July 30, 2026 • 50 mins
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One of the most misunderstood words in math ed right now is "fluency", so Vanessa invited an expert on the podcast to demystify it: educator Christina Tondevold. Christina calls herself a "recovering traditionalist" - she committed to stop teaching students in the same ineffective ways she was taught as a student.
They discuss a ton of practical strategies you can bring to your classroom, such as:
- showing students how connected math is (in class and in their lives)
- building fluency on 3 balanced pillars: efficiency, accuracy, and flexibility
- teaching students to learn math by teaching them to be problem solvers
If you enjoy this conversation, sign up for Christina's free 3-day virtual summit August 10-12, 2026 featuring Vanessa and a ton of other incredible speakers!
About Christina: (Website)
Christina Tondevold is a Recovering Traditionalist - she previously taught mathematics traditionally and expected the students to parrot back what she taught them. Now she gets to work with teachers in developing students’ mathematical understandings in a balanced way by developing conceptual understanding while working on procedural fluency through her site BuildMathMinds.com where you can get PD at Your Fingertips.
Contact us:
- Vanessa Vakharia: Instagram, TikTok, Email
- Math Therapy: Text the Podcast
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Christina Tondevold (00:03):
at five years old We aren't expecting
kids to come to baseball, beingable to hit the ball into the
outfield, We aren't expectingevery kid to win, every kid to
be perfect.
We are laying a foundation ofwe're all here, we're learning.
Unfortunately for some kids,they end up getting coaches who
are all about winning, and allabout getting it right, and then
(00:24):
guess what happens?
They don't love the sportanymore, and they stop doing it.
And that's exactly what we'redoing in mathematics, it becomes
only about the winning, onlyabout being perfect.
Flexibility is the piece thatgets everybody feeling like they
can do this, that they have apart.
And yet we have to balance it alittle with, accuracy and
(00:45):
efficiency do matter, but if weput too much focus on that, that
becomes an issue, and then kidsare performing out of fear,
Vanessa Vakharia (00:56):
Hello, and welcome to another amazing
episode of Math Therapy, thepodcast that unpacks math trauma
and helps you build a betterrelationship with math.
I'm your host, Vanessa Vakharia,and I'm here today to get you
pumped up about going back toschool.
And yeah, I know, what abuzzkill when it's still summer
and, like, 10,000 degrees out,but it's coming, so why not get
(01:17):
fired up about it?
A new school year brings so manypossibilities, one of which is
the chance to redefine our termsin the classroom so they empower
us, and today's word is one ofthe most vulgar F words in all
of math (01:29):
fluency.
We keep hearing that we can't,like, teach students to be
fluent in mathematics while alsohonoring their progress and
thinking, but today's guest,Christina Tondevold, joins me to
tell you that that is total BS,and yes, you can have both.
Christina is a self-proclaimedrecovering traditionalist who
initially taught mathematics byexpecting students to parrot
(01:49):
back to her what she taughtthem.
But she now works with teachersin developing students'
mathematical understandings in afar more balanced way,
developing conceptualunderstanding while working on
procedural fluency.
She does this through her sitebuildmathminds.com, where you
can get PD literally at yourfingertips.
She's a powerhouse.
She is, like, the person I thinkabout when someone says fluency,
(02:12):
and that's why I decided she wasthe person I had to talk to
about reclaiming this F-bomb.
If you think that timing thingsin math will ruin a kid's life,
and if you've ever been like,"Well, yes, I want my students
to feel good about math andtheir thinking and themselves,
but I also need them to befluent in math, and it feels
impossible to do both," or ifyou've previously thought, just
like me, that fluency equalsspeed at the expense of all
(02:35):
else, this episode is for you.
And if you're like,"Sorry, Idon't even know what fluency
means, period, why it'simportant, or why I should give
a fuck," well, this episode isdefinitely for you.
All right, enough from me.
Here's my convo with the amazingChristina Tondevold.
Christina, welcome to thepodcast
Christina Tondevold (02:55):
Thank you for having me.
I am excited to be able to chatwith you.
Vanessa Vakharia (02:59):
I love how your, the first thing on your
website says that you are arecovering traditionalist, and I
kinda wanna just start there.
I wanna know a bit more aboutthat.
What does that mean?
Christina Tondevold (03:09):
When I started sharing things online, I
decided to call my blog that,The Recovering Traditionalist,
because it really is a journey,and I feel like I'm never fully
done.
You know?
Like I'm, i'm not just a thinkernow.
It is really hard to get out ofour traditional ways of teaching
mathematics because if, assumethat, you know, people my age,
(03:34):
uh, I'm nearing mid-life, thatwe all kind of grew up with very
traditional style of teaching ofhere's the procedure, learn it,
memorize it, follow the steps,and you'll get to the correct
answer, and that was howeverything was graded in math,
was did you follow the steps?
Did you get the right answer?
That was the way that I taught,was still very traditional.
(03:57):
I stood up there and gavestudents the notes and taught
them the procedure, and thenexpected them to practice it as
a whole group.
And then when they got to theindependent practice time, it
was like hands were going up,and I did not have another way
to help them.
I just would repeat the rulesand steps,'cause that's all I
(04:18):
knew.
Vanessa Vakharia (04:19):
I wanna make sure I'm tracking here that when
you say traditionalist, you arereferring to, um, a, a historic
way of teaching math that relieson procedure.
Is that correct?
Like, we're relying more onprocedure, we're on...
Okay,
Christina Tondevold (04:36):
Yeah, and, and for years though, I think
it's, you know, as everything ineducation, the pendulum swings.
And so the pendulum swingingaway from the traditional style
of teaching into more lettingkids think and play around with
mathematics, um, w- kind of wenta little too far to where it
(04:56):
was, let's just let kids playand discover.
And but we have to remember it'sguided instruction still.
It's not just letting them play.
It is letting them play andexplore, but we still have to
use that information to thenpull them, push them along their
trajectory of learning.
(05:16):
It's not just let them play andflounder, right?
We need to learn how they'rethinking and then use that to
guide our instruction to movethem through mathematical
understandings.
Vanessa Vakharia (05:30):
Yeah, it does feel like the guided piece is
what, when we hear about this inthe media, gets missed.
And I, I, I'm actually curious,like, did we ever actually just,
like, let kids play andflounder, or was there just,
like, an idea that we...
Like, were we ever like,"Oh,we're actually not teaching
anything"?
Like, just, I don't know.
Like, I know that there are someschools or, like, communities
(05:50):
where that happens, but I feellike that was never, like, the
instruction to teachers wasnever like,"Let them just, like,
vibe," and, like, the end,right?
Like, it was like,"Let's figureout, like, how they're learning,
what draws their interest, like,toward what their tendencies
are," and then exactly like yousaid,"Let's use that to guide
how we're gonna teach a certainconcept.
Like, let's prov-" Right?
Christina Tondevold (06:12):
I could say even from, like, personal
experience, but also stories,like my own children's
experience
Vanessa Vakharia (06:19):
Yep
Christina Tondevold (06:20):
Um, I have four kids ranging from 18 right
now to 12.
and there have been times where,I mean, they've had a whole
range of types of teachers,especially around mathematics.
but there have been a few havetaken things that they've
learned and, like, wanting kids,you know, what we talk about of
(06:43):
letting kids solve the problems,uh, not telling them how to
solve it, kind of to an extreme
Vanessa Vakharia (06:52):
Okay
Christina Tondevold (06:53):
"Here's the problem," and they, and then,
like, if they are flounderingand they aren't even sure where
to start or anything, th- thenthe teacher's like,"Well, figure
it out.
What can you
Vanessa Vakharia (07:03):
Okay
Christina Tondevold (07:04):
you know, a little, like, not just play and
discover, but even as we'reopen, giving kids an open task,
and
Vanessa Vakharia (07:11):
open
Christina Tondevold (07:12):
yeah, too open, and we just, like, let
them flounder a little too muchsometimes.
Vanessa Vakharia (07:17):
I would love to actually talk about this
because I think that this is oneof the biggest issues that I'm
hearing right now fromeducators, is like they know
that the move isn't to, like, beso prescriptive, right?
They're like,"Okay, I get thatI'm not supposed to give the kid
a problem and then, like, astep-by-step formula on how to
solve it.
I understand that.
But at the same token, I knowI'm not supposed to just be
like,'Okay, well figure it out.
(07:39):
Like, see ya.
I'm gonna go eat a peanut buttersandwich.'" Like, do you know
what I mean?
Like, that's not the move.
So it's like, but I also do feellike teachers are constantly
being, like, wrist-slapped fordoing too little or too much.
This feels like a Goldilockssituation, actually, right?
Like, it's like
Christina Tondevold (07:55):
Yes
Vanessa Vakharia (07:56):
too cold.
What was it?
It was too hot or too cold, theporridge, I think, right?
And then there was, like, themiddle.
What are some tips you can giveon, like, what you might ask
yourself in terms of what theright balance might be?
Like, what is that, that not toohot, not too cold bowl of
porridge?
Like, what should they do?
Christina Tondevold (08:14):
In general what I try to keep in mind Is I
don't want to start by telling.
Actually, okay, so w- in ourtalk that we had a couple days
ago, we mentioned our friendRaj, right?
Vanessa Vakharia (08:28):
Oh my God, Raj, what a vibe.
Christina Tondevold (08:30):
Raj is so fun.
So in I got to chat with Raj fora thing that we have upcoming
that Vanessa's a part of, andone of the things he mentioned
to me that still is- is on mybrain is that we can always go
back to direct instruction.
But our default has been, let mefirst tell you how to solve it,
(08:52):
and then you work on parrotingback and mimicking what I've
just told you.
So instead, like, to just getstarted and, give kids a
problem.
Just give them a problem, andsee what they think.
And you should always have inmind, though, where you're
wanting to go with them.
(09:13):
Like, what is the ultimate goal?
And, a lot of times we think ourgoals are the standards of
students will be able to blahblah blah.
It's not about what they're ableto do.
It's about what they understand.
And so we need to keep in mindis it that I want them to
understand about this?
Vanessa Vakharia (09:34):
I love this 'cause, like, uh, what I'm
hearing, and this makes so muchsense, it's like d- direct
instruction or just telling,okay, let's just call it just
telling'cause I hate all thejargon.
Just telling someone is in yourback pocket that you can use any
time, right?
But asking somebody, like askingsomebody to notice for the first
time can only happen in thebeginning.
(09:56):
You can't tell them and then askthem to notice for the first
time, right?
Whereas, like, the telling couldhappen at any time, so it kinda
makes sense to front-load yourinstruction with the stuff that
can only happen at the beginningas like an experiment, right?
Like, to be like,"Oh," like,"what would you do if you saw
this with no information?"'Causeonce they have the information,
they can't like imagine they hadno information and like, right?
(10:18):
Like you can't like you--
Christina Tondevold (10:19):
something
Vanessa Vakharia (10:20):
to unsee
Christina Tondevold (10:21):
pretend
Vanessa Vakharia (10:21):
and you can only be...
Christina Tondevold (10:22):
Yeah
Vanessa Vakharia (10:23):
Exactly.
So I kind of love that of beinglike, fine, like especially for
the teacher who's like,"Oh myGod," but like,"What if I have
to..." It's like, great, you cantell them.
I almost wonder if like a nicelittle therapeutic way to like
acclimatize yourself to thethinking model or, or getting
farther and farther away fromtelling is to even set a timer
(10:44):
and be like,"I'm not gonna tellthem anything for two minutes."
And then the next day be like,"I'm gonna set my timer for
three minutes," like I'm notallowed to tell anything for th-
you know what I mean?
Like you can build yourtolerance from uncertainty this
way.
Christina Tondevold (10:56):
Here's one thing I would recommend.
If your lesson is on doublesplus one, right?
And they aren't getting it inthe first 10 minutes, uh, might
be some deeper issues at, inplay.
Because mathematics is really aweb of understanding, and we try
to teach it in isolation.
(11:17):
Like, here's your doubles,here's your doubles plus one,
here's your make tens.
Or with multiplication, I don'tknow how you learned them, but I
learned them times ones, thentimes twos, then times threes.
Like, total isolation.
Vanessa Vakharia (11:28):
Yep
Christina Tondevold (11:29):
and now we know, like, okay, well, if you
know your tens, those areconnected to your fives.
And twos are c- can help youwith your fours and your eights.
Like,
Vanessa Vakharia (11:37):
We never did that, did we?
Christina Tondevold (11:39):
No.
No, never.
Never.
And, and so I could, I couldenvision, like, you know, I, I
don't want people to take awaythat, oh, okay, today we're
learning our times twosmultiplication facts.
Um, and if they don't have it bythe end, I'm just going to give
them a bunch of flashcards topractice it.
(12:00):
Like, there, there are reallybig things in mathematics that
just take time.
They take time to build.
And one of the things thatreally bugs me in our standards,
actually, is we do a reallygreat job with addition and
subtraction facts because itstarts in kinder, then they,
(12:21):
every state is technicallydifferent.
In, in Canada, yours might looka little different as well.
