November 15, 2023 • 33 mins
Tune in to Episode 5, where we dive back into our season-long discussion of math fluency with classroom teacher Lauren Carr. Listen as Lauren shares how she allows her students to approach mathematical thinking and learning with joy and fun to encourage the development of math fluency.
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Episode Transcript
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Lauren Carr (00:00):
There's an idea of what fluency looks like.
(00:02):
There's these little tests. Yougotta sit there, quiet. Write
all your answers as quickly asyou can. And I'm like, not all
students learn that way.
Bethany Lockhart Johnson (00:13):
Hi! And welcome to another episode
of Math Teacher Lounge. I'mBethany Lockhart Johnson .
Dan Meyer (00:19):
And I'm Dan Meyer.
Bethany Lockhart Johnson (00:20):
You know, Dan, we're in the thick
of our season about fluency.
And I have to do our episodiccheck-in —
Dan Meyer (00:28):
Yes!
Bethany Lockhart Johnson (00:30):
— about how you're feeling about
things. You have two youngsons. I wanna know, how is it
impacting the way that youthink about fluency with your
kiddos?
Dan Meyer (00:43):
Yeah! Thank you for asking by the way. I hope you
are well, also, Bethany. So, toorient the listener, if you
have not been tuning intoprevious episodes, I , Dan
Meyer , former high school mathteacher, have had a little bit
of an uneasy relationship withideas of fluency. Which, for
me, are kind of associated witha lot of negative experiences
that students I taught had hadthroughout K–8. So I'm here, in
(01:07):
this journey, trying to find mylove and excitement for
fluency. I feel excited aboutintroducing new math concepts
with students. About assessingmath knowledge. And Bethany has
been super-helpful, as have ourguests. All of whom have had
tons of enthusiasm. I've gotkids who are in kindergarten
and first grade. I'm watchingthem learn math right now, and
(01:28):
it's been pretty exciting tothink about through the lens of
what we've been chatting about.
For instance, I watched myfirst grader zip on through
some fluency exercises, notrealizing that addition
problems changed to subtractionproblems. So the kid was doing
like six plus four and makingtens real nicely, but then six
plus four becomes six minusfour. And, all of a sudden ,
(01:51):
there's 10 again, which to mesaid like, "OK, this is one of
the tricky parts about fluency— not getting just so anchored
in the operations that we'renot paying attention to what
we're doing." There was that.
And then, like, I had a momentthat I just felt like, Bethany,
if you had seen it, youwould've just fallen on the
sidewalk and been sobbing athow beautiful it was. Sort of
thing you've told me to do.
Which is walking to school, wejust start making fives, you
(02:15):
know. Making fives as a mathnerd dad is "want to do"!
Bethany Lockhart Johnso (02:20):
Making fives out in the wild.
Dan Meyer (02:22):
In the wild! Yeah! And so, we're doing, like, four
plus one , three plus two.
Someone has the bright idea togo from three plus two to two
plus three, and they thinkthey're pulling off a bank
robbery by flipping 'em aroundlike that. That was cool. And
then I had a moment where Ibrought fire to the cave people
when I was like, "Check thisout! You ready for this? Five
(02:43):
plus zero." And everyone'slike, "Oh dad, you're the
best!" So anyway, that's someof my experiences, to see that
my first grade kid then fliparound and say, "You know what
else makes five? 15 minus 10."An d I was like, "Oh, shoot.
OK. Ki d's g ot game."
Bethany Lockhart Johns (03:01):
Nuh-uh!
Dan Meyer (03:01):
I'm serious! I would not lie on the pod. I would lie
off the pod, maybe, but I wouldnot lie on the pod. So I'm
just, like, feeling how theprocedural fluency ties into a
conceptual understanding. Howthat robustness of
understanding then leads intobetter fluency. It is a
cyclical thing going on. Sothanks for letting me riff off
that for a hot second here.
Bethany Lockhart Johnson (03:22):
Yeah, I wanna hear it all, because I
think the part that I'm hearingis that it's becoming this,
like, everyday thing. We justtalk about numbers. And we
decompose numbers. And we lookfor numbers around us. We look
for different ways to makenumbers. And we celebrate
numbers. It's just part of ourday. And that is what I'm
(03:43):
hoping that when we think aboutfluency, I'm hoping that we use
that lens. We've been talkingabout the ways that fluency has
not been done in a productive,joyful way. And we don't want
that for your kids or any kids.
Dan Meyer (03:58):
Any kid. Which is why I'm really excited about
our guest today. We've had alot of people who have been
speaking from a perspective ofacademic literature,
theoretically, "what are wetalking about when we define or
assess or foster fluency?" AndI found it super helpful. I
also have the need, right now,to feel grounded in classroom
(04:22):
practice, and people who aredoing the work, and seeing its
effect on classes full of kids.
I'm super-excited that we haveon Ms. Lauren Carr , who's a
teacher out of SouthernCalifornia, who happens to
teach kindergartners and firstgraders, who are kids that I
have a love-hate, but mostlylove, relationship with right
now. Lauren, in 2016 receivedthe LA Unified School
(04:46):
District's Rookie Teacher ofthe Year award, has been in the
game for nine years, is a UCLAMath Project coach is doing it
all. And here, at the end ofthe week, has been kind enough
to sit down with us and chatabout fluency and how it works
in your classes. So, thanks forbeing with us. Lauren Carr,
appreciate you.
Lauren Carr (05:03):
You're welcome.
I'm happy to be here.
Bethany Lockhart Johnson (05:05):
Thank you for being here.
Lauren Carr (05:07):
Happy to be here.
Dan Meyer (05:09):
Lauren Carr , we have a question we love to get
to know our guests by asking.
And the question is this (05:12):
In what ways have you been
developing fluency in yourpersonal life? Is there an area
where you're like, "Oh, I'mdoing the thing that I ask kids
to do in the math classroomevery day , most days"? What
would that be for you?
Lauren Carr (05:27):
Over the summer I started learning how to sew.
And, I don't think I realizedhow much math goes into sewing
. The amount of timesI've had to measure things. And
then, I don't know, all thenumbers, and keeping track of
(05:47):
everything. And, if you're oneinch off, that throws off your
whole outfit. And so I've beentrying to —
Bethany Lockhart Johnson (05:54):
Wait.
You started with clothing?
Lauren Carr (05:57):
Yes, yes.
Bethany Lockhart Johnso (05:59):
That's impressive!
Dan Meyer (06:01):
Straight for the final, boss .
Lauren Carr (06:02):
Yes, yes.
When I do things, I commit. Igo over the top. I can't just
start something small. I'mlike, if I'm gonna jump in, I'm
gonna jump in. So, I've made mysister a matching set. I made
myself dresses. I made mysister's dog a little bandana
(06:22):
. So I've been trying—
Bethany Lockhart Johnson (06:24):
No pot holders for you, ,
let me tell you. That'sawesome! So, as you've been
learning these new skills, andbuilding your fluency with the
machine, with all the languageof the discipline of sewing,
(06:46):
you said about the measurement,but has it been frustrating?
Have there been moments whenyou're getting to the flow of
it?
