October 4, 2023 • 36 mins
Tune in to our latest episode where we sat down with Dr. Valerie Henry to discuss how math fluency assessments can be redesigned to provide teachers with better data and students with better learning experiences.
Listen today and don’t forget to grab your MTL study guide to track key strategies and make the most of this episode!
For more from Valerie, check out the following resources:
- Learn more from Val and check out her resources on her website FactsWise.
- Dive deeper into fluency with Val and read her blog post Timed Tests – NOT the Way to Build Facts Fluency and NOT the Way to Assess Facts Fluency
- Tune in to Math Teacher Lounge Season 3 Episode 4 to hear Val’s previous conversation on building fluency.
- Join us in the Math Teacher Lounge Facebook Community.
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Dr. Valerie Henry (00:00):
I think assessment and evaluation are
two different things.
Evaluation is often where weput a number to something and
we try and give it a grade.
Assessment is where we'retrying to understand what
students are thinking. And, Ithink they're very different
animals.
Bethany Lockhart Johnson (00:19):
Hi, and welcome to another episode
of Math Teacher Lounge. I amBethany Lockhart Johnson .
Dan Meyer (00:24):
And I am Dan Meyer.
Bethany Lockhart Johnson (00:26):
Dan, we're in fluency land! How you
doing? How you doing?
Dan Meyer (00:30):
I'm getting more and more interested in it. Every
new guest we talk to gives mesome new angle on fluency that
helps me see what an importantpart it is of a student's
development of new ideas, and,I'm also, in my own personal
life, getting excited to seefluency kind of bloom , with
the—
Bethany Lockhart Johnson (00:45):
Wait! Say more about that! Back that
up!
Dan Meyer (00:48):
I'd be happy to; thank you for asking. Yeah,
I've been noticing one of mykids does direct counting no
matter what the sum is. Fourplus three, I'm gonna start at
one, two, three ... seven. Or10 plus 12 — I'm going all the
way back to one, gonnadirect-count that thing for the
first 10, then the next 12. AndI find it more fascinating now.
(01:11):
So, what are the experiencesthat he needs to be able to see
the value of just like, no ,just say, "Hey, here's 10. I'm
here at 10 and now count up 12more," let's say. And , I've
seen the limitations of justsaying, "Hey, do this. You
should do this thing." Well, no, kids' i deas just take longer
to —
Bethany Lockhart Johnso (01:30):
You're not doing that, Dan. You, Math
Teacher Dan, are not tellingyour child, "No, no, no. Solve
it this way."
Dan Meyer (01:38):
No, there's no way to do that! I haven't tried it.
But there's just futility wherethe kid's just not ready for
it. Whatever's going on in hisbrain is so much more powerful
and durable than any words Iwould have to offer. However, I
have been offering variousexperiences — for instance,
this game that we call"Garbage," that has five cards
(02:01):
on top in a row and five cardson bottom in a row. And the
kid's gotta find seven. Atfirst he'd count one, two th—,
five, six , seven, with hisfingers counting. But,
recently, we've had enough ofthose experiences where he just
starts at six. He just says,"That first row is five; I know
this now." Or he's even startedat 10 and gone backwards. And
(02:22):
so, to me ... it's a mystery.
It is a mystery; I love a goodmystery, love a movie mystery,
a book mystery, love a mathmystery. Like, how are these
ideas taking root in his head?
That's where I'm coming fromwith fluency this week, and
kind of excited to talk moretoday about it with you.
Bethany Lockhart Johnson (02:37):
I love hearing that. And, sorry I
jumped on you a little bit,because I thought you were
saying, "No matter how manytimes I tell him that's not how
you do it, he keeps doing it!". What? Who are you ?
Dan Meyer (02:49):
I'm like, "You won't get dinner. There's no dinner
tonight for you.".
Nope. You're gonna startcounting-on if you want a treat
. Yeah, you know me.
Bethany Lockhart Johnson (02:55):
Let me tell you . But, what I love
is that you're giving himrepeated experiences to
practice building thatrelationship with those
numbers, because that isexactly what we celebrate in
our classroom. Right? "Ooh,what if we do this?" And now he
gets it. He sees that five.
Right? Eventually, well, sure,you can keep counting up to
(03:17):
five, but eventually he won'tneed to. He is like, "OK, five,
six, seven, eight." Or, what ifyou give him some larger
numbers? Something like 32 plustwo. He may start at one — I've
seen it — and go all the wayup; but maybe he would hold
that number, that large number,and then count on. But, I could
(03:39):
sit here and tell you—
Dan Meyer (03:40):
You can't help yourself, can you?
Bethany Lockhart Johnson (03:42):
I can't help myself. Because I
love this—
Dan Meyer (03:42):
You're like , "What's the next thing?"
Dr. Valerie Henry (03:44):
—so much! I love the way students think. My
kiddo's two and a half, and I'mnot forcing the
counting, but I do give ampleopportunities for counting. I
love counting with my kiddo andexploring different concepts in
math. But, I think we need moreof this, Dan. We need more of
(04:06):
you sharing what is going on inyour household as your kiddos
are beginning to developfluency.
Dan Meyer (04:13):
Oh, I am game.
Bethany Lockhart Johnson (04:15):
I'll take a daily report.
Dan Meyer (04:16):
The real win of it all is that they ask to play
this game. They don't know thatthey're learning math. So yeah,
I love talking about this withyou. It's grown on me. And I
love the guests that we bringon, and the perspectives they
bring to bear on fluency. Andnone more so than Dr. Val Henry
today.
Bethany Lockhart Johnson (04:37):
If you love talking to our guests,
you are really going to lovetalking to Dr. Val Henry again.
We spoke with Val a few seasonsago about fluency in a shared
episode with Tracy Zager andGraham Fletcher, getting a
couple different perspectiveson fluency. But, today, we are
talking to Dr. Val Henryspecifically about assessment,
(05:00):
but I'm sure the conversationwill run the gamut. She is an
amazing, dare I say, expert onfluency. She's been thinking
about this for decades. Andshe's done research about it,
and developed a program calledFactsWise that I've used in my
own classroom. And she also isa university professor at the
(05:21):
University of California,Irvine, teaching pre-service
teachers and helping themdevelop their relationship with
math as they dive into theirfirst classrooms.
Dan Meyer (05:29):
So I hope you folks enjoy this interview as much as
we did with Dr. Val Henry.
Bethany Lockhart Johnson (05:37):
We are so thrilled to have you
back, Dr. Henry. Welcome, somuch, again to the Lounge.
Thank you so much for joiningus again.
Dr. Valerie Henry (05:47):
Thanks Bethany. And Dan. Thank you
both for inviting me.
Bethany Lockhart Johnson (05:51):
Oh! Did you hear that?
Dan Meyer (05:53):
It was like a dot, dot, dot. It was a very short
pause. I'm happy with how thatwent, honestly. Yeah.
Welcome back, Dr. Henry.
Dr. Valerie Henry (06:00):
Thank you.
