September 20, 2023 • 32 mins
Season 6 of Math Teacher Lounge is here!
This season, we’ll be digging deep into math fluency—exploring what it is, looking into the research around it, and sharing practical tips for building it in math classrooms. Join us as we kick things off this week with Jason Zimba, Amplify’s chief academic officer of STEM!
In our first episode, we sat down with Jason to get a clear understanding of what math fluency is and what we really mean when we talk about it. As a prominent math advocate with many years of experience, he can also help us learn just how important fluency is and how it fits into the standards.
Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
Unlock additional insights with these bonus resources:
- Read Jason’s article, “How I See Addition Facts.”
- Join us in the Math Teacher Lounge Facebook Community.
- Dive into, “Adding It Up: Helping Children Learn Mathematics” and “Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity” at National Academics.
- Check out Appetites: A Cookbook by Anthony Bourdain and Laurie Woolever to cook with Jason.
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Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Jason Zimba (00:00):
The dials are all mixed up on fluency. On the one
(00:02):
hand, I worry that wordproblems and applications get
proceduralized. And if so, thenwe're aiming for fluency with
something that's not aprocedure in the first place.
Bethany Lockhart Johnson (00:13):
Hi, I'm Bethany Lockhart Johnson .
Dan Meyer (00:15):
And I'm Dan Meyer.
Bethany Lockhart Johns (00:16):
Welcome to our new season of Math
Teacher Lounge. Dan! Newseason, new music!
Dan Meyer (00:24):
New lounge, too! I'm loving this new spot. What's in
our new Lounge here right now?
You know, posters on the wallof famous mathematicians from
movies and whatnot .Movies and TV. Better
accommodations, slightly lessgrungy. Beanbag chair.
Bethany Lockhart Johnson (00:37):
The couches have been
steam-cleaned. There's donutson the table. I don't know , it
feels like a fresh start.
Anything ispossible...including defining
fluency, Dan Meyer.
Dan Meyer (00:48):
Defining fluency.
New season for us here. Lastseason, we really got to the
bottom, and I would like to saywe solved entirely, the issue
of math anxiety. < Laughter >Good work to our guests, but
especially to you and to me,Bethany, on that last season's
deep dive into math anxiety.
And we're excited to bring anew deep dive to you folks, on
(01:11):
fluency. We've done an episodeon fluency. Yeah? A couple of
them? Dr. Val Henry , Tracy andGraham. Very popular episodes.
That that gave us the sensethat fluency was an area that
we ought to dive deeper into.
So , Bethany, what's your vibeon fluency? Like, how do you
feel about it? Are you lookingforward to this? What are you
looking forward to?
Bethany Lockhart Johnson (01:30):
Well, should I pretend I don't know
how you feel about it, Dan? Inmy defense, I will say that
when we were thinking about howwe want to spend our collective
time in the Lounge and what wewere hoping to share with the
audiences, I think I was morepushing/gung-ho for the joy in
(01:53):
mathematics season. Mathanxiety, I think you were
onboard. Fluency ... you seemedonboard, but not with the level
of enthusiasm that I washoping. And so I'm thinking
that over the course of thisseason, your enthusiasm will
just continue to grow. How youfeel about that? You think?
Dan Meyer (02:11):
I think it
could ONLY grow. That's the
only direction. Nowthis is an area, gentle
listener ... this is one of therare areas of difference
between Bethany and I. And Iwanna say it's a very loosely
held difference for me. Like,I'm here wanting to believe.
And I'm so excited to haveBethany on this season with me,
(02:31):
' cause Bethany isn't ... Iwould call you enthusiastic
about fluency and what it canoffer students, and fluency as
a lever for more equitableeducation for all kinds of
kids. You're positive about itin ways that I admit that I am
not. And I want to learn more.
I assume when someone Irespect, like you, likes a
(02:52):
thing that I'm not instantlydrawn to, that there's
something there for me tolearn. So if I c ould just
offer to the listener ... I getreally excited by introducing
new stuff. Like, I get excitedby, "So you've learned this old
thing, a nd here's like a wayinto the new thing — a
connection you haven't thoughtof or something surprising
about it." And I find myselfnot super-opinionated about how
(03:15):
the old thing becomes fluent oreven really solidly known. I do
think this is a liability ofmine, a place of growth for me.
And I'm also aware of a lot ofthe ways we develop fluency in
the old stuff. And the thingthat was known can cause some
damage to kids. Like, whenadults reflect on moments in
their childhood where theydecided that math was not for
(03:37):
them, it is often on someworksheet or some drill or some
moment where they could not seethe forest for the tree in
front of them. They lost sightof what a lot of us cherish
about mathematics.
Bethany Lockhart Johnson (03:52):
I applaud you in your open mind,
that you know that the new ISexciting. And I guess where I
come from, living in K–5 land —the land that I love — I see
what a barrier fluency can be.
(04:12):
And I see the way that kiddoswho don't own their addition,
subtraction, multiplication,division facts, the way they
don't own those — and I'mspeaking about fluency, again,
with the basic facts here —that can be such a barrier. And
(04:34):
I think so often the way it'staught or not taught at all is
the real issue, and can be acause of math anxiety. So you
have these kiddos who don'thave access to these facts, or
they don't own them. They don'tknow 'em. And it keeps them
from diving into the juicyparts of math, right? Math is
(04:56):
so much bigger than additionfacts, but because they don't
know those addition facts, itbecomes all math is. And all
you can think about. And whenyou think about math, that's
what you think about. Sothere's two things: There's the
kiddos who don't have them yetand who are then stymied from
enjoying all the things you cando once you have those in your
(05:18):
repertoire, and then you haveschools and teachers who, a lot
of them don't know enough aboutfluency. So they are going to
Teachers Pay Teachers anddownloading timed tests with
just cooler font or whatever,right? And thinking, "Look,
this is themed! This is aHalloween timed test! So
they've gotta get it now,right?" And fortunately, I was
(05:42):
at a school where my principalsent every single teacher, K
through 5, to training. And wedid the training with Dr. Val
Henry, who we've talked to;we'll talk to her again. And
she has a program calledFactsWise. And my favorite part
about it was just how much Ilearned about how facts are
learned, right? Like, Ilearned, how do we learn them.
(06:02):
And learned about long-termmemory, working memory. And it
just really helped me to have abetter, like, joy and sense of
what's possible. And too oftenI have seen teachers, when you
ask them, "Well, how do yourkiddos learn their facts?" Or
"What do you do in yourclassroom?" a lot of them don't
have any plan at all. Orthey're like, "Oh, well ,
they'll just get it." Or, "Oh,yeah, at the end of every week,
(06:23):
we do a timed test." And weknow that's not how kiddos
learn it.
Dan Meyer (06:27):
I think that speaks to what I'm excited about for
this season with you, Bethany,is to come to an appreciation
of the sophistication ofdeveloping fluency for kids,
with kids. Like I know thesophistication of introducing
new material, like ideas ofcognitive disequilibrium or
(06:48):
intellectual need or workedexamples. It feels so rich to
me. And I think that I canagree fluency is important, but
in my head, what's conjured upare these very direct routes
from not being fluent to beingfluent. They just kind of
charge in a direct line, by wayof these worksheets, these
downloadables. Whereas you haveseen, I think, through folks
that we'll interview, I hope,the sophistication there. And
(07:11):
how there are different pathspossible from not being fluent
to being fluent, that canactually lead through
mathematical joy and conceptualrichness and the stuff that I
more innately gravitatetowards. So I'm excited about
it. We got a great set ofguests lined up here. And I'd
just love to intro our firstguest of the new season.