Lauren Carr (06:53):
Yes. A lot of frustrating moments. Like I
said, I'm always I wanna justget it done. And so, sometimes
I'll sit with a pattern and I'mlike, "I'm gonna finish this
right now." And then I keepmaking mistake after mistake
after mistake. And then I'mlike, "You know what? I need to
take a break." And so, I'vebeen OK with taking breaks. And
then there's some times, I'vejust let it kind of happen,
(07:16):
when I haven't used a pattern,I've found that sometimes I'm
doing a little bit better when I just kind of
look at how it fits on my body.
Trying to not be so stuck at ,"Oh, this is the pattern I have
to follow this." Kind of like,what fits on my body? What
headspace am I in right now? DoI need to take a break? Can I
keep going? So it , I'velearned a lot about myself as
(07:38):
just learning something new. Soit's also a good stress
reliever after a long day ofteaching. And I always bring it
back to my kids too. So I'llwear something and I'll—
Bethany Lockhart Johnson (07:50):
You said, "I made this."
Lauren Carr (07:52):
Uh-huh. And I think they're just shocked now
. And I'm like, "Yes, I madethis."
Dan Meyer (07:57):
Where'd your clothes come from? And I was like,
"What?!"
Lauren Carr (07:59):
. It's a
whole lesson.
Bethany Lockhart Johnson (08:01):
I love it!
Lauren Carr (08:01):
It's like, I would love to teach my kindergartners
and my first graders how tosew. 'Cause there's so much
math in it.
Bethany Lockhart Johnson (08:07):
I love that that brings you calm
. I love that thatbrings you calm . It does not
sound calming to me. But here'sthe beautiful thing: You're
seeing what happens when youwork through, when you
persevere. So, thank you forsharing that with us! Now, you
mentioned your kinders, yourfirst graders, which I could
(08:27):
have a whole conversation withyou about combo classes, but
we'll save that for anothertime. .
Lauren Carr (08:31):
Yes.
Bethany Lockhart Johnson (08:32):
I love seeing people teach. I
love teaching, but I lovethere's such a joy in being in
someone's teaching space,right? So if I had the chance
to visit your classroom, if we— OK, Dan, you can come too. If
Dan and I had the chance tovisit your classroom, I'm so
(08:54):
curious, what would you hope Iwould see? Or what would you
hope I would experience aboutyour teaching philosophy? Or
the kind of space that you'retrying to create for yourself
but also for your students?
Lauren Carr (09:07):
Yes. So, I hope when you step into my
classroom, you feel a lot oflove. I think that's one thing
that I really want. I want mykids to feel safe and loved in
the classroom. Specifically inmath. Honestly, my class is
never quiet. So you'llnever step into my classroom
(09:29):
when it's quiet. They're alwayshaving conversations. You're
always hearing them askingquestions, moving around,
wiggling. Doing all the funstuff. But, my teaching
philosophy is verystudent-centered. It's a lot of
student choice, student voice.
And so, I hope when you maybe,possibly, come to my classroom
, you would hear a lot ofstudent students talking and
(09:52):
not as much me up there justtalking. The students bring so
much knowledge and experiencesto the classroom. And I really
enjoy just listening to them,and then giving them questions
and things to nudge themforward. And so, that's the
space that I hope everyonefeels. 'Cause usually when I
(10:14):
step in there, I feel that . So I'm hoping
everybody else feels that whenthey step into my classroom.
Dan Meyer (10:19):
That's great to hear! And I hope that one day
we're all in the same roomenjoying your teaching.
For some people, some forms offluency feel like the opposite
of what you're describing.
Sometimes, the way that fluencyhas been tried, teachers, pure
of heart, have tried to developfluency, result in kids not
feeling they can be themselvesor contribute actively. That
(10:42):
they have to be kind ofprogrammed. And so I would love
to know like, how do you makethis fluency? How do you weave
fluency into this space thatyou've created, that feels so
full of life and love?
Lauren Carr (10:53):
Sometimes, when you hear fluency, you just
think of those timed tests. Andwhen I was younger, thinking
about those timed tests andjust the stress that came with
it. We won't see those littletimed tests in my class. It's a
lot of counting collections anda lot of counting, a lot of
(11:15):
word problems, number talkimages, different hands-on
experiences where students arehaving fun with numbers and
also real-world experiences.
Today, a parent brought in somedonuts, and so we ended up just
having a conversation about,"There's 20 of us, and there's
only 10 donuts. What are wegonna have to do?" And so just
(11:38):
that real-world experience, andthat's fluency. They were able
to say, "OK, I think we gottacut it in half." And that's
first graders! They were like,"Yeah! Cut it in half so that
everybody can have a littlepiece." And so, those little
experiences, a lot of thosetypes of experiences, I feel
like build fluency. And knowingthat it's going to be OK to
kind of make mistakes. Andhaving conversations and asking
(12:00):
questions. And I think thatreally helps with fluency.
Dan Meyer (12:04):
Was that a gift to you? Were you happy that a
parent brought donuts in? Orwas that like, "Oh great, you
brought donuts in. Wonderful,thank you." Is that a good
thing to bring to K–1 comboteacher?
Lauren Carr (12:14):
They were given at the end of the day. So, it was
the last—
Dan Meyer (12:17):
OK, nice! Perfect!
Lauren Carr (12:18):
She came in the morning, but I said , "OK, end
of the day." Once we go home,there we go.
Dan Meyer (12:22):
That's a nine-year veteran teacher right there!
Bethany Lockhart Johnson (12:25):
Yeah, this is no rookie of the year
here . This is no rookie .
Dan Meyer (12:29):
So I'd love to dig in a little bit more here on
fluency. You've described abunch of different kinds of
curricula, or activities, thatI think are, like for a
secondary teacher like me,aren't, I'm not super familiar
with counting collections, forinstance. And the others you
mentioned. So I'd love a littlemore elaboration here perhaps
on what those are. And I'm alsocurious about when the donuts
(12:52):
came in, and you had thismoment of numeracy with the
students around the donuts,like, my idea about fluency has
not included the kind ofone-off, interesting,
real-world applicationexperience. Help me out here.
That moment is what the fluencyhas meant to support. Like,
(13:14):
using fluency, thatdevelopment, and developing
your kid's sense of being mathdoers, and having an identity
as a mathematician, is thething that enables them to be
mathematical in that moment.
The donuts. But, the donutsthemselves, in my
understanding, are not afluency-developing activity
themselves. So, there's twoquestions there. One about how
(13:35):
much did the kind ofreal-world, one-off activities
develop fluency? And I'd justlove to know more specifics
about the activities youmentioned that have developed
fluency for your students.
Lauren Carr (13:47):
I'll start with the counting collections. So
counting collections, they'rean activity where students are
given an amount of objects andthey're asked to count them in
a way that makes sense to them.
And so, in kinder and first,they're working on cardinality.
Extending the countingsequence. One-to-one
correspondence. Actually firstgrade. That's what we're
(14:11):
working on with countingcollections.
Dan Meyer (14:14):
I'm still working on that. So, no disrespect.
Lauren Carr (14:16):
. Yeah, so
that's a great activity to work
on those things. Then they'rejust counting. And then I come
and ask questions. How did theycount it? Why did they count it
that way? And then they mightstart counting by ones. And
then they might start countingby fives. The collections might
start getting bigger. And thenthey're like, "I've got a
thousand little rocks. Am Igonna count those little rocks
(14:38):
by ones?" And so they startmaking sense of does this make
sense? Does this not makesense? And then the fluency
comes with counting, likeskip-counting those collections
in different ways. And so,sometimes they're counting the
same collection over anextended period of time, a lot
of different ways. That'sbuilding their fluency. And
(14:59):
it's fun! Counting collectionsare, like, my favorite
activity.