Bethany Lockhart Johnson (06:01):
It's actually kind of appropriate,
because we recently chattedwith Jason Zimba, who we were
really excited to get a peekinto his brain and how he
thinks about fluency andmathematics in general. And, I
(06:21):
worked on Dan a bit, becauseDan's been a little less than
enthusiastic about fluency. ButI'm telling you, ever since we
had you on the show, we've hadthese questions buzzing around
about fluency. And it keepscoming up. And we knew we had
to have you back. And, in fact,you're really the inspiration
for this whole season. ... Dan, before we ask any questions,
(06:45):
share a little bit, just togive a little framework about
your perspective, because Ithink it's good she knows what
she's getting into.
Dan Meyer (06:52):
Sure, that's fair. I do feel like you're asking me
to share with Val what it is Ifind uncomfortable a bout the
work of fluency that she'sinto, but I'll just go with it.
As a math educator, I've alwaysbeen really excited about
introducing the new. I've beena little bit less excited about
fluency. Especially because Ithink a lot of the way fluency
(07:12):
is developed in studentsnowadays constitutes a lot of
people's negative memories ofmath class. I don't w anna
associate fluency completelywith those bad vibes, but
thinking about the endlessworksheets or Mad Minutes, or
just those kinds of traumaticexperiences, a lot of them have
been in the fluency realm. Andso I've been a little bit ...
(07:33):
cold to it, let's just say.
Bethany is warm to fluency; Iwo uld s ay warm-to-hot. And
I've really enjoyed talkingwith Bethany about how to
develop math fluency in kids,especially as we both have
really young kids, and thinkingabout how they develop those
ideas. So , I wanna believe. Iwan t to be a believer here.
So, I'm excited about thisseason, excited to have you on
(07:55):
the show.
Dr. Valerie Henry (07:56):
Well, Dan, I have to tell you, I was
cool-to-cold about fluency 20years ago. So I'd been doing a
lot of professionaldevelopment, a lot of it around
algebraic thinking back inthose days. And I'd go out and
work with teachers and withstudents, and the teachers
would say, "But we can't doalgebraic thinking with our
(08:19):
kids, because they're notfluent."
Dan Meyer (08:23):
They don't know the basics.
Dr. Valerie Henry (08:24):
Or, I'd work on problem solving. And they'd
say, "They can't do that,because they're not fluent."
And I'd go in, and I'd sort ofshow them that kids can do a
lot of great math thinking,even if or before they're
fluent. So I was reallyresistant to this; but every
single upper grade teacher thatI talked to brought up fluency
(08:46):
as a roadblock. So when I wentback to school to get my Ed.D.,
I decided that I would reallyinvestigate this. What is going
on with this? And so bylearning about how other
countries really do a betterjob often with fluency teaching
and learning, I decided maybeit was worth looking at from a
(09:10):
different perspective thanworksheets or timed tests, that
kind of thing, so that we couldget away from those negatives.
Dan Meyer (09:17):
I appreciate that background enormously. I feel
like we have a new kinship, youand me, here . It does
resonate with me that the newstuff that excites me is often
much more challenging tostudents if they struggle with
some of those basics. If theystruggled with prerequisite
skills, foundational skills,... I don't know what word
(09:39):
would be most appropriate here.
But that as a mission, as yourdesire to understand those
skills, because they supportthese other skills that also
interest you, that's a helpfulroute in for me in this
conversation. Whatever that'sworth. Thank you.
Dr. Valerie Henry (09:54):
Cool. I'll also say one more thing that
has really stuck with me overthe years. I had a teaching
assistant who grew up in China,I believe, and learned her
early mathematics in China.
Very fluent in English, so shewas helping me with a graduate
(10:16):
course. And I said, "One of thethings we're gonna be looking
at is basic facts fluency." Andshe said, "Well, what's that?"
And I thought, "OK, maybe shedoesn't understand the word
fluency." So I explained thatand she said, "Yeah, yeah,
yeah; I get that." And then Isaid, "Basic, like between one
(10:36):
and 20." And she said, "Yeah, Iget that, but why are you
calling them facts?" And Isaid, "Well ... because ..."
and she said, "Well, let meexplain. In China, when we grew
up, we learned that one plusone was two, and then
everything else was arelationship that was built off
(11:01):
of one plus one is two. Theyaren't facts; they are
relationships, and areprovable." She said, "Facts are
things that you can't reallyknow unless somebody tells
you." So I'll just share thatas an insight that I have into
this whole language of basicfacts fluency. I hate to call
(11:23):
it that now, but that's what Ithink a lot of people
understand what we're talkingabout when we reference it that
way.
Bethany Lockhart Johnson (11:29):
This is really a helpful
perspective, Val, and ... I'msaying Val—
Dr. Valerie Henry (11:34):
That's fine.
Bethany Lockhart Johnson (11:35):
Dan, you continue to call her Dr.
Henry.
Dr. Valerie Henry (11:38):
I'm way more comfortable with Val.
Bethany Lockhart Johnson (11:41):
It was my joy to get to learn from
you at University ofCalifornia, Irvine. And, I felt
like the way that youapproached your pre-service
teachers was like you werehelping us to heal our
relationship with math. Andsomething that I learned from
you was really a new way tothink about assessment. And
(12:04):
when we think about fluency,people have been jumping in
with, "Well, timed tests."Right? Or, we gave the example
of like, Teachers Pay Teachers.
They pull up a themed timedtest; and, therefore, if I give
it to you every Friday, you'regonna get it. And I know some
of your research has beenspecifically why timed tests
are problematic, why they don'twork. Right? Why they aren't
(12:25):
enough. But, you had a biggerpicture of assessment. And I'm
wondering if you could share alittle bit about that.
Dr. Valerie Henry (12:33):
So, when I was growing up, teachers often
thought that assessment woulddrive students to become
fluent, without really anythingelse happening in the
classroom. Maybe an occasionalworksheet, maybe an occasional
around-the-world kind of game,or something. But most of the
(12:55):
time it was assumed that youwould go home; you would
somehow learn those basic factson your own; and the testing
would compel you to keepworking at it at home. So
assessment was sort of seen asa force that would require kids
(13:18):
— that would compel them — tomake sense and become fluent.
My theory is — and this is whatwe do in every other subject —
we teach the subject to thestudents, we work with them, we
give them learning experiences,and then we assess. To find out
(13:41):
how far they've come towardsmeeting the learning goals we
have. And the assessmentdoesn't happen without the
learning experiences in theclassroom. And I often talk
with my student teachers aboutthis: We would never think
about saying, "Go home andlearn how to read and we'll
just test you every Friday;and, therefore, you will learn
(14:03):
how to read." So I don't seewhy we're doing that with math
fact fluency. It's sofoundational to mathematics,
and it gives everybody such asense of confidence and number
sense. Why are we assuming thatwe shouldn't be teaching it ?
And so when I say teaching, Idon't mean lecturing; I mean
(14:26):
providing learning experiences.
Dan Meyer (14:29):
You're describing a diminished sense of what
fluency is. If it is possibleto teach it just through
assessing it, that implies adefinition of fluency that I
think the rest of your workspeaks to the opposite idea.
That it is rich, requirespersistent development on the
part of a teacher, work fromthe student. That's just an
(14:53):
interesting dichotomy that nowwe're moving into this other
way of thinking about fluency.