(07:31):
Happens to be Jason Zimba,Amplify's Chief Academic
Officer of STEM. He's beenthinking about math fluency in
depth for years. We hope thiswill be a great introduction
into a season-long explorationof this topic.
Bethany Lockhart Johnson (07:44):
We hope you enjoy our conversation
with Jason Zimba.
Dan Meyer (07:50):
Welcome, Jason Zimba, to the show. We're happy
to have you here.
Jason Zimba (07:54):
Thank you. I'm glad to be here.
Dan Meyer (07:55):
We know that fluency is one of many buckets of
mathematical ideas andcompetencies you care a lot
about. So we're really happy toget your time here to help us
break some initial ground onthe area of what is fluency and
why should we care so muchabout it.
Bethany Lockhart Johnson (08:10):
But before we get into that, I
mean, we need to get to knowyou a little bit more, Jason
Zimba! So we'recurious: What's something
outside of math where you'vedeveloped, or you are currently
developing, fluency? I figureyou're pretty fluent with the
math facts.
Jason Zimba (08:29):
Well, you know, a lot of fluencies I think we
develop as kids. Shoe-tying,the combination lock on your
locker in the high schoolhallway. But there is something
I have made a concerted effortto become fluent in over the
last 10 years, which isroasting a chicken. I was
following food blogs and otherthings. I grew up in a diner,
(08:50):
and making food was always apart of life. And I noticed
that people were always on aquest for the perfect roast
chicken recipe. And they werelike, "Oh, this recipe will
finally help you get it right."And, "This is the ideal recipe
for roasting a chicken." And Idecided to go another way. I
got a cookbook for Christmas.
It was Anthony Bourdain'sAppetites book. And he had a
(09:12):
recipe for roasting a chickenthat looked pretty good, looked
legitimate, you know?
Legitimate chef. And I said,I'm just gonna get good at this
one. I'm gonna stop hunting forthe perfect chicken recipe. I'm
just gonna learn how to roastthe crap out of this recipe for
chicken. And so I started doingthat and I've roasted about 30,
(09:33):
40 chickens in the exact sameway to the point where now, if
I'm walking past the grocerystore, I don't need an
ingredient list. I can justwalk in. I know what I need. I
prep the chicken withoutopening the book. And I know
the temperatures and the times.
But of course, every chicken'sa little different. So you
can't just apply an algorithmfor having a nice roast
(09:56):
chicken. The weights aredifferent, you know, the way
the legs go is a littledifferent. The lemon you have
might be a different size. AndI have found that a much more
rewarding way to go about itthan to constantly be hoping
that I would find the idealroast chicken recipe.
Dan Meyer (10:10):
It feels like we might return to this anecdote
over and over again.This conversation. There's a
lot going on here. I, myself,am wondering, like, that 30th
chicken versus the first —you've mentioned that you don't
have the things you don't haveto do anymore. But are there
things that you now can dobecause your mind is no longer
occupied by the steps of therecipe? Ways that you're more
(10:33):
flexible with the chicken?
Jason Zimba (10:35):
Well, one thing is, I no longer need it to be a
weekend where I have five hoursto futz around and mess up the
kitchen. There are more windowsof time available to me now,
when we can have that. Or ifI'm staying over at someone
else's house and poking around,I could do it. I don't need
home-field advantage to roastthe chicken.
Dan Meyer (10:56):
As Bethany and I talked about before our
interview began, I'm in theprocess of trying to awaken my
own enthusiasm for fluency. Imean, I have some, but it's not
my first-round draft pick ofareas of math that excite me.
And what you're describinghere, how it enables you to do
more things or better ordifferently for how you're
(11:17):
fluent with chicken preparation is pretty exciting. But
we're kind of talking aroundthe issue here. I'd love to
hear from you. If you're on atrain with a stranger, and they
get to know you a little bit inthat way you do sometimes on a
train, and were to ask you, "Sowhat is fluency, anyway?" how
would you offer them adefinition?
Jason Zimba (11:39):
Well, so there was a reference book, a National
Academies report that came outa little over 20 years ago
called Adding It Up. And ithas, I think, a definition of
fluency in math — proceduralfluency — that is still useful.
It covers a lot of the diversecases that are covered under
fluency. But as a generalconcept, the definition there
(12:00):
is "skill in carrying outprocedures flexibly,
accurately, efficiently, andappropriately." And that's a
careful, committee-styledefinition. I think in a very
informal way, maybe you couldsay it's getting the right
answer to a routine sort ofproblem without struggling over
it. And I might even saythere's even a more informal
(12:23):
... maybe it means similar towhen we say someone's fluent in
a foreign language. It's nothalting. To be fluent is to
flow. I think it even comesfrom a Latin word that means
fluid.
Bethany Lockhart Johnson (12:34):
So Dan loves to say how much I
love talking about fluency. Andit's true, because I have seen
the power when somebody isreally fluent and when they are
not. And I'm speaking right nowin, like, math facts. I'm K–5,
but it feels like whenever I'veheard you talk about fluency,
(12:58):
your definition of fluency, itstretches beyond basic
arithmetic facts. And for me, Iso often stay there in that
land, in that bucket. What aresome other big buckets of math
fluency you think about thatmaybe us in the K–5 world are
not thinking about? Or justdon't see right away?
Jason Zimba (13:23):
There are a lot of places where this plays out.
Starting in kindergarten, thereare some important kindergarten
fluencies. Reciting the numberword list in order. Physically
executing the cardinal countingprocedure takes practice in
coordination. Writing thenumerals from 0 to 9.
Subitizing and conceptualsubitizing. You might think of
(13:44):
those as forms of fluency andkind of a capstone at that
level of comfortably findingsums and differences within 5.
So there's a lot offoundational fluency work there
on the entry into thisdiscipline. And then over the
next few years, fluency withmulti-digit calculation grows.
And then, growing into middleschool, fluency with
(14:06):
rational-number arithmeticbecomes a focus in grades 6 and
7. And in rational-numberarithmetic, that is , like
doing algebra with numbers, thecalculation in elementary
grades is not only algorithmic,and in middle grades and high
school, it seldom is. And thenat the sixth grade, sixth
through high school, we havefluency with variable
(14:27):
expressions. Symbol pushing.
It's a wordless, but stillsomehow almost verbal sort of
fluency, with properties ofoperations as the grammar of
the language. So there are alot of buckets of it, and it
changes and morphs as we moveup through the grades. I would
say I consider fact recalldifferent from fluency. Recall
(14:48):
is remembering or just knowing,whereas fluency refers to a
calculation process which iswritten or mental.
Bethany Lockhart Johnson (14:54):
That feels like a really important
distinction. And you know, Iactually ... OK, the first time
I met you was at a conference,and afterwards, you know, you
had this long line of people toask you questions and I had all
these questions and you werevery clear in redirecting my
thinking. Which was important,because I was...
you're like, "No, Bethany,that's not modeling." I'm like,
(15:17):
"But I don't get it!" You'relike, "But it's not modeling."