But typically in the UnitedStates, um, it's second grade
that it talks about being fluentwith addition and subtraction
within 20, which is your, yourquote, unquote facts.
So they have kindergarten, theyhave first, they have second
grade that they are building anunderstanding of what addition
(12:43):
and subtraction are.
And then by the end of secondgrade, they're supposed to have
become fluent with it.
Well, then, here in the UnitedStates, then third grade comes
along, and all of a suddenthey're supposed to master
multiplication and divisionfacts all in one grade level.
Like, that's, I mean, that is anunrealistic thing.
Um, and so I'm just saying,like, sometimes our standards
(13:08):
are great in giving us time tobuild these things for kids, and
sometimes it's just thrown at usand then we're like,"I've gotta
get kids fluent with these allin one year?" And so we get the
pressure of, oh, I just gottatell you, I've just gotta tell
you.
But there's a lot underneaththat we can build that will help
(13:29):
them be able to see a lot ofconnections, and the more
connections we can make, theeasier it is to recall info.
Vanessa Vakharia (13:35):
I'm gonna be honest here.
I'm listening to this, and I'mstressed.
Like, I'm listening to it, andI'm like,"Oh my God," there are
so many variables here.
Again, no pun intended.
But there's so much going on,right?
Like, you're kinda like, you'rekinda like, l- like, there's a
lot of messages.
And this is interesting.
I remember talking to anothereducator earlier this week, and
(13:55):
she was like,"You know,sometimes teachers just want,
like, what are the questions Ishould ask?
What are the rules I shouldfollow?" And it's like, y- this
is where your teacher'sintuition comes in, right?
Like, as educators, we arehealers.
We have an intuition.
We have experience.
We know that certain studentsneed this.
We can feel the energy of aclass when things are being
understood and not.
And I feel like we have to,like, pause and be like,"Listen,
(14:16):
we're saying a lot of thingshere, and none of these are
prescriptive." You kinda justhave to feel it out and trust
that you're doing the rightthing.
That being said, it's kind ofhard to hear, you know, that in
grade three we have thisbasically, like, impossible
standard, and it's gonna bereally, really hard, but also,
you gotta just, like, know whatthey need to understand about
the standard, and it's not aboutthe standard.
(14:38):
It's about them.
Right?
Like, it's like, oh, my God.
And now-- And, like, I, I getthat almost in a way this is
supposed to chill people out, tobe like,"Don't worry so much
about the standard.
Just, like, make sure they'reunderstanding some stuff that's
gonna be important." But whatif...
Can we take a step back and,like, forget the content, forget
the actual things, and, like,what is something that a
teacher, especially a beginningteacher who's hearing all this,
(15:00):
what's something that might givethem a bit of hope and relief
to-- if they're l- kind of like,"Yeah, man, like, this feels
hard.
It feels like some kids aren'tgonna be, like, getting all this
content.
It feels like I've gotta do toomuch." Like, what is your, like,
go-to, like, just remember this,this, this thing.
Like, j- what-- Like, do youhave something?
Christina Tondevold (15:19):
Yep.
Vanessa Vakharia (15:20):
Oh, okay, great.
Christina Tondevold (15:21):
Is not a set of isolated things.
It's all connected.
And so it does seem overwhelmingwhen you, like, you open up even
your standards and you're like,"Oh my gosh, I have to get all
of this in this grade?"Especially when w- I have
students maybe coming with somegaps or two back.
(15:44):
and when I saw mathematics is soconnected, opened up a whole
world for me.
Like, I was middle school, so Iw- at one point I was doing
sixth, seventh, eighth grade.
Um, in the, in the sixth gradetextbook, there's a chapter on
decimals, there's a chapter onfractions, there's a chapter on
(16:07):
percents Those are all the samething.
Vanessa Vakharia (16:12):
Yeah.
Christina Tondevold (16:13):
Tho-
Vanessa Vakharia (16:13):
I love it
Christina Tondevold (16:14):
the same types of numbers, yet we teach
them in isolation withoutconnecting them together.
Fractions are, you know, like apart of a whole.
I mean, that's a simplifiedversion of it, right?
It's
Vanessa Vakharia (16:27):
I loved it.
It was cute.
Yeah
Christina Tondevold (16:30):
decimals are just special fractions
because they have denominatorsthat are a power of 10.
They're a 10th, 1000th, right?
And then percents are evenspecialer because they are out
of 100.
So it's a fraction, but always,you know, percents are basi-
based out of what it is out of100 of something.
(16:51):
And yet those are not connectedtogether.
I didn't learn them as connectedtogether, and I didn't teach
them as connected together, andthen I had this group of kids in
front of me, uh, when we getdone with it, and they don't see
those connections.
Like, once I realized howconnected mathematics was, it
made me really start to look atthe textbook, the standards, and
(17:15):
say,"Okay, hold on.
So these are all listedindividually, but what actually
connects together?" And there isgreat, a great document out
there, um, by Achieve the Core,and it talks about the...
I mean, they're not the powerstandards.
That's not the phrase that theyuse.
I think they call them contentemphases.
(17:35):
but it's like what's the majorwork at each grade level?
And then they also talk aboutwhat ones are connected, they
support that major work.
And then it also shows whichones are just additional.
Like ex- for example,kindergarten, basically
everything is connected to thes- the work.
(17:55):
The major work in kindergartenis getting kids to count,
understand how numbers work, youknow, like the, the, the number
system of how things work, and alittle bit of addition and
subtraction.
Well, everything you're doing,if you're working on geometry
stuff, of recognizing shapes,and then you ask a kid,"So how
(18:16):
many circles do you have?"You're really also working on
counting.
Like, it's all
Vanessa Vakharia (18:21):
It's all co- Well, I also feel like it's like
this is, like, a message of hopeto be like anytime you're
working on anything, you'reworking on something else, too.
Like, you're getting more bangfor your buck than you think.
So it's like I really like thatexample of being like fractions,
percentages, and decimals.
You're looking at it being like,"I've got three chapters to
teach," right?
When really it's like what if welook at it as, like, you have
(18:44):
one chapter with some tentacles.
You know what I m- oh, I hatedthat I said that.
I'm sorry.
That grossed me out.
But do you know what I mean?
Like, you have, like, onechapter with, like, w- like, if
you teach fractions, you've nowtaught, you've taught a third of
percentages.
You know, if you teach fractionsand decimals, you've taught
two-thirds of percentages.
Once you close it off by being,like, percentages, now you've
(19:05):
taught the entire thing.
Oh my God, I just turned thechapters into a fraction.
Did you see what I did there?
I think that worked, right?
Like, right, right, right?
I think, as we know, time is,like, one of the biggest
struggles for teachers, and it'salways like,"I'm running out of
time, I'm running out of time."So if you can feel like you're
doing more, like, th- whateverwork you're doing now is
investing in all the futurechapters.
(19:26):
Like, if they're understandingfractions, they've already
understood a third ofpercentages.
You're getting there.
Like, you're filling that.
I do really like the way oflooking at- I Can I switch gears
for a sec?
Christina Tondevold (19:37):
absolutely
Vanessa Vakharia (19:38):
Okay, you've said a word several times, and
it is what I think of when Ithink of you.
And it's a word I feel we throwaround a lot in math ed and
don't define, and that word isfluency.
You've said fluency, kids beingfluent, and I think when people
hear fluency, what they think ofis speed, and I know that we're
missing the mark on that, and Ifeel like you're, like, one of
(20:00):
the fluency experts in my world,and I would love to hear from
you what fluency means.
Christina Tondevold (20:07):
So I will say everything I learned is from
other people.
Again, I, once I start seeingconnections, I, I learn
something over here fromsomebody and something here, and
I bring it together to make itmake sense for me.
Vanessa Vakharia (20:20):
Yeah
Christina Tondevold (20:20):
so I, I really love Susan Jo Russell's
definition of fluency.
She had a article back in 2000called Computational Fluency.
It was published by NCTM,National Council of Teachers of
Mathematics.
And she talked about threethings that make up fluency, one
is efficiency.
We do need to be fast.
(20:41):
I mean, that is part of And Ifeel like fast has kind of
gotten a bad rap
Vanessa Vakharia (20:46):
Yeah, agree
Christina Tondevold (20:47):
of all the trauma that comes with it, that
the way that we have used speedand timed activities in the past
has been harmful.
But the, the need to beefficient and fast still is a
part of our world.
We do want to be able to getthings done quickly.
(21:08):
Um, and, and this isn't just formathematics.
This, this version of fluency,uh, for those that are
listening, think of anything youfeel like you are fluent at or
trying to become fluent at.
Vanessa Vakharia (21:19):
Like a language obviously we'd think of
Christina Tondevold (21:20):
A language.
Yeah, yeah.
If you're fluent at driving yourcity that you live in, right?
You are efficient.
You know the fastest way to getsomewhere.
Vanessa Vakharia (21:30):
we've used speed and timed in a way that
was harmful, can you say a bitmore?
Like, how have we used it?
Christina Tondevold (21:36):
The classic of the timed tests of you have
to get this many in a minute,and then you, uh, switch papers
and somebody grades you.
You know, and so everybody'sseeing it.
And then, um, if you don't get80 problems in a minute, I'm
totally exaggerating, but 80problems in a minute, you have
(21:57):
to stay in at recess, and youdon't get your name up on the
wall with a star that you haveachieved, uh, this thing or
whatever it was.
I mean, f- there for a while,the multiplication sundae, I
don't know who started that, uh,but it was, like, everywhere
that you would get a scoop forevery, you know, you learned
(22:18):
your
Vanessa Vakharia (22:18):
Like actual ice cream?
Christina Tondevold (22:20):
Like, they would make a sundae.
And then when you got yoursundae complete, you could have,
like, you got to join in on theice cream sundae.
Like, I
Vanessa Vakharia (22:30):
Wait,
Christina Tondevold (22:30):
was
Vanessa Vakharia (22:31):
what?
Christina Tondevold (22:31):
years ago.
Vanessa Vakharia (22:32):
didn't have this.
I would like an ice creamsundae.
Okay
Christina Tondevold (22:36):
right?
But everybody who, who was goodat it loved that.
But those kids who struggled andnever achieved that 80 in a
minute or whatever it might havebeen, uh, never got their scoop
on the wall, never got toparticipate in the, the sundae
party that everybody else gotto.
So the timed activities, thosetimed tests, the mad minutes,
(22:59):
all of that was used aspunitive.
It was as a punishment, not assome- And we thought it would
motivate kids.
We thought if they got to seetheir name with a star up there,
that would motivate them.
Vanessa Vakharia (23:13):
and that's the thing, it's like, I mean, this
is a whole other conversation ofhow do we define motivation,
because like, okay, I guess itdid motivate some kids, but like
out of fear, right?
Like, it's like, yeah, likethat's like not really
motivation exact- Like it ismotivation, but it's like
Christina Tondevold (23:30):
true.
Vanessa Vakharia (23:31):
of motivation that we like want Let's just
like for argument's sake say weare gonna time you to do like 20
questions in a minute, or 10questions in a minute, whatever.
There's gonna be no sundae,there's gonna be no star,
there's gonna be no nothing, butyou're still gonna be timed.
Would that be okay?
Is it the way we treated theentire thing as...
Yeah?
Okay.
Christina Tondevold (23:51):
Yeah, yeah.
So actually, the researcharound- so there's, uh, a What
Works Clearinghouse and theInstitute for Educational
Sciences, IES.
Um, two groups look at all theresearch that's out there
because we can say,"Oh, well,research says this, research
says that." That might be onestudy, right?
(24:14):
What Works Clearinghouse and theIES puts together these practice
guides.
And, um, back in 2009, they didthe first one that I ever saw,
maybe there was one before it,but the first one I ever saw for
what works with students who arestruggling with mathematics.
And then in 2021, they justreleased, an updated one.
I said just released.
(24:34):
That was, like, five years ago.
Uh,
Vanessa Vakharia (24:36):
it
Christina Tondevold (24:37):
very many people know about it.
We,
Vanessa Vakharia (24:39):
Yeah
Christina Tondevold (24:40):
So this document has six recommendations
that have strong researchevidence to back them up for
what works.
One of them is timed activities.
So
Vanessa Vakharia (24:53):
what works for fluency
Christina Tondevold (24:55):
f- for, no, just mathematics in general.
Vanessa Vakharia (24:58):
Oh, okay
Christina Tondevold (24:59):
So it's, um, what works for students who
are struggling with mathematics.
It's actually a guide for t- forintervention, what intervention
should look like aroundmathematics.
So there's things like, um,vocabulary, like getting clear
on vocabulary helps kids, beingprecise in your language, using
word problems, using lots ofrepresentations in mathematics,
(25:21):
so models.
Um, everybody seems to be, tolove the first five
recommendations, and then thesixth recommendation is to use
timed activities.
And people are kind of a littlelike, hmm, I don't konw about
this."
Vanessa Vakharia (25:37):
I'm so into this because this is juicy,
'cause it's kind of like I'mjust, I don't know, I'm
processing this with you rightnow, but it's like you're right.
We have our backs up with speed.
As soon as someone says speed,I'm like Like as soon as a kid
is like,"I'm not fast," I'mlike,"Oh my God." Like, that's
not the thing.