Dr. Valerie Henry (14:58):
Yes. And I think it goes directly back to
the idea that if we thought offluency as learning facts,
things that could be put into asong, or things that could be
chanted, and that could belearned just through verbal
memory, then we thought of itas something that you could
(15:20):
just test over and over. But,if we think of fluency as these
relationships, and findingstrategies that can make
connections between somethingthat we know ... like, I know
two plus two is four, sotherefore I can use that to
help me figure out that twoplus three is five, without
(15:41):
having to memorize two plusthree is five on its own,
without making connections.
Bethany Lockhart Johnson (15:49):
I'm curious if you can talk about
what has assessment looked liketo you in your research, where
you were able to really seethose relationships students
were building with thesenumbers, with these facts? And
how is that maybe differentthan what we wanna get away
from ?
Dr. Valerie Henry (16:08):
Absolutely.
So, when I first startedreading the literature about
fluency, one of the things Irealized was that the
psychologists who actuallyspecialize in studying the
challenges of fluency inmathematics do one-on-one
assessments. So that they canreally hear students not only
(16:32):
say the answer correctly orincorrectly and they can get a
sense of how long it took themto come up with their answer,
but they also get to ask themthis really important question.
Which is, "How did you get thatanswer?" And so, one-on-one
assessments are so differentthan timed tests, in a couple
(16:56):
of different ways. The firstone is that you actually find
out how fluent — I'm gonna moveaway from whether or not
they're fluent — but how fluentthey are with the fact, with
the math problem. As opposed toon a timed test, which
typically has 20, 50, or a 100problems. And students
(17:22):
completed it and you have nounderstanding of how they
completed it. Whether they wereskip-counting on their fingers,
whether they were jumpingaround and going, "OK, five
times seven is 35, so now I'mgonna look for seven times
five, because now it's in myshort-term memory, and then I'm
gonna do 35 divided by sevenand 35 divided by five," all
(17:47):
without really having beenfluent with any of those. Just
capitalizing on skip-countingand short-term memory. So, 1:1
assessment taught me a lotabout how to really understand
what's happening with students.
I'm gonna stop there, becausethere's a whole other picture ,
(18:07):
which is, is one-on-oneassessment practical in the
average classroom on a regularbasis?
Dan Meyer (18:14):
Something I wanna say I love about the one-on-one
assessment idea is that I thinkit's something so radicalizing
for a math teacher, to becomeaware that students have
interesting ideas all the time.
Even if those ideas don't fitinto really precise boxes. Like
(18:36):
the sort that are expressed ona timed test. And it sounds
like these 1:1 assessments dida lot of work on you to help
you see that, "Oh, what's goingon in the development of
fluency is much moresophisticated than a lot of the
timed test assessments I gavecredit for." I'm just curious,
what were a couple of the bigtakeaways that you had as you
(18:58):
did these 1:1 assessments?
Dr. Valerie Henry (19:00):
I've done thousands of one-on-one
assessments with students fromkindergarten all the way
through eighth grade, and,well, actually, even higher.
And, one of the things that hasreally resonated with me is
that students do come up withfairly similar strategies.
(19:21):
Either because they've inventedthem themselves, or because
they've had learningexperiences that have helped
them develop these relationalideas. So when I ask a student,
"What's six plus nine?" there'susually a small handful of
(19:42):
different strategies thatstudents will tell me about.
One is they just know it.
Another is that they counted ontheir fingers. Or in their
head. Which is not quite atfluency level for me yet. But,
then the others are thingslike, "Well, I gave one from
the six to the nine and thatmade 10; so now I have 10 plus
(20:03):
five." Another is, "Well, Ijust temporarily added 10 to
six, that was one too many, sothen I subtracted one." It's a
little bit different strategy.
Another is, "I might havethought of it as seven plus
seven plus one." And then I'vehad one first grader ever say
(20:26):
that he knew that that fourplus nine was 13 and that he
just needed to add two more toget to 15. Nobody else has ever
come up with that idea! Justthat one little guy. So, yes,
you do have a lot of studentscapitalizing on making tens,
sometimes using doubles, andsometimes using a fact that
(20:49):
they knew that just helped thembuild relationships even if it
wasn't one of the standards.
Dan Meyer (20:55):
So these are really interesting ways of thinking
that aren't visible to teachersfrom a worksheet or printed
timed test , where there's anumber and maybe some scratches
where students carriedsomething. Or something like
that. And you're describingwhat's visible to you, what's
present in these one-on-oneinterviews. I wonder what's
(21:15):
possible, though, in thelogistics of a classroom?
You're able to do this as aresearcher or a consultant. And
I'm curious how you'd helpteachers who have different
logistical demands than you d oi n your role. How can they
capture the best of yourone-on-one assessments within
the constraints of a classroom?
The time constraints, thestudent constraints?
Dr. Valerie Henry (21:38):
There are a couple of different ways that I
think about this. One is, whenI wanna understand what
strategy students are using, Iask them to share their
thinking. Either in the smallgroup setting or in the whole
class setting. I usuallyalternate a little mini lesson,
(21:59):
where we do something usuallywith manipulatives or some kind
of visual on the board, withgames. And even when the kids
are playing the games, I willoften ask that the students
share their strategy thinkingas they're responding with
their answers. So, they mightbe playing a little card game,
(22:22):
where they have the nine faceup on the table and they'll
pick up another card and it'llsay four plus nine. And they'll
say, "The answer's 13," andthen their next job is to
explain to their partner howthey got 13. That's one way
(22:42):
that, as I'm circulating theroom, I get to feel like I'm
hearing what's inside theirhead. Even though I'm not doing
a one-on-one assessment withthem. And I work with teachers,
then, to use that same kind ofapproach for hearing students'
strategy thinking. Sometimesthey're actually showing it
(23:03):
with a manipulative, inaddition to or instead of
verbalizing it. So we oftenhave them use number racks or
10 Frames, depending on whetherwe're doing add/subtract or
multiply/divide. Themanipulatives change a little
bit, but they're sharing theirthinking either verbally or
with the manipulatives.
Dan Meyer (23:26):
I love that you're talking about teachers becoming
sensitized, through all theirsenses, to the different ways
that students are developingfluency, even verbally,
non-verbally, throughmanipulatives. And there's
something that's so specialabout that, where a teacher
becomes like a fine-tunedantenna for all the different
ways students are being smartand fluent in class. I don't
(23:46):
wanna diminish that by asking,"But what about the logistics?"
But I'm kind of curious. As ateacher is moving around, and
is assessing students in a veryreal way, while students aren't
even really aware that they'rebeing assessed, how should the
teacher make good use of thatdata to support the student's
development? I know what to dowith the timed test that has 19
(24:09):
outta 20. I put the 19 in mygrade book. But what are some
productive ways to use all ofthat data, sensory data almost,
to support a student?