And I wanted to sit there andjust have this whole
conversation with you. Butthere were a lot of people in
the room who also wanted to sitthere and have this huge
conversation. But had we satdown and I'd pulled out my list
of things that I wanna talk toJason Zimba about, fluency
would absolutely be on there.
(15:37):
'Cause I am a big fluencycheerleader. But then when I'm
having conversations with othereducators, you know, they don't
wanna hear my cheer, JasonZimba. They don't wanna hear
it. They want research. Theywant, "tell me the research!"
So maybe you can sharejust some of the research out
there on building fluency inthe primary grades.
Jason Zimba (15:57):
Well, there's one helpful body of evidence
summarized in a NationalAcademies report called
Mathematics Learning in EarlyChildhood: Paths Toward
Excellence and Equity. And youcan find discussions there, for
example, about importantkindergarten fluencies. So one
of them I mentioned before isbeing able to recite the number
(16:18):
word list in order. And so thatreport will cite research about
that question, and what's knownabout the learning trajectories
in a question like that, andwhy it matters, why that
fluency is important. So thenumber word list becomes a
tool. If you think about anearly childhood way of adding 6
+ 3, you might hold 6 in yourhead and using your fingers to
(16:40):
keep track, count 7, 8, 9. Youmay not notice it, but you're
using a remembered number wordlist as a powerful tool there.
You can get a sense of what anaccomplishment that is if you
try to add F plus C, using thealphabet. And you'll find
yourself a bit tongue-tied asyou try to do it that way.
Dan Meyer (17:02):
I would like to ask you how you feel as though the
standards around fluency havebeen taken up , nationally.
What is your take? W hat aresuccesses and what are areas of
growth?
Jason Zimba (17:14):
Well, first thing I would say is there's so many
questions that the standardsdon't answer for an educator,
for a curriculum developer, fora test developer. And so the
early years were a lot aboutdiscussing and settling those
things. Even a question like,"Should I do flashcards?" You
know, it's not answered there.
But in terms of how thecountry's doing with fluencies,
(17:37):
I'm not sure we know. And thatstrikes me as peculiar. NAEP,
for example, doesn't break thisout cleanly. I have a weak
hypothesis — I don't have gooddata for it , so I can't defend
it very strongly — maybe it'smore of a worry. Which is that
the dials are all mixed up onfluency. On the one hand, I
worry that word problems andapplications and problems about
(17:59):
the connective tissue of math,like the distributed property,
or the concept of a function,get proceduralized. And if so,
then we're aiming for fluencywith something that's not a
procedure in the first place.
There's another dial to worryabout, is whether discomfort
with repetitive practice isshort-changing students of the
power and the confidence thatfluency can bring. That dial
(18:23):
swings to the negative, too ,where fluency's done poorly or
disproportionately orhumiliatingly or glancingly and
ineffectually. There's anequity threat if a school
systematically deprivesmarginalized students of the
intellectual work and theintellectual joy and societal
power of the discipline. I'vewalked hallways that were
(18:45):
papered with multiplicationfacts so that students could
practice them duringtransitions, but where I saw
very little intellection washappening in the math classroom
itself.
Dan Meyer (18:55):
That's really helpful. Yeah. One wondering I
have here, in thinking aboutyou roasting chickens or me,
and my touchstone here islearning to do a thing in a
sport. And like shooting fromthe same spot on the court over
and over again. And actuallynot feeling any type of
negative way about it. Like,feeling like this has purpose
(19:17):
for me and is productive. Andto contrast that with what
happens in math classes, I'mreally struck by what you're
saying about how we areinjecting fluency where it
doesn't belong, perhaps doingword problems of a similar kind
of template over and overagain. Which is maybe not the
intent. And also denyingstudents , out of some, I
think, healthy fear that Ishare, of the power of fluency.
(19:40):
And I wonder if part of it isnot knowing or not being able
to communicate to studentswhere fluency in math shows up
in the game of math. Whereasyou, when you're roasting a
chicken, I imagine you have atleast in some part in your mind
the destination. Like the pointof the journey is this will be
sustenance for friends orfamily and me. I know why I'm
(20:01):
shooting from this spot ahundred times is I'm gonna
shoot from this spot again in amoment where it matters. And I
guess I do have this wondering,and perhaps you can comment on
it, is communicating thepurpose of the fluency a
necessary aspect here? How arewe doing there ? How can
teachers make that clear tostudents, that we are not doing
this for its own sake, but thatit is part of a " game" or part
(20:24):
of a "meal"?
Jason Zimba (20:26):
Yeah, you know, there's a huge literature on
motivation—intrinsicmotivation. And I have not
commanded that literature, so Iwon't try to speak too in too
much detail about it. But I dothink that you're not going to
get very far with therepetitive work if someone is
not invested in understandingand agreeing that this is gonna
(20:49):
do something for them, if thisis not gonna help them. You
know, I agree with pretty muchall the extant critiques of
fluency implementation, exceptwhere they've led people to
discount the importance offluency itself, or misconstrue
state standards about it. Andthere are pitfalls everywhere.
You know, even to go back tothe chicken analogy, the early
(21:09):
phases of this can beunpleasant ... in that case,
for the people eating thechicken I made. You know? But
eventually you get the rewards.
And being able to visualizethat and wanting it to take the
steps to move towards it isimportant, tfo have ownership
of that. But withoutaccidentally or intentionally
conveying the idea that this isthe subject, and conveying the
(21:32):
idea that to be fast IS to begood at this. There are a lot
of accidental or maybe evenjust unexamined value
statements about the academicdiscipline of math that can
leak through this. And that'sreally unfortunate. All the
questions of time and timing ofthings ... I'm reminded,
(21:53):
though, of a discussion, Dan,that you and I had once, about
the zone of proximaldevelopment and how when we're
learning new ideas all thetime, and constantly stretching
our brains with that, it can bekind of tiring. And it can be
relaxing, in a way, just to bata ping pong ball back and
(22:14):
forth, you know, withregularity, and problems that
you've seen before, and justalmost clear your head by
coming up against routinechallenges. So it's a different
mode. It might even might evenbe compensatory to the hard
intellectual work and the headyapplication work that we can be
doing in math sometimes.
Dan Meyer (22:34):
Shout out to Dr.
Gerardo Ramirez from our lastseason on math anxiety, who ,
as an antidote to math anxiety,proposed ritualizing the
process of giving kids an oldtest just so they could reflect
and have a moment of concretereflection on how far they've
come and what was harder is noweasy, what was halting is now
(22:56):
fluent.
Bethany Lockhart Johnso (22:57):
Before we wrap up, I'm processing what
you're saying and I love thatwhenever I hear you speak about
this, and I think this is gonnabe the case for our audience,
too, you're gonna help us pushour thinking beyond what is
just labeled fluency. And Ithink that's so important, and
that's what we're hoping to do.
So thank you for that. I havetwo questions that are just
(23:18):
gonna poke ... this is justabout the chicken, really fast.
And then I do have one morefluency question. I know you
didn't do all 30simultaneously, but when you
finish the roast chicken — andmaybe it's 'cause I have a
small family — do you do, like,a salad? Like, a chicken salad?