Dan Meyer (15:03):
It sounds like it'll take you a long distance. What
I'm hearing now is thatstudents will reveal to you
that they are fluent when theystart adopting new strategies
for counting. I'm not hearingyou formally assess their
understanding of cardinality orskip-counting. It's like all of
(15:24):
a sudden, I don't need todirect-count like, six of
these. I see a five and thenone more. Is that an indicator
to you that, "Oh, OK, we aredeveloping fluency here." It
has been developed in some way.
Lauren Carr (15:36):
Yes, it is! They'll start, like I said, by
ones. And then when they startmaking connections from the
counting collections to maybethe choral-counts, where we're
counting altogether. Andthey're able to decompose the
numbers or the countingcollection to the word problem.
They're making thoseconnections. And so, yes, that
(15:57):
starts to tell me like, "Oh,they're starting to recognize
the patterns." They're startingto see patterns. And start to
see the patterns everywhereelse. And then, yes, that's
where I'm able to say, "OK,we're building our fluency."
Dan Meyer (16:09):
I think K–5 folks will know what choral-counting
is and counting collections andall these things. But, it was
really helpful to hear youspell out those different kinds
of fluency building activities,which we haven't heard so far,
I don't think from many of ourguests. Which is why we've got
you on.
Lauren Carr (16:27):
Yay!
Bethany Lockhart Johnson (16:27):
So, for me, definitely, counting
collections brings me a levelof joy. Not just collect — my
husband's like, "Why are yousaving these bag ties? Why?!"
It allows me to have my littlecollections, and it's for my
classroom. But no, really,there's so much richness that
(16:49):
we see coming out of theseopportunities for students to
count. And to make sense ofword problems and
problem-solving. But, I alsowant to address, what about the
teacher who says, "Yeah, we'vebeen doing counting
collections, but my studentsstill can't add, or can't
(17:11):
subtract, you know, five minusfour or two plus three, or
whatever." When I ask them, orwhen I give them an opportunity
and assess them, they're stillnot understanding or fluent
according to the standards. AndI ask that because I think we
understand that there's fluencyin the bigger sense of fluency,
(17:31):
with numbers and compositionand decomposition, but then
there's also the standards,right? So, I'm just curious,
how does that fit in with thekind of folks who push back and
ask you more specifics aboutaddition and subtraction, the
way they might picture itinitially?
Lauren Carr (17:49):
I hear that. And I hear the fluency. They have to
be able to add quickly to beable to add on to other
activities. It's the foundationfor, like, multiplication,
division. But I think that theyare mastering the standards
(18:11):
through fluency with likecounting collections and
things. I think it just looksdifferent. And I think there's
ways to assess fluency withaddition and subtraction that's
not punitive, where it'ssomething that's gonna stress
students out. And so when itcomes to the standards, yes,
like in first grade, thestandards is to be able to add
(18:33):
and subtract fluently within20. So yes, we are playing math
games where we're adding andsubtracting fluently within 20.
We might have a little sheetwith different
number-sentences, but they'reasked to solve the ones that
are less than five or more thanfive. That's still building
(18:54):
fluency. Yes, you wanna be ableto go quickly, but sometimes we
don't. Like, honestly, I'm justthinking about me sometimes
when it comes to percentageswhen I'm shopping and trying to
know the percentage of a sale.
Of course I wanna be able toknow it fast but, in that
moment, I don't really need toknow it that fast. I think it's
(19:19):
like, "Why are we trying to goso fast?" On one end, I'm like,
yes. Like I said, yes, we wannabe able to add and subtract
quickly. And then some of us,we are working on our own at
our own speed.
Bethany Lockhart Johnson (19:35):
I've been in schools where the
school was very gung-ho and wasvery focused on some fluency
goals, and kind of telling thestory of fluency K–5, right?
And that was a really rareexperience. And then I've had
other situations where itwasn't talked about at all,
right? And, and it was more putoff like, "Oh, well the parents
(19:57):
will practice those things athome." Right? So I bring it up
because I think it's sofascinating to hear. There's so
many times we hear aboutfluency and it's very
antithetical. Like, the wayfluency is taught antithetical
to how you're talking aboutyour classroom culture, right?
So if your students areexperiencing joy, if your
(20:19):
classroom is not quiet, 'causethey're engaged, they're in it,
they're present. I think I amhearing you say that,
simultaneously, they arebecoming flexible thinkers with
numbers and withproblem-solving. Is that what
I'm hearing? I wanna make sureI'm understanding.
Lauren Carr (20:39):
Yes, for sure. I hope all of those experiences
make space for them to befluent with numbers, and have
fun with numbers, and seenumbers everywhere. See numbers
in the real world. Yeah! That'swhat I want! And I don't want
them to see numbers and think,"Oh, I don't know how to do
(20:59):
this quickly, so I can't doit." Or, "This doesn't make
sense to me. And so it's notrelevant to me, so I'm not
gonna do it." Or, "I have tosit here and be quiet during
math time . That's the oppositeof what I want." And so I think
by making space for the joy,and having fun, and having a
positive math identity, I thinkstudents will build fluency.
Dan Meyer (21:23):
You've described yourself as someone who is
interested in students learningabout justice in the world
through math class, not inother classes, but in this
class, through theseactivities. And I just wonder
if you could speak to how thedifferent approaches to
fluency, we've talked about theones that you've been pursuing
with your kids and other onesthat are out there that other
kids have experienced, howthose contribute to a student's
(21:44):
sense of who I am in the world.
Can they do that? Is that toolofty? You have a goal for
fluency? Or have you seen thatcontribute to a student's sense
of what justice looks like inthe world?
Lauren Carr (21:55):
So we start with math as, like, patterns. Math
is all about seeing patternswith numbers. And you can use
math to see patterns in theworld. We start small with the
numbers, and then we start tosee patterns in all types of
different subjects. So it'slike seeing patterns in and
(22:19):
issues of injustice in theworld. Patterns of nature.
We're seeing patternseverywhere. I think that's one
way that in those real-worldexperiences they're able to see
patterns and make thoseconnections.
Dan Meyer (22:34):
Yeah, that's helpful. There could be
activities or experiencesstudents have in math class
where they're noticing wherepatterns are maintained and
when patterns break. I feellike kids of this age have a
sensory experience of fairnessor unfairness. Like, we should
all get half of a donut. Andthen, if that pattern gets
(22:56):
disrupted, it's perhaps a kidwho has some fluency with
numbers can notice that moreeasily than kids who don't.
Does that sound accurate to howkids develop these ideas?
Lauren Carr (23:09):
Yeah, I think so.
Coming back to the donuts (23:10):
The students that have had a lot of
experience, hands-onexperiences, with little
parties and having donuts, andbeing able to count the donuts
— how many donuts there are.
How do we share donuts? — thosestudents can bring that to the
problem. And then be able tofluently say like, "Oh, I know
(23:31):
that we're gonna split these upquickly. This makes sense to
me, because I've had a lot ofexperiences talking about these
things and seeing thesepatterns."