Dr. Valerie Henry (24:19):
Great question. And my top
recommendation for that is totake a class list, make some
columns on your class list, andstart writing in some things
that you are interested inlooking for or looking at. So,
if I were working on addingnines, let's say, I might write
(24:40):
in, "Student uses plus 10," or"Student makes a 10," or
"Student uses a doublesapproach," or "Student counts
with their fingers," "Studentcounts in their head." I might
list all of those at the top ofthose columns. And so as I'm
walking around, I'm able tojust start making a quick check
(25:03):
mark, maybe having some roomover on the side so that I can
write a note if it's somethingunique that I wanna attend to,
and I can start then lookingafter that one 10-minute
session, or a few 10-minutefluency sessions, I can now
look at my chart and see, "Wow,a lot of students are using
(25:23):
plus 10, but I've got threethat are still counting on
their fingers." So now I knowthat there are three students
that maybe need some extrasupport, maybe need some extra
time with a manipulative, tohelp with that. I can also see
that the majority of mystudents are building fluency
(25:44):
quite easily with their plusnines. So, we can start moving
on to the minus nines, ifthat's the approach we're
taking.
Bethany Lockhart Johnson (25:53):
I wanted to say, Val, just how
much I respect and appreciatethe way that you listen to
students. And, for me, that iswhat this assessment kind of
all boils down to. You areteaching students to think
flexibly about numbers. You'redoing these routines, and these
games, and these share-outs,and spending time supporting
(26:18):
students in having experienceworking with these numbers. And
the assessment is just a pieceof that. The assessment comes,
like you said, during the gamesas you're walking around, or
during a share out after thestudents are playing the games.
But, really, I hope that ourlisteners are taking from this,
like Dan said, using yoursenses as a teacher, how much
(26:40):
you are listening to students.
I know you did this as yourresearch. But you just so
respect students' thinking. Andthat is something that I think
is so powerful. And so,assessments weren't just
something to squeeze in thereand then you don't do anything
with what you find. You'rereally listening to them and
(27:01):
valuing their thinking.
Dr. Valerie Henry (27:03):
I think that's such an important
perspective about assessment.
Because I think assessment andevaluation are two different
things. Evaluation is oftenwhere we put a number to
something and we try and giveit a grade. Assessment is where
we're trying to understand whatstudents are thinking and able
(27:25):
to do, what they need supportwith, what they're ready to
move on from. And I thinkthey're very different animals.
And so, putting a number on apiece of paper doesn't help me
know what to do next with mystudents. But listening and
engaging with them does let meknow what's the next thing that
(27:48):
I can do to help them.
Dan Meyer (27:49):
Yeah, what you're describing to me has much more
in common with my asking afriend, "How is your
day-to-day?" than any kind ofmath assessment that I think a
lot of us are familiar with.
You're seeking to understand.
It's conversational. I likethat distinction between
assessment and evaluation. WhenI ask, "How was your day?" I'm
not trying to evaluate youranswer in any way , just
(28:10):
understand you a little bitbetter.
Dr. Valerie Henry (28:11):
Definitely.
So I have had teachers askwhether this writing things on
a chart as I'm listening, or aswe're circulating around
watching students, is goodenough to put on a report card.
And so I've asked a fewprincipals, "What would you
(28:33):
think if your teacher stoppedgiving timed tests, or stopped
grading worksheets, and didthis approach of listening in
and understanding wherestudents are in their thinking
and marking it down on a pieceof paper? Would that be good
enough in terms of reportingback to parents how students
(28:55):
are doing on a report card?"And at least the principals
that I've talked to have said,"Absolutely! That's a
completely responsible way ofgrading fluency, if you have to
grade it."
Bethany Lockhart Johnson (29:09):
Val, I was in an Uber in Colorado
and I thought of you. Becausethe Uber driver was like, "Oh,
what do you do?" We weretalking. I was there for a math
conference. And her firstreaction was, "Ugh!" She's
like, "A conference where youjust talk about math?!" And
then she immediately launchedinto, "Oh, I hear those
(29:30):
standards they're asking kids... that's not even how kids
think." She went into thiswhole thing, and she's like,
"What is it even all about?"And the first thing that came
to mind, I said, "Well, if Iasked you to add what's nine
plus seven?" And she said,"16." And I said, "Well, how
did you get that? You got thatpretty fast." And she said,
(29:52):
"Well, I don't know, I guess Itook something from the seven
to make it a 10, and I made 10plus six." Right? And I said,
"That's it. Yeah, exactly.
That's it. Right? You brokeapart those numbers. You're
thinking about those numbersflexibly; that's what we want
to happen in our classroom,that our students feel like
(30:14):
they can manipulate numbers,and think about it in new ways,
and share their thinking." AndI tell you, Val, I was thinking
of you when I asked her that,and I think she gave me a
pretty good rating as apassenger, if not for that
story . No, but forreals though, it was a really
good reminder for me that somany of us have these negative
(30:36):
experience with fluency, withmathematics, with assessment.
Right? And when it'sconversational, and when it's
just a part of like, "Let'stalk about this. What went on
in your brain? How are youthinking about it?" It can be
really positive.
Dr. Valerie Henry (30:51):
What's really fascinating is that
students love to talk abouttheir thinking. And they feel
very special when the teacherlistens to them individually.
Sometimes we can listen to themindividually by doing a
one-on-one assessment.
Sometimes we can just interruptthe little activity or game
(31:15):
they're doing with a partnerand say, "I just would love to
hear how you thought about thatone; I wanna know." And so, the
logistics, kind of back toDan's question of one--on-one
assessment versus thiscirculating as students are
(31:35):
interacting with themathematics, usually with a
partner, is that you caninteract one-on-one with the
student for 10 seconds and theyget that same sort of
validation, and you get to hearwhat they're thinking. Or you
can spend five minutes withthem doing a full-on sit-down
(31:56):
with one student kind ofone-on-one assessment. And the
reality is, most teachers arefinding that those quick
10-second interactions are moreviable in the classroom than
the "sit-down one-on-one withevery one of your 30 students,
(32:16):
once a week" kind ofassessments.
Bethany Lockhart Johnson (32:19):
Val, before we go, I'm wondering, is
there a final message orthought that you want to leave
our listeners with?
Dr. Valerie Henry (32:26):
One of the things that I've been so
impressed by over the lastseveral years, as Common Core
instructional materials havebecome more available is how
much more confident teachershave become with relationships
related to tens. Because thisis what we see from countries
(32:47):
that really have very strongfluency programs, is that they
invest their time in tens. IfIt's adding and subtracting,
they're making sure that theirstudents know that one plus
nine is 10 and two plus eightis 10. I have a Korean
first-grade textbook wherestudents spend an entire
(33:11):
chapter learning how to makeall of the ways to make 10. Not
one lesson. One chapter out oftheir 10 chapters. And then,
the next chapters are about howdo you use tens to work with
numbers? So, for instance,seven plus eight. Alot of
(33:32):
American teachers in the pasthave thought that, "Well, we
should teach kids to do sevenplus seven plus one." But,
that's not what I've read andseen in other countries'
approaches. They're constantlyand consistently building
making tens. So, seven pluseight, the most likely approach
(33:54):
of students from these othercountries would be to give two
to the eight and then have 10plus five is 15. I've been
really impressed by the factthat teachers understand more
strategies. Because theirinstructional materials are
emphasizing that. The thingthat I'd love for teachers to
(34:18):
think more about is why othercountries emphasize making tens
and de-emphasize doubles. I'vedone a little analysis. And
doubles, and doubles plus one,limit the number of facts you
can solve up within ... up to20. And they absolutely limit
(34:43):
what you can do within 100. Forinstance, how many problems
beyond 20 really work withdoubles plus one? If I ask,
"What's 38 plus 49?" Doublesplus one doesn't help me at
all, but making a 10 helps. SoI think that's one of the
things I've been reallyimpressed by is this shift
(35:03):
towards tens thinking.
