay.
Okay.
Pam Harris (14:14):
I dive and choose what to do.
That's the crux of thedifference between a strategy
and an algorithm.
Vanessa Vakharia (14:22):
I think you just, I think you just,
something clicked, even thoughliterally what happened is you
threw a bunch of numbers intothe ether and that some No, it
was, it kind of worked because Ithink, I think something you
said just clicked where you saidthe difference is that you're
thinking about the numbers.
There I think is it.
Is that with a traditionalalgorithm of just line up the
(14:44):
digits by place value and add,there is zero thinking.
You are simply following.
If however, you have a boatloadof, not a boatload, but you've
got a range of strategies tochoose from that require a small
set that require your priorknowledge and thinking and you
get to be empowered to say, I'mgonna choose this because I know
this, all of a sudden thestudent is in the seat of power,
(15:06):
they're thinking and they're notjust following and now it is no
longer simply an algorithm.
Did I get it?
Pam Harris (15:12):
And they're using their agency.
I'd throw that in.
Yes.
Vanessa Vakharia (15:15):
Their agency.
I love it.
Pam Harris (15:16):
have agency, they get to choose, they get to,
they, they get to be
Vanessa Vakharia (15:19):
I got to choose
Pam Harris (15:20):
they get to be influenced by the numbers.
And then say, for this, for thisproblem, I think I'm actually,
how about No.
Ooh, this, I have, I have, Ihave my, my oldest son, I was
teaching high school math, knewwhat I was doing.
Vanessa, I could tell you every,give me a high school problem, I
knew the algorithm, I knew thesteps well because if I didn't,
(15:41):
I would have major impostersyndrome.
So I knew that in order to be ahigh school math teacher, I
needed to know all the things.
But what I knew was to recognizewhich algorithm to do and then
be able to do those steps.
What I didn't ever do was letthe problems influence how I
would attack the problem.
My young son was growing up andhe would logic his way through
(16:04):
problems.
I literally went to him one dayand I was, I just had a
conversation with my kids'teachers who were saying, Pam,
we're kind of concerned that ourkids don't know facts anymore
because we've been told not togive him time fact math and so
we stopped'cause we don't wannagive him math anxiety.
So we stopped giving him timefact math tests'cause we don't
wanna give him math anxiety andnow they don't know their facts
anymore.
Is that important?
(16:24):
And I was like, that'simportant.
Like kids need to know theirfacts.
I went home to my own kid, but,but just like you, I don't wanna
give kids math anxiety.
So this is,
Vanessa Vakharia (16:31):
Right.
Pam Harris (16:32):
was fussing with this.
I'm a high school math teacher.
Think I know everything.
I know it sounds so arrogant,but y'all, I had to be that
almost to be able to survive inthat, that place.
Anyway, I went home to my ownkid and I'm thinking in my head,
do you know your multiplicationfacts?
And I, what I asked him was, doyou know your fives?
I just picked one.
And he said no.
(16:52):
And I was like, I'm sorry, what?
Like, dude, thou shalt know thyfacts.
Like this is I, I, as a mathteacher, I panicked like my own
personal kid has to know his Flike he's got.
So in that panicking, he goes,mom, mom, mom, you don't have to
know your fives if you know yourtens.
And I said, what?
And he goes, you don't have toknow your fives if you know your
(17:14):
tens.
I was like, dude, I heard whatyou said.
I don't know what you mean.
Like Vanessa, at that point inmy life I could not follow.
Now maybe some of your listenersare like, duh Pam.
Well you can look down on me allyou want, but I am the product
of the current system.
Vanessa Vakharia (17:26):
Yeah.
Yeah, yeah.
Pam Harris (17:27):
I was a very successful high school math
teacher who had no idea what hemeant.
Now many, your listeners arelike, I don't either, Pam tell
me.
So I said to him, give me anexample.
said, okay, let's say that youdon't know five times nine.
Well do you know 10 times nine?
That's 95 is half of 10.
So half of 90 is 45.
To which I said, good heavens,that is nine times five.
(17:48):
Does that work every time?
Give me another example.
he said, okay, what about fivetimes 23?
Vanessa?
I'm thinking about single digitfacts and he's playing around
with a pattern withrelationships that can find five
times 23.
So in that moment I was like,wait, okay, 10 times 23 is 230
(18:09):
five is half of 10.
So half of 230 is 115.
And then I literally had to sayto myself, is that five times
23?
I did the algorithm to make
Vanessa Vakharia (18:17):
Yeah, yeah,
Pam Harris (18:18):
but then I thought if you have 10 groups of things
and you cut it in half, you'llhave five groups of things.
And times 10 is so brilliant inour Base
Vanessa Vakharia (18:26):
yeah, yeah, yeah.
Pam Harris (18:27):
that it makes it a relationship worth knowing.
Does that, does that track?
Vanessa Vakharia (18:32):
It totally tracks.
