S6-E06: Nurturing fluency through student strengths

Join us for Episode 6, where we discuss how to take an asset-based approach to building math fluency with John W. Staley, Ph.D., who has spent decades in math classrooms. In this episode Dr. Staley shares his experiences and research to provide strategies on how to utilize student strengths to encourage growth.

For more from Dr. Staley, check out the following resources:

• Follow John on X at @JStaley06.
• Learn more from John by checking out his NCTM articles.
• Read John’s book, High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice.
• Read John’s book, Middle School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice.
  
  

Episode Transcript

Speaker 1 (00:00):
We have to look at mathematics as a story that we
tell students across the gradesK to 12. And what we are all is
the conveyors of a chapter inthis progression of the story.

Speaker 2 (00:12):
Welcome back folks to Math Teacher Lounge. I'm one
of your co-hosts, Dan Meyer,

Speaker 3 (00:17):
And I'm your other co-host, Bethany Lockhart
Johnson .

Speaker 2 (00:20):
And if you folks notice a little extra charisma
or vibe between Bethany and Ithis recording, it's because
Bethany and I got to hang outin person, a real rare
occurrence for us. Uh , yeah .
Bethany was up here with , uh,fam and, and my home. And , uh,
yeah. Bethany , what was your ,uh, what was your take on the ,
uh, on the whole situation? Youknow, I gimme a thumbs up,
thumbs down. How was it neatenough for you? You know , talk

(00:41):
to us about it.

Speaker 3 (00:43):
On the Meyer household. Well, you know,
anytime I get to see you, Dan,which is usually at
conferences, this was like awhole nother level. You invited
me into your home to hang outwith your wonderful family. Uh
, the only thing missing wasthat I really did, like, I was
serious. I told you thisbeforehand. I really did think
I was gonna get to play some ofthose like fluency math games

(01:05):
with your kiddos. Yeah. Yeah.
And that did not happen. Infact, I think once I gave them
some Halloween stickers, theywere done. They were like, but
you know. Yeah . You said,actually, could you stop
calling them math games? Is Ibelieve what you told me,
.

Speaker 2 (01:20):
You , yeah.
You, you served your purpose indelivering a fantastic little
treat for them. And then theywere off scurrying into their,
you know, their rabbit's den orwhatever to go GNA on it. And ,
uh, yeah. And we had, we had,we had, we had aspirations for
like, doing some socialcontent, you know, to try to
make our producer Martin happy.
Yes . You know, we had somereels ideas. I thought I was
gonna have, you know, figureout all my fluency stuff.

(01:41):
'cause I had a , you know, KAlegit K five specialist in my
home. So I was gonna putBethany to work with my kids.
But really, we just like , hada, had a good time just hanging
out, talking, talking shop,talking family, that kind of
thing. It was a real treat tohang out with you. Hey ,

Speaker 3 (01:54):
Thanks. And if I come to your home and you
immediately present me with afall cocktail and then feed me
an amazing dinner, I probablywill get a little distracted
off the fluency stuff. Sorry.
But I will tell you. Okay. Danhad a really fun idea for a
reel . Do you wanna share it?
Dan?

Speaker 2 (02:12):
I'll , I'll , I'll share it 'cause it probably
won't get made. Okay. And Iwanna clarify on the front end.
Okay. I'm, I'm a secondary guy,so I'm , I want to like set the
bar real low for myself so low.
I can step over it with thisright here. So I had this idea,
all right , which was that ,um, I got a ping pong table in
my backyard, right? And Ilearned about coral counting
recently from Bethany and otherfolks on the call, right? Where
, you know , you can start atany number and go up around a

(02:33):
circle by a fixed amount maybe.
So one kid says six, next kidsays nine, next kid says 12,
and so on. So here's what I wasthinking is me, Bethany pinging
pong in it, all right ? Tabletennis in it. And , uh, we
start just doing choral byones. So like, I hit the ball
over one, Bethany hits two,three. And whenever someone
misses that, then is the newstarting number. And the new,

(02:53):
the new what , what do you callit? You know, the new skip
amount. So if we make it tofour, then we go 4, 8, 12. If I
blow it there, it's like 12,24, 36, whatever's after that.
Who even knows ? Butyou gotta like, kind of ,
there's a little bit of timepressure, you know? 'cause the
ball's coming, the ball'scoming and uh , you gotta hit
the , gotta hit that back. So Iwas feeling pretty good about
that. Never . We never did it.

(03:14):
But you can all imagine howfunny and heartwarming and a
little bit profound the reelwould've been on a , on Insta.
You can , you can imagine inyour mind's eye,

Speaker 3 (03:25):
I did not see this pinging pong table you speak
of. But if you had like,greeted me with paddle in hand,
I would've been ready to go.
I've been like, let's go. Andalso, I wanna clarify that in
coral counting, one of thebeauties is the coral nature of
it, where you're countingtogether. So like you have, so
it's not like a popcorn, Danhas to tell me

Speaker 2 (03:46):
Person on the spot.

Speaker 3 (03:47):
Yeah. Okay . I know it's that we're counting
together. So if I don't knowwhat like a multiple of 12 is,
because you missed the ball,love that on the , you know, I
mean, just in case you missedit, I would , you know, I would
then we're doing it together sothere's no pressure and it's
just joy in counting. So let's,let's take that pressure off
that we would've been countingtogether. Mm-Hmm.
,

Speaker 2 (04:07):
I love that. That like, if 24 plus 12, I'm like,
ah , I know it's 30 some , youknow, but not 36. Then like,
there's like, I can kind oflike get , get happy about, we
all said 30 and I , I said 30.
I was a part of that. And I waslike, you know, not quite at
six yet, but can contribute.
So, hey , I'm learning here.
Thank you for that, Bethany.
It's

Speaker 3 (04:24):
All about learning Dan Meyer , it's all about
learning. It

Speaker 2 (04:26):
Is about learning. I wanted to offer one quick
thing, fluency wise has beenhappy in our lives around here.
Got kids in k and one, as I'vementioned before, they're like
in the official, you know,learning math thing in , in
formal school environments.
And, you know, I'm so gratefulto have a little bit of time
and energy at the end of myday. I'm not working two jobs.
I can sit down and do a little,you know, work with them,
homework of different sorts.