Dan Meyer (35:05):
That's great to get your perspective there, Val. I
know that, as the Common Corefirst rolled out, a lot of
parents were very uncomfortablewith some of the changes,
especially around fluency. It'sreally been a generational
project, as the students whowere coming up in the Common
Core are slowly becomingteachers. It's just great to
have your perspective on thesetwo snapshots, before and
(35:25):
after, and what has changed.
And the value of 10. So, thankyou so much for coming on with
us again. Again, you inspiredthe whole season. It's j ust
been great to have a moment todive deeper into fluency with
you. And t r ade i deas. Thankyou so much.
Dr. Valerie Henry (35:40):
You're welcome. And I look forward to
hearing from teachers, as maybethey get a chance to think more
about assessment and fluency.
Bethany Lockhart Johnso (35:50):
Thanks so much, Val.
Dan Meyer (35:52):
Thanks so much for listening to our conversation
with Dr. Val Henry, creator ofFactsWise.
Bethany Lockhart Johnson (35:57):
Check out the show notes for more
information on Dr. Val Henryand FactsWise. Let us know what
you thought of this episode inour Facebook discussion group,
Math Teacher Lounge (36:06):
The Community. We're still early in
this new season, so let us knowwhat you'd like to hear about
when it comes to math fluency.
You can share your questions,your ideas, your thoughts, your
wonderings. And make sure youcatch all the episodes in this
new season by subscribing toMath Teacher Lounge wherever
you get your podcasts. Andwhile you're there, we'd really
(36:27):
appreciate it if you couldleave us a review. It helps
other listeners find the showand, if you're enjoying it, let
a friend know about it. You canfind more information on all of
Amplify's great shows at ourPodcast Hub. Go to
amplify.com/hub. Thanks againfor listening.
I think assessment and evaluation are
two different things.
Evaluation is often where weput a number to something and
we try and give it a grade.
Assessment is where we'retrying to understand what
students are thinking. And, Ithink they're very different
animals.
Bethany Lockhart Johnson (00:19):
Hi, and welcome to another episode
of Math Teacher Lounge. I amBethany Lockhart Johnson .
Dan Meyer (00:24):
And I am Dan Meyer.
Bethany Lockhart Johnson (00:26):
Dan, we're in fluency land! How you
doing? How you doing?
Dan Meyer (00:30):
I'm getting more and more interested in it. Every
new guest we talk to gives mesome new angle on fluency that
helps me see what an importantpart it is of a student's
development of new ideas, and,I'm also, in my own personal
life, getting excited to seefluency kind of bloom , with
the—
Bethany Lockhart Johnson (00:45):
Wait! Say more about that! Back that
up!
Dan Meyer (00:48):
I'd be happy to; thank you for asking. Yeah,
I've been noticing one of mykids does direct counting no
matter what the sum is. Fourplus three, I'm gonna start at
one, two, three ... seven. Or10 plus 12 — I'm going all the
way back to one, gonnadirect-count that thing for the
first 10, then the next 12. AndI find it more fascinating now.
(01:11):
So, what are the experiencesthat he needs to be able to see
the value of just like, no ,just say, "Hey, here's 10. I'm
here at 10 and now count up 12more," let's say. And , I've
seen the limitations of justsaying, "Hey, do this. You
should do this thing." Well, no, kids' i deas just take longer
to —
Bethany Lockhart Johnso (01:30):
You're not doing that, Dan. You, Math
Teacher Dan, are not tellingyour child, "No, no, no. Solve
it this way."
Dan Meyer (01:38):
No, there's no way to do that! I haven't tried it.
But there's just futility wherethe kid's just not ready for
it. Whatever's going on in hisbrain is so much more powerful
and durable than any words Iwould have to offer. However, I
have been offering variousexperiences — for instance,
this game that we call"Garbage," that has five cards
(02:01):
on top in a row and five cardson bottom in a row. And the
kid's gotta find seven. Atfirst he'd count one, two th—,
five, six , seven, with hisfingers counting. But,
recently, we've had enough ofthose experiences where he just
starts at six. He just says,"That first row is five; I know
this now." Or he's even startedat 10 and gone backwards. And
(02:22):
so, to me ... it's a mystery.
It is a mystery; I love a goodmystery, love a movie mystery,
a book mystery, love a mathmystery. Like, how are these
ideas taking root in his head?
That's where I'm coming fromwith fluency this week, and
kind of excited to talk moretoday about it with you.
Bethany Lockhart Johnson (02:37):
I love hearing that. And, sorry I
jumped on you a little bit,because I thought you were
saying, "No matter how manytimes I tell him that's not how
you do it, he keeps doing it!"
Dan Meyer (02:49):
I'm like, "You won't get dinner. There's no dinner
tonight for you."
Nope. You're gonna startcounting-on if you want a treat
. Yeah, you know me.
Bethany Lockhart Johnson (02:55):
Let me tell you . But, what I love
is that you're giving himrepeated experiences to
practice building thatrelationship with those
numbers, because that isexactly what we celebrate in
our classroom. Right? "Ooh,what if we do this?" And now he
gets it. He sees that five.
Right? Eventually, well, sure,you can keep counting up to
(03:17):
five, but eventually he won'tneed to. He is like, "OK, five,
six, seven, eight." Or, what ifyou give him some larger
numbers? Something like 32 plustwo. He may start at one — I've
seen it — and go all the wayup; but maybe he would hold
that number, that large number,and then count on. But, I could
(03:39):
sit here and tell you—
Dan Meyer (03:40):
You can't help yourself, can you?
Bethany Lockhart Johnson (03:42):
I can't help myself. Because I
love this—
Dan Meyer (03:42):
You're like , "What's the next thing?"
Dr. Valerie Henry (03:44):
—so much! I love the way students think. My
kiddo's two and a half, and I'mnot forcing
counting, but I do give ampleopportunities for counting. I
love counting with my kiddo andexploring different concepts in
math. But, I think we need moreof this, Dan. We need more of
(04:06):
you sharing what is going on inyour household as your kiddos
are beginning to developfluency.
Dan Meyer (04:13):
Oh, I am game.
Bethany Lockhart Johnson (04:15):
I'll take a daily report.
Dan Meyer (04:16):
The real win of it all is that they ask to play
this game. They don't know thatthey're learning math. So yeah,
I love talking about this withyou. It's grown on me. And I
love the guests that we bringon, and the perspectives they
bring to bear on fluency. Andnone more so than Dr. Val Henry
today.
Bethany Lockhart Johnson (04:37):
If you love talking to our guests,
you are really going to lovetalking to Dr. Val Henry again.
We spoke with Val a few seasonsago about fluency in a shared
episode with Tracy Zager andGraham Fletcher, getting a
couple different perspectiveson fluency. But, today, we are
talking to Dr. Val Henryspecifically about assessment,
(05:00):
but I'm sure the conversationwill run the gamut. She is an
amazing, dare I say, expert onfluency. She's been thinking
about this for decades. Andshe's done research about it,
and developed a program calledFactsWise that I've used in my
own classroom. And she also isa university professor at the
(05:21):
University of California,Irvine, teaching pre-service
teachers and helping themdevelop their relationship with
math as they dive into theirfirst classrooms.