I love this story, by the way.
Pam Harris (18:35):
I'm gonna suggest that that relationship, that
five is half of 10, is one ofthe small set of major
multiplication relationshipsthat we need to build in kids.
Like I could've thought thatway, if I knew it was a thing,
if I'd had a teacher say, Hey,it's sort of important that you
know five is half of 10, andlook how you can use it,
would've used it.
Like I could have let thatinfluence how I solve things,
but nobody ever shared that withme.
(18:56):
So Vanessa, my work isinterviewing, studying naturally
math people and going, wait,wait, wait, wait.
How do you do that?
Oh,
Vanessa Vakharia (19:05):
What's a naturally mathy person?
Pam Harris (19:06):
Ok i'm gonna suggest, and I know there are
good math minds out there, matheducation, people who would
disagree with me on this, and Iwould love to have the
respectful conversation withthem.
I think we all have naturaltalents.
you're
Vanessa Vakharia (19:19):
Okay.
Pam Harris (19:20):
the video, you'll notice there's a basketball
behind me.
Vanessa Vakharia (19:23):
Yeah.
Pam Harris (19:23):
a baller.
I played semi-pro basketball inSwitzerland.
the game.
Um, I, I, I think I have somenatural talent.
To play that game.
But I gotta be honest, therewere people who were much better
than me.
One of the reasons why I was anygood is I worked blooming hard
at it.
So I had some natural talent.
I put a lot of effort into it.
I think my personal kid, thestory I just told, has some
(19:47):
natural talent to run into a lowdose of mathematical patterns
and pull them together make newrelationships in his head.
And now that he owns those, pullthose together, uh, he ran into
the same low dose of patterns weall do.
And for whatever reason, he hadboth the, the sort of talent and
the interest.
(20:07):
Like I think both of those gotogether.
If you have the talent and theinterest, I think pull out a
favorite athlete of yours.
Ooh, Alanis Morissette.
Did I get a name?
I think she has some naturaltalent.
Vanessa Vakharia (20:22):
Dying
Pam Harris (20:22):
She's
Vanessa Vakharia (20:23):
fam.
I love you an athlete,
Pam Harris (20:27):
Well, okay, because, so, so we should probably tell
everybody, you introduced me toAlanis Morissette.
You were like comparing I Ihadn't heard of her before.
Vanessa Vakharia (20:36):
but you know who she is now, right?
Do you know that song?
Pam Harris (20:38):
no, not really.
Sorry.
Vanessa Vakharia (20:40):
like rain on my wedding day.
Pam Harris (20:43):
to it.
Now I know it.
Vanessa Vakharia (20:44):
You've never heard that song?
Pam Harris (20:45):
before then.
I don't think so.
Vanessa Vakharia (20:47):
Really?
Okay.
No problem.
Go on.
Pam Harris (20:49):
me
Vanessa Vakharia (20:49):
It's fine.
Pam Harris (20:49):
ignorant.
Maybe that's probably
Vanessa Vakharia (20:51):
No, no, no, it's fine.
It's totally cool.
Yeah.
I'm not trying to shame you.
Pam Harris (20:54):
has natural talent and drive and eth work ethic
and, and when after interestshe's interest in it.
So I'm gonna suggest there arenaturally mathy people who a,
have maybe some natural talentor, or have enough natural
interest that they go for it.
And either one of those isenough for them to sort of take
interest.
Here's the rub, not the rub.
(21:15):
Here's my point.
We can all be mathy people, butwe have to know what the actual
mathy thing is.
I
Vanessa Vakharia (21:25):
Oh, boy.
Okay.
Yep.
Pam Harris (21:27):
I want, I want we, everybody can do more real math
than fake math.
I know you hate those words.
Sorry.
Vanessa Vakharia (21:34):
Oh my God.
Okay, so there's so muchhappening here.
Okay, so first of all.
Pam Harris (21:38):
take a
Vanessa Vakharia (21:38):
Let's just, let's take a drink.
We'll both take a drink.
What water?
Okay.
Decaf latte for me.
Okay.
So, mm, but electrolytes aregonna be next, so I'm gonna need
to hydrate for what's happeningnext.
Okay.
So first, I guess we probablydon't have time to go into this.
I will have to respectfullydisagree about the term
"naturally mathy", we, we likelydon't have to, and I'll only
(21:58):
say, I'm actually, I'm gonnarespectfully disagree because
that's cool.
But my actual question I don'twanna tell, I wanna ask.
No, I, I'm gonna respectfullydisagree'cause I'm wondering if
this is an opinion you have orsomething that's corroborated by
evidence.
Because all of the evidence I'veseen is that there is no.
Um, you know though, no, becauseit's such a big conversation.
(22:21):
'cause are we talking about likeat birth they pop out and
they're naturally mathy?
Or are we talking aboutculturally they become more
naturally mathy because there'sno actual scientific evidence
that there is like a mathy genein the brain.