(04:47):
And , uh, we're doing some,some mathy stuff. And they said
to me, can you time me? And Iwas like, wait, what? And it
kind of hit me a little bit and, uh, come to find out that
like, they get timed in schooland they wanted to kind of like
do the timing thing at home. Ijust wanna say, you know, I
felt a little bit of conflicthere. I wanna say just straight
up, my kids' teachers areincredible, love them , could

(05:10):
not do what they do. Andobviously over the course of
this, our season here, I'vebeen working issues out about
fluency and, you know, how tobalance a kid's joy in math and
their ability to work themathematics fluently. Anyway,
I'm, I'm still thinking aboutit. I was glad if nothing else,
that they weren't liketraumatized by the timing.
Yeah. Uh , you know , that ,that's nice that they weren't

(05:30):
freaking out about that or, orshrinking back. But it did
raise questions for me aboutlike, is this part of the
nature of math? Or like, isthis extra?

Speaker 3 (05:39):
Yeah, I mean, we, we had our whole season about math
anxiety and you know, the timetest came up a bit and we had
one of our guests who was like,there's a space for time test .
We kind of like, thought aboutthat and we're like , uh, but
will teachers do it in a waythat's not traumatizing? You
know, I have some questions.
Yeah. I would maybe ask like,how does timing show up in AK

(06:01):
or first grade classroom? Like,what is the, the goal there?
And again, your kiddos seemedexcited, wanted you to time
them, but is that theexperience for all kids? We
don't know. But it might beinteresting in a very, like,
Hey, I respect what you'redoing sort of way . But I'm
also curious, can we talk alittle bit about how this shows
up in the classroom? Becausethat seems Yeah, that is,

(06:23):
that's, maybe it's just becauseyou usually time them in every
other aspect of their life,Dan, you're like, you know,

Speaker 2 (06:29):
Do the potty stuff faster, fast . Um , Bethany, I
, I love your confidence in me,but do you, what part of our
experience together makes youthink that I could gracefully
thread the needle between beingencouraging and respectful and
also asking a sincere butinterested question about why
you're timing my kid .
Uh, I'll do my best at somepoint .

Speaker 3 (06:47):
Do your best, do your best or, or , um, le why
don't I met your wife? Whydon't we leave that to your
wife? Because she is charming.
She's fabulous. Yeah . There .
So let , we'll leave it tothere . There you go . But you
know what, though, this is areally great invitation, Dan,
to like, for our listeners tobe listening to what kinds of
conversations are coming home.
You know, what kind oflanguage, how are kids talking

(07:07):
about math, talking aboutreading? Because once our
kiddos are in that moreformalized schooling
environment, we don't reallyknow what's happening, right?
So how can we even just tune ina little bit to hear, are they
saying things that kind ofgreat against the way we're
hoping to think about math orhave conversations about math

(07:29):
in our home? And how can wemake sure we're not having our
kiddos traumatized by that,that language, by the , those
exercises. So I, I wanna , Iwanna hear more. Please keep
the stories coming. Dan will

Speaker 2 (07:41):
Do. And I, I think we should like , uh, we're
lucky enough to have , uh,really smart guests on the
calls , uh, in the , in theseason, who can help us sort
some of these issues out. So Imight just like be selfish here
and ask about my own situationof our, of our current guest.
Um, to tee up the currentepisode here. Just to recap
where we've been in our season,you should hit the back catalog
if you haven't. We've talkedabout assessment of fluency

(08:02):
with Dr. Val Henry. We'vetalked about how to balance
fluency and use that to developenthusiasm for math and problem
solving with Dr. Art Brody .
And we've talked aboutdeveloping fluency in a
classroom setting that alsoreally prioritizes listening
and conversation betweenstudents with , uh, with Lauren
Carr. It's been a fantasticseason. We also had, of course,
Jason Ziba on , uh, to talkabout the nature of fluency

(08:25):
itself. Been a, been awhirlwind. And we have on the
call today Dr. John Staley ,who's gonna talk with us about
how to develop these kinds ofskills we're talking about in
teachers at a system level.
John has seen it all. Um, Johnhas worked with the Baltimore
County Public Schools fornearly three decades in roles
such as teacher of middle andhigh school, math coordinator

(08:47):
of secondary mathematics,director of math, pre-K to 12,
and currently the coordinatorof special projects. So we're
excited to talk all thingsfluency with John here. Uh ,
but especially right now , uh,about my own children. You
know, what's up, what , youknow, how , how welcome
and how would you handle this?
What should I do here? big welcome to

Speaker 1 (09:05):
John . Hey , hey , hey, Dan. I'm , I'm taking
notes from you on this one'cause we have a grandson who's
, um, okay, he's almost 20months and we're not quite
doing that time fluency withthem yet. But I'm hoping the
same thing that you're hopingthat as teachers think through
what that does for students.
The question I ask on the frontend is, how does that impact

(09:26):
their confidence? And so, K 1,2, 3, as you keep moving across
the grades, when do studentswho aren't as fast as the other
ones begin to believe thatmaybe they're not as good as
math at math? Mm-Hmm .
with doing itbecause they can't do it within
this certain time limit, thiscertain speed. They're not the
first one to finish. And sothat's always the minute that

(09:46):
timer goes on, that's always a,I'm wondering what's gonna
happen as far as not whether ornot they can do it and get
there, but how it begins tochip away at a student's sense
of confidence and willingnessto go try and do and show what
they can do. So all of that iswhat I'm thinking about with
you for your kids that are inkindergarten, first. Our

(10:08):
grandson is not quite thereyet, but , um, you know, just
thinking about how that hasplayed itself out even with our
own children.

Speaker 3 (10:15):
Thank you so much for being here. Dr. Staley and
I, I got John .

Speaker 1 (10:20):
Yeah , yeah , please. John

Speaker 3 (10:22):
, thank you for being here. I, and I really
appreciate you saying that. I,I have a two and a half year
old , so you know, K one andI'm a kindergarten teacher. So
you think about our kiddos,we're trying to help them build
language of the discipline.
We're helping them like makesense of what is math and
seeing math all around them.