Dan Meyer (05:29):
So I hope you folks enjoy this interview as much as
we did with Dr. Val Henry.
Bethany Lockhart Johnson (05:37):
We are so thrilled to have you
back, Dr. Henry. Welcome, somuch, again to the Lounge.
Thank you so much for joiningus again.
Dr. Valerie Henry (05:47):
Thanks Bethany. And Dan. Thank you
both for inviting me.
Bethany Lockhart Johnson (05:51):
Oh! Did you hear that?
Dan Meyer (05:53):
It was like a dot, dot, dot. It was a very short
pause. I'm happy with how thatwent, honestly.
Welcome back, Dr. Henry.
Dr. Valerie Henry (06:00):
Thank you.
Bethany Lockhart Johnson (06:01):
It's actually kind of appropriate,
because we recently chattedwith Jason Zimba, who we were
really excited to get a peekinto his brain and how he
thinks about fluency andmathematics in general. And, I
(06:21):
worked on Dan a bit, becauseDan's been a little less than
enthusiastic about fluency. ButI'm telling you, ever since we
had you on the show, we've hadthese questions buzzing around
about fluency. And it keepscoming up. And we knew we had
to have you back. And, in fact,you're really the inspiration
for this whole season. ... Dan, before we ask any questions,
(06:45):
share a little bit, just togive a little framework about
your perspective, because Ithink it's good she knows what
she's getting into.
Dan Meyer (06:52):
Sure, that's fair. I do feel like you're asking me
to share with Val what it is Ifind uncomfortable a bout the
work of fluency that she'sinto, but I'll just go with it.
As a math educator, I've alwaysbeen really excited about
introducing the new. I've beena little bit less excited about
fluency. Especially because Ithink a lot of the way fluency
(07:12):
is developed in studentsnowadays constitutes a lot of
people's negative memories ofmath class. I don't w anna
associate fluency completelywith those bad vibes, but
thinking about the endlessworksheets or Mad Minutes, or
just those kinds of traumaticexperiences, a lot of them have
been in the fluency realm. Andso I've been a little bit ...
(07:33):
cold to it, let's just say.
Bethany is warm to fluency; Iwo uld s ay warm-to-hot. And
I've really enjoyed talkingwith Bethany about how to
develop math fluency in kids,especially as we both have
really young kids, and thinkingabout how they develop those
ideas. So , I wanna believe. Iwan t to be a believer here.
So, I'm excited about thisseason, excited to have you on
(07:55):
the show.
Dr. Valerie Henry (07:56):
Well, Dan, I have to tell you, I was
cool-to-cold about fluency 20years ago. So I'd been doing a
lot of professionaldevelopment, a lot of it around
algebraic thinking back inthose days. And I'd go out and
work with teachers and withstudents, and the teachers
would say, "But we can't doalgebraic thinking with our
(08:19):
kids, because they're notfluent."
Dan Meyer (08:23):
They don't know the basics.
Dr. Valerie Henry (08:24):
Or, I'd work on problem solving. And they'd
say, "They can't do that,because they're not fluent."
And I'd go in, and I'd sort ofshow them that kids can do a
lot of great math thinking,even if or before they're
fluent. So I was reallyresistant to this; but every
single upper grade teacher thatI talked to brought up fluency
(08:46):
as a roadblock. So when I wentback to school to get my Ed.D.,
I decided that I would reallyinvestigate this. What is going
on with this? And so bylearning about how other
countries really do a betterjob often with fluency teaching
and learning, I decided maybeit was worth looking at from a
(09:10):
different perspective thanworksheets or timed tests, that
kind of thing, so that we couldget away from those negatives.
Dan Meyer (09:17):
I appreciate that background enormously. I feel
like we have a new kinship, youand me, here
resonate with me that the newstuff that excites me is often
much more challenging tostudents if they struggle with
some of those basics. If theystruggled with prerequisite
skills, foundational skills,... I don't know what word
(09:39):
would be most appropriate here.
But that as a mission, as yourdesire to understand those
skills, because they supportthese other skills that also
interest you, that's a helpfulroute in for me in this
conversation. Whatever that'sworth. Thank you.
Dr. Valerie Henry (09:54):
Cool. I'll also say one more thing that
has really stuck with me overthe years. I had a teaching
assistant who grew up in China,I believe, and learned her
early mathematics in China.
Very fluent in English, so shewas helping me with a graduate
(10:16):
course. And I said, "One of thethings we're gonna be looking
at is basic facts fluency." Andshe said, "Well, what's that?"
And I thought, "OK, maybe shedoesn't understand the word
fluency." So I explained thatand she said, "Yeah, yeah,
yeah; I get that." And then Isaid, "Basic, like between one
(10:36):
and 20." And she said, "Yeah, Iget that, but why are you
calling them facts?" And Isaid, "Well ... because ..."
and she said, "Well, let meexplain. In China, when we grew
up, we learned that one plusone was two, and then
everything else was arelationship that was built off
(11:01):
of one plus one is two. Theyaren't facts; they are
relationships, and areprovable." She said, "Facts are
things that you can't reallyknow unless somebody tells
you." So I'll just share thatas an insight that I have into
this whole language of basicfacts fluency. I hate to call
(11:23):
it that now, but that's what Ithink a lot of people
understand what we're talkingabout when we reference it that
way.
Bethany Lockhart Johnson (11:29):
This is really a helpful
perspective, Val, and ... I'msaying Val—
Dr. Valerie Henry (11:34):
That's fine.
Bethany Lockhart Johnson (11:35):
Dan, you continue to call her Dr.
Henry.
Dr. Valerie Henry (11:38):
I'm way more comfortable with Val.
Bethany Lockhart Johnson (11:41):
It was my joy to get to learn from
you at University ofCalifornia, Irvine. And, I felt
like the way that youapproached your pre-service
teachers was like you werehelping us to heal our
relationship with math. Andsomething that I learned from
you was really a new way tothink about assessment. And
(12:04):
when we think about fluency,people have been jumping in
with, "Well, timed tests."Right? Or, we gave the example
of like, Teachers Pay Teachers.
They pull up a themed timedtest; and, therefore, if I give
it to you every Friday, you'regonna get it. And I know some
of your research has beenspecifically why timed tests
are problematic, why they don'twork. Right? Why they aren't
(12:25):
enough. But, you had a biggerpicture of assessment. And I'm
wondering if you could share alittle bit about that.
Dr. Valerie Henry (12:33):
So, when I was growing up, teachers often
thought that assessment woulddrive students to become
fluent, without really anythingelse happening in the
classroom. Maybe an occasionalworksheet, maybe an occasional
around-the-world kind of game,or something. But most of the
(12:55):
time it was assumed that youwould go home; you would
somehow learn those basic factson your own; and the testing
would compel you to keepworking at it at home. So
assessment was sort of seen asa force that would require kids
(13:18):
— that would compel them — tomake sense and become fluent.