With the leftovers the nextday? No, I'm
serious! Because this is a realthing! If I have a roast
(23:39):
chicken, what do I do the nextday?
Jason Zimba (23:41):
Well ... let's take something just very
cut-and-dried, and very boring,in a way. Let's say ... the
standard edition algorithm.
Bethany Lockhart Johnson (23:52):
You can bring it back. I love it so
much.
Jason Zimba (23:54):
There is
intellectual content to it,
which is kind of interesting.
You know, you do those puzzles,the missing-digit puzzles, and
sometimes they hinge onrealizations or insights like,
"Huh, the only digit I evercarry is a 1 — what's up with
that?" And so you can even dosome real math on those things,
and learn things over time. Andso, likewise, with roasting a
(24:16):
chicken — I was gonna bring itback to the chicken — you learn
things over time. Like , in myview, the smaller the chicken,
the better it works. So I'm ona quest in my shopping all the
time to find the littlestchicken that I can find there.
And then, secondly, a new skillbuilds up from it, which is now
I almost always do a homemadestock from the chicken bones
(24:37):
when I do that. So then, when Imake a chicken soup later on,
it's better. So it's not theend of everything. It opens up
new avenues for you.
Bethany Lockhart Johnson (24:47):
It opens up. Thank you. I would've
had to try to wrap my m–, youknow — I would've kept thinking
about it . But I wannamake sure we include in our
show notes something that youpublished a while back, and I
remember reading it ages ago,where you shared a little bit
about your Saturday school thatyou did with your kiddos, and
(25:09):
the way you practiced additionfacts together. And I wanna
make sure we share that,because I feel like it's such a
fun ... I love peeking into theway that someone who has such a
wide breadth of knowledge andjust ... I don't know, what do
you do with your kids to teachthem this? I just love it. And
(25:32):
I'm wondering, is thereanything else you wanna share,
that you wanna make sureeducators — or maybe parents —
know about the way we approachthis work, moving forward? We
just came off of a math anxietyseason, and we're trying to
really move away frommath anxiety. And we know that
(25:54):
just thinking about fluencyfacts can really stir that up
for some people. So, anyperspective you wanna share?
Jason Zimba (26:02):
Yeah, I'll say something about the Saturday
school that I did with my kidswhen they were little. At
different times in their matheducation , I saw ways that I
wanted to step in and maybejust buff things up a bit. And
so we did that with additionfacts. And one of the things
about flashcards is you shouldspend most of the time on the
(26:24):
facts that are known but notyet remembered. Understood, but
not yet remembered. A lot ofrepetitive practice ends up
wasting time because it doesn'tconcentrate on exactly the
parts that are needed. So,nowadays, technology will do
this for you. But I invented amethod for this, where once the
fact was remembered, it wouldgo into a box, and they owned
(26:45):
it then. And then, at the endof the session, they could dump
out the box and color in orhighlight the parts of the
chart that belonged to them.
And that was very motivating.
And I'll say, knowing I wasgonna come on today and talk
about fluency, I interviewed mykids, who are now teenagers,
and said, you know, "What didyou think about that? Are you
(27:07):
glad we did that? Was thathorrible? Did you hate all
that?" And they said, "Well, Ididn't always ... I had better
things to do with my Saturday,mostly, in the mornings." You
know, which involved, like, MyLittle Pony or Wild Kratts or
whatever, whatever was theobsession of the age. But they
said, "I'm glad we did it. It'sjust good to just know it." And
(27:27):
I think that has something todo with how we stayed
motivated, how we kept theiridentities intact, in doing
this work. It's sensitive work,it's soul craft . And I would
say that when you say, "What doI wish people understood about
fluency?" I might broaden thatquestion beyond educators, to
(27:49):
more broadly, all of usAmericans. And I wish we had a
stronger view of what math isand what math education is.
Namely, a kind of educationwith the depth and
transformative power ofeducation in all of its other
forms, too. And math educationis not only techniques , but
also disciplinary patterns ofknowledge and thought a nd
(28:10):
student metacognition andidentity formation. It's a big
ball of wax. And to concentrateon this part of it is
important, but the challenge isalways to do that without
losing sight of the whole.
Dan Meyer (28:22):
That's really exciting. I wanna say just one
thing about what I love aboutwhat you shared about Saturday
school, that I think is absentfrom a lot of fluency practice
I see in schools. Which is thisrepresentation of what has been
... if not completed, able tobe set aside. I think a lot of
the ways fluency shows up inschools is in worksheets or
(28:42):
activities where it feels asthough it may as well be
endless. There'sprobably more worksheets where
that one came from. There'sprobably other math facts or
whatever in the drawer. Butthis sense that "I have
accomplished something" — and Iheard that also in your
discussion of the zone ofproximal development, and how
we need to have moments toreflect on what has been
(29:02):
learned and what is what iseasy that was previously hard —
I hope that over the course ofour conversations with more
guests, we'll learn more andmore techniques for humanizing
fluency in that way. Reallyappreciate it.
Bethany Lockhart Johnson (29:14):
Yeah.
Thank you so much for yourtime. Thank you, Jason Zimba,
for being with us and answeringall of our questions so
patiently, just like you did inthat conference room when the
line was stretched out thedoor. And, you know, just thank
you. We really appreciate youcontinuing to share your
perspective and your years ofknowledge. Thank you. Thank
you, thank you.
Jason Zimba (29:35):
Thank you, both. I enjoyed the conversation.
Bethany Lockhart Johnson (29:41):
Dan, I want you to remember the way
it felt when your child firstmade a squiggle on the paper
that they recognized as thenumber 5. And they also knew
that that squiggle meant fivethings, and you could break it
apart in all different ways,and oh my goodness, they have
five fingers on one hand! Thatlevel of joy, that is new,
(30:03):
right? A newness. And I feellike we both came out of this
conversation with Jason Zimba alittle bit newer, a little bit
fresher. New things to thinkabout. I really, really enjoyed
that conversation, and it bodesreally well for this season .
I'm so excited, Dan. How areyou feeling?
Dan Meyer (30:20):
Yeah, I am 10% more of a believer. I'm definitely
reconsidering my vegetarianbona fides; Jason's
description of roast chicken ,not gonna lie, got a little
mouth-watering there. But yeah,I think I recognize, in the
kids in my life, and in Jason'sdescriptions, and yours, what a
(30:41):
joy it is to be able to do athing less haltingly, more
easily , than I did before. AndI hope to find a way to thread
the needle to accomplish thatwhile also avoiding some of the
more negative and well-knownoutcomes of how fluency is
taught. Maybe especially inmiddle and upper grades.
(31:01):
Exciting conversation all theway, though.
Bethany Lockhart Johnso (31:03):
Right.
And then that thing, that thingthat you now own and know? Then
that thing you don't even thinkabout anymore. 'Cause you've
got it. It's in there. And itlets you do all that other
stuff, right? We're not stillthinking about addition facts,
'cause you've got it. But itfuels you, right? It's the
foundation that allows you tothen do all this other cool
stuff. So yes, I'm excitedabout this season. And thank
(31:26):
you, listeners, for being withus, for our diving into our
sixth season. We've got a lotmore in store for you. And in
fact, this season we'rereleasing episodes even more
frequently. We are very excitedabout that. We have lots of
great conversations coming up.