(10:43):
And if we are bringing in thattimed nature, I love how you
put it, like, at some point forsome of our students, it's,
they're gonna make meaning outof that, right? If their time
either goes down, doesn'timprove or does improve, like,
we don't know how they're gonnamake meaning of it. And, and so
thank you for saying that, andthank you for being here. Yes.

(11:04):
You're coordinator of specialprojects, so little did you
know your special project isDan Meyer . So , he ,
he's got, he's got a doozy of a, a question for you, right?
?

Speaker 2 (11:13):
I am a project. Yeah ,

Speaker 1 (11:14):
I understand that .

Speaker 2 (11:15):
Could I ask you a question? We've asked some
guests and found reallyilluminating here, John , which
is , uh, you know, we talkabout fluency in math and a lot
of ideas flood into the mindfor a lot of math folks. So we
wanna take it outta math for asecond. And we're curious, is
there an area of your life aspersonal as you wanna make it
here, that where you feel likeyou've been developing fluency
yourself? What is it? How'sthat, how's that process been

(11:37):
for you?

Speaker 1 (11:39):
Um, yeah. The , the one area is , um, I would just
put it, and so let's gopersonal. My quiet time with
God. You know, I , I try on a,on a regular basis, daily to
have quiet time when, you know, um, that might entail a whole
bunch of different things fromlistening to music, to reading
the Bible, to journaling, tojust prayer, to just sitting

(12:01):
and being quiet. So I've gotdifferent things that I can do
within that quiet time. But asI think about from day to day
to day, it's always a growth inprocess for me. So, in other
words, there are days when I'mthinking I'm doing well with
it. There's days when I'mlight. And the consistency of
doing it across the days issomething that I continue to
myself step back and look at.

(12:22):
And, and I take that timepersonal because there are days
when I know, okay, man, Ididn't give much time. And
there's days when I know, okay,I put in time. And so the goal
is how do I think aboutcontinue to build, grow, and
develop? I've got multiplestrategies that I can bring
into it. So as I think aboutquote unquote building that
fluency, I'm thinking aboutwhich strategies do I need?

(12:44):
Which ones do I want to usethat day? And quite often from
day to day , it depends onwhat's happening with me in
life, what's happening with meand my, my wife Karen, and our
children, our grandchildren,and the situations that have
come our way. So fluency willvary, but that idea of my time
with God helps me with dealingwith situations that come up.

Speaker 2 (13:07):
I appreciate you sharing that. It's , uh, it's
real personal. And I'm , I'mthinking, you know, about how
often in fluency development,there's an element of feedback
attached to it. You know, like,I wanna, if I'm developing
fluency, you know, in the, inthe, in the kitchen, it's like,
well, how do people receive myfall cocktail, let's say? Or,
and , uh, when you're talkingabout , uh, you know,
discipline that's spiritual andyou know, how you get feedback

(13:30):
on how you're doing , uh, feelslike a real interesting part ,
uh, takes a real sensitivity toknow like, how am I doing with
this , uh, this process ondeveloping fluency? And that's
really interesting.

Speaker 3 (13:43):
I also wanna to flag that. Like, it's that
consistency, right? You talkedabout that consistency. And
when we're thinking aboutfluency like that, we're doing
it consistently. And not onlythe feedback, but that growth,
right? That growth with, like,it's gonna change, it's gonna
evolve. Now here, Dan Meyer ,what if Dr. Staley, what if you

(14:05):
put a time pressure on that?
What if you said , youhave to get it down by this
time, or you have to get an icecream scoop to show that you
have mastered these verses orwhatever your walk is looking
like. Hmm . Is it , is thatgonna change your relationship
with your journey? I wonder,see , I'm still thinking about

(14:25):
this question, Dan

Speaker 1 (14:28):
And that idea of feedback , um, Dan and time,
when you put both of thosetogether, 'cause you think
about days when I'm thinking,okay, I need to be spending 15
minutes, 20 minutes, 30minutes, and I spend three
minutes, or I spend fiveminutes. It's gotta be a
nonjudgmental zone, especiallyas you think through and
process self. So as you thinkabout your children, Dan, as
they process what they're doing, uh, when they no longer enjoy

(14:52):
you, timing them at home, Ooh ,I wonder what's going on. And
it's not because of somethingthat you've done that's changed
it, but it's because of somekind of interaction with
something in the space of whereit's happened. So like, what I
don't do is run around sayingto my wife, Hey, you know, I
spent 15 minutes with Godtoday, 10 minutes, 12 minutes,
two minutes, because I, I don'twant it to be in a judgmental

(15:14):
space. And so that time elementof how much time do I spend or
don't spend, that's, that's,that's me. That's an individual
piece that I have tointernalize. So

Speaker 3 (15:24):
Thank you so much for that perspective, John .
It's so, it's not only helps usget to know you better, but
it's also like in my brain, allthese little connections are
zing. And, and thinking abouthow that, that evolution, your
journey with that, how that'sgonna impact the way you
approach it tomorrow, right?
The way you approach yourconversation or you walk
tomorrow. Yeah . And anyway,thank you for that. Um, you

(15:46):
know, you, you identified apotential risk when it comes to
fluency development thatoftentimes fluency can be used
as an excuse to hold kids backfrom progressing in math. And
I'm wondering if you can talk alittle bit about that concern,
because I don't know if folkseven sometimes see it. They may
say, oh, well kid's not fluent,therefore they may not have

(16:10):
access to a certain aspect ofthe material as quickly. But
you're talking about on an evenbigger level, like actually
holding them back from their,from building a further
relationship with math orprogressing in math. Maybe you
can give an example of howyou've seen that in your
career.