My theory is — and this is whatwe do in every other subject —
we teach the subject to thestudents, we work with them, we
give them learning experiences,and then we assess. To find out
(13:41):
how far they've come towardsmeeting the learning goals we
have. And the assessmentdoesn't happen without the
learning experiences in theclassroom. And I often talk
with my student teachers aboutthis: We would never think
about saying, "Go home andlearn how to read and we'll
just test you every Friday;and, therefore, you will learn
(14:03):
how to read." So I don't seewhy we're doing that with math
fact fluency. It's sofoundational to mathematics,
and it gives everybody such asense of confidence and number
sense. Why are we assuming thatwe shouldn't be teaching it ?
And so when I say teaching, Idon't mean lecturing; I mean
(14:26):
providing learning experiences.
Dan Meyer (14:29):
You're describing a diminished sense of what
fluency is. If it is possibleto teach it just through
assessing it, that implies adefinition of fluency that I
think the rest of your workspeaks to the opposite idea.
That it is rich, requirespersistent development on the
part of a teacher, work fromthe student. That's just an
(14:53):
interesting dichotomy that nowwe're moving into this other
way of thinking about fluency.
Dr. Valerie Henry (14:58):
Yes. And I think it goes directly back to
the idea that if we thought offluency as learning facts,
things that could be put into asong, or things that could be
chanted, and that could belearned just through verbal
memory, then we thought of itas something that you could
(15:20):
just test over and over. But,if we think of fluency as these
relationships, and findingstrategies that can make
connections between somethingthat we know ... like, I know
two plus two is four, sotherefore I can use that to
help me figure out that twoplus three is five, without
(15:41):
having to memorize two plusthree is five on its own,
without making connections.
Bethany Lockhart Johnson (15:49):
I'm curious if you can talk about
what has assessment looked liketo you in your research, where
you were able to really seethose relationships students
were building with thesenumbers, with these facts? And
how is that maybe differentthan what we wanna get away
from
Dr. Valerie Henry (16:08):
Absolutely.
So, when I first startedreading the literature about
fluency, one of the things Irealized was that the
psychologists who actuallyspecialize in studying the
challenges of fluency inmathematics do one-on-one
assessments. So that they canreally hear students not only
(16:32):
say the answer correctly orincorrectly and they can get a
sense of how long it took themto come up with their answer,
but they also get to ask themthis really important question.
Which is, "How did you get thatanswer?" And so, one-on-one
assessments are so differentthan timed tests, in a couple
(16:56):
of different ways. The firstone is that you actually find
out how fluent — I'm gonna moveaway from whether or not
they're fluent — but how fluentthey are with the fact, with
the math problem. As opposed toon a timed test, which
typically has 20, 50, or a 100problems. And students
(17:22):
completed it and you have nounderstanding of how they
completed it. Whether they wereskip-counting on their fingers,
whether they were jumpingaround and going, "OK, five
times seven is 35, so now I'mgonna look for seven times
five, because now it's in myshort-term memory, and then I'm
gonna do 35 divided by sevenand 35 divided by five," all
(17:47):
without really having beenfluent with any of those. Just
capitalizing on skip-countingand short-term memory. So, 1:1
assessment taught me a lotabout how to really understand
what's happening with students.
I'm gonna stop there, becausethere's a whole other picture ,
(18:07):
which is, is one-on-oneassessment practical in the
average classroom on a regularbasis?
Dan Meyer (18:14):
Something I wanna say I love about the one-on-one
assessment idea is that I thinkit's something so radicalizing
for a math teacher, to becomeaware that students have
interesting ideas all the time.
Even if those ideas don't fitinto really precise boxes. Like
(18:36):
the sort that are expressed ona timed test. And it sounds
like these 1:1 assessments dida lot of work on you to help
you see that, "Oh, what's goingon in the development of
fluency is much moresophisticated than a lot of the
timed test assessments I gavecredit for." I'm just curious,
what were a couple of the bigtakeaways that you had as you
(18:58):
did these 1:1 assessments?
Dr. Valerie Henry (19:00):
I've done thousands of one-on-one
assessments with students fromkindergarten all the way
through eighth grade, and,well, actually, even higher.
And, one of the things that hasreally resonated with me is
that students do come up withfairly similar strategies.
(19:21):
Either because they've inventedthem themselves, or because
they've had learningexperiences that have helped
them develop these relationalideas. So when I ask a student,
"What's six plus nine?" there'susually a small handful of
(19:42):
different strategies thatstudents will tell me about.
One is they just know it.
Another is that they counted ontheir fingers. Or in their
head. Which is not quite atfluency level for me yet. But,
then the others are thingslike, "Well, I gave one from
the six to the nine and thatmade 10; so now I have 10 plus
(20:03):
five." Another is, "Well, Ijust temporarily added 10 to
six, that was one too many, sothen I subtracted one." It's a
little bit different strategy.
Another is, "I might havethought of it as seven plus
seven plus one." And then I'vehad one first grader ever say
(20:26):
that he knew that that fourplus nine was 13 and that he
just needed to add two more toget to 15. Nobody else has ever
come up with that idea! Justthat one little guy. So, yes,
you do have a lot of studentscapitalizing on making tens,
sometimes using doubles, andsometimes using a fact that
(20:49):
they knew that just helped thembuild relationships even if it
wasn't one of the standards.
Dan Meyer (20:55):
So these are really interesting ways of thinking
that aren't visible to teachersfrom a worksheet or printed
timed test , where there's anumber and maybe some scratches
where students carriedsomething. Or something like
that. And you're describingwhat's visible to you, what's
present in these one-on-oneinterviews. I wonder what's
(21:15):
possible, though, in thelogistics of a classroom?
You're able to do this as aresearcher or a consultant. And
I'm curious how you'd helpteachers who have different
logistical demands than you d oi n your role. How can they
capture the best of yourone-on-one assessments within
the constraints of a classroom?
The time constraints, thestudent constraints?
Dr. Valerie Henry (21:38):
There are a couple of different ways that I
think about this. One is, whenI wanna understand what
strategy students are using, Iask them to share their
thinking. Either in the smallgroup setting or in the whole
class setting. I usuallyalternate a little mini lesson,
(21:59):
where we do something usuallywith manipulatives or some kind
of visual on the board, withgames. And even when the kids
are playing the games, I willoften ask that the students
share their strategy thinkingas they're responding with
their answers. So, they mightbe playing a little card game,
(22:22):
where they have the nine faceup on the table and they'll
pick up another card and it'llsay four plus nine. And they'll
say, "The answer's 13," andthen their next job is to
explain to their partner howthey got 13. That's one way
(22:42):
that, as I'm circulating theroom, I get to feel like I'm
hearing what's inside theirhead. Even though I'm not doing
a one-on-one assessment withthem. And I work with teachers,
then, to use that same kind ofapproach for hearing students'
strategy thinking. Sometimesthey're actually showing it
(23:03):
with a manipulative, inaddition to or instead of
verbalizing it. So we oftenhave them use number racks or
10 Frames, depending on whetherwe're doing add/subtract or
multiply/divide. Themanipulatives change a little
bit, but they're sharing theirthinking either verbally or
with the manipulatives.
Dan Meyer (23:26):
I love that you're talking about teachers becoming
sensitized, through all theirsenses, to the different ways
that students are developingfluency, even verbally,
non-verbally, throughmanipulatives. And there's
something that's so specialabout that, where a teacher
becomes like a fine-tunedantenna for all the different
ways students are being smartand fluent in class. I don't
(23:46):
wanna diminish that by asking,"But what about the logistics?"