And to be sure that you catchall the episodes in this new
season, be sure that yousubscribe to Math Teacher
(31:48):
Lounge on the podcast platformof your choosing.
Dan Meyer (31:51):
And hit us up if you have your own ideas you wanna
share, at MTLShow on X,formerly known as Twitter, or
at the Math Teacher Loungecommunity on Facebook. We'd
love to hear from you howyou're thinking about fluency
as well.
Bethany Lockhart Johnson (32:03):
And check out our show notes! We
have that blog post we weretalking about, about Jason's
Saturday school and rumor hasit , we might even put in that
chicken recipe.
Dan Meyer (32:12):
Thanks so much, team. Bye.
The dials are all mixed up on fluency. On the one
(00:02):
hand, I worry that wordproblems and applications get
proceduralized. And if so, thenwe're aiming for fluency with
something that's not aprocedure in the first place.
Bethany Lockhart Johnson (00:13):
Hi, I'm Bethany Lockhart Johnson .
Dan Meyer (00:15):
And I'm Dan Meyer.
Bethany Lockhart Johns (00:16):
Welcome to our new season of Math
Teacher Lounge. Dan! Newseason, new music!
Dan Meyer (00:24):
New lounge, too! I'm loving this new spot. What's in
our new Lounge here right now?
You know, posters on the wallof famous mathematicians from
movies and whatnot .
accommodations, slightly lessgrungy. Beanbag chair.
Bethany Lockhart Johnson (00:37):
The couches have been
steam-cleaned. There's donutson the table. I don't know , it
feels like a fresh start.
Anything ispossible...including defining
fluency, Dan Meyer.
Dan Meyer (00:48):
Defining fluency.
New season for us here. Lastseason, we really got to the
bottom, and I would like to saywe solved entirely, the issue
of math anxiety. < Laughter >Good work to our guests, but
especially to you and to me,Bethany, on that last season's
deep dive into math anxiety.
And we're excited to bring anew deep dive to you folks, on
(01:11):
fluency. We've done an episodeon fluency. Yeah? A couple of
them? Dr. Val Henry , Tracy andGraham. Very popular episodes.
That that gave us the sensethat fluency was an area that
we ought to dive deeper into.
So , Bethany, what's your vibeon fluency? Like, how do you
feel about it? Are you lookingforward to this? What are you
looking forward to?
Bethany Lockhart Johnson (01:30):
Well, should I pretend I don't know
how you feel about it, Dan? Inmy defense, I will say that
when we were thinking about howwe want to spend our collective
time in the Lounge and what wewere hoping to share with the
audiences, I think I was morepushing/gung-ho for the joy in
(01:53):
mathematics season. Mathanxiety, I think you were
onboard. Fluency ... you seemedonboard, but not with the level
of enthusiasm that I washoping. And so I'm thinking
that over the course of thisseason, your enthusiasm will
just continue to grow. How youfeel about that? You think?
Dan Meyer (02:11):
only direction.
listener ... this is one of therare areas of difference
between Bethany and I. And Iwanna say it's a very loosely
held difference for me. Like,I'm here wanting to believe.
And I'm so excited to haveBethany on this season with me,
(02:31):
' cause Bethany isn't ... Iwould call you enthusiastic
about fluency and what it canoffer students, and fluency as
a lever for more equitableeducation for all kinds of
kids. You're positive about itin ways that I admit that I am
not. And I want to learn more.
I assume when someone Irespect, like you, likes a
(02:52):
thing that I'm not instantlydrawn to, that there's
something there for me tolearn. So if I c ould just
offer to the listener ... I getreally excited by introducing
new stuff. Like, I get excitedby, "So you've learned this old
thing, a nd here's like a wayinto the new thing — a
connection you haven't thoughtof or something surprising
about it." And I find myselfnot super-opinionated about how
(03:15):
the old thing becomes fluent oreven really solidly known. I do
think this is a liability ofmine, a place of growth for me.
And I'm also aware of a lot ofthe ways we develop fluency in
the old stuff. And the thingthat was known can cause some
damage to kids. Like, whenadults reflect on moments in
their childhood where theydecided that math was not for
(03:37):
them, it is often on someworksheet or some drill or some
moment where they could not seethe forest for the tree in
front of them. They lost sightof what a lot of us cherish
about mathematics.
Bethany Lockhart Johnson (03:52):
I applaud you in your open mind,
that you know that the new ISexciting. And I guess where I
come from, living in K–5 land —the land that I love — I see
what a barrier fluency can be.
(04:12):
And I see the way that kiddoswho don't own their addition,
subtraction, multiplication,division facts, the way they
don't own those — and I'mspeaking about fluency, again,
with the basic facts here —that can be such a barrier. And
(04:34):
I think so often the way it'staught or not taught at all is
the real issue, and can be acause of math anxiety. So you
have these kiddos who don'thave access to these facts, or
they don't own them. They don'tknow 'em. And it keeps them
from diving into the juicyparts of math, right? Math is
(04:56):
so much bigger than additionfacts, but because they don't
know those addition facts, itbecomes all math is. And all
you can think about. And whenyou think about math, that's
what you think about. Sothere's two things: There's the
kiddos who don't have them yetand who are then stymied from
enjoying all the things you cando once you have those in your
(05:18):
repertoire, and then you haveschools and teachers who, a lot
of them don't know enough aboutfluency. So they are going to
Teachers Pay Teachers anddownloading timed tests with
just cooler font or whatever,right? And thinking, "Look,
this is themed! This is aHalloween timed test! So
they've gotta get it now,right?" And fortunately, I was
(05:42):
at a school where my principalsent every single teacher, K
through 5, to training. And wedid the training with Dr. Val
Henry, who we've talked to;we'll talk to her again. And
she has a program calledFactsWise. And my favorite part
about it was just how much Ilearned about how facts are
learned, right? Like, Ilearned, how do we learn them.
(06:02):
And learned about long-termmemory, working memory. And it
just really helped me to have abetter, like, joy and sense of
what's possible. And too oftenI have seen teachers, when you
ask them, "Well, how do yourkiddos learn their facts?" Or
"What do you do in yourclassroom?" a lot of them don't
have any plan at all. Orthey're like, "Oh, well ,
they'll just get it." Or, "Oh,yeah, at the end of every week,
(06:23):
we do a timed test." And weknow that's not how kiddos
learn it.
Dan Meyer (06:27):
I think that speaks to what I'm excited about for
this season with you, Bethany,is to come to an appreciation
of the sophistication ofdeveloping fluency for kids,
with kids. Like I know thesophistication of introducing
new material, like ideas ofcognitive disequilibrium or
(06:48):
intellectual need or workedexamples. It feels so rich to
me. And I think that I canagree fluency is important, but
in my head, what's conjured upare these very direct routes
from not being fluent to beingfluent. They just kind of
charge in a direct line, by wayof these worksheets, these
downloadables. Whereas you haveseen, I think, through folks
that we'll interview, I hope,the sophistication there. And
(07:11):
how there are different pathspossible from not being fluent
to being fluent, that canactually lead through
mathematical joy and conceptualrichness and the stuff that I
more innately gravitatetowards. So I'm excited about
it. We got a great set ofguests lined up here. And I'd
just love to intro our firstguest of the new season.