But you're kind of right.
Like, there's nothing inherentlywrong with wanting to be
(25:58):
efficient with something, let'ssay, but there's so much baggage
that has come with it that I nowthink we're almost doing an
over-correct.
Like, the pendulum is swingingwhere we're like, oh my God,
like, no, like, speed doesn'tmatter at all.
But, like, doesn't make s- whatif it took an hour for someone
to add two plus two?
Like, we would- like, that,that's too long.
(26:20):
That's not good
Christina Tondevold (26:21):
Yeah.
So we, again, it's a thing ofbalance, right?
Like, we shouldn't be onlyfocusing on efficiency.
That is only, I'm gonna use afraction again, one third,
Vanessa Vakharia (26:32):
Okay, tell us the other things.
Yeah.
Okay, I love it, I love it.
Wow, we are doing the wholeunit.
Yeah, 30.3.333.
Oh my God, we're, we just didit.
We just converted them all.
We just taught, we just taughtthree chapters of math in one
second.
Christina Tondevold (26:47):
There we go.
Vanessa Vakharia (26:48):
Oh my God.
Okay
Christina Tondevold (26:49):
efficiency is one piece.
Let me get all three of them outso then we can
Vanessa Vakharia (26:52):
Okay.
Christina Tondevold (26:53):
it,
Vanessa Vakharia (26:53):
Yes, yes, yes
Christina Tondevold (26:54):
all together.
So efficiency is the speed part.
And then accuracy.
Correct answers do matter.
And again, the pendulum swungaway from
Vanessa Vakharia (27:04):
ChatGPT, yes.
Oh my God
Christina Tondevold (27:06):
You know, it's been like, oh, it doesn't
matter if they get it
Vanessa Vakharia (27:09):
Hmm.
Christina Tondevold (27:09):
or wrong.
Vanessa Vakharia (27:10):
Oh my God
Christina Tondevold (27:11):
thinking.
I'm sorry.
Correct answers do still matterin
Vanessa Vakharia (27:15):
It matters
Christina Tondevold (27:16):
They need right answers.
Accuracy is important.
yeah, it is important to look attheir thinking, but they also
need to be told when it's wrong,like,
Vanessa Vakharia (27:29):
Oh my God.
Yep
Christina Tondevold (27:30):
That matters.
And then the third one isflexibility.
Vanessa Vakharia (27:35):
What's that?
Christina Tondevold (27:36):
that's been my focus is because for the
longest...
I mean, I've been doing this along time.
I started teaching, I graduatedcollege in 2000.
So I have been in the educationspace for a long time, and
focusing on building numbersense and, and flexibility for
(27:58):
more than 15 years of that time.
and so I have pushed heavily ongetting teachers to focus on
flexibility.
Vanessa Vakharia (28:07):
What is it?
What is that?
Christina Tondevold (28:10):
about, uh, that in a
Vanessa Vakharia (28:10):
Doing math when on, in a handstand while
doing the splits
Christina Tondevold (28:14):
yeah, yeah.
Let's see how, how good yourdownward dog is or whatever, you
know.
Um, but the hard part is thatthat put the focus away from the
first two of accuracy andefficiency.
So I'm gonna talk aboutflexibility, but do not take
away that that is the only thingwe need to build.
Vanessa Vakharia (28:33):
We're just defining it
Christina Tondevold (28:35):
And I've, I've had to, like, say that now
because I've put so muchemphasis on flexibility and
people have, have gone all theway to the
Vanessa Vakharia (28:43):
Okay
Christina Tondevold (28:43):
the other side.
So flexibility is just havingalternate routes.
So let's go back to, you know,if you're, if you feel like
you're fluent driver in yourcity, what happens if there's an
accident and
Vanessa Vakharia (28:56):
Oh, God.
Oof.
Christina Tondevold (28:58):
Do
Vanessa Vakharia (28:58):
I'm stuck.
Christina Tondevold (28:59):
to get there without
Vanessa Vakharia (29:00):
No, absolutely not.
Christina Tondevold (29:03):
You're not
Vanessa Vakharia (29:04):
I am not.
Christina Tondevold (29:05):
your...
right?
Vanessa Vakharia (29:06):
I'm not
Christina Tondevold (29:07):
That's, and that's essentially what our kids
are.
So they might have one way to doit, and that's also been an, an
issue is, like, once all thesedifferent strategies came
around, it's like, well, if kidshave one way to do it, that's
fine.
They don't need to know otherways.
what if that one way doesn'twork on that problem?
Vanessa Vakharia (29:25):
okay?
I'm gonna do a little recap forthe listeners, and for myself,
quite frankly.
Okay, there are three aspects tofluency.
We have efficiency, which has todo with speed.
We have accuracy, which has todo with getting the right
answer.
And we have flexibility, whichhas to do with being able to, to
do things in different waysdepending on the circumstances.
Context dependent.
(29:45):
Having to...
Okay, so now...
Christina Tondevold (29:47):
love that.
Yeah.
Vanessa Vakharia (29:48):
Okay.
Oh my God, thanks.
Okay, so now I'm like, oh myGod, you are so right that we
have g- we have completelyover-corrected.
It's almost like, becauseflexibility wasn't a thing when,
you know, like 20 years ago, wedidn't care about it.
We only cared about efficiencyand accuracy.
Now we're like,"Oh my God,flexibility," like,"We left you
(30:09):
out." Now we're gonna, like,focus on flex- it also feels
like, to me, flexibility is likethe feel-good one of the gang.
It's like, and you know what Imean?
It's like, oh, you'll feel good.
Don't worry about getting itright.
Don't worry about being fast.
Christina Tondevold (30:22):
Yeah, it's like everybody wins kind of
Vanessa Vakharia (30:25):
Everybody wa- so it's giving participation
ribbon.
Oh my God.
what?
Christina Tondevold (30:30):
I mean, we need that.
We need everybody to feel likethey have a starting point, like
they have a way to contribute,like they have a way to
participate in mathematics.
That's, we do want that.
I'm not saying it's a bad thing,
Vanessa Vakharia (30:43):
I'm having a real epiphany.
I'm like,"Oh my God." I dothink, I do think...
You know all the haters on theinternet that are like,"Oh my
God, they're treating kids likesnowflakes"?
I don't know if I'm using thatright, but do you know what I
mean?
Like, participation ribbon, da,da, da, da, da, da.
It's like they're not actuallyentirely wrong, okay?
So, like, let me just say that,right?
It's like I get where they'recoming with this.
(31:05):
Like, for sure, if we reallywere like,"Don't worry, take two
hours to add two plus twotogether.
Don't worry if two plus twoequals five or six or seven,
but, like, as long as you'redoing something, you get an A+,"
that would be a problem.
I agree, that is a problem.
But I think what's actuallyhappening, and tell me if I'm
wrong here, I feel likeflexibility is not only useful,
(31:27):
but it is the inroad for themath-anxious student into doing
what is needed to get to anefficient, accurate place.
The flexibility is the thing wecan be like,"Look, do it
whatever way.
We can reward you becauseeveryone has their own way of
doing things." Now you feel moreconfident, and because you're
feeling more confident, you'renot gonna freak out when you get
something wrong or you're tooslow.
(31:48):
You're gonna keep at it becauseyou have some con...
Like, am I onto something?
You know what I'm saying?
Christina Tondevold (31:52):
Absolutely.
And, and as, as an, um, a sportsmom, you
Vanessa Vakharia (31:57):
Okay
Christina Tondevold (31:58):
I can see the analogy too with the
participation trophies and the,and the entry points in, right?
Like, if, if at five years oldwe're expecting kids to come to
baseball, being able to hit theball into the outfield, and know
which- where to throw it, andknow which way to go.
Because, uh, if you've everseen, like, play T-ball, they
(32:19):
hit the ball and then they'llrun to, like, third base, not
first ba- Like, you know,they're learning
Vanessa Vakharia (32:23):
Oh, cute.
Right
Christina Tondevold (32:25):
not They don't have the accuracy and, uh,
all the, that stuff down.
And, and so we do that buildthat and, and allow for all kids
to have an entry point, right?
We aren't expecting every kid towin, every kid to be perfect.
We are laying a foundation ofwe're all here, we're learning,
(32:45):
right?
And then unfortunatelysometimes, uh, for some kids,
they end up getting coaches whoare all about winning, and all
about getting it right, and willyell, and all of that kind of
stuff.
And then guess what happens?
They don't love the sportanymore, and they stop doing it.
And that's exactly what we'redoing in mathematics, is that we
might be having these entrypoints, you know.
(33:07):
Like, again, we've, we've goneto the wayside where we're just
letting everybody come in andhave this entry point piece, but
we also need to balance thatwith, hey, they Uh, like, we do
need to get to the efficiencyand accuracy part, but even then
it's still flexibility.
The flexibility still matters.
It's not like flexibility goesaway.
(33:28):
that's unfortunately sometimeswe see in sports, is it becomes
only about the winning, onlyabout being perfect.
And then kids are playing out offear because they're, uh, s-
scared their coach is gonna yellat them or bench them because
they did something wrong, right?
Like, there, there's differentstyles of coaching, for sure.
I've done Uh, this is part of akeynote that I do.
(33:49):
Um, so it's something I lovetalking about.
But the same is true for us aseducators, that we- that
flexibility is the piece thatgets everybody feeling like they
can do this, that they have apart.
And yet we have to balance it alittle with, you know, accuracy
and efficiency do matter, but ifwe put too much focus on that,
(34:10):
that becomes an issue, and thenkids are performing out of fear,
and they're motivated onlybecause those external things
that they're afraid of.
Vanessa Vakharia (34:21):
I wanna bring this all home for us here, which
is gonna be a bit hard, and thatkind of is a baseball metaphor
that I'm sort of using, I think.
Christina Tondevold (34:29):
Yeah,
Vanessa Vakharia (34:30):
right?
Uh, is that where it comes from?
Is it like ra- is it-- Oh, myGod, Christina, wow, we are
basically sports commentators.
Okay, this is gonna be hard totrack'cause I have about 30
thoughts in my mind, but hereare some of them.
The first is, I think we have torecognize, for anyone listening,
I don't think anyone who thinksthis listens to my podcast, but
if you are listening and you'relike,"I hate this flexibility
(34:53):
stuff.
It's all about speed andaccuracy," I'm so glad you're
listening.
Actually, thank you for taking achance on the podcast.
Thank you for being here, andhere's what I wanna say.
If you're like,"Well, exactly,like, we are losing those things
at the expense of flexibility,"here is, here is my thought on
that.
I actually think we have torecognize that historically math
has been such ananxiety-inducing subject that so
(35:13):
few students are willing to walkin the door.
And because of that, it behoovesus, I don't know what behooves
means, but it feels like it fitsin the sentence.
Christina Tondevold (35:23):
Yes
Vanessa Vakharia (35:23):
It behooves us to actually put an emphasis on
flexible thinking as a startingpoint because it allows the most
flexibility in terms of who canwalk in the door.
Because, you know, there are notmany ways to think incorrectly.
If you're thinking, if you'redoing something in any way, you
are doing something, and that iswhat flexibility is all about,
right?
So, like, it kind of makes sensefor us to be really emphasizing
(35:45):
that so we can get all thepeople in the door.
Once they're in the door, weare, we are dedicated as
educators to helping them solvethe problem and get the correct
answer and to do so efficiently.
But, like, let us, let usemphasize flexibility for a bit,
because the lack of flexibilityis what has led to so much math
anxiety, hence so few peoplewalking in the door.
(36:06):
What do we think so far?
Christina Tondevold (36:07):
Mm-hmm.
Absolutely.
Vanessa Vakharia (36:08):
Okay, so great.
So that's nice.
But now you're making me thinktoo, we've now really centered
on the concept of fluency,right?
But it kinda, I know thatfluency isn't the only goal in
math, right?
Christina Tondevold (36:21):
well, so that could
Vanessa Vakharia (36:23):
It feels like,
Christina Tondevold (36:24):
right?
I
Vanessa Vakharia (36:25):
it feels pretty good.
It feels like it covers a lot ofbases.
Oh my God!
Christina Tondevold (36:30):
We're just gonna keep at it.
Vanessa Vakharia (36:32):
Okay
Christina Tondevold (36:33):
um, I've had to really rethink my own
understanding of the purpose ofmathematics,
Vanessa Vakharia (36:39):
Okay
Christina Tondevold (36:41):
My traditional view of mathematics
was I use mathematics and solveproblems, like, I'm just doing
math.
However, to me, and, and I gotthis from, we in the United
States call it Singapore math,Ban Har says,"It's just math,
(37:02):
but we do it in Singapore." Andtheir focus is
Vanessa Vakharia (37:07):
Hmm.
Christina Tondevold (37:08):
We want kids to be problem-solvers, and
we do that with mathematics.
Um, and so fluency, uh, likeeven in the United States,
though, even with thisflexibility piece, we still do
have this push of get themfluent, fluent, fluent, fluent.
When, is mathematics, like,being fluent in mathematics,
(37:28):
like, the end-all be-all?