Bethany Lockhart Johnson (23:41):
So, last season was about math
anxiety. And something thatcame up again and again when we
were talking is the anxietyfolks had around assessment,
and around perceived judgmentof their math competency. And
so, thinking about how we lookat patterns and justice, I feel
(24:07):
like with fluency instruction,if done poorly, it can really
exacerbate inequalities, right?
And I'm wondering how you thinkabout that in terms of when
you're in that kind ofsituation, wanting to celebrate
students who are bringing thisknowledge about their
experience. I've had lots ofopportunities to count and to
experience these parties. Andthen I also have students who
(24:30):
this is all new for them,right? Or they bring a
different fund of knowledge tothe conversation.
Lauren Carr (24:36):
My teaching philosophy in general is social
justice-centered andanti-racist. It centers
students' thinking andstudents' voices. I always say
"empowering students," but theyhave the power. But giving
space for students to recognizetheir own power. With fluency,
I used to think that ifstudents are sitting there kind
(24:58):
of quiet, listening to what I'msaying, being able to tell me
exactly what I just said, I waslike, "OK, this is going well."
And I think it's also because Iused to be like that. I was
that math kid that was like,"Just tell me what I need to
do, and I'm going to do it."And so when I started getting
older, and the math startedgetting harder, and I started
(25:20):
to think a little bit,I was like, "Oh, wait a minute,
I don't know, because I've beentold how to do this math my
whole life." And I didn't wantthat for my students. I want
them to be able to be loud,have fun, ask questions. I'm
not going to tell them theanswer. And I think one thing I
(25:40):
always tell my students is it'snot about the answer. It's
about how you get to theanswer. Those little
conversations going into wordproblems and counting
collections. All those things Ifeel are also part of fluency.
I'm always talking about math.
I feel like I'm the person atthe school that's always
talking about math. And peopleare always just like, "Oh,
(26:03):
there she goes again." Then,whenever fluency comes up in
spaces, there's an idea of whatfluency looks like . The idea
that there's these littletests. You gotta sit there
quiet. Write all your answersas quickly as you can. And I'm
like, not all students learnthat way. Not all students are
(26:24):
going to get it that way. And,it's not equitable. I believe
it's not equitable. And so, Iwant teachers to see, like, my
classroom where we're doingcounting collections. We're
having fun. We're having theseconversations about math.
Seeing math everywhere we go.
(26:45):
Recognizing patterns everywherewe go. And that's building
fluency. Those experiences arebuilding fluency. That's what
fluency looks like to me. Andeven just thinking about today,
we have these beautiful muralsat our school, and my students
just look was just lookingaround. He's like, "Hey, I
noticed a pattern!" And Ithought it was the colors that
(27:06):
he was going to notice. But, itended up being the arrows. One
arrow was going up, one arrowwas going down, one arrow was
going up. And I was like,"Wow!" So that to me, those
experiences where he's lookingat something in the space and
recognizing a pattern andsharing it, those experiences
are going to help him befluent. And how excited he was
(27:27):
to just share with me that hesaw a pattern at our school.
Dan Meyer (27:38):
Yeah , I'm trying to get a sense of you around
fluency versus the conceptionof how a lot of people
experienced it. And one thing Ifeel like I'm hearing, right or
wrong, I don't know, is thatwhereas a lot of teachers might
see their job as to give outthe paper that has the problems
on them, and that is the thingthat develops fluency. What I
(28:01):
feel like I've heard you talkabout is doing so much work to
help students realize you havegood ideas, but you're also
kind of a provider ofexperiences, like a box of new
stuff to count up. And then,the cool thing you do, like
lots of folks could do that,but what you do feels like
(28:21):
naming a kid's strategy as athing of value. A thing you
did. And knowing what to offerthem next in response to keep
helping them develop that. Andthat feels like a very
different approach to fluencythan what a lot of people are
used to. Different kinds ofskills to develop. It's very
fun to hear. Thank you so much!It's been a real pleasure to
(28:44):
have you on. Learn more aboutyou and your work.
Lauren Carr (28:46):
You're welcome. It was a pleasure. I love talking
about math. I can talk aboutmath all the time, every day,
all day.
Bethany Lockhart Johnso (28:53):
You're welcome in the Lounge anytime.
Dan Meyer (28:56):
We're here 'til 1:00 AM some nights just talking
about math. It gets a littlebit nuts. Wow, Bethany, what a
ride! So fun to hear fromsomeone doing the work in the
classroom day in, day out.
What'd you take away there?
Bethany Lockhart Johnson (29:10):
These conversations we're having,
it's definitely expanding mynotion of the idea of fluency,
right? Because I think when Ienvisioned the season, I came
in with a much narrowerdefinition. Really thinking
about the California statestandards, and really thinking
about like computationalfluency in terms of how that
(29:32):
can be a barrier or a realfoundation for students.
Thinking about ways to seefluency happening, in a broader
sense, is I think reallyhelpful. And it's a good
reminder when we're thinkingabout cultivating classroom
community. What about you, DanMeyer?
Dan Meyer (29:51):
Yeah, all of that! And I loved Lauren's
description of attending tostudent identities, even while
we're asking them to do stuffthat's difficult, and even
sometimes repetitive. Whatstuck out to me was the moment
when Lauren was talking abouthow you're not gonna count to a
thousand by ones, so what canwe do here? And like, just how
(30:13):
necessity is the mother ofinvention of fluency, of the
need for fluency. I thoughtthat was pretty special. It
takes a certain kind of teacherto say, "OK, I'm not just gonna
have you develop fluency forits own sake, but develop
fluency in order to becomeproficient at a particular task
that you understand. And thatis interesting to you." That
felt, like, next-level. Thatfelt like rookie of the year,
(30:36):
like nine-year veteran typeteaching moves to me. So, that
was really exciting.
Bethany Lockhart Johnson (30:41):
Well, and also, for folks listening,
we see each other virtually aswe're recording. And I hope,
and I think it will comeacross, when you hear the way
Lauren talks about her studentsand her classroom, but to see
the joy emanating fromLauren as she's talking about
her students, as she's talkingabout mathematics, as she's
(31:03):
talking about creating aclassroom culture like that. We
want to share that. We want ourstudents to experience that joy
and that, I don't know, freedomaround talking about math. And
seeing math, and exploring mathand problem-solving, even when
it's not coming easily, so tospeak. So yeah, that was a
(31:27):
pleasure. And I thank you allfor listening with us. And
hopefully you're enjoying thisseason. We'd love to know what
you think about Ms . LaurenCarr's strategy for developing
fluency. Or maybe you haveother ideas of your own that
you'd like to share about thisseason, or about what you do in
your classroom. Please join theconversation in our Facebook
discussion group, Math TeacherLounge: The Community. And you
(31:49):
can also reach us at X,formerly known as Twitter, at
MTL Show. We have plenty moreto come on this season of Math
Teacher Lounge.
Dan Meyer (32:00):
And you folks can keep up with all of it by
subscribing to our podcast onall the platforms. And we would
love for you to support ourwork here. Get the word out by
rating and leaving a reviewwherever you get your fine
podcast products. Bethany andI, we read all of them. And I
do mean we read ALL of them.
And we read them to our lovedones, and parents, and friends.
(32:22):
So just keep that in mind asyou fill out that review. Just
think about what you're saying,and would you like this to be
read to Dan's mom? You know, ? So we'll be back in
just a couple weeks. In themeantime, here's a quick tease
of what's to come.