(07:31):
Happens to be Jason Zimba,Amplify's Chief Academic
Officer of STEM. He's beenthinking about math fluency in
depth for years. We hope thiswill be a great introduction
into a season-long explorationof this topic.
Bethany Lockhart Johnson (07:44):
We hope you enjoy our conversation
with Jason Zimba.
Dan Meyer (07:50):
Welcome, Jason Zimba, to the show. We're happy
to have you here.
Jason Zimba (07:54):
Thank you. I'm glad to be here.
Dan Meyer (07:55):
We know that fluency is one of many buckets of
mathematical ideas andcompetencies you care a lot
about. So we're really happy toget your time here to help us
break some initial ground onthe area of what is fluency and
why should we care so muchabout it.
Bethany Lockhart Johnson (08:10):
But before we get into that, I
mean, we need to get to knowyou a little bit more, Jason
Zimba!
outside of math where you'vedeveloped, or you are currently
developing, fluency? I figureyou're pretty fluent with the
math facts.
Jason Zimba (08:29):
Well, you know, a lot of fluencies I think we
develop as kids. Shoe-tying,the combination lock on your
locker in the high schoolhallway. But there is something
I have made a concerted effortto become fluent in over the
last 10 years, which isroasting a chicken. I was
following food blogs and otherthings. I grew up in a diner,
(08:50):
and making food was always apart of life. And I noticed
that people were always on aquest for the perfect roast
chicken recipe. And they werelike, "Oh, this recipe will
finally help you get it right."And, "This is the ideal recipe
for roasting a chicken." And Idecided to go another way. I
got a cookbook for Christmas.
It was Anthony Bourdain'sAppetites book. And he had a
(09:12):
recipe for roasting a chickenthat looked pretty good, looked
legitimate, you know?
Legitimate chef. And I said,I'm just gonna get good at this
one. I'm gonna stop hunting forthe perfect chicken recipe. I'm
just gonna learn how to roastthe crap out of this recipe for
chicken. And so I started doingthat and I've roasted about 30,
(09:33):
40 chickens in the exact sameway to the point where now, if
I'm walking past the grocerystore, I don't need an
ingredient list. I can justwalk in. I know what I need. I
prep the chicken withoutopening the book. And I know
the temperatures and the times.
But of course, every chicken'sa little different. So you
can't just apply an algorithmfor having a nice roast
(09:56):
chicken. The weights aredifferent, you know, the way
the legs go is a littledifferent. The lemon you have
might be a different size. AndI have found that a much more
rewarding way to go about itthan to constantly be hoping
that I would find the idealroast chicken recipe.
Dan Meyer (10:10):
It feels like we might return to this anecdote
over and over again.
lot going on here. I, myself,am wondering, like, that 30th
chicken versus the first —you've mentioned that you don't
have the things you don't haveto do anymore. But are there
things that you now can dobecause your mind is no longer
occupied by the steps of therecipe? Ways that you're more
(10:33):
flexible with the chicken?
Jason Zimba (10:35):
Well, one thing is, I no longer need it to be a
weekend where I have five hoursto futz around and mess up the
kitchen. There are more windowsof time available to me now,
when we can have that. Or ifI'm staying over at someone
else's house and poking around,I could do it. I don't need
home-field advantage to roastthe chicken.
Dan Meyer (10:56):
As Bethany and I talked about before our
interview began, I'm in theprocess of trying to awaken my
own enthusiasm for fluency. Imean, I have some, but it's not
my first-round draft pick ofareas of math that excite me.
And what you're describinghere, how it enables you to do
more things or better ordifferently for how you're
(11:17):
fluent with chicken preparation
we're kind of talking aroundthe issue here. I'd love to
hear from you. If you're on atrain with a stranger, and they
get to know you a little bit inthat way you do sometimes on a
train, and were to ask you, "Sowhat is fluency, anyway?" how
would you offer them adefinition?
Jason Zimba (11:39):
Well, so there was a reference book, a National
Academies report that came outa little over 20 years ago
called Adding It Up. And ithas, I think, a definition of
fluency in math — proceduralfluency — that is still useful.
It covers a lot of the diversecases that are covered under
fluency. But as a generalconcept, the definition there
(12:00):
is "skill in carrying outprocedures flexibly,
accurately, efficiently, andappropriately." And that's a
careful, committee-styledefinition. I think in a very
informal way, maybe you couldsay it's getting the right
answer to a routine sort ofproblem without struggling over
it. And I might even saythere's even a more informal
(12:23):
... maybe it means similar towhen we say someone's fluent in
a foreign language. It's nothalting. To be fluent is to
flow. I think it even comesfrom a Latin word that means
fluid.
Bethany Lockhart Johnson (12:34):
So Dan loves to say how much I
love talking about fluency. Andit's true, because I have seen
the power when somebody isreally fluent and when they are
not. And I'm speaking right nowin, like, math facts. I'm K–5,
but it feels like whenever I'veheard you talk about fluency,
(12:58):
your definition of fluency, itstretches beyond basic
arithmetic facts. And for me, Iso often stay there in that
land, in that bucket. What aresome other big buckets of math
fluency you think about thatmaybe us in the K–5 world are
not thinking about? Or justdon't see right away?
Jason Zimba (13:23):
There are a lot of places where this plays out.
Starting in kindergarten, thereare some important kindergarten
fluencies. Reciting the numberword list in order. Physically
executing the cardinal countingprocedure takes practice in
coordination. Writing thenumerals from 0 to 9.
Subitizing and conceptualsubitizing. You might think of
(13:44):
those as forms of fluency andkind of a capstone at that
level of comfortably findingsums and differences within 5.
So there's a lot offoundational fluency work there
on the entry into thisdiscipline. And then over the
next few years, fluency withmulti-digit calculation grows.
And then, growing into middleschool, fluency with
(14:06):
rational-number arithmeticbecomes a focus in grades 6 and
7. And in rational-numberarithmetic, that is , like
doing algebra with numbers, thecalculation in elementary
grades is not only algorithmic,and in middle grades and high
school, it seldom is. And thenat the sixth grade, sixth
through high school, we havefluency with variable
(14:27):
expressions. Symbol pushing.
It's a wordless, but stillsomehow almost verbal sort of
fluency, with properties ofoperations as the grammar of
the language. So there are alot of buckets of it, and it
changes and morphs as we moveup through the grades. I would
say I consider fact recalldifferent from fluency. Recall
(14:48):
is remembering or just knowing,whereas fluency refers to a
calculation process which iswritten or mental.
Bethany Lockhart Johnson (14:54):
That feels like a really important
distinction. And you know, Iactually ... OK, the first time
I met you was at a conference,and afterwards, you know, you
had this long line of people toask you questions and I had all
these questions and you werevery clear in redirecting my
thinking. Which was important,because I was
you're like, "No, Bethany,that's not modeling." I'm like,
(15:17):
"But I don't get it!" You'relike, "But it's not modeling."
And I wanted to sit there andjust have this whole
conversation with you. Butthere were a lot of people in
the room who also wanted to sitthere and have this huge
conversation. But had we satdown and I'd pulled out my list
of things that I wanna talk toJason Zimba about, fluency
would absolutely be on there.