That's all.
Something to add on is have youever read, um, Outliers by
Malcolm Gladwell?
Pam Harris (22:39):
And, do I think that some people have a math gene and
some people don't?
Absolutely not.
We all have the math gene.
Do I think some people paybasketball better than others?
Yes.
Is that because they were in thegym a lot with their dad, who
was the coach?
Vanessa Vakharia (22:53):
Yeah.
Pam Harris (22:53):
so as from a young kid, they had a ball in their
hands.
Like, so my high school coach,we, we called his kids gym rats.
Like he, his
Vanessa Vakharia (23:00):
Yeah.
Pam Harris (23:01):
in the gym.
Were they?
And, and then they grew up tobe, uh, basketball coaches as
well.
that because they were naturallybasketball players or is it
because they grew up in the gymwith a
Vanessa Vakharia (23:10):
Yeah.
Yeah, yeah,
Pam Harris (23:11):
So I think nature, nurture, there's a lot of, um,
I, when I meet people who say,Ooh, I've always thought about
numbers that way, and I justassumed everybody else did too.
Are you
Vanessa Vakharia (23:22):
yeah.
Pam Harris (23:22):
that you didn't?
And I'll smile and I go, Ididn't.
And
Vanessa Vakharia (23:24):
Mm-hmm.
Pam Harris (23:25):
at me like, really?
if I ask that person, did youhave some, so I would call that
person kind of naturally mathfor
Vanessa Vakharia (23:33):
Okay.
Pam Harris (23:34):
As they were growing up, they played with
relationships.
I did not,
Vanessa Vakharia (23:39):
Yeah.
Okay.
Pam Harris (23:39):
thought about using relationships and they assumed
the rest of us did too, or theyweren't sure why the rest of us
weren't.
did not.
Many people that I meet, themajority of the math teachers I
work with will say to me, I waslike, you, Pam, believed that
math was wrote, memorizing andmimicking.
And that's what I did.
I did not, I never played withnumbers.
Now, I, I don't know if thereason some people kind of did
(24:03):
that on their own was because.
They had a natural inclination,more talent, or it was because
they had more interest or it wasbecause they had a mom, a dad,
an uncle, an aunt a a, someother significant person in
their life who played withnumbers with them.
So often when I meet that personI'll say, did anybody play with
numbers with you when you were akid and they'd say oh my gosh,
(24:23):
my granddad would put me on hisknee and we played cards and we
always had to figure out ourscore.
And like often, often, so thiswas research I would love to do
when I have a minute, be tolike, like they have some
influential person who early intheir life helped them do the
mental actions of math then thatset them on the course of math.
(24:47):
And sure, that could be, thatcould absolutely be true.
Vanessa Vakharia (24:51):
Okay, so then we're kind of fine.
Then.
You know what, actually, I thinkyou and I are so funny in this
way because I am, so, like, Ithink it's, for us, most of our
like quote unquote disagreementsare simply in language.
Pam Harris (25:03):
Yeah.
Vanessa Vakharia (25:04):
I actually think we're saying the same
thing.
'cause when you say"naturallymathy", it sounds like you're
like, some people are just kindof born with this, like abil.
But you're not saying that atall.
You're you're not saying that atall.
And that's exactly, and you knowwhat, all the research actually
corroborates what you aresaying, which is what outliers
is all about.
Which is when we look at thesepeople that are like the most
skilled mathematicians orathletes or whatever it is
(25:24):
usually nothing genetic.
It is about this 10,000 hours ofpractice.
Right.
And whether you get that
Pam Harris (25:28):
born.
Glad.
We'll also talk about right whenthe, when the hockey players in
Canada were born,
Vanessa Vakharia (25:33):
at different times of the year.
Yeah,
Pam Harris (25:35):
year.
So if they were born so thatthey were the oldest kids in
their
Vanessa Vakharia (25:38):
exactly.
Pam Harris (25:39):
magically they looked like they had more
talent.
So Yeah, absolutely.
I, I completely can.
I think you are right.
I think often where you and Iare have to, where we dive in to
have a longer conversation iswhen there's some vocabulary
that we're like,
Vanessa Vakharia (25:52):
It is a vocab.
Pam Harris (25:53):
do, what do we mean.
Vanessa, I just wanna encourageanybody listening to this
podcast, we in math education,need to have more conversations
like this where we don't justnod at each other and
Vanessa Vakharia (26:04):
Mm-hmm.
Pam Harris (26:04):
yeah, you're good.
So sure, I'm gonna agree.
Like, we need to parse out whatwe're talking about because too
many people think we're all onthe same page when I don't know
that we are
Vanessa Vakharia (26:14):
Yes.
Pam Harris (26:15):
the same page, when in fact we are.
Vanessa Vakharia (26:18):
Which is actually, you know what's so
ironic about this?
Which by the way, AlanisMorissette's, uh, key song was
called, isn't it Ironic?