Speaker (32:38):
We have to look at mathematics as a story that we
tell students across thegrades, K to 12. And what we
are is the conveyors of achapter in this progression of
the story. If we look at it asan isolated chapter, then the
question really becomes, whatam I doing to my students and
(32:59):
for my students?
Dan Meyer (33:00):
Thanks for listening folks.
Bethany Lockhart Johnson (33:02):
Bye!
There's an idea of what fluency looks like.
(00:02):
There's these little tests. Yougotta sit there, quiet. Write
all your answers as quickly asyou can. And I'm like, not all
students learn that way.
Bethany Lockhart Johnson (00:13):
Hi! And welcome to another episode
of Math Teacher Lounge. I'mBethany Lockhart Johnson .
Dan Meyer (00:19):
And I'm Dan Meyer.
Bethany Lockhart Johnson (00:20):
You know, Dan, we're in the thick
of our season about fluency.
And I have to do our episodiccheck-in —
Dan Meyer (00:28):
Yes!
Bethany Lockhart Johnson (00:30):
— about how you're feeling about
things. You have two youngsons. I wanna know, how is it
impacting the way that youthink about fluency with your
kiddos?
Dan Meyer (00:43):
Yeah! Thank you for asking by the way. I hope you
are well, also, Bethany. So, toorient the listener, if you
have not been tuning intoprevious episodes, I , Dan
Meyer , former high school mathteacher, have had a little bit
of an uneasy relationship withideas of fluency. Which, for
me, are kind of associated witha lot of negative experiences
that students I taught had hadthroughout K–8. So I'm here, in
(01:07):
this journey, trying to find mylove and excitement for
fluency. I feel excited aboutintroducing new math concepts
with students. About assessingmath knowledge. And Bethany has
been super-helpful, as have ourguests. All of whom have had
tons of enthusiasm. I've gotkids who are in kindergarten
and first grade. I'm watchingthem learn math right now, and
(01:28):
it's been pretty exciting tothink about through the lens of
what we've been chatting about.
For instance, I watched myfirst grader zip on through
some fluency exercises, notrealizing that addition
problems changed to subtractionproblems. So the kid was doing
like six plus four and makingtens real nicely, but then six
plus four becomes six minusfour. And, all of a sudden ,
(01:51):
there's 10 again, which to mesaid like, "OK, this is one of
the tricky parts about fluency— not getting just so anchored
in the operations that we'renot paying attention to what
we're doing." There was that.
And then, like, I had a momentthat I just felt like, Bethany,
if you had seen it, youwould've just fallen on the
sidewalk and been sobbing athow beautiful it was. Sort of
thing you've told me to do.
Which is walking to school, wejust start making fives, you
(02:15):
know. Making fives as a mathnerd dad is "want to do"!
Bethany Lockhart Johnso (02:20):
Making fives out in the wild.
Dan Meyer (02:22):
In the wild! Yeah! And so, we're doing, like, four
plus one , three plus two.
Someone has the bright idea togo from three plus two to two
plus three, and they thinkthey're pulling off a bank
robbery by flipping 'em aroundlike that. That was cool. And
then I had a moment where Ibrought fire to the cave people
when I was like, "Check thisout! You ready for this? Five
(02:43):
plus zero." And everyone'slike, "Oh dad, you're the
best!" So anyway, that's someof my experiences, to see that
my first grade kid then fliparound and say, "You know what
else makes five? 15 minus 10."An d I was like, "Oh, shoot.
OK. Ki d's g ot game."
Bethany Lockhart Johns (03:01):
Nuh-uh!
Dan Meyer (03:01):
I'm serious! I would not lie on the pod. I would lie
off the pod, maybe, but I wouldnot lie on the pod. So I'm
just, like, feeling how theprocedural fluency ties into a
conceptual understanding. Howthat robustness of
understanding then leads intobetter fluency. It is a
cyclical thing going on. Sothanks for letting me riff off
that for a hot second here.
Bethany Lockhart Johnson (03:22):
Yeah, I wanna hear it all, because I
think the part that I'm hearingis that it's becoming this,
like, everyday thing. We justtalk about numbers. And we
decompose numbers. And we lookfor numbers around us. We look
for different ways to makenumbers. And we celebrate
numbers. It's just part of ourday. And that is what I'm
(03:43):
hoping that when we think aboutfluency, I'm hoping that we use
that lens. We've been talkingabout the ways that fluency has
not been done in a productive,joyful way. And we don't want
that for your kids or any kids.
Dan Meyer (03:58):
Any kid. Which is why I'm really excited about
our guest today. We've had alot of people who have been
speaking from a perspective ofacademic literature,
theoretically, "what are wetalking about when we define or
assess or foster fluency?" AndI found it super helpful. I
also have the need, right now,to feel grounded in classroom
(04:22):
practice, and people who aredoing the work, and seeing its
effect on classes full of kids.
I'm super-excited that we haveon Ms. Lauren Carr , who's a
teacher out of SouthernCalifornia, who happens to
teach kindergartners and firstgraders, who are kids that I
have a love-hate, but mostlylove, relationship with right
now. Lauren, in 2016 receivedthe LA Unified School
(04:46):
District's Rookie Teacher ofthe Year award, has been in the
game for nine years, is a UCLAMath Project coach is doing it
all. And here, at the end ofthe week, has been kind enough
to sit down with us and chatabout fluency and how it works
in your classes. So, thanks forbeing with us. Lauren Carr,
appreciate you.
Lauren Carr (05:03):
You're welcome.
I'm happy to be here.
Bethany Lockhart Johnson (05:05):
Thank you for being here.
Lauren Carr (05:07):
Happy to be here.
Dan Meyer (05:09):
Lauren Carr , we have a question we love to get
to know our guests by asking.
And the question is this (05:12):
In what ways have you been
developing fluency in yourpersonal life? Is there an area
where you're like, "Oh, I'mdoing the thing that I ask kids
to do in the math classroomevery day , most days"? What
would that be for you?
Lauren Carr (05:27):
Over the summer I started learning how to sew.
And, I don't think I realizedhow much math goes into sewing
then, I don't know, all thenumbers, and keeping track of
(05:47):
everything. And, if you're oneinch off, that throws off your
whole outfit. And so I've beentrying to —
Bethany Lockhart Johnson (05:54):
Wait.
You started with clothing?
Lauren Carr (05:57):
Bethany Lockhart Johnso (05:59):
That's impressive!
Dan Meyer (06:01):
Straight for the final, boss .
Lauren Carr (06:02):
Yes, yes
When I do things, I commit. Igo over the top. I can't just
start something small. I'mlike, if I'm gonna jump in, I'm
gonna jump in. So, I've made mysister a matching set. I made
myself dresses. I made mysister's dog a little bandana
(06:22):
Bethany Lockhart Johnson (06:24):
No pot holders for you,
let me tell you. That'sawesome! So, as you've been
learning these new skills, andbuilding your fluency with the
machine, with all the languageof the discipline of sewing,
(06:46):
you said about the measurement,but has it been frustrating?
Have there been moments whenyou're getting to the flow of
it?
Lauren Carr (06:53):
Yes. A lot of frustrating moments. Like I
said, I'm always I wanna justget it done. And so, sometimes
I'll sit with a pattern and I'mlike, "I'm gonna finish this
right now." And then I keepmaking mistake after mistake
after mistake. And then I'mlike, "You know what? I need to
take a break." And so, I'vebeen OK with taking breaks. And
then there's some times, I'vejust let it kind of happen,
(07:16):
when I haven't used a pattern,I've found that sometimes I'm
doing a little bit better
look at how it fits on my body.