Speaker 1 (16:25):
Um, here , easiest part, let's continue with Dan's
story. This time testing, thistime testing of facts. Um,
which quite often really ispeople linking this idea of
fluency to automaticity, torecall, to memorization. So how
many facts do I have memorized,especially if I'm going through
and I'm doing it so quick thatI have to be boom, snap, snap,

(16:48):
snap right there. If I'm astudent who processes, I need
time to think a little bit andprocess. When I'm put in those
situations where that kind offluency is, is elevated, that's
where, man, I could be all overthe place. I can shut down the
anxiety's kicking and thingslike that. But that one fluency
is about fact, fluency aboutthe memorization. The

(17:11):
automaticity, quite often it'saddition type problems. Um,
it's your quote unquote youraddition facts. It might be
some subtraction facts thatmight be held to within 10,
within 20. Um, and later on itbecomes your multiplication
facts. So my students don'tknow their multiplication facts
or types of words that youhear. And that's quite often

(17:32):
about the middle of thir thirdgrade, fourth grade, fifth
grade, where that becomes adominant set of importance that
people chase. And when that'shappening, you start to see
groupings. You start to seepeople grouping students who
can't quickly and fluentlyrecall them, AKA memorize them,
right? But often sometimes yousee memorization without

(17:54):
understanding of what theymean. Memorization or
multiplication facts can happenfor students with some drills
and practices and games andthings like that. But if
students don't understand whatthe multiplication means behind
that fact that they just spitout, that's another piece of
it. So as you think about howthat plays out in groupings in
elementary schools, then itchanges into identification for

(18:17):
students to go into differentmath courses, especially as
they go into middle school,which is when I say different
math courses, we're talkingabout tracking beginning to
happen based off of can Ifluently recall? We're not even
talking really about proceduralfluency yet. Can I do addition
and subtraction and do itwithin a timely manner? Do I

(18:40):
have a strategy that I can use?
So a lot of it's fact then itshifts to computational
fluency. It leads into who wesee as who can and can't
because they get put intodifferent groups. Some of those
groups get identified early,third, fourth, fifth grade,
next thing you know, they're indifferent sixth grade classes.
And that leads into, ultimatelywhen you step into high school,

(19:04):
people looking at what camefrom fluency in elementary
leading into who you're deemingas being ready or not ready for
algebra. It just has thattrickle up effect that really
is mindful of not what studentscan show and do. And also it
impacts their confidence. Yousee students coming into middle

(19:27):
school and their confidencebegin to crumble and begin to
be shaken. I haven't gone outand studied this, but I would
almost say it's connected tothis idea of what they can do
and how fast they can do it ingrades three, four, and five.
Prior to that man they'redoing, doing , doing . They're
trying, trying, trying. Thenwhen they stop showing that

(19:50):
willingness to try, thatwillingness to raise their
hands because they're not fastenough, we gotta step back and
say, what's going on here?

Speaker 2 (19:58):
Yeah. It's interesting. You're really
describing a , a , aself-fulfilling prophecy as it
were, where like, students whoare told you are not this or
that will wind up living intothose expectations, be they,
you know, higher or lower forkids. Um, and it all seems to
start from these assessmentsthat humans flawed, wonderful
humans are making about thekids in front of them , uh,

(20:20):
evaluations and , and judgmentsthat are in inflected with
every kind of, of bias andhistory of the person, but also
their ideas about what fluencyis. And you've, you've spoken
about , uh, you put a name tothis, I think is , uh, really
effective, which is , uh, fakefluency indicators. I think you
kind of hovered a little bitover some of those in your
answer just there. Um , butit's interesting to me that

(20:41):
like the fake fluencyindicators like hurt both kind
of kids. They hurt the kidsthat get advanced who don't
have the understanding that youdescribed. Mm-Hmm .
. And they hurtthe kids who have the
understanding, but don'tmeasure up against this quote
unquote fake fluency indicator.
So I'd love if you like, couldyou put a few under that
umbrella of fake fluencyindicator, what are some of the

(21:02):
ways that systems and teachersevaluate students as fluent or
not that you think should bereconsidered or considered more
deeply?

Speaker 1 (21:10):
Um, man. Okay. How much time do we have today,
? No, let's , um, let'sstart with just one, the first
one thinking about andconnecting to this idea of how
fast can students recall thesefacts? So let me, maybe it's a
32nd, maybe it's a one minuteto reproduce these facts. That
right there, when you startthinking about fact recall and

(21:31):
I'll, I won't call it factfluency, but fact recall within
a certain time limit, thatright there begins to be one
indicator that says are arethey doers or math or not doers
or math. The idea is, are theythinkers of math? And the
question we have to ask ourselfabout that practice of timing
them is how does that helpsupport their thinking and

(21:52):
making of sense in mathematicsclassroom as people who do work
in math, when was the last timeyou were asked to reproduce or
do something within a 32ndtimeframe? And the question
becomes, is that a practicethat mathematicians have to do
on a regular? And people willsay, oh, they have to be able
to recall certain facts. Sowhen you think about what comes

(22:14):
up sometimes as the faked mathindicators or these readiness
indicators, that piece rightthere, computational fluencies.
So when you think about canstudents add or subtract and
let's say with additionalsubtraction , um, it's a
continuum for computations. Andso when you think about the
computational continuum, youhave to think about where are

(22:36):
students in the space? How dothey have strategies that help
them with adding andsubtracting and doing problems
that involve additional andsubtraction so that they're
able to accurately andefficiently produce an answer,
produce a solution, develop a ,uh, a problem solution to a
problem that you put in frontof. So as you think about

(22:57):
whether or not you wanna say,yes, they're ready, or no,
they're not, and this is aplace where I need to slow them
down or not slow them down. Youhave to ask yourself that
question quite often with theseindicators I've seen in high
school or middle school, whenyou start to say algebra
readiness or students ready toquote unquote study the formal
course of algebra. Now how arewe gonna define that formal

(23:20):
course? It's often words like,my students don't know their
facts, my students don't havegood numbers since , well, the
questions that I ask in thosequestions, what we have to push
in on, and what I've pushed inon with teachers and teams is,
okay, tell me which numberfacts or what facts don't they
know , um, so that we can workon them . Oh, well , uh, and

(23:42):
sometimes they don't have theirmultiplication facts memorized.
They don't have those down pat. Sometimes it's their work
around fractions. And so wehave to dig in up underneath of
it . So what's important aboutfractions when we talk about
algebra readiness? Is itbecause they can't do the
operations or they strugglewith doing the operations or
they take time to do theoperations? Or is it because