Or is it that we want kids to becapable thinkers and
problem-solvers, and we
Vanessa Vakharia (37:39):
it sounds...
Christina Tondevold (37:40):
through mathematics
Vanessa Vakharia (37:41):
But hold on, fluency sounds, the tenets of
fluency, efficiency, accuracy,and flexibility, is that not
what it takes to solve aproblem?
Christina Tondevold (37:52):
It is, but it's, it's, it's flipping how
we're looking at it.
Like, the end-all be-all...
'Cause okay, so, um, let me seeif I can reframe this too.
Like, I always thought, like,even on, when I first started
becoming more of a recoveringtraditionalist, I still thought
my job is to teach themathematical skills, to help
them understand the mathematicalskills, like the operations,
Vanessa Vakharia (38:15):
Yes
Christina Tondevold (38:16):
that they can solve problems, right?
Vanessa Vakharia (38:20):
it
Christina Tondevold (38:20):
can solve problems.
When I heard Dr.
Bonhar talk, he said,"Our goalis to help kids be
problem-solvers, and thebyproduct of that is they learn
some math skills along the way."And so it's the rever- Like,
just
Vanessa Vakharia (38:39):
Oh,
Christina Tondevold (38:40):
is our
Vanessa Vakharia (38:41):
yep, yep, yep, yep, yep
Christina Tondevold (38:42):
wa- I was still focusing on help my kids
learn the math skills, help mykids learn the math skills, and
if they become greatproblem-solvers, that's a great
byproduct.
But instead
Vanessa Vakharia (38:53):
hear you.
Christina Tondevold (38:53):
let's put
Vanessa Vakharia (38:54):
I hear you
Christina Tondevold (38:54):
And so even if we're like,"Okay, fluency
will hit all of that stuff,"it's still we're putting the
focus on fluency, fluency,fluency, and then if they become
thinkers, eh, a great byproductof that.
Vanessa Vakharia (39:08):
Oh, wait, 'cause it kind of seems like
fluency, if we think about thew- you remember, you were, like,
fluent in driving, fluent incooking.
It almost feels like fluency isdependent on the thing you're
fluent in.
You can't just be, like, fluentin life.
Whereas you can be aproblem-solver in every domain,
fluency is domain-specific, andright now we're talking about
fluency in the domain ofmathematics.
Oh my God.
(39:29):
Oh my God.
Okay.
And I think, we're gonna wraphere, but it's okay that we
don't have a conclusion.
I actually think it is for theeducator listening or whoever
listening to be like,"Huh, whatis my approach going to be?"
Right?
Like, what is it?
Like, is it, is it going to befluency first, problem-solving
second, or is it gonna be pro-Like, and again, I actually
(39:52):
don't know that there is ageneric answer.
I think it can depend on yoursituation, on the student.
Maybe a student's reallyinterested in some mathematical
concept, and through that theydevelop fluency, and through
that they learn how to solveproblems.
Maybe a student's...
Right?
Like, do, do you think, do youthink there's a right answer to
this?
Christina Tondevold (40:11):
well, I would encourage, I guess, um,
maybe it's the recoveringtraditionalist in me that we
start opening our mind to maybeit is more about the
problem-solving si- piece of it,and that when we have that as
the center goal, it makes allthe other things seem easier it
(40:35):
all connects back to that onething.
like fluency with math factsstill connects to that because
we do...
If, like, if we're out solvingthe, like, some problem comes to
mind when we're out there, we doneed to be quick that so that we
can figure something out in themoment, right?
Like, I, know.
(40:55):
I- it's a good conversation tokeep going and a, a, a good one
to really think and grapplewith.
Vanessa Vakharia (41:01):
Yeah, think about it
Christina Tondevold (41:02):
the center focus of this,
Vanessa Vakharia (41:04):
we're ta- w- you know, a lot of people
listening are, teach math.
And I'm like,
Christina Tondevold (41:08):
Mm-hmm.
Vanessa Vakharia (41:09):
Have math as a gateway.
Like, I, I mean, I love math,but I don't particularly, I'm
not like,"Math is the mostimportant thing." I'm like, math
is just the most beautifulgateway to so many things.
And one of the gateways that itopens up is the ability to
problem solve, right?
Y- yes, you're learning contentand you're learning skills, and
you're becoming fluent in thisand that, but at the end of the
day, the, the broader skillsyou're learning is how to solve
(41:30):
a problem, right?
So I guess I'm kind of thinking,like, because at your disposal,
what you have is math contentthat you have to teach.
Christina Tondevold (41:41):
Mm-hmm.
Mm-hmm.
Vanessa Vakharia (41:43):
that's kinda what you, you're supposed to be
doing anyways.
I don't know, I'm stuck at thatend of that sentence.
But I'm kind of like, so if you,if through teaching a child to
be fluent in math facts, thatwas your way to teach them to be
a problem solver, that almostseems like starting with the
(42:04):
trees instead of the forest.
Christina Tondevold (42:07):
Yeah, it's an interesting conversation of
just, um, trying to grapplewith, you know, all these things
that come at us.
You know, there's, oh, well, oh,now we should be doing which one
doesn't belong, and now weshould be doing
Vanessa Vakharia (42:20):
Cat
Christina Tondevold (42:21):
word prob- Like, there's so many different,
like, things that we can bedoing in the math classroom, and
now, like, high-qualityinstructional materials and, and
all of those pieces that getthrown at educators.
And so whether you have beenteaching for 30 years or you've
been teaching for three years,you've probably already noticed
(42:42):
this pendulum swing andbandwagon.
You're getting on the bandwagonof this new next thing, and then
guess what?
We're gonna hop off that here insix months, a year, maybe two
years from now.
And so it's not about the thingsthat come along.
we really do need to think aboutthe bigger picture what our goal
(43:07):
is when we are helping studentslearn mathematics.
Um, and I think that's somethingwe all need to grapple with a
little.
Vanessa Vakharia (43:14):
Well, this is perfect,'cause I was gonna say,
can you leave th- us withsomething?
It is summer.
I want you to leave us with a,like, what's something we can do
right now so that when we getinto the classroom, you know,
when school starts again, wefeel more centered?
And I think that's the thing, isto think about what you feel
your purpose is up there infront of the classroom.
(43:35):
What is the point of what you'redoing?
What's the point, and then letyour answer to that question
guide how you teach.
Christina Tondevold (43:41):
Let your own answer to that, and then
what you're hearing from yourstudents where they are in their
learning guide the instructionmoving forward.
Vanessa Vakharia (43:51):
Ugh.
Okay, this was so fun.
I have two questions to ask youthat I ask every podcast guest,
and you have 30 seconds toanswer both of them.
But I do have to tell you,
Christina Tondevold (44:01):
Speed.
Vanessa Vakharia (44:02):
this is...
Christina Tondevold (44:02):
I
Vanessa Vakharia (44:03):
Right?
You gotta be fluent.
You gotta be fluent.
Okay.
Someone's listening to thispodcast, they're like,"I love
everything Christina said.
Honestly, that's sointeresting," and like,"Yeah,
for sure, maybe I have some mathtrauma," like maybe that's not
why I'm good at math, buthonestly the truth is I'm just
not a math person.
How do you respond?
Christina Tondevold (44:19):
Mm.
you have a wrong version of mathbecause your version is probably
like mine.
I th- I had the opposite.
I thought I was good at mathuntil I had to go teach it, I
learned that I was good atarithmetic, mathematics.
(44:40):
And so you may see yourself asnot good, but you've been not
good at the arithmetic part ofmathematics, of getting correct
answers, and there's so muchmore to math beyond just correct
answers.
It is about a problem solver,and so, and everybody's good at
that.
Vanessa Vakharia (45:01):
It's so hard right now because I know I don't
have time for what I'm about tosay, but I'm gonna have to say
it.
Christina Tondevold (45:08):
Okay
Vanessa Vakharia (45:08):
I really don't like...
This is not your fault, okay?
And I love your response, but Idon't like that in the response
you put yourself down.
And the reason I don't like thatyou put yourself down is, is I
don't like this new trend ingeneral, and I'm not saying
you're, like, sorry, but I don'tlike this trend of us in, in
order to include more people inmath, we now have to exclude
(45:31):
people who were included.
I don't like this'cause I feellike it's like arithmetic is a
part of math, and you were goodat arithmetic.
It's not like it wasn't real.
Sorry, Christina.
I shouldn't be yelling at you
Christina Tondevold (45:42):
No, that's a good point because I say it a
lot, um, and you're making mereflect on that part of it that
I, I was good at a certain partof mathematics.
Vanessa Vakharia (45:53):
great.
No one's good at every part ofmathematics, even like prolific
mathematicians.
It's not like they're...
There's like game theory expertsthat don't know shit about like
calculus.
It doesn't mean that they'relike,"I was never actually g-
Sorry, this is like I shouldn'tbe taking this out on you,
especially within the timeconfines that I gave you.
Okay.
Christina Tondevold (46:12):
We're all on this journey.
That's why I call myself arecovering traditionalist.
Like, there are times thatsomebody needs to hold a mirror
to me and be like,"No, Idon't...
You're n- you're not saying thatcorrectly," or, or,"Rethink
about how you think about that."
Vanessa Vakharia (46:25):
Um, the n- final question, I swear to God.
final question is, if you couldpick one thing to change about
the way math is taught inschool, what would it be?
One thing
Christina Tondevold (46:34):
Hmm, balance.
Vanessa Vakharia (46:36):
Hmm.
I love that
Christina Tondevold (46:37):
of balance becau- and it goes with our
theme of the pendulum.
I wish I could tie baseball intothis somehow, uh, but I don't
see that.
Uh, that we, we swing one way,we swing the other, and, and we
realize that's not working, andso we'll swing all the way to
the other way.
And we need some of both all thetime.
(46:58):
We, we do need some timedactivities.
We need kids to be able to playand discover and guide their
instruction.
We need, um, sometimes we need alot of practice.
You know, when textbooks havemoved one way and it's like a
lot of contextual problems anddiscovery, and then those
textbooks are lacking inpractice, and we do need t- time
(47:20):
to practice things.
So we, if I could changeanything, it would be to find a
way to have some balance of bothsides of these pendulums that we
find in math education.
Vanessa Vakharia (47:34):
I love this.
And honestly, to really take ushome, David has texted me, I
think your landing metaphor maybe what you were looking for.
Not sure if it really is it.
He said,"Gotta play both offenseand defense to win a ball game
Christina Tondevold (47:50):
Yeah.
Vanessa Vakharia (47:51):
Honestly, this was such a treat.
I've had so many epiphanies.
It was so great talking to you.
I can't believe how manymetaphors we wove into one
another.
Like, I, I feel it was trulyprolific.
Um, thank you so, so much for
Christina Tondevold (48:06):
for asking me, and it's fun to get to chat
with you, and hope to get tomeet you in person one of these
days at a conference.
So
Vanessa Vakharia (48:14):
me too, and I'm really excited for the World
Series when the Blue Jayshopefully make it again, because
this time when I jump on thebandwagon, I know that I have a
baseball girly to talk to aboutall the things.
Christina Tondevol (48:24):
terminology, I'm
Vanessa Vakharia (48:26):
I do.
Christina Tondevold (48:27):
Yeah.
Vanessa Vakharia (48:28):
See you on the field.
Is that what they say?
No?
Christina Tondevold (48:32):
Play ball.
Vanessa Vakharia (48:36):
Okay, I'm dying to hear what you guys
think because honestly I feellike my entire relationship with
fluency has changed, especiallywhen I start thinking about
using that word in contextsother than math, right?
Like, the word is not polarizedwhen it comes to languages.
Why has it been so polarized inmath?
And I'm really curious ifChristina shared anything that
changed your mind and might evenchange your practice this
(48:57):
upcoming school year, or if shesaid anything that made you
double down on what you alreadythink and what you're already
doing.
Either way, we wanna hear fromyou.
Text the podcast, hit the linkin your show notes.
It literally says,"Text us," sotext us.
Also, if you want more of me andChristina, I'll be speaking at
her free virtual thinking summitAugust 10th, 11th, and 12th.
You should totally come.
(49:18):
It's completely free, and thereare such awesome speakers like
Pam Harris, Zak Champagne,Deborah Peart, Juliana Tapper,
Mike Flynn.
I could go o- Brittany Hege.
Like, there are so many peoplethat you know and love that are
gonna be speaking at this thing,and it's totally free.
So head to the show notes.
The link is in there to registerfor free, so come.
As always, thank you guys forlistening.
(49:39):
I would love for you to do allthe things I always ask you to
do, like share this episode witha friend, rate and review the
podcast, that stuff makes such abig difference to a small little
operation like ours that isgrowing thanks to you and the
amazing work you're doing outthere.
But also, I know we're busy.
I know you are booked and busy.
I know the last days of summerare approaching, and you have a
(50:01):
million other things to do, soif you don't wanna do any of
that stuff, that's cool.
Just have the best day ever, andI will catch you back here next
week uh, David, I have aproducer's note from about half
an hour ago when we were tryingto find that fairy tale.
He's now said,"You've run out ofpitchers in your bullpen and
(50:22):
putting position players on themound at this point", I don't
know what that means.