Trying to not be so stuck at ,"Oh, this is the pattern I have
to follow this." Kind of like,what fits on my body? What
headspace am I in right now? DoI need to take a break? Can I
keep going? So it , I'velearned a lot about myself as
(07:38):
just learning something new. Soit's also a good stress
reliever after a long day ofteaching. And I always bring it
back to my kids too. So I'llwear something and I'll—
Bethany Lockhart Johnson (07:50):
You said, "I made this."
Lauren Carr (07:52):
Uh-huh. And I think they're just shocked now
. And I'm like, "Yes, I madethis."
Dan Meyer (07:57):
Where'd your clothes come from? And I was like,
"What?!"
Lauren Carr (07:59):
Bethany Lockhart Johnson (08:01):
I love it!
Lauren Carr (08:01):
It's like, I would love to teach my kindergartners
and my first graders how tosew. 'Cause there's so much
math in it.
Bethany Lockhart Johnson (08:07):
I love that that brings you calm
sound calming to me. But here'sthe beautiful thing: You're
seeing what happens when youwork through, when you
persevere. So, thank you forsharing that with us! Now, you
mentioned your kinders, yourfirst graders, which I could
(08:27):
have a whole conversation withyou about combo classes, but
we'll save that for anothertime.
Lauren Carr (08:31):
Yes.
Bethany Lockhart Johnson (08:32):
I love seeing people teach. I
love teaching, but I lovethere's such a joy in being in
someone's teaching space,right? So if I had the chance
to visit your classroom, if we— OK, Dan, you can come too. If
Dan and I had the chance tovisit your classroom, I'm so
(08:54):
curious, what would you hope Iwould see? Or what would you
hope I would experience aboutyour teaching philosophy? Or
the kind of space that you'retrying to create for yourself
but also for your students?
Lauren Carr (09:07):
Yes. So, I hope when you step into my
classroom, you feel a lot oflove. I think that's one thing
that I really want. I want mykids to feel safe and loved in
the classroom. Specifically inmath. Honestly, my class is
never quiet
(09:29):
when it's quiet. They're alwayshaving conversations. You're
always hearing them askingquestions, moving around,
wiggling. Doing all the funstuff. But, my teaching
philosophy is verystudent-centered. It's a lot of
student choice, student voice.
And so, I hope when you maybe,possibly, come to my classroom
, you would hear a lot ofstudent students talking and
(09:52):
not as much me up there justtalking. The students bring so
much knowledge and experiencesto the classroom. And I really
enjoy just listening to them,and then giving them questions
and things to nudge themforward. And so, that's the
space that I hope everyonefeels. 'Cause usually when I
(10:14):
step in there, I feel that
everybody else feels that whenthey step into my classroom.
Dan Meyer (10:19):
That's great to hear! And I hope that one day
we're all in the same roomenjoying your teaching
For some people, some forms offluency feel like the opposite
of what you're describing.
Sometimes, the way that fluencyhas been tried, teachers, pure
of heart, have tried to developfluency, result in kids not
feeling they can be themselvesor contribute actively. That
(10:42):
they have to be kind ofprogrammed. And so I would love
to know like, how do you makethis fluency? How do you weave
fluency into this space thatyou've created, that feels so
full of life and love?
Lauren Carr (10:53):
Sometimes, when you hear fluency, you just
think of those timed tests. Andwhen I was younger, thinking
about those timed tests andjust the stress that came with
it. We won't see those littletimed tests in my class. It's a
lot of counting collections anda lot of counting, a lot of
(11:15):
word problems, number talkimages, different hands-on
experiences where students arehaving fun with numbers and
also real-world experiences.
Today, a parent brought in somedonuts, and so we ended up just
having a conversation about,"There's 20 of us, and there's
only 10 donuts. What are wegonna have to do?" And so just
(11:38):
that real-world experience, andthat's fluency. They were able
to say, "OK, I think we gottacut it in half." And that's
first graders! They were like,"Yeah! Cut it in half so that
everybody can have a littlepiece." And so, those little
experiences, a lot of thosetypes of experiences, I feel
like build fluency. And knowingthat it's going to be OK to
kind of make mistakes. Andhaving conversations and asking
(12:00):
questions. And I think thatreally helps with fluency.
Dan Meyer (12:04):
Was that a gift to you? Were you happy that a
parent brought donuts in? Orwas that like, "Oh great, you
brought donuts in. Wonderful,thank you." Is that a good
thing to bring to K–1 comboteacher?
Lauren Carr (12:14):
They were given at the end of the day. So, it was
the last—
Dan Meyer (12:17):
OK, nice! Perfect!
Lauren Carr (12:18):
She came in the morning, but I said , "OK, end
of the day." Once we go home,there we go.
Dan Meyer (12:22):
That's a nine-year veteran teacher right there!
Bethany Lockhart Johnson (12:25):
Yeah, this is no rookie of the year
here . This is no rookie
Dan Meyer (12:29):
So I'd love to dig in a little bit more here on
fluency. You've described abunch of different kinds of
curricula, or activities, thatI think are, like for a
secondary teacher like me,aren't, I'm not super familiar
with counting collections, forinstance. And the others you
mentioned. So I'd love a littlemore elaboration here perhaps
on what those are. And I'm alsocurious about when the donuts
(12:52):
came in, and you had thismoment of numeracy with the
students around the donuts,like, my idea about fluency has
not included the kind ofone-off, interesting,
real-world applicationexperience. Help me out here.
That moment is what the fluencyhas meant to support. Like,
(13:14):
using fluency, thatdevelopment, and developing
your kid's sense of being mathdoers, and having an identity
as a mathematician, is thething that enables them to be
mathematical in that moment.
The donuts. But, the donutsthemselves, in my
understanding, are not afluency-developing activity
themselves. So, there's twoquestions there. One about how
(13:35):
much did the kind ofreal-world, one-off activities
develop fluency? And I'd justlove to know more specifics
about the activities youmentioned that have developed
fluency for your students.
Lauren Carr (13:47):
I'll start with the counting collections. So
counting collections, they'rean activity where students are
given an amount of objects andthey're asked to count them in
a way that makes sense to them.
And so, in kinder and first,they're working on cardinality.
Extending the countingsequence. One-to-one
correspondence. Actually firstgrade. That's what we're
(14:11):
working on with countingcollections.
Dan Meyer (14:14):
I'm still working on that. So, no disrespect.
Lauren Carr (14:16):
on those things. Then they'rejust counting. And then I come
and ask questions. How did theycount it? Why did they count it
that way? And then they mightstart counting by ones. And
then they might start countingby fives. The collections might
start getting bigger. And thenthey're like, "I've got a
thousand little rocks. Am Igonna count those little rocks
(14:38):
by ones?" And so they startmaking sense of does this make
sense? Does this not makesense? And then the fluency
comes with counting, likeskip-counting those collections
in different ways. And so,sometimes they're counting the
same collection over anextended period of time, a lot
of different ways. That'sbuilding their fluency. And
(14:59):
it's fun! Counting collectionsare, like, my favorite
activity.