(24:04):
they don't understand howfraction sense goes into
proportional reasoning? Andthat right there for algebra
readiness is more importantbecause when you don't
understand proportionalreasoning, ooh , that hurts you
later on when you start to talkabout slope and rate of change
and everything along thoselines, which have nothing to do

(24:24):
with the computations ofadding, subtracting multiple or
dividing fractions or have verylittle to do, I won't say
nothing because you use some ofthat skillset there also. So we
have to think about what wewanna label as those
gatekeepers that will keepstudents from progressing along
their math trajectory. They'rein a pre-K to 12 or AK to 12

(24:47):
math learning trajectory. Andso we really have to think
about how we can continue tomove students forward and build
their skills, their knowing,their depth of understanding
when it comes to content versususing these as stop gaps . And
the stop gaps might not be inthe way we design courses, so
we put 'em in this course orthat course, but it's about the

(25:09):
mindset that we as theteachers, we as those
supporting teachers bring intothe classroom. When we talk
about students, when we talkabout their skillsets , when we
talk about what they can andcannot do, and how do we shift
that language from talkingabout what they can't do and
what they don't have to, whatthey can do and what they bring
with that we can build from

Speaker 3 (25:30):
That . I love the way that you're framing that
it's not just about thestudents, right? What the power
that teachers and the educatorshave and taking the results of
a times test or taking whatthey're seeing, like you said,
as an indicator that they'renot ready, that power that they
have, and how can we helpteachers have a deeper sense of

(25:55):
where students are at or, ormore, maybe not deeper, but a ,
um, a broader look at whatmathematics can look like. It's
not just about the speed, it'snot just about this number on
the test. Like you said, my,that student may be able to
recite six times seven , youknow, they may have memorized
the verses to the fluencylyrics, right? But they mm-hmm

(26:17):
. don't have theunderstanding of what that
actually means. And how can youas a teacher use your knowledge
to help hone into like, whereis that, where's the actual
gap? Where's the actual spacethat they need support in?
Rather than just send 'em homewith more time tests or say
practice these flashcards more.

(26:38):
That feels really huge to me,and it feels like a, a call an
invitation to teachers.

Speaker 1 (26:43):
True. And, and Bethany, what you mentioned
about that space. So we have tothink about with our students,
we have to stop thinking aboutjust, I have them for this one
year is I have 'em from a oneyear and it's a handoff process
I'm getting them from andthey're going to. So that idea
of where's the space andwhere's the handoff and what do

(27:04):
I need to work on is reallycritical. Especially I will say
now here we are in 2023 and weare what, a couple of years out
of schools having responded tothe Covid pandemic. And we know
over the course of thatpandemic students had different
learning experiences, let'sjust put it that way. So we're

(27:25):
still thinking we need to stillbe thinking and still working.
We cannot have fixed all thedifferent things that happened
during that pandemic for somestudents who got richer
learning experiences and somestudents for which that
learning experiences was not asrich as we would like for it to
be. So we have to keep thinkingabout what's the vertical
nature of mathematics and howfrom year to year, especially

(27:49):
when it comes to, and I'll goto computational fluency, how
we go about building anddeveloping that computational
fluency from year to year. Sowhen you said teachers need to
step back and recognize wherestudents are so true, so true.
Because if this is where youare, that's where you are now,
how do I help you go to yournext? What's your next? And

(28:12):
that's the importance of meunderstanding the vertical
nature of how computation growsand develops for addition, for
subtraction, formultiplication, and I'll say
for division also. But reallyif you think about addition and
multiplication, those two areso powerful and lead into
algebra readiness. It's so keyand critical in elementary

(28:36):
school when you think aboutdecomposition of numbers versus
just going with this quoteunquote a standard algorithm
that we teach procedurallysometimes, but just
decomposition of numbers. Justone tens , hundreds, thousands
placed . And studentsunderstanding how to take a
number and and decompose itinto those three. And then
adding that, that sets them upfor later on when they're

(28:58):
simplifying algebraicexpressions, when they're
adding like terms andeverything. If I understand
constants , if I understandlinear and then quadratic
terms, I can equate that towhat we did with one's tens and
hundreds. And so this is theimportance of me as a teacher
and those who are supportingteachers providing that space

(29:19):
and time for vertical work tohappen that allows us to
connect with what they learnedearlier grades and how they
learned it. Now, I don't needto know all the problems in the
procedure , but I need to knowhow the conceptual
understanding was laid that ledto the procedural at that grade
level so that as I'm buildingin the later grades, I can

(29:40):
build from it . Multiplicationis another example. In third
grade, when you start tointroduce it, if you rush to
the fact fluency ofmultiplication, multiplication
facts and the procedural piece,which really is not really
quote unquote in many placesrequired until fifth grade, but
if I just rush at theprocedures, I overstep the

(30:03):
ability to use place value anda grid method in grade three to
introduce it. Well, it's a nicevisual, it also helps 'em with
place value. But then later onwhen I get to algebra and I'm
teaching multiplication ofpolynomials, if I use a grid
method there, the , theconnection of those two just
from what you did. I rememberworking with some third grade a

(30:25):
team at a school years ago, andthe third grade teachers sort
of wanted to skip that method.
And I shared with them where itgoes and said, you're laying a
foundation for later on whenI'm using algebra tiles to
really use algebra tiles or adifferent kind of manipulative
tool that visually shows them.
And I can easily just layer innumbers or algebraic

(30:46):
expressions. And so theimportance of understanding
where you begin and where someof the foundational pieces are
beginning in grade 3, 4, 5, andgrade one and two also, if
addition is attractionespecially and how that plays
up into the upper grades andprepare students with their
algebra readiness, it givesteachers something to build
from. No, as a high schoolteacher, I'm not gonna totally

(31:09):
activate prior knowledge fromdoing a one sense hundreds
addition problem, but I have,because the place value piece
is so critical withunderstanding the terms within
an expression.