Okay, here are the twoquestions.
You have 30 seconds for each,okay?
Christina Tondevold (50:29):
Toss me a softball question here.
Vanessa Vakharia (50:31):
Oh my God.
All right.
Christina Tondevold (50:33):
that
Vanessa Vakharia (50:33):
I,
Christina Tondevold (50:34):
to hit out of the park?
Vanessa Vakharia (50:35):
I do know that, from when I watched the
Blue Jays World Series.
A soft toss.
So here are two soft tosses thatyou have 30 seconds to answer.
Okay.
at five years old We aren't expecting
kids to come to baseball, beingable to hit the ball into the
outfield, We aren't expectingevery kid to win, every kid to
be perfect.
We are laying a foundation ofwe're all here, we're learning.
Unfortunately for some kids,they end up getting coaches who
are all about winning, and allabout getting it right, and then
(00:24):
guess what happens?
They don't love the sportanymore, and they stop doing it.
And that's exactly what we'redoing in mathematics, it becomes
only about the winning, onlyabout being perfect.
Flexibility is the piece thatgets everybody feeling like they
can do this, that they have apart.
And yet we have to balance it alittle with, accuracy and
(00:45):
efficiency do matter, but if weput too much focus on that, that
becomes an issue, and then kidsare performing out of fear,
Vanessa Vakharia (00:56):
Hello, and welcome to another amazing
episode of Math Therapy, thepodcast that unpacks math trauma
and helps you build a betterrelationship with math.
I'm your host, Vanessa Vakharia,and I'm here today to get you
pumped up about going back toschool.
And yeah, I know, what abuzzkill when it's still summer
and, like, 10,000 degrees out,but it's coming, so why not get
(01:17):
fired up about it?
A new school year brings so manypossibilities, one of which is
the chance to redefine our termsin the classroom so they empower
us, and today's word is one ofthe most vulgar F words in all
of math (01:29):
fluency.
We keep hearing that we can't,like, teach students to be
fluent in mathematics while alsohonoring their progress and
thinking, but today's guest,Christina Tondevold, joins me to
tell you that that is total BS,and yes, you can have both.
Christina is a self-proclaimedrecovering traditionalist who
initially taught mathematics byexpecting students to parrot
(01:49):
back to her what she taughtthem.
But she now works with teachersin developing students'
mathematical understandings in afar more balanced way,
developing conceptualunderstanding while working on
procedural fluency.
She does this through her sitebuildmathminds.com, where you
can get PD literally at yourfingertips.
She's a powerhouse.
She is, like, the person I thinkabout when someone says fluency,
(02:12):
and that's why I decided she wasthe person I had to talk to
about reclaiming this F-bomb.
If you think that timing thingsin math will ruin a kid's life,
and if you've ever been like,"Well, yes, I want my students
to feel good about math andtheir thinking and themselves,
but I also need them to befluent in math, and it feels
impossible to do both," or ifyou've previously thought, just
like me, that fluency equalsspeed at the expense of all
(02:35):
else, this episode is for you.
And if you're like,"Sorry, Idon't even know what fluency
means, period, why it'simportant, or why I should give
a fuck," well, this episode isdefinitely for you.
All right, enough from me.
Here's my convo with the amazingChristina Tondevold.
Christina, welcome to thepodcast
Christina Tondevold (02:55):
Thank you for having me.
I am excited to be able to chatwith you.
Vanessa Vakharia (02:59):
I love how your, the first thing on your
website says that you are arecovering traditionalist, and I
kinda wanna just start there.
I wanna know a bit more aboutthat.
What does that mean?
Christina Tondevold (03:09):
When I started sharing things online, I
decided to call my blog that,The Recovering Traditionalist,
because it really is a journey,and I feel like I'm never fully
done.
You know?
Like I'm, i'm not just a thinkernow.
It is really hard to get out ofour traditional ways of teaching
mathematics because if, assumethat, you know, people my age,
(03:34):
uh, I'm nearing mid-life, thatwe all kind of grew up with very
traditional style of teaching ofhere's the procedure, learn it,
memorize it, follow the steps,and you'll get to the correct
answer, and that was howeverything was graded in math,
was did you follow the steps?
Did you get the right answer?
That was the way that I taught,was still very traditional.
(03:57):
I stood up there and gavestudents the notes and taught
them the procedure, and thenexpected them to practice it as
a whole group.
And then when they got to theindependent practice time, it
was like hands were going up,and I did not have another way
to help them.
I just would repeat the rulesand steps,'cause that's all I
(04:18):
knew.
Vanessa Vakharia (04:19):
I wanna make sure I'm tracking here that when
you say traditionalist, you arereferring to, um, a, a historic
way of teaching math that relieson procedure.
Is that correct?
Like, we're relying more onprocedure, we're on...
Okay,
Christina Tondevold (04:36):
Yeah, and, and for years though, I think
it's, you know, as everything ineducation, the pendulum swings.
And so the pendulum swingingaway from the traditional style
of teaching into more lettingkids think and play around with
mathematics, um, w- kind of wenta little too far to where it
(04:56):
was, let's just let kids playand discover.
And but we have to remember it'sguided instruction still.
It's not just letting them play.
It is letting them play andexplore, but we still have to
use that information to thenpull them, push them along their
trajectory of learning.
(05:16):
It's not just let them play andflounder, right?
We need to learn how they'rethinking and then use that to
guide our instruction to movethem through mathematical
understandings.
Vanessa Vakharia (05:30):
Yeah, it does feel like the guided piece is
what, when we hear about this inthe media, gets missed.
And I, I, I'm actually curious,like, did we ever actually just,
like, let kids play andflounder, or was there just,
like, an idea that we...
Like, were we ever like,"Oh,we're actually not teaching
anything"?
Like, just, I don't know.
Like, I know that there are someschools or, like, communities
(05:50):
where that happens, but I feellike that was never, like, the
instruction to teachers wasnever like,"Let them just, like,
vibe," and, like, the end,right?
Like, it was like,"Let's figureout, like, how they're learning,
what draws their interest, like,toward what their tendencies
are," and then exactly like yousaid,"Let's use that to guide
how we're gonna teach a certainconcept.
Like, let's prov-" Right?
Christina Tondevold (06:12):
I could say even from, like, personal
experience, but also stories,like my own children's
experience
Vanessa Vakharia (06:19):
Yep
Christina Tondevold (06:20):
Um, I have four kids ranging from 18 right
now to 12.
and there have been times where,I mean, they've had a whole
range of types of teachers,especially around mathematics.
but there have been a few havetaken things that they've
learned and, like, wanting kids,you know, what we talk about of
(06:43):
letting kids solve the problems,uh, not telling them how to
solve it, kind of to an extreme
Vanessa Vakharia (06:52):
Okay
Christina Tondevold (06:53):
"Here's the problem," and they, and then,
like, if they are flounderingand they aren't even sure where
to start or anything, th- thenthe teacher's like,"Well, figure
it out.
What can you
Vanessa Vakharia (07:03):
Okay
Christina Tondevold (07:04):
you know, a little, like, not just play and
discover, but even as we'reopen, giving kids an open task,
and
Vanessa Vakharia (07:11):
open
Christina Tondevold (07:12):
yeah, too open, and we just, like, let
them flounder a little too muchsometimes.
Vanessa Vakharia (07:17):
I would love to actually talk about this
because I think that this is oneof the biggest issues that I'm
hearing right now fromeducators, is like they know
that the move isn't to, like, beso prescriptive, right?
They're like,"Okay, I get thatI'm not supposed to give the kid
a problem and then, like, astep-by-step formula on how to
solve it.
I understand that.
But at the same token, I knowI'm not supposed to just be
like,'Okay, well figure it out.
(07:39):
Like, see ya.
I'm gonna go eat a peanut buttersandwich.'" Like, do you know
what I mean?
Like, that's not the move.
So it's like, but I also do feellike teachers are constantly
being, like, wrist-slapped fordoing too little or too much.
This feels like a Goldilockssituation, actually, right?
Like, it's like
Christina Tondevold (07:55):
Yes
Vanessa Vakharia (07:56):
too cold.
What was it?
It was too hot or too cold, theporridge, I think, right?
And then there was, like, themiddle.
What are some tips you can giveon, like, what you might ask
yourself in terms of what theright balance might be?
Like, what is that, that not toohot, not too cold bowl of
porridge?
Like, what should they do?
Christina Tondevold (08:14):
In general what I try to keep in mind Is I
don't want to start by telling.
Actually, okay, so w- in ourtalk that we had a couple days
ago, we mentioned our friendRaj, right?
Vanessa Vakharia (08:28):
Oh my God, Raj, what a vibe.
Christina Tondevold (08:30):
Raj is so fun.
So in I got to chat with Raj fora thing that we have upcoming
that Vanessa's a part of, andone of the things he mentioned
to me that still is- is on mybrain is that we can always go
back to direct instruction.
But our default has been, let mefirst tell you how to solve it,
(08:52):
and then you work on parrotingback and mimicking what I've
just told you.
So instead, like, to just getstarted and, give kids a
problem.
Just give them a problem, andsee what they think.
And you should always have inmind, though, where you're
wanting to go with them.
(09:13):
Like, what is the ultimate goal?
And, a lot of times we think ourgoals are the standards of
students will be able to blahblah blah.
It's not about what they're ableto do.
It's about what they understand.
And so we need to keep in mindis it that I want them to
understand about this?
Vanessa Vakharia (09:34):
I love this 'cause, like, uh, what I'm
hearing, and this makes so muchsense, it's like d- direct
instruction or just telling,okay, let's just call it just
telling'cause I hate all thejargon.
Just telling someone is in yourback pocket that you can use any
time, right?
But asking somebody, like askingsomebody to notice for the first
time can only happen in thebeginning.
(09:56):
You can't tell them and then askthem to notice for the first
time, right?
Whereas, like, the telling couldhappen at any time, so it kinda
makes sense to front-load yourinstruction with the stuff that
can only happen at the beginningas like an experiment, right?
Like, to be like,"Oh," like,"what would you do if you saw
this with no information?"'Causeonce they have the information,
they can't like imagine they hadno information and like, right?
(10:18):
Like you can't like you--
Christina Tondevold (10:19):
something
Vanessa Vakharia (10:20):
to unsee
Christina Tondevold (10:21):
pretend
Vanessa Vakharia (10:21):
and you can only be...
Christina Tondevold (10:22):
Yeah
Vanessa Vakharia (10:23):
Exactly.
So I kind of love that of beinglike, fine, like especially for
the teacher who's like,"Oh myGod," but like,"What if I have
to..." It's like, great, you cantell them.
I almost wonder if like a nicelittle therapeutic way to like
acclimatize yourself to thethinking model or, or getting
farther and farther away fromtelling is to even set a timer
(10:44):
and be like,"I'm not gonna tellthem anything for two minutes."
And then the next day be like,"I'm gonna set my timer for
three minutes," like I'm notallowed to tell anything for th-
you know what I mean?
Like you can build yourtolerance from uncertainty this
way.
Christina Tondevold (10:56):
Here's one thing I would recommend.
If your lesson is on doublesplus one, right?
And they aren't getting it inthe first 10 minutes, uh, might
be some deeper issues at, inplay.
Because mathematics is really aweb of understanding, and we try
to teach it in isolation.
(11:17):
Like, here's your doubles,here's your doubles plus one,
here's your make tens.
Or with multiplication, I don'tknow how you learned them, but I
learned them times ones, thentimes twos, then times threes.
Like, total isolation.
Vanessa Vakharia (11:28):
Yep
Christina Tondevold (11:29):
and now we know, like, okay, well, if you
know your tens, those areconnected to your fives.
And twos are c- can help youwith your fours and your eights.
Like,
Vanessa Vakharia (11:37):
We never did that, did we?
Christina Tondevold (11:39):
No.
No, never.
Never.
And, and so I could, I couldenvision, like, you know, I, I
don't want people to take awaythat, oh, okay, today we're
learning our times twosmultiplication facts.
Um, and if they don't have it bythe end, I'm just going to give
them a bunch of flashcards topractice it.
(12:00):
Like, there, there are reallybig things in mathematics that
just take time.
They take time to build.
And one of the things thatreally bugs me in our standards,
actually, is we do a reallygreat job with addition and
subtraction facts because itstarts in kinder, then they,
(12:21):
every state is technicallydifferent.
In, in Canada, yours might looka little different as well.
But typically in the UnitedStates, um, it's second grade
that it talks about being fluentwith addition and subtraction
within 20, which is your, yourquote, unquote facts.
So they have kindergarten, theyhave first, they have second
grade that they are building anunderstanding of what addition
(12:43):
and subtraction are.
And then by the end of secondgrade, they're supposed to have
become fluent with it.
Well, then, here in the UnitedStates, then third grade comes
along, and all of a suddenthey're supposed to master
multiplication and divisionfacts all in one grade level.
Like, that's, I mean, that is anunrealistic thing.