Dan Meyer (15:03):
It sounds like it'll take you a long distance. What
I'm hearing now is thatstudents will reveal to you
that they are fluent when theystart adopting new strategies
for counting. I'm not hearingyou formally assess their
understanding of cardinality orskip-counting. It's like all of
(15:24):
a sudden, I don't need todirect-count like, six of
these. I see a five and thenone more. Is that an indicator
to you that, "Oh, OK, we aredeveloping fluency here." It
has been developed in some way.
Lauren Carr (15:36):
Yes, it is! They'll start, like I said, by
ones. And then when they startmaking connections from the
counting collections to maybethe choral-counts, where we're
counting altogether. Andthey're able to decompose the
numbers or the countingcollection to the word problem.
They're making thoseconnections. And so, yes, that
(15:57):
starts to tell me like, "Oh,they're starting to recognize
the patterns." They're startingto see patterns. And start to
see the patterns everywhereelse. And then, yes, that's
where I'm able to say, "OK,we're building our fluency."
Dan Meyer (16:09):
I think K–5 folks will know what choral-counting
is and counting collections andall these things. But, it was
really helpful to hear youspell out those different kinds
of fluency building activities,which we haven't heard so far,
I don't think from many of ourguests. Which is why we've got
you on.
Lauren Carr (16:27):
Yay!
Bethany Lockhart Johnson (16:27):
So, for me, definitely, counting
collections brings me a levelof joy. Not just collect — my
husband's like, "Why are yousaving these bag ties? Why?!"
It allows me to have my littlecollections, and it's for my
classroom. But no, really,there's so much richness that
(16:49):
we see coming out of theseopportunities for students to
count. And to make sense ofword problems and
problem-solving. But, I alsowant to address, what about the
teacher who says, "Yeah, we'vebeen doing counting
collections, but my studentsstill can't add, or can't
(17:11):
subtract, you know, five minusfour or two plus three, or
whatever." When I ask them, orwhen I give them an opportunity
and assess them, they're stillnot understanding or fluent
according to the standards. AndI ask that because I think we
understand that there's fluencyin the bigger sense of fluency,
(17:31):
with numbers and compositionand decomposition, but then
there's also the standards,right? So, I'm just curious,
how does that fit in with thekind of folks who push back and
ask you more specifics aboutaddition and subtraction, the
way they might picture itinitially?
Lauren Carr (17:49):
I hear that. And I hear the fluency. They have to
be able to add quickly to beable to add on to other
activities. It's the foundationfor, like, multiplication,
division. But I think that theyare mastering the standards
(18:11):
through fluency with likecounting collections and
things. I think it just looksdifferent. And I think there's
ways to assess fluency withaddition and subtraction that's
not punitive, where it'ssomething that's gonna stress
students out. And so when itcomes to the standards, yes,
like in first grade, thestandards is to be able to add
(18:33):
and subtract fluently within20. So yes, we are playing math
games where we're adding andsubtracting fluently within 20.
We might have a little sheetwith different
number-sentences, but they'reasked to solve the ones that
are less than five or more thanfive. That's still building
(18:54):
fluency. Yes, you wanna be ableto go quickly, but sometimes we
don't. Like, honestly, I'm justthinking about me sometimes
when it comes to percentageswhen I'm shopping and trying to
know the percentage of a sale.
Of course I wanna be able toknow it fast but, in that
moment, I don't really need toknow it that fast. I think it's
(19:19):
like, "Why are we trying to goso fast?" On one end, I'm like,
yes. Like I said, yes, we wannabe able to add and subtract
quickly. And then some of us,we are working on our own at
our own speed.
Bethany Lockhart Johnson (19:35):
I've been in schools where the
school was very gung-ho and wasvery focused on some fluency
goals, and kind of telling thestory of fluency K–5, right?
And that was a really rareexperience. And then I've had
other situations where itwasn't talked about at all,
right? And, and it was more putoff like, "Oh, well the parents
(19:57):
will practice those things athome." Right? So I bring it up
because I think it's sofascinating to hear. There's so
many times we hear aboutfluency and it's very
antithetical. Like, the wayfluency is taught antithetical
to how you're talking aboutyour classroom culture, right?
So if your students areexperiencing joy, if your
(20:19):
classroom is not quiet, 'causethey're engaged, they're in it,
they're present. I think I amhearing you say that,
simultaneously, they arebecoming flexible thinkers with
numbers and withproblem-solving. Is that what
I'm hearing? I wanna make sureI'm understanding.
Lauren Carr (20:39):
Yes, for sure. I hope all of those experiences
make space for them to befluent with numbers, and have
fun with numbers, and seenumbers everywhere. See numbers
in the real world. Yeah! That'swhat I want! And I don't want
them to see numbers and think,"Oh, I don't know how to do
(20:59):
this quickly, so I can't doit." Or, "This doesn't make
sense to me. And so it's notrelevant to me, so I'm not
gonna do it." Or, "I have tosit here and be quiet during
math time . That's the oppositeof what I want." And so I think
by making space for the joy,and having fun, and having a
positive math identity, I thinkstudents will build fluency.
Dan Meyer (21:23):
You've described yourself as someone who is
interested in students learningabout justice in the world
through math class, not inother classes, but in this
class, through theseactivities. And I just wonder
if you could speak to how thedifferent approaches to
fluency, we've talked about theones that you've been pursuing
with your kids and other onesthat are out there that other
kids have experienced, howthose contribute to a student's
(21:44):
sense of who I am in the world.
Can they do that? Is that toolofty? You have a goal for
fluency? Or have you seen thatcontribute to a student's sense
of what justice looks like inthe world?
Lauren Carr (21:55):
So we start with math as, like, patterns. Math
is all about seeing patternswith numbers. And you can use
math to see patterns in theworld. We start small with the
numbers, and then we start tosee patterns in all types of
different subjects. So it'slike seeing patterns in and
(22:19):
issues of injustice in theworld. Patterns of nature.
We're seeing patternseverywhere. I think that's one
way that in those real-worldexperiences they're able to see
patterns and make thoseconnections.
Dan Meyer (22:34):
Yeah, that's helpful. There could be
activities or experiencesstudents have in math class
where they're noticing wherepatterns are maintained and
when patterns break. I feellike kids of this age have a
sensory experience of fairnessor unfairness. Like, we should
all get half of a donut. Andthen, if that pattern gets
(22:56):
disrupted, it's perhaps a kidwho has some fluency with
numbers can notice that moreeasily than kids who don't.
Does that sound accurate to howkids develop these ideas?
Lauren Carr (23:09):
Yeah, I think so.
Coming back to the donuts (23:10):
The students that have had a lot of
experience, hands-onexperiences, with little
parties and having donuts, andbeing able to count the donuts
— how many donuts there are.
How do we share donuts? — thosestudents can bring that to the
problem. And then be able tofluently say like, "Oh, I know
(23:31):
that we're gonna split these upquickly. This makes sense to
me, because I've had a lot ofexperiences talking about these
things and seeing thesepatterns."
Bethany Lockhart Johnson (23:41):
So, last season was about math
anxiety. And something thatcame up again and again when we
were talking is the anxietyfolks had around assessment,
and around perceived judgmentof their math competency. And
so, thinking about how we lookat patterns and justice, I feel
(24:07):
like with fluency instruction,if done poorly, it can really
exacerbate inequalities, right?