Um, what's ironic is that so farthis whole podcast has actually,
this whole interview has justbeen about language.
What is an algorithm?
What do we mean when we'resaying algorithm?
You know, it's funny, it's likewhen we use the term common
sense, it bugs me'cause I'mlike, my common sense is not the
(26:38):
same as someone else's commonsense, right?
So it's like there's nodefinition of common sense that
we're all gonna be like, wellit's common sense that blah,
blah, blah.
Because depending what you grewup, depending what your values
are, it's not common.
It's actually not common.
And like when we use the termalgorithm, we don't all mean the
same thing.
So we're having thisconversation and we're actually
saying completely differentthings because we have a
different definition than we'regoing on.
(26:59):
And actually as mathematiciansisn't the number one rule to
define our terms, isn't thatliterally what we're supposed to
do before we get into anyproblem?
Pam Harris (27:07):
It
Vanessa Vakharia (27:07):
Okay.
So,
Pam Harris (27:08):
would be a good idea.
Yeah.
This is, this is tricky andsuper subtle and so let me
Vanessa Vakharia (27:11):
Okay.
Pam Harris (27:12):
what
Vanessa Vakharia (27:13):
Hmm.
Pam Harris (27:13):
You and I, which I love by the way.
Thank you.
We are not.
these terms so that everybodyhas to use our definitions.
We're defining these terms sothat you and I can have a
conversation
Vanessa Vakharia (27:25):
Yes.
Pam Harris (27:26):
we can understand what each other means.
We're not commanding everybodynow take on our definitions.
Vanessa Vakharia (27:32):
Yeah.
This isn't like going in thedictionary of Pam and Vanessa.
Pam Harris (27:35):
Uh,
Vanessa Vakharia (27:35):
No,
Pam Harris (27:36):
uh, me trying to be arrogant to say I know best of
what the
Vanessa Vakharia (27:39):
no.
Pam Harris (27:40):
and everybody
Vanessa Vakharia (27:40):
Love it.
Pam Harris (27:41):
I wanted to
Vanessa Vakharia (27:41):
Thank you for clarifying that.
Actually, no, I really, reallyliked that.
Pam Harris (27:44):
Yeah.
Vanessa Vakharia (27:45):
We're making sure we're speaking the same
language so that we're actually,
Pam Harris (27:48):
we can't have a
Vanessa Vakharia (27:48):
or we can't have a conversation.
Yeah, exactly.
This is just, I mean, there's somuch here.
You know what I wanna ask younow?
Pam Harris (27:55):
Yes.
Vanessa Vakharia (27:56):
Just to, to bring it all together.
You at one point said, ourstudents deserve, to, learn
these reasoning skills.
You know, we don't need them tojust pump out an answers
anymore.
They, we, they deserve this, andwe are robbing them for that.
If we don't um, facilitate that.
How do you think learning in theway that you're proposing versus
learning the standard algorithmactually shapes math identity?
(28:18):
you know, obviously this is apodcast about math, trauma and
math, anxiety.
How do you think teaching oneway versus the other plays into
that?
Pam Harris (28:25):
Huge, so if I'm in a math class and the teacher says,
here is math.
I'm gonna give you a problem.
I'm gonna work it out.
Now we're gonna do it together.
Now you go mimic exactly what Ijust told you to do.
Then the student has no agencyand this, the math becomes this
thing that I'm, uh, uh, I, what,what I do is, is mimic what you
(28:48):
have told me to do.
And then if I like that, if I'm,if I'm rewarded for that now,
I've created, uh, an identityof, ooh, I'm good at, and, and
it was exactly the identity Icreated.
Like I, I was, I was a nerd.
I didn't have friends, whatever,but hey, I, I won round the
world, Arlene Wheeler.
I wonder if she would everlisten to this.
Vanessa Vakharia (29:08):
Who's that?
Pam Harris (29:09):
she was my third grade nemesis.
Well, third grade she won theaward in middle
Vanessa Vakharia (29:13):
Should we find her?
Pam Harris (29:14):
two.
Oh, I love that.
We, it was the two of us thatwere, we were always like, like
we were the quickest we aroundthe world.
It was the two of us that werealways at the end.
Vanessa Vakharia (29:23):
Mm-hmm.
Pam Harris (29:23):
division first, like all the things.
I got this identity that I wassmart and I,
Vanessa Vakharia (29:29):
Okay.
Pam Harris (29:29):
math.
I've heard you kinda talk abouthow, I like your take on that by
the way, that we have thiscultural sort of assumption that
if you're good at math, you'resmart.
Vanessa Vakharia (29:38):
Yeah, it's gross.
Pam Harris (29:39):
I'm just gonna say if you're quick at math.
even good, but if
Vanessa Vakharia (29:44):
Mm.
Mm-hmm.
Yeah.
Pam Harris (29:45):
cause you gotta define good, right?
Vanessa Vakharia (29:47):
Totally.