Um, and so I'm just saying,like, sometimes our standards
(13:08):
are great in giving us time tobuild these things for kids, and
sometimes it's just thrown at usand then we're like,"I've gotta
get kids fluent with these allin one year?" And so we get the
pressure of, oh, I just gottatell you, I've just gotta tell
you.
But there's a lot underneaththat we can build that will help
(13:29):
them be able to see a lot ofconnections, and the more
connections we can make, theeasier it is to recall info.
Vanessa Vakharia (13:35):
I'm gonna be honest here.
I'm listening to this, and I'mstressed.
Like, I'm listening to it, andI'm like,"Oh my God," there are
so many variables here.
Again, no pun intended.
But there's so much going on,right?
Like, you're kinda like, you'rekinda like, l- like, there's a
lot of messages.
And this is interesting.
I remember talking to anothereducator earlier this week, and
(13:55):
she was like,"You know,sometimes teachers just want,
like, what are the questions Ishould ask?
What are the rules I shouldfollow?" And it's like, y- this
is where your teacher'sintuition comes in, right?
Like, as educators, we arehealers.
We have an intuition.
We have experience.
We know that certain studentsneed this.
We can feel the energy of aclass when things are being
understood and not.
And I feel like we have to,like, pause and be like,"Listen,
(14:16):
we're saying a lot of thingshere, and none of these are
prescriptive." You kinda justhave to feel it out and trust
that you're doing the rightthing.
That being said, it's kind ofhard to hear, you know, that in
grade three we have thisbasically, like, impossible
standard, and it's gonna bereally, really hard, but also,
you gotta just, like, know whatthey need to understand about
the standard, and it's not aboutthe standard.
(14:38):
It's about them.
Right?
Like, it's like, oh, my God.
And now-- And, like, I, I getthat almost in a way this is
supposed to chill people out, tobe like,"Don't worry so much
about the standard.
Just, like, make sure they'reunderstanding some stuff that's
gonna be important." But whatif...
Can we take a step back and,like, forget the content, forget
the actual things, and, like,what is something that a
teacher, especially a beginningteacher who's hearing all this,
(15:00):
what's something that might givethem a bit of hope and relief
to-- if they're l- kind of like,"Yeah, man, like, this feels
hard.
It feels like some kids aren'tgonna be, like, getting all this
content.
It feels like I've gotta do toomuch." Like, what is your, like,
go-to, like, just remember this,this, this thing.
Like, j- what-- Like, do youhave something?
Christina Tondevold (15:19):
Yep.
Vanessa Vakharia (15:20):
Oh, okay, great.
Christina Tondevold (15:21):
Is not a set of isolated things.
It's all connected.
And so it does seem overwhelmingwhen you, like, you open up even
your standards and you're like,"Oh my gosh, I have to get all
of this in this grade?"Especially when w- I have
students maybe coming with somegaps or two back.
(15:44):
and when I saw mathematics is soconnected, opened up a whole
world for me.
Like, I was middle school, so Iw- at one point I was doing
sixth, seventh, eighth grade.
Um, in the, in the sixth gradetextbook, there's a chapter on
decimals, there's a chapter onfractions, there's a chapter on
(16:07):
percents Those are all the samething.
Vanessa Vakharia (16:12):
Yeah.
Christina Tondevold (16:13):
Tho-
Vanessa Vakharia (16:13):
I love it
Christina Tondevold (16:14):
the same types of numbers, yet we teach
them in isolation withoutconnecting them together.
Fractions are, you know, like apart of a whole.
I mean, that's a simplifiedversion of it, right?
It's
Vanessa Vakharia (16:27):
I loved it.
It was cute.
Yeah
Christina Tondevold (16:30):
decimals are just special fractions
because they have denominatorsthat are a power of 10.
They're a 10th, 1000th, right?
And then percents are evenspecialer because they are out
of 100.
So it's a fraction, but always,you know, percents are basi-
based out of what it is out of100 of something.
(16:51):
And yet those are not connectedtogether.
I didn't learn them as connectedtogether, and I didn't teach
them as connected together, andthen I had this group of kids in
front of me, uh, when we getdone with it, and they don't see
those connections.
Like, once I realized howconnected mathematics was, it
made me really start to look atthe textbook, the standards, and
(17:15):
say,"Okay, hold on.
So these are all listedindividually, but what actually
connects together?" And there isgreat, a great document out
there, um, by Achieve the Core,and it talks about the...
I mean, they're not the powerstandards.
That's not the phrase that theyuse.
I think they call them contentemphases.
(17:35):
but it's like what's the majorwork at each grade level?
And then they also talk aboutwhat ones are connected, they
support that major work.
And then it also shows whichones are just additional.
Like ex- for example,kindergarten, basically
everything is connected to thes- the work.
(17:55):
The major work in kindergartenis getting kids to count,
understand how numbers work, youknow, like the, the, the number
system of how things work, and alittle bit of addition and
subtraction.
Well, everything you're doing,if you're working on geometry
stuff, of recognizing shapes,and then you ask a kid,"So how
(18:16):
many circles do you have?"You're really also working on
counting.
Like, it's all
Vanessa Vakharia (18:21):
It's all co- Well, I also feel like it's like
this is, like, a message of hopeto be like anytime you're
working on anything, you'reworking on something else, too.
Like, you're getting more bangfor your buck than you think.
So it's like I really like thatexample of being like fractions,
percentages, and decimals.
You're looking at it being like,"I've got three chapters to
teach," right?
When really it's like what if welook at it as, like, you have
(18:44):
one chapter with some tentacles.
You know what I m- oh, I hatedthat I said that.
I'm sorry.
That grossed me out.
But do you know what I mean?
Like, you have, like, onechapter with, like, w- like, if
you teach fractions, you've nowtaught, you've taught a third of
percentages.
You know, if you teach fractionsand decimals, you've taught
two-thirds of percentages.
Once you close it off by being,like, percentages, now you've
(19:05):
taught the entire thing.
Oh my God, I just turned thechapters into a fraction.
Did you see what I did there?
I think that worked, right?
Like, right, right, right?
I think, as we know, time is,like, one of the biggest
struggles for teachers, and it'salways like,"I'm running out of
time, I'm running out of time."So if you can feel like you're
doing more, like, th- whateverwork you're doing now is
investing in all the futurechapters.
(19:26):
Like, if they're understandingfractions, they've already
understood a third ofpercentages.
You're getting there.
Like, you're filling that.
I do really like the way oflooking at- I Can I switch gears
for a sec?
Christina Tondevold (19:37):
absolutely
Vanessa Vakharia (19:38):
Okay, you've said a word several times, and
it is what I think of when Ithink of you.
And it's a word I feel we throwaround a lot in math ed and
don't define, and that word isfluency.
You've said fluency, kids beingfluent, and I think when people
hear fluency, what they think ofis speed, and I know that we're
missing the mark on that, and Ifeel like you're, like, one of
(20:00):
the fluency experts in my world,and I would love to hear from
you what fluency means.
Christina Tondevold (20:07):
So I will say everything I learned is from
other people.
Again, I, once I start seeingconnections, I, I learn
something over here fromsomebody and something here, and
I bring it together to make itmake sense for me.
Vanessa Vakharia (20:20):
Yeah
Christina Tondevold (20:20):
so I, I really love Susan Jo Russell's
definition of fluency.
She had a article back in 2000called Computational Fluency.
It was published by NCTM,National Council of Teachers of
Mathematics.
And she talked about threethings that make up fluency, one
is efficiency.
We do need to be fast.
(20:41):
I mean, that is part of And Ifeel like fast has kind of
gotten a bad rap
Vanessa Vakharia (20:46):
Yeah, agree
Christina Tondevold (20:47):
of all the trauma that comes with it, that
the way that we have used speedand timed activities in the past
has been harmful.
But the, the need to beefficient and fast still is a
part of our world.
We do want to be able to getthings done quickly.
(21:08):
Um, and, and this isn't just formathematics.
This, this version of fluency,uh, for those that are
listening, think of anything youfeel like you are fluent at or
trying to become fluent at.
Vanessa Vakharia (21:19):
Like a language obviously we'd think of
Christina Tondevold (21:20):
A language.
Yeah, yeah.
If you're fluent at driving yourcity that you live in, right?
You are efficient.
You know the fastest way to getsomewhere.
Vanessa Vakharia (21:30):
we've used speed and timed in a way that
was harmful, can you say a bitmore?
Like, how have we used it?
Christina Tondevold (21:36):
The classic of the timed tests of you have
to get this many in a minute,and then you, uh, switch papers
and somebody grades you.
You know, and so everybody'sseeing it.
And then, um, if you don't get80 problems in a minute, I'm
totally exaggerating, but 80problems in a minute, you have
(21:57):
to stay in at recess, and youdon't get your name up on the
wall with a star that you haveachieved, uh, this thing or
whatever it was.
I mean, f- there for a while,the multiplication sundae, I
don't know who started that, uh,but it was, like, everywhere
that you would get a scoop forevery, you know, you learned
(22:18):
your
Vanessa Vakharia (22:18):
Like actual ice cream?
Christina Tondevold (22:20):
Like, they would make a sundae.
And then when you got yoursundae complete, you could have,
like, you got to join in on theice cream sundae.
Like, I
Vanessa Vakharia (22:30):
Wait,
Christina Tondevold (22:30):
was
Vanessa Vakharia (22:31):
what?
Christina Tondevold (22:31):
years ago.
Vanessa Vakharia (22:32):
didn't have this.
I would like an ice creamsundae.
Okay
Christina Tondevold (22:36):
right?
But everybody who, who was goodat it loved that.
But those kids who struggled andnever achieved that 80 in a
minute or whatever it might havebeen, uh, never got their scoop
on the wall, never got toparticipate in the, the sundae
party that everybody else gotto.
So the timed activities, thosetimed tests, the mad minutes,
(22:59):
all of that was used aspunitive.
It was as a punishment, not assome- And we thought it would
motivate kids.
We thought if they got to seetheir name with a star up there,
that would motivate them.
Vanessa Vakharia (23:13):
and that's the thing, it's like, I mean, this
is a whole other conversation ofhow do we define motivation,
because like, okay, I guess itdid motivate some kids, but like
out of fear, right?
Like, it's like, yeah, likethat's like not really
motivation exact- Like it ismotivation, but it's like
Christina Tondevold (23:30):
true.
Vanessa Vakharia (23:31):
of motivation that we like want Let's just
like for argument's sake say weare gonna time you to do like 20
questions in a minute, or 10questions in a minute, whatever.
There's gonna be no sundae,there's gonna be no star,
there's gonna be no nothing, butyou're still gonna be timed.
Would that be okay?
Is it the way we treated theentire thing as...
Yeah?
Okay.
Christina Tondevold (23:51):
Yeah, yeah.
So actually, the researcharound- so there's, uh, a What
Works Clearinghouse and theInstitute for Educational
Sciences, IES.
Um, two groups look at all theresearch that's out there
because we can say,"Oh, well,research says this, research
says that." That might be onestudy, right?
(24:14):
What Works Clearinghouse and theIES puts together these practice
guides.
And, um, back in 2009, they didthe first one that I ever saw,
maybe there was one before it,but the first one I ever saw for
what works with students who arestruggling with mathematics.
And then in 2021, they justreleased, an updated one.
I said just released.
(24:34):
That was, like, five years ago.
Uh,
Vanessa Vakharia (24:36):
it
Christina Tondevold (24:37):
very many people know about it.
We,
Vanessa Vakharia (24:39):
Yeah
Christina Tondevold (24:40):
So this document has six recommendations
that have strong researchevidence to back them up for
what works.
One of them is timed activities.
So
Vanessa Vakharia (24:53):
what works for fluency
Christina Tondevold (24:55):
f- for, no, just mathematics in general.
Vanessa Vakharia (24:58):
Oh, okay
Christina Tondevold (24:59):
So it's, um, what works for students who
are struggling with mathematics.
It's actually a guide for t- forintervention, what intervention
should look like aroundmathematics.
So there's things like, um,vocabulary, like getting clear
on vocabulary helps kids, beingprecise in your language, using
word problems, using lots ofrepresentations in mathematics,
(25:21):
so models.
Um, everybody seems to be, tolove the first five
recommendations, and then thesixth recommendation is to use
timed activities.
And people are kind of a littlelike, hmm, I don't konw about
this."
Vanessa Vakharia (25:37):
I'm so into this because this is juicy,
'cause it's kind of like I'mjust, I don't know, I'm
processing this with you rightnow, but it's like you're right.
We have our backs up with speed.
As soon as someone says speed,I'm like Like as soon as a kid
is like,"I'm not fast," I'mlike,"Oh my God." Like, that's
not the thing.
But you're kind of right.
Like, there's nothing inherentlywrong with wanting to be
(25:58):
efficient with something, let'ssay, but there's so much baggage
that has come with it that I nowthink we're almost doing an
over-correct.
Like, the pendulum is swingingwhere we're like, oh my God,
like, no, like, speed doesn'tmatter at all.
But, like, doesn't make s- whatif it took an hour for someone
to add two plus two?
Like, we would- like, that,that's too long.
(26:20):
That's not good
Christina Tondevold (26:21):
Yeah.
So we, again, it's a thing ofbalance, right?