(15:37):
'Cause I am a big fluencycheerleader. But then when I'm
having conversations with othereducators, you know, they don't
wanna hear my cheer, JasonZimba. They don't wanna hear
it. They want research. Theywant, "tell me the research!"
there on building fluency inthe primary grades.
Jason Zimba (15:57):
Well, there's one helpful body of evidence
summarized in a NationalAcademies report called
Mathematics Learning in EarlyChildhood: Paths Toward
Excellence and Equity. And youcan find discussions there, for
example, about importantkindergarten fluencies. So one
of them I mentioned before isbeing able to recite the number
(16:18):
word list in order. And so thatreport will cite research about
that question, and what's knownabout the learning trajectories
in a question like that, andwhy it matters, why that
fluency is important. So thenumber word list becomes a
tool. If you think about anearly childhood way of adding 6
+ 3, you might hold 6 in yourhead and using your fingers to
(16:40):
keep track, count 7, 8, 9. Youmay not notice it, but you're
using a remembered number wordlist as a powerful tool there.
You can get a sense of what anaccomplishment that is if you
try to add F plus C, using thealphabet. And you'll find
yourself a bit tongue-tied asyou try to do it that way.
Dan Meyer (17:02):
I would like to ask you how you feel as though the
standards around fluency havebeen taken up , nationally.
What is your take? W hat aresuccesses and what are areas of
growth?
Jason Zimba (17:14):
Well, first thing I would say is there's so many
questions that the standardsdon't answer for an educator,
for a curriculum developer, fora test developer. And so the
early years were a lot aboutdiscussing and settling those
things. Even a question like,"Should I do flashcards?" You
know, it's not answered there.
But in terms of how thecountry's doing with fluencies,
(17:37):
I'm not sure we know. And thatstrikes me as peculiar. NAEP,
for example, doesn't break thisout cleanly. I have a weak
hypothesis — I don't have gooddata for it , so I can't defend
it very strongly — maybe it'smore of a worry. Which is that
the dials are all mixed up onfluency. On the one hand, I
worry that word problems andapplications and problems about
(17:59):
the connective tissue of math,like the distributed property,
or the concept of a function,get proceduralized. And if so,
then we're aiming for fluencywith something that's not a
procedure in the first place.
There's another dial to worryabout, is whether discomfort
with repetitive practice isshort-changing students of the
power and the confidence thatfluency can bring. That dial
(18:23):
swings to the negative, too ,where fluency's done poorly or
disproportionately orhumiliatingly or glancingly and
ineffectually. There's anequity threat if a school
systematically deprivesmarginalized students of the
intellectual work and theintellectual joy and societal
power of the discipline. I'vewalked hallways that were
(18:45):
papered with multiplicationfacts so that students could
practice them duringtransitions, but where I saw
very little intellection washappening in the math classroom
itself.
Dan Meyer (18:55):
That's really helpful. Yeah. One wondering I
have here, in thinking aboutyou roasting chickens or me,
and my touchstone here islearning to do a thing in a
sport. And like shooting fromthe same spot on the court over
and over again. And actuallynot feeling any type of
negative way about it. Like,feeling like this has purpose
(19:17):
for me and is productive. Andto contrast that with what
happens in math classes, I'mreally struck by what you're
saying about how we areinjecting fluency where it
doesn't belong, perhaps doingword problems of a similar kind
of template over and overagain. Which is maybe not the
intent. And also denyingstudents , out of some, I
think, healthy fear that Ishare, of the power of fluency.
(19:40):
And I wonder if part of it isnot knowing or not being able
to communicate to studentswhere fluency in math shows up
in the game of math. Whereasyou, when you're roasting a
chicken, I imagine you have atleast in some part in your mind
the destination. Like the pointof the journey is this will be
sustenance for friends orfamily and me. I know why I'm
(20:01):
shooting from this spot ahundred times is I'm gonna
shoot from this spot again in amoment where it matters. And I
guess I do have this wondering,and perhaps you can comment on
it, is communicating thepurpose of the fluency a
necessary aspect here? How arewe doing there ? How can
teachers make that clear tostudents, that we are not doing
this for its own sake, but thatit is part of a " game" or part
(20:24):
of a "meal"?
Jason Zimba (20:26):
Yeah, you know, there's a huge literature on
motivation—intrinsicmotivation. And I have not
commanded that literature, so Iwon't try to speak too in too
much detail about it. But I dothink that you're not going to
get very far with therepetitive work if someone is
not invested in understandingand agreeing that this is gonna
(20:49):
do something for them, if thisis not gonna help them. You
know, I agree with pretty muchall the extant critiques of
fluency implementation, exceptwhere they've led people to
discount the importance offluency itself, or misconstrue
state standards about it. Andthere are pitfalls everywhere.
You know, even to go back tothe chicken analogy, the early
(21:09):
phases of this can beunpleasant ... in that case,
for the people eating thechicken I made. You know? But
eventually you get the rewards.
And being able to visualizethat and wanting it to take the
steps to move towards it isimportant, tfo have ownership
of that. But withoutaccidentally or intentionally
conveying the idea that this isthe subject, and conveying the
(21:32):
idea that to be fast IS to begood at this. There are a lot
of accidental or maybe evenjust unexamined value
statements about the academicdiscipline of math that can
leak through this. And that'sreally unfortunate. All the
questions of time and timing ofthings ... I'm reminded,
(21:53):
though, of a discussion, Dan,that you and I had once, about
the zone of proximaldevelopment and how when we're
learning new ideas all thetime, and constantly stretching
our brains with that, it can bekind of tiring. And it can be
relaxing, in a way, just to bata ping pong ball back and
(22:14):
forth, you know, withregularity, and problems that
you've seen before, and justalmost clear your head by
coming up against routinechallenges. So it's a different
mode. It might even might evenbe compensatory to the hard
intellectual work and the headyapplication work that we can be
doing in math sometimes.
Dan Meyer (22:34):
Shout out to Dr.
Gerardo Ramirez from our lastseason on math anxiety, who ,
as an antidote to math anxiety,proposed ritualizing the
process of giving kids an oldtest just so they could reflect
and have a moment of concretereflection on how far they've
come and what was harder is noweasy, what was halting is now
(22:56):
fluent.
Bethany Lockhart Johnso (22:57):
Before we wrap up, I'm processing what
you're saying and I love thatwhenever I hear you speak about
this, and I think this is gonnabe the case for our audience,
too, you're gonna help us pushour thinking beyond what is
just labeled fluency. And Ithink that's so important, and
that's what we're hoping to do.
So thank you for that. I havetwo questions that are just
(23:18):
gonna poke ... this is justabout the chicken, really fast.
And then I do have one morefluency question. I know you
didn't do all 30simultaneously, but when you
finish the roast chicken — andmaybe it's 'cause I have a
small family — do you do, like,a salad? Like, a chicken salad?
With the leftovers the nextday?
serious! Because this is a realthing! If I have a roast
(23:39):
chicken, what do I do the nextday?
Jason Zimba (23:41):
Well ... let's take something just very
cut-and-dried, and very boring,in a way. Let's say ... the
standard edition algorithm.
Bethany Lockhart Johnson (23:52):
You can bring it back. I love it so
much.
Jason Zimba (23:54):
which is kind of interesting.