Totally.
Pam Harris (29:48):
my identity was based on the fact that I was
quick.
And then I became a high schoolmath teacher, and I thought I
was the god of math.
Imagine my dismay when Irealized wasn't doing the mental
actions that other people weredoing it all.
I was memorizing and mimicking,and there was this whole other
world.
Now imagine my joy when Irealized I could do that too.
(30:09):
I just needed to know it was athing.
I bought into the myth and it,it sh completely shaped my
identity.
Now I realize I, I can do thattoo.
I can be in that club and maybebetter, because this is my life
mission, I can invite everyoneelse into that club, like the
real club.
Vanessa Vakharia (30:30):
Okay.
Okay.
I was asking about, you know,how does, uh, teaching
algorithmically and throughmimicking affect, you know,
one's math identity?
And there's kind of two partshere.
On the one hand, you and yourpal, Arlene Wheeler, which if
anyone knows where she is,please do locate her.
You actually formed a verystrong, confident math identity
as a result of this procedure,uh, sorry, as, as a result of
(30:52):
being taught this way becauseyou were, for a while, because
you were able to nail this.
Okay.
So on the one hand, we've gottwo kids here who form a very
strong math identity.
They're quote unquote good atit.
They're quick at it.
They can follow the steps.
However, later in life, whenthat becomes challenged in a
sense because they are presentedwith math in a different way,
all of a sudden that identitykind of collapses.
(31:14):
There's a bit of an identitycrisis, and then there's this
beautiful plot twist romcomending where you discover math
in a whole new light and you'relike, I can do it to like
beautiful, cool, some ups anddowns.
Now forget you and Arlene.
Let's think about the rest ofthe class who are watching you
and Arlene just kill it.
And they're like, oh my God, wesuck.
Pam Harris (31:33):
Yeah.
Vanessa Vakharia (31:34):
So now not only like, you know, we have
this like kind of partialsuccess story with you two, you
and Arlene, that then later endsup in a bit of an existential
crisis, but the rest of theclass is not quote unquote good
at math in this way, and theydon't feel good.
They aren't presented with anyother options.
They just leave the classthinking, well I guess I'm not a
math person and I'm not good atit.
Pam Harris (31:55):
Uh yes.
And what a tragedy.
Because
Vanessa Vakharia (31:57):
and what a tragedy.
Pam Harris (31:59):
in reality, they are a math person and they
Vanessa Vakharia (32:01):
Mm-hmm.
Pam Harris (32:01):
can math if they just need to know it's a thing,
and, and
Vanessa Vakharia (32:05):
Well, yeah,
Pam Harris (32:06):
get experiences to help them build their brain to
be able to math more and more.
Vanessa Vakharia (32:12):
Well, and the crazy thing is everyone is at a
disadvantage in this situation,including the two of you or
whoever it was that formed apositive math identity.
Because like my mind is nowgoing somewhere else here where
I have never thought about it inthis way of thinking like.
You know how there's all thesedis, this, you know, hoop law
now about people being like,well, why can't we just teach it
(32:33):
this way?
There are people who are good atit and those are the people who
are good at math, whatever.
You're kind of living proof ofbeing like, well, hold on.
And now this doesn't, this isnot a general statement, this
doesn't apply to everyone, but alot of people who get through
this system and feel good aboutit, it's not even happening for
the reason that I think we'd alllike, which is like we'd all,
like everyone to deeplyunderstand mathematics and
(32:55):
numbers.
I'm not saying that peopledon't, I really believe that a
lot of people who are, who havebeen taught through this, uh,
mimicking an algorithmic way, Ibeing included, and many of us
being included still have, youknow, number sense and deep
reasoning skills and all of thisstuff.
They've just gained it in adifferent way because they
certainly didn't learn it atschool kind of thing.
Pam Harris (33:15):
Yeah.
Yeah,
Vanessa Vakharia (33:16):
Sorry, I'm saying a million things at once,
but I guess I'm kind of like,where I'm, I'm kind of trying to
get to is like, it's kind ofcrazy to think that we're trying
so deeply to protect this way ofteaching that actually didn't
service most people.
Even those who felt good at mathwere actually being robbed.
Pam Harris (33:37):
Yeah.
Agreed.
Agreed.
And can I add a third
Vanessa Vakharia (33:40):
Oh, say that again.
I liked it.
Pam Harris (33:42):
agree with you.
Vanessa Vakharia (33:42):
Okay.
Yes.
A third group.
Pam Harris (33:45):
add a third group because
Vanessa Vakharia (33:46):
Yeah.
Pam Harris (33:47):
people listening who while they were being taught
algorithmic mimicking, throughit kinda like my kid and said,
Ooh, I could logic my waythrough that.
And they use relationships andconnections and think that the
way they were able to do thesereal math mental actions is
because they were shownalgorithms.
Vanessa Vakharia (34:08):
Mm-hmm.