Like, we shouldn't be onlyfocusing on efficiency.
That is only, I'm gonna use afraction again, one third,
Vanessa Vakharia (26:32):
Okay, tell us the other things.
Yeah.
Okay, I love it, I love it.
Wow, we are doing the wholeunit.
Yeah, 30.3.333.
Oh my God, we're, we just didit.
We just converted them all.
We just taught, we just taughtthree chapters of math in one
second.
Christina Tondevold (26:47):
There we go.
Vanessa Vakharia (26:48):
Oh my God.
Okay
Christina Tondevold (26:49):
efficiency is one piece.
Let me get all three of them outso then we can
Vanessa Vakharia (26:52):
Okay.
Christina Tondevold (26:53):
it,
Vanessa Vakharia (26:53):
Yes, yes, yes
Christina Tondevold (26:54):
all together.
So efficiency is the speed part.
And then accuracy.
Correct answers do matter.
And again, the pendulum swungaway from
Vanessa Vakharia (27:04):
ChatGPT, yes.
Oh my God
Christina Tondevold (27:06):
You know, it's been like, oh, it doesn't
matter if they get it
Vanessa Vakharia (27:09):
Hmm.
Christina Tondevold (27:09):
or wrong.
Vanessa Vakharia (27:10):
Oh my God
Christina Tondevold (27:11):
thinking.
I'm sorry.
Correct answers do still matterin
Vanessa Vakharia (27:15):
It matters
Christina Tondevold (27:16):
They need right answers.
Accuracy is important.
yeah, it is important to look attheir thinking, but they also
need to be told when it's wrong,like,
Vanessa Vakharia (27:29):
Oh my God.
Yep
Christina Tondevold (27:30):
That matters.
And then the third one isflexibility.
Vanessa Vakharia (27:35):
What's that?
Christina Tondevold (27:36):
that's been my focus is because for the
longest...
I mean, I've been doing this along time.
I started teaching, I graduatedcollege in 2000.
So I have been in the educationspace for a long time, and
focusing on building numbersense and, and flexibility for
(27:58):
more than 15 years of that time.
and so I have pushed heavily ongetting teachers to focus on
flexibility.
Vanessa Vakharia (28:07):
What is it?
What is that?
Christina Tondevold (28:10):
about, uh, that in a
Vanessa Vakharia (28:10):
Doing math when on, in a handstand while
doing the splits
Christina Tondevold (28:14):
yeah, yeah.
Let's see how, how good yourdownward dog is or whatever, you
know.
Um, but the hard part is thatthat put the focus away from the
first two of accuracy andefficiency.
So I'm gonna talk aboutflexibility, but do not take
away that that is the only thingwe need to build.
Vanessa Vakharia (28:33):
We're just defining it
Christina Tondevold (28:35):
And I've, I've had to, like, say that now
because I've put so muchemphasis on flexibility and
people have, have gone all theway to the
Vanessa Vakharia (28:43):
Okay
Christina Tondevold (28:43):
the other side.
So flexibility is just havingalternate routes.
So let's go back to, you know,if you're, if you feel like
you're fluent driver in yourcity, what happens if there's an
accident and
Vanessa Vakharia (28:56):
Oh, God.
Oof.
Christina Tondevold (28:58):
Do
Vanessa Vakharia (28:58):
I'm stuck.
Christina Tondevold (28:59):
to get there without
Vanessa Vakharia (29:00):
No, absolutely not.
Christina Tondevold (29:03):
You're not
Vanessa Vakharia (29:04):
I am not.
Christina Tondevold (29:05):
your...
right?
Vanessa Vakharia (29:06):
I'm not
Christina Tondevold (29:07):
That's, and that's essentially what our kids
are.
So they might have one way to doit, and that's also been an, an
issue is, like, once all thesedifferent strategies came
around, it's like, well, if kidshave one way to do it, that's
fine.
They don't need to know otherways.
what if that one way doesn'twork on that problem?
Vanessa Vakharia (29:25):
okay?
I'm gonna do a little recap forthe listeners, and for myself,
quite frankly.
Okay, there are three aspects tofluency.
We have efficiency, which has todo with speed.
We have accuracy, which has todo with getting the right
answer.
And we have flexibility, whichhas to do with being able to, to
do things in different waysdepending on the circumstances.
Context dependent.
(29:45):
Having to...
Okay, so now...
Christina Tondevold (29:47):
love that.
Yeah.
Vanessa Vakharia (29:48):
Okay.
Oh my God, thanks.
Okay, so now I'm like, oh myGod, you are so right that we
have g- we have completelyover-corrected.
It's almost like, becauseflexibility wasn't a thing when,
you know, like 20 years ago, wedidn't care about it.
We only cared about efficiencyand accuracy.
Now we're like,"Oh my God,flexibility," like,"We left you
(30:09):
out." Now we're gonna, like,focus on flex- it also feels
like, to me, flexibility is likethe feel-good one of the gang.
It's like, and you know what Imean?
It's like, oh, you'll feel good.
Don't worry about getting itright.
Don't worry about being fast.
Christina Tondevold (30:22):
Yeah, it's like everybody wins kind of
Vanessa Vakharia (30:25):
Everybody wa- so it's giving participation
ribbon.
Oh my God.
what?
Christina Tondevold (30:30):
I mean, we need that.
We need everybody to feel likethey have a starting point, like
they have a way to contribute,like they have a way to
participate in mathematics.
That's, we do want that.
I'm not saying it's a bad thing,
Vanessa Vakharia (30:43):
I'm having a real epiphany.
I'm like,"Oh my God." I dothink, I do think...
You know all the haters on theinternet that are like,"Oh my
God, they're treating kids likesnowflakes"?
I don't know if I'm using thatright, but do you know what I
mean?
Like, participation ribbon, da,da, da, da, da, da.
It's like they're not actuallyentirely wrong, okay?
So, like, let me just say that,right?
It's like I get where they'recoming with this.
(31:05):
Like, for sure, if we reallywere like,"Don't worry, take two
hours to add two plus twotogether.
Don't worry if two plus twoequals five or six or seven,
but, like, as long as you'redoing something, you get an A+,"
that would be a problem.
I agree, that is a problem.
But I think what's actuallyhappening, and tell me if I'm
wrong here, I feel likeflexibility is not only useful,
(31:27):
but it is the inroad for themath-anxious student into doing
what is needed to get to anefficient, accurate place.
The flexibility is the thing wecan be like,"Look, do it
whatever way.
We can reward you becauseeveryone has their own way of
doing things." Now you feel moreconfident, and because you're
feeling more confident, you'renot gonna freak out when you get
something wrong or you're tooslow.
(31:48):
You're gonna keep at it becauseyou have some con...
Like, am I onto something?
You know what I'm saying?
Christina Tondevold (31:52):
Absolutely.
And, and as, as an, um, a sportsmom, you
Vanessa Vakharia (31:57):
Okay
Christina Tondevold (31:58):
I can see the analogy too with the
participation trophies and the,and the entry points in, right?
Like, if, if at five years oldwe're expecting kids to come to
baseball, being able to hit theball into the outfield, and know
which- where to throw it, andknow which way to go.
Because, uh, if you've everseen, like, play T-ball, they
(32:19):
hit the ball and then they'llrun to, like, third base, not
first ba- Like, you know,they're learning
Vanessa Vakharia (32:23):
Oh, cute.
Right
Christina Tondevold (32:25):
not They don't have the accuracy and, uh,
all the, that stuff down.
And, and so we do that buildthat and, and allow for all kids
to have an entry point, right?
We aren't expecting every kid towin, every kid to be perfect.
We are laying a foundation ofwe're all here, we're learning,
(32:45):
right?
And then unfortunatelysometimes, uh, for some kids,
they end up getting coaches whoare all about winning, and all
about getting it right, and willyell, and all of that kind of
stuff.
And then guess what happens?
They don't love the sportanymore, and they stop doing it.
And that's exactly what we'redoing in mathematics, is that we
might be having these entrypoints, you know.
(33:07):
Like, again, we've, we've goneto the wayside where we're just
letting everybody come in andhave this entry point piece, but
we also need to balance thatwith, hey, they Uh, like, we do
need to get to the efficiencyand accuracy part, but even then
it's still flexibility.
The flexibility still matters.
It's not like flexibility goesaway.
(33:28):
that's unfortunately sometimeswe see in sports, is it becomes
only about the winning, onlyabout being perfect.
And then kids are playing out offear because they're, uh, s-
scared their coach is gonna yellat them or bench them because
they did something wrong, right?
Like, there, there's differentstyles of coaching, for sure.
I've done Uh, this is part of akeynote that I do.
(33:49):
Um, so it's something I lovetalking about.
But the same is true for us aseducators, that we- that
flexibility is the piece thatgets everybody feeling like they
can do this, that they have apart.
And yet we have to balance it alittle with, you know, accuracy
and efficiency do matter, but ifwe put too much focus on that,
(34:10):
that becomes an issue, and thenkids are performing out of fear,
and they're motivated onlybecause those external things
that they're afraid of.
Vanessa Vakharia (34:21):
I wanna bring this all home for us here, which
is gonna be a bit hard, and thatkind of is a baseball metaphor
that I'm sort of using, I think.
Christina Tondevold (34:29):
Yeah,
Vanessa Vakharia (34:30):
right?
Uh, is that where it comes from?
Is it like ra- is it-- Oh, myGod, Christina, wow, we are
basically sports commentators.
Okay, this is gonna be hard totrack'cause I have about 30
thoughts in my mind, but hereare some of them.
The first is, I think we have torecognize, for anyone listening,
I don't think anyone who thinksthis listens to my podcast, but
if you are listening and you'relike,"I hate this flexibility
(34:53):
stuff.
It's all about speed andaccuracy," I'm so glad you're
listening.
Actually, thank you for taking achance on the podcast.
Thank you for being here, andhere's what I wanna say.
If you're like,"Well, exactly,like, we are losing those things
at the expense of flexibility,"here is, here is my thought on
that.
I actually think we have torecognize that historically math
has been such ananxiety-inducing subject that so
(35:13):
few students are willing to walkin the door.
And because of that, it behoovesus, I don't know what behooves
means, but it feels like it fitsin the sentence.
Christina Tondevold (35:23):
Yes
Vanessa Vakharia (35:23):
It behooves us to actually put an emphasis on
flexible thinking as a startingpoint because it allows the most
flexibility in terms of who canwalk in the door.
Because, you know, there are notmany ways to think incorrectly.
If you're thinking, if you'redoing something in any way, you
are doing something, and that iswhat flexibility is all about,
right?
So, like, it kind of makes sensefor us to be really emphasizing
(35:45):
that so we can get all thepeople in the door.
Once they're in the door, weare, we are dedicated as
educators to helping them solvethe problem and get the correct
answer and to do so efficiently.
But, like, let us, let usemphasize flexibility for a bit,
because the lack of flexibilityis what has led to so much math
anxiety, hence so few peoplewalking in the door.
(36:06):
What do we think so far?
Christina Tondevold (36:07):
Mm-hmm.
Absolutely.
Vanessa Vakharia (36:08):
Okay, so great.
So that's nice.
But now you're making me thinktoo, we've now really centered
on the concept of fluency,right?
But it kinda, I know thatfluency isn't the only goal in
math, right?
Christina Tondevold (36:21):
well, so that could
Vanessa Vakharia (36:23):
It feels like,
Christina Tondevold (36:24):
right?
I
Vanessa Vakharia (36:25):
it feels pretty good.
It feels like it covers a lot ofbases.
Oh my God!
Christina Tondevold (36:30):
We're just gonna keep at it.
Vanessa Vakharia (36:32):
Okay
Christina Tondevold (36:33):
um, I've had to really rethink my own
understanding of the purpose ofmathematics,
Vanessa Vakharia (36:39):
Okay
Christina Tondevold (36:41):
My traditional view of mathematics
was I use mathematics and solveproblems, like, I'm just doing
math.
However, to me, and, and I gotthis from, we in the United
States call it Singapore math,Ban Har says,"It's just math,
(37:02):
but we do it in Singapore." Andtheir focus is
Vanessa Vakharia (37:07):
Hmm.
Christina Tondevold (37:08):
We want kids to be problem-solvers, and
we do that with mathematics.
Um, and so fluency, uh, likeeven in the United States,
though, even with thisflexibility piece, we still do
have this push of get themfluent, fluent, fluent, fluent.
When, is mathematics, like,being fluent in mathematics,
(37:28):
like, the end-all be-all?
Or is it that we want kids to becapable thinkers and
problem-solvers, and we
Vanessa Vakharia (37:39):
it sounds...
Christina Tondevold (37:40):
through mathematics
Vanessa Vakharia (37:41):
But hold on, fluency sounds, the tenets of
fluency, efficiency, accuracy,and flexibility, is that not
what it takes to solve aproblem?
Christina Tondevold (37:52):
It is, but it's, it's, it's flipping how
we're looking at it.
Like, the end-all be-all...
'Cause okay, so, um, let me seeif I can reframe this too.