You know, you do those puzzles,the missing-digit puzzles, and
sometimes they hinge onrealizations or insights like,
"Huh, the only digit I evercarry is a 1 — what's up with
that?" And so you can even dosome real math on those things,
and learn things over time. Andso, likewise, with roasting a
(24:16):
chicken — I was gonna bring itback to the chicken — you learn
things over time. Like , in myview, the smaller the chicken,
the better it works. So I'm ona quest in my shopping all the
time to find the littlestchicken that I can find there.
And then, secondly, a new skillbuilds up from it, which is now
I almost always do a homemadestock from the chicken bones
(24:37):
when I do that. So then, when Imake a chicken soup later on,
it's better. So it's not theend of everything. It opens up
new avenues for you.
Bethany Lockhart Johnson (24:47):
It opens up. Thank you. I would've
had to try to wrap my m–, youknow — I would've kept thinking
about it
show notes something that youpublished a while back, and I
remember reading it ages ago,where you shared a little bit
about your Saturday school thatyou did with your kiddos, and
(25:09):
the way you practiced additionfacts together. And I wanna
make sure we share that,because I feel like it's such a
fun ... I love peeking into theway that someone who has such a
wide breadth of knowledge andjust ... I don't know, what do
you do with your kids to teachthem this? I just love it. And
(25:32):
I'm wondering, is thereanything else you wanna share,
that you wanna make sureeducators — or maybe parents —
know about the way we approachthis work, moving forward? We
just came off of a math anxietyseason, and we're trying to
really
(25:54):
just thinking about fluencyfacts can really stir that up
for some people. So, anyperspective you wanna share?
Jason Zimba (26:02):
Yeah, I'll say something about the Saturday
school that I did with my kidswhen they were little. At
different times in their matheducation , I saw ways that I
wanted to step in and maybejust buff things up a bit. And
so we did that with additionfacts. And one of the things
about flashcards is you shouldspend most of the time on the
(26:24):
facts that are known but notyet remembered. Understood, but
not yet remembered. A lot ofrepetitive practice ends up
wasting time because it doesn'tconcentrate on exactly the
parts that are needed. So,nowadays, technology will do
this for you. But I invented amethod for this, where once the
fact was remembered, it wouldgo into a box, and they owned
(26:45):
it then. And then, at the endof the session, they could dump
out the box and color in orhighlight the parts of the
chart that belonged to them.
And that was very motivating.
And I'll say, knowing I wasgonna come on today and talk
about fluency, I interviewed mykids, who are now teenagers,
and said, you know, "What didyou think about that? Are you
(27:07):
glad we did that? Was thathorrible? Did you hate all
that?" And they said, "Well, Ididn't always ... I had better
things to do with my Saturday,mostly, in the mornings." You
know, which involved, like, MyLittle Pony or Wild Kratts or
whatever, whatever was theobsession of the age. But they
said, "I'm glad we did it. It'sjust good to just know it." And
(27:27):
I think that has something todo with how we stayed
motivated, how we kept theiridentities intact, in doing
this work. It's sensitive work,it's soul craft . And I would
say that when you say, "What doI wish people understood about
fluency?" I might broaden thatquestion beyond educators, to
(27:49):
more broadly, all of usAmericans. And I wish we had a
stronger view of what math isand what math education is.
Namely, a kind of educationwith the depth and
transformative power ofeducation in all of its other
forms, too. And math educationis not only techniques , but
also disciplinary patterns ofknowledge and thought a nd
(28:10):
student metacognition andidentity formation. It's a big
ball of wax. And to concentrateon this part of it is
important, but the challenge isalways to do that without
losing sight of the whole.
Dan Meyer (28:22):
That's really exciting. I wanna say just one
thing about what I love aboutwhat you shared about Saturday
school, that I think is absentfrom a lot of fluency practice
I see in schools. Which is thisrepresentation of what has been
... if not completed, able tobe set aside. I think a lot of
the ways fluency shows up inschools is in worksheets or
(28:42):
activities where it feels asthough it may as well be
endless.
that one came from. There'sprobably other math facts or
whatever in the drawer. Butthis sense that "I have
accomplished something" — and Iheard that also in your
discussion of the zone ofproximal development, and how
we need to have moments toreflect on what has been
(29:02):
learned and what is what iseasy that was previously hard —
I hope that over the course ofour conversations with more
guests, we'll learn more andmore techniques for humanizing
fluency in that way. Reallyappreciate it.
Bethany Lockhart Johnson (29:14):
Yeah.
Thank you so much for yourtime. Thank you, Jason Zimba,
for being with us and answeringall of our questions so
patiently, just like you did inthat conference room when the
line was stretched out thedoor. And, you know, just thank
you. We really appreciate youcontinuing to share your
perspective and your years ofknowledge. Thank you. Thank
you, thank you.
Jason Zimba (29:35):
Thank you, both. I enjoyed the conversation.
Bethany Lockhart Johnson (29:41):
Dan, I want you to remember the way
it felt when your child firstmade a squiggle on the paper
that they recognized as thenumber 5. And they also knew
that that squiggle meant fivethings, and you could break it
apart in all different ways,and oh my goodness, they have
five fingers on one hand! Thatlevel of joy, that is new,
(30:03):
right? A newness. And I feellike we both came out of this
conversation with Jason Zimba alittle bit newer, a little bit
fresher. New things to thinkabout. I really, really enjoyed
that conversation, and it bodesreally well for this season .
I'm so excited, Dan. How areyou feeling?
Dan Meyer (30:20):
Yeah, I am 10% more of a believer. I'm definitely
reconsidering my vegetarianbona fides;
description of roast chicken ,not gonna lie, got a little
mouth-watering there. But yeah,I think I recognize, in the
kids in my life, and in Jason'sdescriptions, and yours, what a
(30:41):
joy it is to be able to do athing less haltingly, more
easily , than I did before. AndI hope to find a way to thread
the needle to accomplish thatwhile also avoiding some of the
more negative and well-knownoutcomes of how fluency is
taught. Maybe especially inmiddle and upper grades.
(31:01):
Exciting conversation all theway, though.
Bethany Lockhart Johnso (31:03):
Right.
And then that thing, that thingthat you now own and know? Then
that thing you don't even thinkabout anymore. 'Cause you've
got it. It's in there. And itlets you do all that other
stuff, right? We're not stillthinking about addition facts,
'cause you've got it. But itfuels you, right? It's the
foundation that allows you tothen do all this other cool
stuff. So yes, I'm excitedabout this season. And thank
(31:26):
you, listeners, for being withus, for our diving into our
sixth season. We've got a lotmore in store for you. And in
fact, this season we'rereleasing episodes even more
frequently. We are very excitedabout that. We have lots of
great conversations coming up.
And to be sure that you catchall the episodes in this new
season, be sure that yousubscribe to Math Teacher
(31:48):
Lounge on the podcast platformof your choosing.
Dan Meyer (31:51):
And hit us up if you have your own ideas you wanna
share, at MTLShow on X,formerly known as Twitter, or
at the Math Teacher Loungecommunity on Facebook. We'd
love to hear from you howyou're thinking about fluency
as well.
Bethany Lockhart Johnson (32:03):
And check out our show notes! We
have that blog post we weretalking about, about Jason's
Saturday school and rumor hasit , we might even put in that
chicken recipe.
Dan Meyer (32:12):
Thanks so much, team. Bye.
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