Pam Harris (34:08):
Like they almost can't, they almost can't
separate it out.
Vanessa Vakharia (34:11):
Yep.
Yep.
Pam Harris (34:12):
this is the way we should teach because it worked
for me.
So does that make sense?
In other words, there's me who,
Vanessa Vakharia (34:17):
I wanna talk about this.
Pam Harris (34:18):
it didn't actually work for me.
And I'm clear on that.
But there are people who aresuccessfully math, they're doing
the mental
Vanessa Vakharia (34:24):
Yep.
Pam Harris (34:24):
and they think it's because of the way they were
taught.
And I'm gonna respectfullyinvite the, that if you're
listening, I respectfully inviteyou to consider if your teacher
hadn't given you things tomimic?
What if your teacher hadactually helped you, knew, knew
the things you were developingon your own, helped you do that
intentionally.
What if they had set upexperiences for you so you could
(34:47):
have developed those things youkind of did on your own,
quicker, faster, better, becausethe teacher knew what they were
and helped you intentionallybuild it.
Think of how far and fast youcould have gone if you hadn't
had to do it on your own.
Does that make sense?
I don't think
Vanessa Vakharia (35:03):
it makes, it makes so much sense.
Pam Harris (35:05):
to try to parse out.
How
Vanessa Vakharia (35:07):
No, I.
Pam Harris (35:07):
how did you become the person you are?
Well, of course it was theexperiences that that created
me.
I respectfully submit that whenyou were shown an algorithm for
whatever reason, I don't knowwhy you were able to see things
through that the rest of us werenot, if we were taught
differently, all of us couldhave done what you did in spite
of the way you were taught.
Vanessa Vakharia (35:27):
Uh, you know what I think is, I think it's
just a really hard ask.
I, I don't think it'simpossible.
I think it's actually, this iswhat like, you know, most
therapy is, is this idea oflike, let's try and deeply
reflect on what, um, you know,we weren't just quote unquote
born this way or, you know,these things all played a role,
but I actually think it's reallyhard to be like, okay, so
(35:47):
imagine you were taughtcompletely differently because
like, it is so hard to parsethose two things apart.
Like even I'm trying to do itbecause obviously I've kind of
fall into this camp of beinglike, yeah, I was taught the
algorithm, but I still havethese deep reasoning skills and
I was able to buildrelationships.
And I imagine, and I think thismight be only because I've sat
through a couple of your lessonsand been like, oh my gosh.
(36:09):
You know, like, I think, I thinkpeople need to experience it in
order to, you know, there's thisthing I read.
Okay, I think you're gonna likethis actually.
So my a, a lot of my work isbased around this phrase by Joe
Dispenza, who's like.
Let's call him a pseudoscientist.
Um, he's like spiritual science,but I love what he says.
(36:29):
He says, uh, his whole phraseis, believe, behave, become.
It's like you have a belief.
So maybe I believe that whatyou're saying could be true.
You know, I believe that maybewhat you're saying is could be
true.
If I was taught in thisdifferent way, I'd have a
different relationship withmath.
I changed my behavior.
So I go to one of your sessions,I actually see it in action and
I'm like, oh my God, thisactually has changed the way I
(36:50):
think.
And now I've become a personwho's like, yep, you know what?
I really believe that this canwork and now I'm gonna teach
this way.
'Cause when I sat in yourproblem strings lesson, like
I've heard of it, I've read thebook, whatever.
I get it.
I was like, this sounds cool,but I, my entire body was on
fire.
Like, I was like, oh mygoodness.
It's that.
Aha.
That's when we know something tobe true.
Pam Harris (37:12):
I love that.
And, and you're not people willsay to me, that's what you mean?
Like, they'll sit in a sessionwith their ma with their jaw
open.
Vanessa Vakharia (37:21):
Yeah.
Pam Harris (37:22):
Yeah.
And, and I'll be honest, I, Idid too when I ran into Kathy
Fasno, so she's an elementarymath researcher.
When I watched her, when Iwatched kids, it wasn't really
watching the teacher at first.
It was, it was like me watchinglearning happening live.
I was like, I want that, I wantthat.
I want, I want to.
And I had to experience it.
(37:43):
And then now my goal is to helpus all experience it.
Yeah.
Vanessa Vakharia (37:47):
Well, and if you think about it when you're
teaching a lesson, what you do,this is actually gonna be
interesting'cause we're gonnapresent together soon.
I, I notice this, you guide usthrough the experience and then
you explain what you did, right?
So you're not intellectualizingit first.
You're giving us the experiencefirst, and then you're unpacking
it anyways, k.
Fine, fine.
We really do have to wrap thisup.
But my point is, the whole thingis
Pam Harris (38:09):
You have a point?
Vanessa Vakharia (38:10):
well, I, I, I know it's, I don't have a point,
but there is one thing I wannasay.
I,
Pam Harris (38:13):
Okay.