Like, I always thought, like,even on, when I first started
becoming more of a recoveringtraditionalist, I still thought
my job is to teach themathematical skills, to help
them understand the mathematicalskills, like the operations,
Vanessa Vakharia (38:15):
Yes
Christina Tondevold (38:16):
that they can solve problems, right?
Vanessa Vakharia (38:20):
it
Christina Tondevold (38:20):
can solve problems.
When I heard Dr.
Bonhar talk, he said,"Our goalis to help kids be
problem-solvers, and thebyproduct of that is they learn
some math skills along the way."And so it's the rever- Like,
just
Vanessa Vakharia (38:39):
Oh,
Christina Tondevold (38:40):
is our
Vanessa Vakharia (38:41):
yep, yep, yep, yep, yep
Christina Tondevold (38:42):
wa- I was still focusing on help my kids
learn the math skills, help mykids learn the math skills, and
if they become greatproblem-solvers, that's a great
byproduct.
But instead
Vanessa Vakharia (38:53):
hear you.
Christina Tondevold (38:53):
let's put
Vanessa Vakharia (38:54):
I hear you
Christina Tondevold (38:54):
And so even if we're like,"Okay, fluency
will hit all of that stuff,"it's still we're putting the
focus on fluency, fluency,fluency, and then if they become
thinkers, eh, a great byproductof that.
Vanessa Vakharia (39:08):
Oh, wait, 'cause it kind of seems like
fluency, if we think about thew- you remember, you were, like,
fluent in driving, fluent incooking.
It almost feels like fluency isdependent on the thing you're
fluent in.
You can't just be, like, fluentin life.
Whereas you can be aproblem-solver in every domain,
fluency is domain-specific, andright now we're talking about
fluency in the domain ofmathematics.
Oh my God.
(39:29):
Oh my God.
Okay.
And I think, we're gonna wraphere, but it's okay that we
don't have a conclusion.
I actually think it is for theeducator listening or whoever
listening to be like,"Huh, whatis my approach going to be?"
Right?
Like, what is it?
Like, is it, is it going to befluency first, problem-solving
second, or is it gonna be pro-Like, and again, I actually
(39:52):
don't know that there is ageneric answer.
I think it can depend on yoursituation, on the student.
Maybe a student's reallyinterested in some mathematical
concept, and through that theydevelop fluency, and through
that they learn how to solveproblems.
Maybe a student's...
Right?
Like, do, do you think, do youthink there's a right answer to
this?
Christina Tondevold (40:11):
well, I would encourage, I guess, um,
maybe it's the recoveringtraditionalist in me that we
start opening our mind to maybeit is more about the
problem-solving si- piece of it,and that when we have that as
the center goal, it makes allthe other things seem easier it
(40:35):
all connects back to that onething.
like fluency with math factsstill connects to that because
we do...
If, like, if we're out solvingthe, like, some problem comes to
mind when we're out there, we doneed to be quick that so that we
can figure something out in themoment, right?
Like, I, know.
(40:55):
I- it's a good conversation tokeep going and a, a, a good one
to really think and grapplewith.
Vanessa Vakharia (41:01):
Yeah, think about it
Christina Tondevold (41:02):
the center focus of this,
Vanessa Vakharia (41:04):
we're ta- w- you know, a lot of people
listening are, teach math.
And I'm like,
Christina Tondevold (41:08):
Mm-hmm.
Vanessa Vakharia (41:09):
Have math as a gateway.
Like, I, I mean, I love math,but I don't particularly, I'm
not like,"Math is the mostimportant thing." I'm like, math
is just the most beautifulgateway to so many things.
And one of the gateways that itopens up is the ability to
problem solve, right?
Y- yes, you're learning contentand you're learning skills, and
you're becoming fluent in thisand that, but at the end of the
day, the, the broader skillsyou're learning is how to solve
(41:30):
a problem, right?
So I guess I'm kind of thinking,like, because at your disposal,
what you have is math contentthat you have to teach.
Christina Tondevold (41:41):
Mm-hmm.
Mm-hmm.
Vanessa Vakharia (41:43):
that's kinda what you, you're supposed to be
doing anyways.
I don't know, I'm stuck at thatend of that sentence.
But I'm kind of like, so if you,if through teaching a child to
be fluent in math facts, thatwas your way to teach them to be
a problem solver, that almostseems like starting with the
(42:04):
trees instead of the forest.
Christina Tondevold (42:07):
Yeah, it's an interesting conversation of
just, um, trying to grapplewith, you know, all these things
that come at us.
You know, there's, oh, well, oh,now we should be doing which one
doesn't belong, and now weshould be doing
Vanessa Vakharia (42:20):
Cat
Christina Tondevold (42:21):
word prob- Like, there's so many different,
like, things that we can bedoing in the math classroom, and
now, like, high-qualityinstructional materials and, and
all of those pieces that getthrown at educators.
And so whether you have beenteaching for 30 years or you've
been teaching for three years,you've probably already noticed
(42:42):
this pendulum swing andbandwagon.
You're getting on the bandwagonof this new next thing, and then
guess what?
We're gonna hop off that here insix months, a year, maybe two
years from now.
And so it's not about the thingsthat come along.
we really do need to think aboutthe bigger picture what our goal
(43:07):
is when we are helping studentslearn mathematics.
Um, and I think that's somethingwe all need to grapple with a
little.
Vanessa Vakharia (43:14):
Well, this is perfect,'cause I was gonna say,
can you leave th- us withsomething?
It is summer.
I want you to leave us with a,like, what's something we can do
right now so that when we getinto the classroom, you know,
when school starts again, wefeel more centered?
And I think that's the thing, isto think about what you feel
your purpose is up there infront of the classroom.
(43:35):
What is the point of what you'redoing?
What's the point, and then letyour answer to that question
guide how you teach.
Christina Tondevold (43:41):
Let your own answer to that, and then
what you're hearing from yourstudents where they are in their
learning guide the instructionmoving forward.
Vanessa Vakharia (43:51):
Ugh.
Okay, this was so fun.
I have two questions to ask youthat I ask every podcast guest,
and you have 30 seconds toanswer both of them.
But I do have to tell you,
Christina Tondevold (44:01):
Speed.
Vanessa Vakharia (44:02):
this is...
Christina Tondevold (44:02):
I
Vanessa Vakharia (44:03):
Right?
You gotta be fluent.
You gotta be fluent.
Okay.
Someone's listening to thispodcast, they're like,"I love
everything Christina said.
Honestly, that's sointeresting," and like,"Yeah,
for sure, maybe I have some mathtrauma," like maybe that's not
why I'm good at math, buthonestly the truth is I'm just
not a math person.
How do you respond?
Christina Tondevold (44:19):
Mm.
you have a wrong version of mathbecause your version is probably
like mine.
I th- I had the opposite.
I thought I was good at mathuntil I had to go teach it, I
learned that I was good atarithmetic, mathematics.
(44:40):
And so you may see yourself asnot good, but you've been not
good at the arithmetic part ofmathematics, of getting correct
answers, and there's so muchmore to math beyond just correct
answers.
It is about a problem solver,and so, and everybody's good at
that.
Vanessa Vakharia (45:01):
It's so hard right now because I know I don't
have time for what I'm about tosay, but I'm gonna have to say
it.
Christina Tondevold (45:08):
Okay
Vanessa Vakharia (45:08):
I really don't like...
This is not your fault, okay?
And I love your response, but Idon't like that in the response
you put yourself down.
And the reason I don't like thatyou put yourself down is, is I
don't like this new trend ingeneral, and I'm not saying
you're, like, sorry, but I don'tlike this trend of us in, in
order to include more people inmath, we now have to exclude
(45:31):
people who were included.
I don't like this'cause I feellike it's like arithmetic is a
part of math, and you were goodat arithmetic.
It's not like it wasn't real.
Sorry, Christina.
I shouldn't be yelling at you
Christina Tondevold (45:42):
No, that's a good point because I say it a
lot, um, and you're making mereflect on that part of it that
I, I was good at a certain partof mathematics.
Vanessa Vakharia (45:53):
great.
No one's good at every part ofmathematics, even like prolific
mathematicians.
It's not like they're...
There's like game theory expertsthat don't know shit about like
calculus.
It doesn't mean that they'relike,"I was never actually g-
Sorry, this is like I shouldn'tbe taking this out on you,
especially within the timeconfines that I gave you.
Okay.
Christina Tondevold (46:12):
We're all on this journey.
That's why I call myself arecovering traditionalist.
Like, there are times thatsomebody needs to hold a mirror
to me and be like,"No, Idon't...
You're n- you're not saying thatcorrectly," or, or,"Rethink
about how you think about that."
Vanessa Vakharia (46:25):
Um, the n- final question, I swear to God.
final question is, if you couldpick one thing to change about
the way math is taught inschool, what would it be?
One thing
Christina Tondevold (46:34):
Hmm, balance.
Vanessa Vakharia (46:36):
Hmm.
I love that
Christina Tondevold (46:37):
of balance becau- and it goes with our
theme of the pendulum.
I wish I could tie baseball intothis somehow, uh, but I don't
see that.
Uh, that we, we swing one way,we swing the other, and, and we
realize that's not working, andso we'll swing all the way to
the other way.
And we need some of both all thetime.
(46:58):
We, we do need some timedactivities.
We need kids to be able to playand discover and guide their
instruction.
We need, um, sometimes we need alot of practice.
You know, when textbooks havemoved one way and it's like a
lot of contextual problems anddiscovery, and then those
textbooks are lacking inpractice, and we do need t- time
(47:20):
to practice things.
So we, if I could changeanything, it would be to find a
way to have some balance of bothsides of these pendulums that we
find in math education.
Vanessa Vakharia (47:34):
I love this.
And honestly, to really take ushome, David has texted me, I
think your landing metaphor maybe what you were looking for.
Not sure if it really is it.
He said,"Gotta play both offenseand defense to win a ball game
Christina Tondevold (47:50):
Yeah.
Vanessa Vakharia (47:51):
Honestly, this was such a treat.
I've had so many epiphanies.
It was so great talking to you.
I can't believe how manymetaphors we wove into one
another.
Like, I, I feel it was trulyprolific.
Um, thank you so, so much for
Christina Tondevold (48:06):
for asking me, and it's fun to get to chat
with you, and hope to get tomeet you in person one of these
days at a conference.
So
Vanessa Vakharia (48:14):
me too, and I'm really excited for the World
Series when the Blue Jayshopefully make it again, because
this time when I jump on thebandwagon, I know that I have a
baseball girly to talk to aboutall the things.
Christina Tondevol (48:24):
terminology, I'm
Vanessa Vakharia (48:26):
I do.
Christina Tondevold (48:27):
Yeah.
Vanessa Vakharia (48:28):
See you on the field.
Is that what they say?
No?
Christina Tondevold (48:32):
Play ball.
Vanessa Vakharia (48:36):
Okay, I'm dying to hear what you guys
think because honestly I feellike my entire relationship with
fluency has changed, especiallywhen I start thinking about
using that word in contextsother than math, right?
Like, the word is not polarizedwhen it comes to languages.
Why has it been so polarized inmath?
And I'm really curious ifChristina shared anything that
changed your mind and might evenchange your practice this
(48:57):
upcoming school year, or if shesaid anything that made you
double down on what you alreadythink and what you're already
doing.
Either way, we wanna hear fromyou.
Text the podcast, hit the linkin your show notes.
It literally says,"Text us," sotext us.
Also, if you want more of me andChristina, I'll be speaking at
her free virtual thinking summitAugust 10th, 11th, and 12th.
You should totally come.
(49:18):
It's completely free, and thereare such awesome speakers like
Pam Harris, Zak Champagne,Deborah Peart, Juliana Tapper,
Mike Flynn.
I could go o- Brittany Hege.
Like, there are so many peoplethat you know and love that are
gonna be speaking at this thing,and it's totally free.
So head to the show notes.
The link is in there to registerfor free, so come.
As always, thank you guys forlistening.
(49:39):
I would love for you to do allthe things I always ask you to
do, like share this episode witha friend, rate and review the
podcast, that stuff makes such abig difference to a small little
operation like ours that isgrowing thanks to you and the
amazing work you're doing outthere.
But also, I know we're busy.
I know you are booked and busy.
I know the last days of summerare approaching, and you have a
(50:01):
million other things to do, soif you don't wanna do any of
that stuff, that's cool.
Just have the best day ever, andI will catch you back here next
week uh, David, I have aproducer's note from about half
an hour ago when we were tryingto find that fairy tale.
He's now said,"You've run out ofpitchers in your bullpen and
(50:22):
putting position players on themound at this point", I don't
know what that means.
Okay, here are the twoquestions.
You have 30 seconds for each,okay?
Christina Tondevold (50:29):
Toss me a softball question here.
Vanessa Vakharia (50:31):
Oh my God.
All right.
Christina Tondevold (50:33):
that
Vanessa Vakharia (50:33):
I,
Christina Tondevold (50:34):
to hit out of the park?
Vanessa Vakharia (50:35):
I do know that, from when I watched the
Blue Jays World Series.
A soft toss.
So here are two soft tosses thatyou have 30 seconds to answer.
Okay.
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