And I'm wondering how you thinkabout that in terms of when
you're in that kind ofsituation, wanting to celebrate
students who are bringing thisknowledge about their
experience. I've had lots ofopportunities to count and to
experience these parties. Andthen I also have students who
(24:30):
this is all new for them,right? Or they bring a
different fund of knowledge tothe conversation.
Lauren Carr (24:36):
My teaching philosophy in general is social
justice-centered andanti-racist. It centers
students' thinking andstudents' voices. I always say
"empowering students," but theyhave the power. But giving
space for students to recognizetheir own power. With fluency,
I used to think that ifstudents are sitting there kind
(24:58):
of quiet, listening to what I'msaying, being able to tell me
exactly what I just said, I waslike, "OK, this is going well."
And I think it's also because Iused to be like that. I was
that math kid that was like,"Just tell me what I need to
do, and I'm going to do it."And so when I started getting
older, and the math startedgetting harder, and I started
(25:20):
to think a little bit
I don't know, because I've beentold how to do this math my
whole life." And I didn't wantthat for my students. I want
them to be able to be loud,have fun, ask questions. I'm
not going to tell them theanswer. And I think one thing I
(25:40):
always tell my students is it'snot about the answer. It's
about how you get to theanswer. Those little
conversations going into wordproblems and counting
collections. All those things Ifeel are also part of fluency.
I'm always talking about math.
I feel like I'm the person atthe school that's always
talking about math. And peopleare always just like, "Oh,
(26:03):
there she goes again." Then,whenever fluency comes up in
spaces, there's an idea of whatfluency looks like . The idea
that there's these littletests. You gotta sit there
quiet. Write all your answersas quickly as you can. And I'm
like, not all students learnthat way. Not all students are
(26:24):
going to get it that way. And,it's not equitable. I believe
it's not equitable. And so, Iwant teachers to see, like, my
classroom where we're doingcounting collections. We're
having fun. We're having theseconversations about math.
Seeing math everywhere we go.
(26:45):
Recognizing patterns everywherewe go. And that's building
fluency. Those experiences arebuilding fluency. That's what
fluency looks like to me. Andeven just thinking about today,
we have these beautiful muralsat our school, and my students
just look was just lookingaround. He's like, "Hey, I
noticed a pattern!" And Ithought it was the colors that
(27:06):
he was going to notice. But, itended up being the arrows. One
arrow was going up, one arrowwas going down, one arrow was
going up. And I was like,"Wow!" So that to me, those
experiences where he's lookingat something in the space and
recognizing a pattern andsharing it, those experiences
are going to help him befluent. And how excited he was
(27:27):
to just share with me that hesaw a pattern at our school.
Dan Meyer (27:38):
Yeah , I'm trying to get a sense of you around
fluency versus the conceptionof how a lot of people
experienced it. And one thing Ifeel like I'm hearing, right or
wrong, I don't know, is thatwhereas a lot of teachers might
see their job as to give outthe paper that has the problems
on them, and that is the thingthat develops fluency. What I
(28:01):
feel like I've heard you talkabout is doing so much work to
help students realize you havegood ideas, but you're also
kind of a provider ofexperiences, like a box of new
stuff to count up. And then,the cool thing you do, like
lots of folks could do that,but what you do feels like
(28:21):
naming a kid's strategy as athing of value. A thing you
did. And knowing what to offerthem next in response to keep
helping them develop that. Andthat feels like a very
different approach to fluencythan what a lot of people are
used to. Different kinds ofskills to develop. It's very
fun to hear. Thank you so much!It's been a real pleasure to
(28:44):
have you on. Learn more aboutyou and your work.
Lauren Carr (28:46):
You're welcome. It was a pleasure. I love talking
about math. I can talk aboutmath all the time, every day,
all day.
Bethany Lockhart Johnso (28:53):
You're welcome in the Lounge anytime.
Dan Meyer (28:56):
We're here 'til 1:00 AM some nights just talking
about math. It gets a littlebit nuts. Wow, Bethany, what a
ride! So fun to hear fromsomeone doing the work in the
classroom day in, day out.
What'd you take away there?
Bethany Lockhart Johnson (29:10):
These conversations we're having,
it's definitely expanding mynotion of the idea of fluency,
right? Because I think when Ienvisioned the season, I came
in with a much narrowerdefinition. Really thinking
about the California statestandards, and really thinking
about like computationalfluency in terms of how that
(29:32):
can be a barrier or a realfoundation for students.
Thinking about ways to seefluency happening, in a broader
sense, is I think reallyhelpful. And it's a good
reminder when we're thinkingabout cultivating classroom
community. What about you, DanMeyer?
Dan Meyer (29:51):
Yeah, all of that! And I loved Lauren's
description of attending tostudent identities, even while
we're asking them to do stuffthat's difficult, and even
sometimes repetitive. Whatstuck out to me was the moment
when Lauren was talking abouthow you're not gonna count to a
thousand by ones, so what canwe do here? And like, just how
(30:13):
necessity is the mother ofinvention of fluency, of the
need for fluency. I thoughtthat was pretty special. It
takes a certain kind of teacherto say, "OK, I'm not just gonna
have you develop fluency forits own sake, but develop
fluency in order to becomeproficient at a particular task
that you understand. And thatis interesting to you." That
felt, like, next-level. Thatfelt like rookie of the year,
(30:36):
like nine-year veteran typeteaching moves to me. So, that
was really exciting.
Bethany Lockhart Johnson (30:41):
Well, and also, for folks listening,
we see each other virtually aswe're recording. And I hope,
and I think it will comeacross, when you hear the way
Lauren talks about her studentsand her classroom, but to see
the joy emanating
her students, as she's talkingabout mathematics, as she's
(31:03):
talking about creating aclassroom culture like that. We
want to share that. We want ourstudents to experience that joy
and that, I don't know, freedomaround talking about math. And
seeing math, and exploring mathand problem-solving, even when
it's not coming easily, so tospeak. So yeah, that was a
(31:27):
pleasure. And I thank you allfor listening with us. And
hopefully you're enjoying thisseason. We'd love to know what
you think about Ms . LaurenCarr's strategy for developing
fluency. Or maybe you haveother ideas of your own that
you'd like to share about thisseason, or about what you do in
your classroom. Please join theconversation in our Facebook
discussion group, Math TeacherLounge: The Community. And you
(31:49):
can also reach us at X,formerly known as Twitter, at
MTL Show. We have plenty moreto come on this season of Math
Teacher Lounge.
Dan Meyer (32:00):
And you folks can keep up with all of it by
subscribing to our podcast onall the platforms. And we would
love for you to support ourwork here. Get the word out by
rating and leaving a reviewwherever you get your fine
podcast products. Bethany andI, we read all of them. And I
do mean we read ALL of them.
And we read them to our lovedones, and parents, and friends.
(32:22):
So just keep that in mind asyou fill out that review. Just
think about what you're saying,and would you like this to be
read to Dan's mom? You know,
just a couple weeks. In themeantime, here's a quick tease
of what's to come.
Speaker (32:38):
We have to look at mathematics as a story that we
tell students across thegrades, K to 12. And what we
are is the conveyors of achapter in this progression of
the story. If we look at it asan isolated chapter, then the
question really becomes, whatam I doing to my students and
(32:59):
for my students?
Dan Meyer (33:00):
Thanks for listening folks.
Bethany Lockhart Johnson (33:02):
Bye!
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