Vanessa Vakharia (38:14):
I wanna make clear, I think, at least from my
end, but you can definitelyobviously chime in that if
you're listening to this andyou're a teacher who teaches
through algorithms, okay.
I personally wanna make it very,very clear,
Pam Harris (38:25):
right?
We're not
Vanessa Vakharia (38:26):
which we're not, not only are we not blaming
because like, you know, yeah.
Pam Harris (38:32):
right.
We're not.
We're not.
We're
Vanessa Vakharia (38:33):
There's nothing bad happening.
Pam Harris (38:35):
we're?
Vanessa Vakharia (38:36):
I wanna make it so clear.
I wanna make it so clear thatit's like, Hey, first of all, we
all learn to teach this way, sowhatever you're up to.
Totally cool.
We all have the same mission.
We all want kids to developreasoning skills.
if you are doing that, you arenot doing something wrong.
And this whole episode is meantto be like, oh my God, we're
robbing kids like you are notrobbing kids.
Everything's cool.
I'm sure they're learning,they're, you know, you're
(38:57):
helping them feel confident.
You're helping them build theiridentity.
That is the most importantthing.
And if you're interested inperhaps shifting a little and
exploring how you might teach ina different way, maybe you'll
like it, there's an opportunity.
Would you agree?
Pam Harris (39:12):
Absolutely.
Yes.
Yes.
Very positive.
we know better, we can dobetter.
I'm suggesting there might besomething worth investigating,
worth experiencing
Vanessa Vakharia (39:21):
Yeah.
Pam Harris (39:22):
that you might find, um, will help you shift you're
teaching to reach more studentsin less time.
Vanessa Vakharia (39:30):
Yeah, in less time, that's who doesn't wanna
do that?
And also, I also would imaginethat there are some teachers
that are like, but I don'tunderstand the math fully enough
to be doing all this stuff.
Like I learned throughalgorithms, just so everyone
knows that is me.
Like I'm a trained high schoolmath teacher.
That's Pam.
She's pointing at herself.
(39:50):
That's her.
So.
I would personally invite youtwo to be like, just see what
happens.
Like, take one of theseworkshops, like put, you know,
whatever, if you can see Pampresent, like go do it.
Um, explore it just for your, Iactually think for you, the
listener, and I'm talking tomyself too, it's gonna build
your confidence.
Because what happened is I satin one of these sessions with
Pam and I was like, oh my God,by the way, there's nothing that
(40:11):
intimidates me more thanelementary school math.
Okay.
Like the worst.
Like, I'm just like, oh God.
So I was very intimidated andyeah, right.
I found myself having so manyahas, like sitting quietly in
the back being like, oh my, ohmy God, oh my God.
And I was like, oh my God, Ifeel like I understand more than
I gave myself credit for.
So even if you just go as anexplor, uh, exploratory, session
(40:32):
for yourself, just, I want allteachers to have the confidence
themselves.
And you know, I think so manyteachers have walked away with
so much math trauma from the waywe were taught, I just want you
to have a good experience.
You know, because yeah, just tosee that there's hope.
We can all be learning andgrowing and changing and there's
magic in math and we candiscover that every day.
(40:53):
Tell people where to go before Iwrap up with the final two
questions.
Pam Harris (40:56):
Excellent.
So the first thing I would dois, uh, suggest, wait.
I have a free ebook.
That would be a great place foryou to start.
So you can go tomathisfigureoutable.com/big B.
'cause I think it's big, it's abig, it's a big add to the
world.
That would be a great place foryou to start.
We have the math isFigureoutable podcast where Kim,
we've talked about a little bit,uh, where she And I talk about
(41:17):
all things, Math isFigureoutable from super young
all the way through high school.
Um, another thing that you coulddo is join me on social media at
the hashtag Math Strat Chatwhere I threw out a problem on
Wednesday evenings to peoplefrom around the world chat about
their strategies and comment oneach other's, uh, thinking.
So that's totally fun.
Those would be some super goodways to sort of kick off.
(41:37):
Uh, joining me to make math morefigureoutable.
Vanessa Vakharia (41:41):
Oh my God.
I can't believe we have to endthis.
We didn't even talk about thefake math thing, but I mean,
whatever.
Pam Harris (41:45):
We could send'em to the Debate Math Podcast if they
wanted to hear a little bit
Vanessa Vakharia (41:48):
You can, but I feel like both of us have
changed since then.
Pam Harris (41:51):
well, okay.
Vanessa Vakharia (41:52):
You know, it's not important.
Um, it's not important because Ifeel like it's old news and I
feel like we actually covered itin a way by talking about all
these other things.
Pam Harris (42:00):
Well, it's
Vanessa Vakharia (42:01):
Do you?
Pam Harris (42:01):
mean.
Everything we talked about todayIs the important stuff.
Vanessa Vakharia (42:04):
Is what I mean.
David's doing this, by the way.
He is doing the wrap up.