Speaker 2 (31:21):
Yeah, definitely. I think it's really easy for me
as a teacher, like , uh, toimagine my grade is a silo or
the end of it is a is a gate.
And my job is to give studentseverything they need to get
through that gate. And it'sharder to see students as me
equipping students withresources that they will carry
with them through K to 12. AndI'm really curious, you've

(31:41):
mentioned several times aboutthis kind of this vertical
understanding of mathematics indifferent domains as being
really essential for helpingstudents develop fluency and
for not holding students backunnecessarily. I'm wondering ,
uh, we have administrators wholisten to this show. I'm
curious, do you have ideas forhow to create those moments of
vertical understanding bothwithin a building like say K 5,

(32:02):
6, 8, but also, and especiallylike across buildings, like
getting those K five teacherstalking to nine 12 teachers
saying, Hey, here's what we gotfor you. We're giving these
students this decompositionskills. If you know that's
there, draw on that. Don'tignore that. When kids get to
algebra and they're combininglike terms, are there
structures you put in placefrom your vantage point that
have worked?

Speaker 1 (32:21):
So some of the structures have been around
the, the teams that schoolshave built and developed.
Sometimes it's from aprofessional learning
community. Sometimes it's justfrom grade level teams.
Sometimes it's just , um,content teams. So when you
think about the opportunitiesto provide space for teachers
to grow in this area withvertical nature, you have to

(32:42):
set environments where , um,it's non-threatening. You have
to set an environment where allteachers, so let's go with AK
to five team. When they cometogether, you are bringing in
math that goes across the gradelevels and helping the teachers
see examples, problems, problemsets, and the strategies that
play themselves out. Especiallyif you're using a curriculum

(33:04):
resource. And I, I'll say thatbecause what you wanna see is
the design in the curriculumresource and how that's
exposed. Especially like in alot of , um, schools who are
using a curriculum resourcehave access to it online also.
So it's no longer this , yougotta give each teacher, say K
to five, you gotta give 'em sixteacher edition books for them

(33:25):
to see it, but also focus it.
So don't go try to do all ofthe domains in math in one
year, you know, focus this yearsay, or a year on, let's look
at the addition andsubtraction. 'cause
subtraction, additions sort ofgo together. But just look at
how addition and subtractiongrows and develops across our
curriculum. In AK to fivestructure, if you have a pre-K

(33:49):
to five curriculum structureacross that structure, what are
the key pieces that getelevated each year? So don't
talk about every single littlenuance. Don't go to like every
single lesson the way we tendto , um, take our curriculums
and lay it out and got ahundred plus lessons and this
many on this. But think aboutthe big idea of what's

(34:11):
happening at each other , thegrade levels. And so what's the
big idea of addition thathappens in K 1, 2, 3, 4, 5 ?
What's the big strategies thatwe elevate at that space? What
are the strategies that wespend more time on ? What's the
representations that are used?
What's the tools that are used?
So if we're using number linesin grade K or one or two, how

(34:34):
do we use that number lineacross the grade levels?
Because later on it goes fromwhole numbers on the number
line to fractions on the numberline to decimals on the number
line . So how does it show upand how do we as a teacher team
see it show up with just theuse of a number line? I'll just
use that as one tool. If we'rejust using a number line , how

(34:55):
do we work with that later onso that we're consistent? We're
building from not tearing downwhat teachers in prior grades
have done. And the reason why Isay pick one space, don't,
don't go pick multiple domainsto study in one year because
you say you gotta try to do itall by trying to do it all. You
get very little done , um, thathas meaning and that students

(35:17):
can hold onto that teachers canhold on to . So that's, that's
one, you know, when teachershave that time to really look
at the vertical nature ofadding numbers across K to
five. And then how do I take adocument? How do I create some
kind of resource? Maybe it's aone page or a two pager that I

(35:37):
can hand off to my middleschool so that they can see the
key strategies and how they'vebeen built and developed. And
how do I develop this If I'mworking as a system, how do we
develop a vertical tool thatshows from K to five additional
cross and where it grows sothat my high school teachers
can see, hey, here's where itcomes from, here's where it

(35:57):
came from, here's what theywere doing in elementary that I
can connect to, that I canbuild from, that I can
reactivate. And maybe the spacethat I reactivate is a space
where they were finding joy inmath, third grade, fourth
grade, second grade. Oh, wow.
They boom, a problem like that.
They found joy by the time theygot into middle school where
maybe their confidence startedto shake. They weren't finding

(36:20):
that joy again. And now thatthey're sitting in high school,
they're really like, man, am Ia doer of mathematics? Am I not
a doer? Mathematics? Sometimesyou gotta pop that back in with
a , Hey, this is a problemy'all did back in second grade.
Remember y'all did it with X,Y, z and this and that. Okay,
let's go. We're doing somethingsimilar. But now with algebraic
terms,

Speaker 3 (36:42):
It feels too like it's just so worth it. Like we,
as a teacher, I, I know howpressed we are for time and
especially when like, let's saywe have just a few meetings
with our team a week. If we'relucky, we get to see our team,
right? But if we focus, andlike you're saying, I think

(37:03):
you're inviting us to zoom inon something, let's say
addition and really understandthe story, the progression and
how that grows and builds. Likeif each teacher is holding
their grade level knowledge,but how much richer it'll be if
they're, like you said, able tosee the just, there's their
piece , a piece in the storybecause they're gonna get

(37:25):
students that come in at alldifferent points on that
trajectory, right? Yep . And sothat feels really powerful to
me as a teacher to think themore that I know about that
story, the more, even like whenI'm working with my students
with fluency, it's gonna changethe way I teach those
additions, subtraction,multiplication, division facts,

(37:46):
right? Mm-Hmm. .
Because now I wanna put it inthe context of a bigger story,
right? I want to teach them howthese number facts or being
able to decompose and composenumbers and use strategies, the
power in that, right? I feellike it's gonna really change
the way I teach my students.