I love telling people that.
It's so fun.
Okay, so final two questions.
Quick fire.
I ask every guest.
Pam Harris (42:13):
I'm ready.
Vanessa Vakharia (42:13):
Number one, if there's one thing you could
change about the way math istaught in school is, what would
it be?
Pam Harris (42:21):
Holy.
I would help teachers experiencewhat it means to do the mental
actions of math thing, becausethat would shift everything they
do.
Vanessa Vakharia (42:31):
I love it.
Okay.
So what if a teacher's listeningto this and they're like, you
know, this is so awesome.
It sounds really great, but Ijust, I'm not a math person and
that's just it.
I'm just not a math person.
What would you say?
Pam Harris (42:42):
I would say you're, you're not a math person yet, or
you actually are a math person.
Um, and, and one of my favoritethings to do is to ask them, how
do you think about this problem?
And, and then, and 99% of thetime people will go, well, you
know, that's how you think aboutit, but you're supposed to do
the right way.
And I'm like, what if we couldteach all math the way you just
logiced your way through thatone.
Vanessa Vakharia (43:03):
Oh, I love that.
Well, that's all she wrote.
I mean, it's not, I have like 20more questions, but that's all.
That's all we have time for iton today's segment of Pam and
Vanessa, figure out what wordsand math mean and truly
understand each other.
Thank you so much.
(43:23):
This was so much fun.
Pam Harris (43:25):
You're a gift.
Vanessa Vakharia (43:26):
Oh my God, you're a gift.
This is so sweet.
We should tell Chris and Robthat you know they really were
the start of our love story.
Thanks guys.
The matchmaker, the matchmakers.
Okay, until next time.
Pam Harris (43:37):
Woo.
Vanessa Vakharia (43:39):
Okay, guys, be honest.
When we started that convo, didyou think we'd be besties by the
end of it?
I loved this talk with Pam.
In a world where our differencesand disagreements are amplified.
I just found it so refreshing tohave time for actually nuanced
debate about some math questionsthat people seem to lose their
minds about online, but thatreally shouldn't be so
(44:00):
controversial.
Especially when we all have thesame goal, which is just helping
kids learn and feel confident.
So, I have some homework for youthis week.
Maybe my biggest challenge foryou yet.
I want you to find someone youdisagree with about math or like
anything, and sit down for anhour, okay, that's, that's a
long time.
But like, sit down for like 20minutes and really talk about
(44:21):
it.
See each other's side and trulytry to understand where they're
coming from and where youactually might share common
ground, one piece of commonground.
And, ahem, a good way to breakthe ice with this person might
just be to send them thisepisode.
And whether you try thischallenge out or just wanna
share your thoughts on theepisode, please text the
podcast, DM me on Instagram atthe Math Guru, or email me at
(44:44):
vanessa@themathguru.ca.
Links to do all of those thingsare in the show notes.
Also, my audio book isofficially out and I cannot
believe how many of you guyshave already bought a copy and
are listening to me narrate MathTherapy in my voice, in your
ears, that's actually wild.
You can grab it wherever you buyyour audio books, including
Audible and actually Spotifywhere it just got added like
(45:06):
today.
Finally, my Math Therapy merchline has dropped and I'm dying
for the cute pics you guys aresending me with you in your MT
swag, please keep sending methose, and you can shop the drop
at maththerapy.com/merch.
Math Therapy is hosted by me,Vanessa Vakharia.
It's produced and edited byDavid Kochberg, and our theme
music is by our band, GoodnightSunrise.
(45:28):
Okay, that's it.
Go forth.
Trust yourself.
And remember, your innermathematician is already in
there.
You just have to give them themic.
Pam Harris (45:41):
They're logical relationships, but we're not
logicing our, see, I've made itmy own word.
They're logicing.
We're
Vanessa Vakharia (45:46):
I like it.
Pam Harris (45:46):
logicing our way.
What is on your shirt?
Vanessa Vakharia (45:50):
Brittany Spears, do you know who that is?
Pam Harris (45:51):
do, but I, there's two people on your shirt that,
so they can't be.
Vanessa Vakharia (45:57):
They're, they're both just Brittany.
It's like both, just twodifferent,
Pam Harris (45:59):
right now.
There's
Vanessa Vakharia (46:00):
no,
Pam Harris (46:01):
on your shirt.
Sorry.
Okay.
Pop, pop culture ignorant here.
Vanessa Vakharia (46:07):
I mean, no, you're not ignorant.
You're, you know who BritneySpears is.
Pam Harris (46:10):
mean, ish.
Vanessa Vakharia (46:11):
Yeah, it's just a very poorly designed
shirt.
Pam Harris (46:15):
We won't tell anyone that you said that.
Vanessa Vakharia (46:18):
Okay.
Pam Harris (46:18):
We won't put that out publicly or anything.
Vanessa Vakharia (46:22):
Oh my God.
Okay.
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