(38:07):
And it's gonna mean hopefullywe're printing off less , uh,
you know , cutesy time testsand just saying, here, memorize
this. But instead we're weavingit into the story of
mathematics because it's onepiece and it can serve us well.
And like you said, or be agatekeeper, if we don't have
that,

Speaker 1 (38:26):
Bethany, the word story is , is key and critical.
We have to look at mathematicsas a story that we tell
students across the grades K to12. And what we are all is the
conveyors of a chapter in thisprogression of the story. If we
look at it as an isolatedchapter, then the question

(38:47):
really becomes, what am I doingto my students and for my
students? So if I'm, if I'mthat teacher and I gotta , it's
gotta be about me staying inthat space. And maybe that's
where my comfort level is atthis time. I invite you to
begin to grow a little bit, andI invite you to begin to look
at small chunks of it. Youmight think that students need

(39:07):
help in everything. Okay? Butwhat I would offer is that you
step back and say, okay, whereare my students' strengths that
I can begin to build from andthat I can begin to help them
with making more sense of thestory of mathematics that I
have to tell them this year.
And by building from thatperspective, it allows me to

(39:28):
continue to keep going if I'mtrying to build from your
deficits what you've beenstruggling on for years. Um, I
think even us as adults, if youtry to say, John , man, we're
going to help you be a , um,run five miles a day. And I
would say to you, yeah, okay,help. I would tell you after a
little bit of time, and if, ifI'm not sure what magic you

(39:49):
have, but I gotta find thetime, the space, the energy to
really want to do it. And ifI've been struggling at that
for a number of years, I'm notsure if I'm going to keep on
wanting to do it. And so ifstudents have been struggling
for a number of years orperceived that struggling, and
that's always the lens that wecome at versus a lens of, Hey,
here's what you can know,here's what you can do, man. I

(40:12):
like the way you were workingwith your number work . I like
the way when we studied thedomain of geometry, wow, you
really got a sense of spatialreasoning and you can really
push in on those parts. Hmm .
Okay. I , I see how you wereconnecting what we do in number
to algebraic thinking. And soI'm thinking about their
strengths in the content area.
Boom. When I elevate that I canbuild from that. When I elevate

(40:36):
your deficits, it's almostlike, yeah, you're strong in
this, but you can't do this.
And so which do we as adultstrigger to help us wanna keep
going and trying? I'm not sureif it's every time you turn
around you saying the, but youcan't, but you still can't do
this. That helps me keep goingand wanting to go. So you got

(40:57):
content strengths, you gotprocess and practices, and then
you even have dispositionstrength. That's , you have to
think about for your students.
And here's the hard part of allthis work. We often think we
wanna do it for all of ourstudents. And when we begin
trying to do it for all of ourstudents, I'm trying to figure
out logistically, how do I doit for this student, this
student, this student, thisstudent, da da da da da . What

(41:19):
I would offer you to thinkabout in some cases is how
about if I pick three students?
How about if I get pick threestudents to really begin to
understand what it means tobuild from their strengths and
asset-based approach. How toidentify what their strengths
are, how to think about how Iactivate prior knowledge based
on their strengths, how I usetheir dispositions to help them

(41:43):
grow. 'cause if I can figure itout for three, then I can begin
to grow it more. But it's, howdo I go about figuring it out
first with a , a manageable waythat I can do it. If I'm an
elementary teacher, I got 20students, 30 students, and I'm
trying to do it for all 30, itmight become overwhelming, let
alone once I move up intomiddle school and I've got, or

(42:04):
if I'm content specific inelementary school , fourth
grade, fifth grade, quite oftenyou see that happening and I've
got all the fourth graders, andmaybe that might be a hundred
of them . You're asking me todo something for a hundred
students. Hmm . Can I do it forthree students first? I think I
can,

Speaker 2 (42:21):
We talked a lot about asset orientation and
various , uh, episodes of thispodcast, and you've talked
about the ways that we canartificially and incorrectly
label someone or something notgood enough, right? And I think
your description of , uh, therunner and the teacher I think
are a great moment to drawthose ideas in where like,
someone you would not wanna seea running coach say to someone
like, you are a runner if, andonly if you are able to run

(42:43):
five miles. Like that coach isgonna be looking at like, okay,
so what do you got? What areyou bringing here? Like, can
you do, can you do four laps,two laps? Do you have like
grit? Do you have, are you ableto like, push through those
moments? You feel absolutelygassed? Mm-hmm .
And in the same way a teacherlistening might say to
themselves right now, oh, likewhat we're talking about here.
Like that's, there's the goodteachers and then there's the
other teachers. And I'm not , Idon't know if I'm one of the
good teachers, but what you'redescribing here I feel like is

(43:05):
interesting to me of likefiguring out what you've got on
a smaller scale before thensaying, okay, like the , like
the , the three kids is, youknow, the two laps, so to
speak, around the track and thefive miles is like the entire
class. And we can just easilycommunicate to ourselves a
deficit orientation of who weare based on the enormity of
the challenge, challenge atfull scale . Anyway , it's just

(43:26):
been a fantastic to chat withyou about all these ideas at a
system scale. Before we go, isthere a final thought or idea
you'd like to leave withlisteners?

Speaker 1 (43:36):
I think two things.
One thing is this idea of wheredo I begin? Especially let's
start thinking about my studentstrengths and building from
there , um, is the first for usto look in the mirror and look
at our beliefs when it comes tocomputational fluency. And when
it comes to this idea of factfluency and, and what are our
beliefs around it . Quite oftenwhat we are doing is what we've

(43:57):
learned and what we believe in. And I'm gonna say beliefs .
Sometimes it's what we've seenfor some students, for pockets
of students. But when we lookat those students who have not
been successful, take a quicklook at that, take a deep look
at that and identify your ownbiases. When it comes to, oh,
if a student by this gradedoesn't have this, they can't
spit off their facts. What doesthat mean? Well, what does that

(44:20):
really mean? And so think aboutthose biases and think about
how we look at students and howwe speak about our students and
what role does speed come inthere versus not come in there.
So that's one piece. The otherpart is really go and take some
time to gain an understandingof computational continuum, the

(44:42):
computational fluency acrossthe grades. I think that part
right there helps you at anygrade level, K to five, six to
eight, nine to 12, understandwhere the math is coming from
and where the math is going.
Why don't I teach certaintricks? Because I know those
tricks don't work when they getto X, Y, Z. And so think about

(45:03):
that and enroll and, and workthere as you keep going and
think through things. And justreally the bottom line with
fluency and everything relatedto fluency, I think we have to
really be critical of ourselvesand think about what impact
does it have on students' senseof identity as math doers, you
know, their self-confidence.
What does it do to them When wethink about and how we execute

(45:27):
our work with fluency, be itfacts. And I'm gonna keep going
back to facts because I thinkthat's the a piece that
automaticity piece is somethingin there that people speak
about with fluency, butcomputational fluency. So how
does it impact theirself-confidence, their
identity, and then their senseof agency, their willingness to
show you what they know andthey can do in multiple ways.

(45:49):
And I think that's the biggestthing. The bottom line message
is fluency will impactstudents' identities and
agencies as math doers. Thequestion we have to ask
ourselves is, and as we watchour students grow across the
years, when does it start tochip away at their
self-confidence? And when doesit continue to help coat their

(46:11):
self-confidence and build iteven stronger? And how do we
shift our process from a, inmany cases, identifying
struggling students, a deficitmindset to more of a strengths
base in a assets-basedapproach? So I'll leave it
right there with that.

Speaker 3 (46:26):
So wonderful. You have such a perspective, you're
able to zoom in, but you'realso able to give us that
bigger picture and help us seethe importance, like you said,
of that vertical understanding.
We really, really deeplyappreciate your time and your
perspective. I think it'sreally gonna help us and
hopefully our listeners, likeyou said, to look in the mirror
and to help reframe the waythat we might be thinking about

(46:48):
it and if we're subconsciouslyor not using that fluency as a
gatekeeper. Thank you so muchfor your time, Dr. Staley .
John. Well thank , thank you ,

Speaker 1 (46:59):
. Thank you, Rob . Thank you for the
opportunity to share.

Speaker 3 (47:05):
Dan , I am so happy that we got to hear Dr . Sta ,
John , that we got tohear his perspective on this.
It also reminded me like,because sometimes I think when
folks think about that verticalunderstanding of like
mathematics, for me anyway, itcan start to feel really
overwhelming, right? Like,there's so much to know, how do
I learn? But it's also aboutthat zooming in, right? On

(47:28):
those particular topics. And itmade me think of like how Val
said, like, where is gonna havethe most impact? So she was
talking about if we're focusingon doubles, well that's only
gonna get you so far. But ifwe're really thinking about
like 10 compliments and we'rethinking about decomposing and
composing 10 and working with10 , like the power that's
gonna have over the course of astudent's mathematical career,

(47:52):
right? Talk to me Dan.

Speaker 2 (47:54):
Yeah. The vertical continuum, that kind of work
was really interesting to me aswas this idea that as you get
higher up into like middle andhigh, maybe even elementary, it
feels, I think like easier tosay kid doesn't know it.

Speaker 3 (48:08):
Yes.

Speaker 2 (48:09):
In ways that like, especially with fractions for
instance, it's like the kidsjust don't know 'em , you know?
And it's like, well, I , Iappreciated John's, you know,
broadening of that perspectivesaying no and doesn't know
that's a binary lights , whichkind of measure. It's more
like, what do they know? Andthere's some things that you
don't know, like the operationswhich can be developed
throughout, for instance,algebra. Whereas ideas of scale

(48:31):
and proportionality, if youdon't know those, that's gonna
create some real fundamentallimitations, right? So I just
appreciated that. I , I , I canthink at elementary, I just
find it hard to imagine ateacher saying, ah , that kid,
you know, doesn't know number.
It's like, well, no , there'slike a lot going on there. So I
, I appreciated the check onmaking that kind of binary
evaluation of a thing that'sreally a continuum and a and a

(48:54):
very vast space. So that wasvery interesting to me.

Speaker 3 (48:57):
But I think that is happening kind of more often
than we think that like, evenhe was talking even like third,
fourth, fifth, are we, yeah .
Are we already starting to saythat about students? Oh , they
don't understand that, or theydon't get that, right. And one
other thing that I wanted toflag too is the way that he
was, I can just imagine himtalking to teachers and to
students and just that assetlens of like, pulling from what

(49:19):
they already know to say, well,you know this, well then yeah,
use that to solve this as ateacher, I wanna be able to
facilitate those connectionsYeah . And help students see
this bigger picture ofmathematics and how it plays
together. And I, I just, what arich conversation and I'm, I'm
really, really glad that we hadthat opportunity. And I wonder

(49:42):
what would happen, Dan, if youasked your kiddos like, sure,
I'll time you, but why? What,what do you wanna be timed for?
Tell me more. Like, why are wetiming? Tell me, you know, and
just see what they say. What doyou think about that, Dan ?
Mm-Hmm . .

Speaker 2 (49:54):
Yeah, they , uh, they , they already, they're
starting to roll their eyes atme . Like, I don't dunno who
taught them that , butI'm getting some, I'm getting
some periodic eye rolls and Ican definitely see some eye
rolls happening there, but I, Imight give it a try. It hasn't
happened a whole lot, the wholetiming request. But I'll , I'll
keep you posted. Believe me,I'll keep you posted. Just
wanna say to you all out there,thank you for listening to our
conversation with Dr. JohnStaley, coordinator, our

(50:16):
special projects with theBaltimore County Public
Schools. You folks can checkout the show notes for links to
connect with Dr. Staley onsocial media here and there. Um
, get in touch with us byjoining our Facebook discussion
group, math Teacher loungecommunity. And I tell you next
time on the show, we'rebringing you a special episode
that I recorded at NCT nm , theNational Council of Teachers of

(50:36):
Mathematics annual Conferencewith Dr. Jennifer Bay Williams.
It's all about games, games,more games, and using games to
develop fluency in particular.
Here's my question. It's anannoying one to start with here
to debrief this. But like, whatis a game? You know,

Speaker 3 (50:52):
Make sure that you don't miss the special episode
recorded at NCTM or any otherepisodes in this season. And
you can do that by subscribingto Math Teacher Lounge on the
podcast platform of yourchoosing . And, you know, while
you're listening, go ahead andwe hope you'll leave us a
rating. Let us know what youthink and let other folks know
what you think of the show. Ifit brought value to you, we

(51:14):
hope you'll share it with , uh,educator in your life. You can
find more information on allthe Amplify shows at our
podcast hub . Go toamplify.com/hub. Thanks so much
for listening.

Speaker 2 (51:25):
Bye.