But I'm kind of curious. As ateacher is moving around, and
is assessing students in a veryreal way, while students aren't
even really aware that they'rebeing assessed, how should the
teacher make good use of thatdata to support the student's
development? I know what to dowith the timed test that has 19
(24:09):
outta 20. I put the 19 in mygrade book. But what are some
productive ways to use all ofthat data, sensory data almost,
to support a student?
Dr. Valerie Henry (24:19):
Great question. And my top
recommendation for that is totake a class list, make some
columns on your class list, andstart writing in some things
that you are interested inlooking for or looking at. So,
if I were working on addingnines, let's say, I might write
(24:40):
in, "Student uses plus 10," or"Student makes a 10," or
"Student uses a doublesapproach," or "Student counts
with their fingers," "Studentcounts in their head." I might
list all of those at the top ofthose columns. And so as I'm
walking around, I'm able tojust start making a quick check
(25:03):
mark, maybe having some roomover on the side so that I can
write a note if it's somethingunique that I wanna attend to,
and I can start then lookingafter that one 10-minute
session, or a few 10-minutefluency sessions, I can now
look at my chart and see, "Wow,a lot of students are using
(25:23):
plus 10, but I've got threethat are still counting on
their fingers." So now I knowthat there are three students
that maybe need some extrasupport, maybe need some extra
time with a manipulative, tohelp with that. I can also see
that the majority of mystudents are building fluency
(25:44):
quite easily with their plusnines. So, we can start moving
on to the minus nines, ifthat's the approach we're
taking.
Bethany Lockhart Johnson (25:53):
I wanted to say, Val, just how
much I respect and appreciatethe way that you listen to
students. And, for me, that iswhat this assessment kind of
all boils down to. You areteaching students to think
flexibly about numbers. You'redoing these routines, and these
games, and these share-outs,and spending time supporting
(26:18):
students in having experienceworking with these numbers. And
the assessment is just a pieceof that. The assessment comes,
like you said, during the gamesas you're walking around, or
during a share out after thestudents are playing the games.
But, really, I hope that ourlisteners are taking from this,
like Dan said, using yoursenses as a teacher, how much
(26:40):
you are listening to students.
I know you did this as yourresearch. But you just so
respect students' thinking. Andthat is something that I think
is so powerful. And so,assessments weren't just
something to squeeze in thereand then you don't do anything
with what you find. You'rereally listening to them and
(27:01):
valuing their thinking.
Dr. Valerie Henry (27:03):
I think that's such an important
perspective about assessment.
Because I think assessment andevaluation are two different
things. Evaluation is oftenwhere we put a number to
something and we try and giveit a grade. Assessment is where
we're trying to understand whatstudents are thinking and able
(27:25):
to do, what they need supportwith, what they're ready to
move on from. And I thinkthey're very different animals.
And so, putting a number on apiece of paper doesn't help me
know what to do next with mystudents. But listening and
engaging with them does let meknow what's the next thing that
(27:48):
I can do to help them.
Dan Meyer (27:49):
Yeah, what you're describing to me has much more
in common with my asking afriend, "How is your
day-to-day?" than any kind ofmath assessment that I think a
lot of us are familiar with.
You're seeking to understand.
It's conversational. I likethat distinction between
assessment and evaluation. WhenI ask, "How was your day?" I'm
not trying to evaluate youranswer in any way , just
(28:10):
understand you a little bitbetter.
Dr. Valerie Henry (28:11):
Definitely.
So I have had teachers askwhether this writing things on
a chart as I'm listening, or aswe're circulating around
watching students, is goodenough to put on a report card.
And so I've asked a fewprincipals, "What would you
(28:33):
think if your teacher stoppedgiving timed tests, or stopped
grading worksheets, and didthis approach of listening in
and understanding wherestudents are in their thinking
and marking it down on a pieceof paper? Would that be good
enough in terms of reportingback to parents how students
(28:55):
are doing on a report card?"And at least the principals
that I've talked to have said,"Absolutely! That's a
completely responsible way ofgrading fluency, if you have to
grade it."
Bethany Lockhart Johnson (29:09):
Val, I was in an Uber in Colorado
and I thought of you. Becausethe Uber driver was like, "Oh,
what do you do?" We weretalking. I was there for a math
conference. And her firstreaction was, "Ugh!" She's
like, "A conference where youjust talk about math?!" And
then she immediately launchedinto, "Oh, I hear those
(29:30):
standards they're asking kids... that's not even how kids
think." She went into thiswhole thing, and she's like,
"What is it even all about?"And the first thing that came
to mind, I said, "Well, if Iasked you to add what's nine
plus seven?" And she said,"16." And I said, "Well, how
did you get that? You got thatpretty fast." And she said,
(29:52):
"Well, I don't know, I guess Itook something from the seven
to make it a 10, and I made 10plus six." Right? And I said,
"That's it. Yeah, exactly.
That's it. Right? You brokeapart those numbers. You're
thinking about those numbersflexibly; that's what we want
to happen in our classroom,that our students feel like
(30:14):
they can manipulate numbers,and think about it in new ways,
and share their thinking." AndI tell you, Val, I was thinking
of you when I asked her that,and I think she gave me a
pretty good rating as apassenger, if not for that
story
good reminder for me that somany of us have these negative
(30:36):
experience with fluency, withmathematics, with assessment.
Right? And when it'sconversational, and when it's
just a part of like, "Let'stalk about this. What went on
in your brain? How are youthinking about it?" It can be
really positive.
Dr. Valerie Henry (30:51):
What's really fascinating is that
students love to talk abouttheir thinking. And they feel
very special when the teacherlistens to them individually.
Sometimes we can listen to themindividually by doing a
one-on-one assessment.
Sometimes we can just interruptthe little activity or game
(31:15):
they're doing with a partnerand say, "I just would love to
hear how you thought about thatone; I wanna know." And so, the
logistics, kind of back toDan's question of one--on-one
assessment versus thiscirculating as students are
(31:35):
interacting with themathematics, usually with a
partner, is that you caninteract one-on-one with the
student for 10 seconds and theyget that same sort of
validation, and you get to hearwhat they're thinking. Or you
can spend five minutes withthem doing a full-on sit-down
(31:56):
with one student kind ofone-on-one assessment. And the
reality is, most teachers arefinding that those quick
10-second interactions are moreviable in the classroom than
the "sit-down one-on-one withevery one of your 30 students,
(32:16):
once a week" kind ofassessments.
Bethany Lockhart Johnson (32:19):
Val, before we go, I'm wondering, is
there a final message orthought that you want to leave
our listeners with?
Dr. Valerie Henry (32:26):
One of the things that I've been so
impressed by over the lastseveral years, as Common Core
instructional materials havebecome more available is how
much more confident teachershave become with relationships
related to tens. Because thisis what we see from countries
(32:47):
that really have very strongfluency programs, is that they
invest their time in tens. IfIt's adding and subtracting,
they're making sure that theirstudents know that one plus
nine is 10 and two plus eightis 10. I have a Korean
first-grade textbook wherestudents spend an entire
(33:11):
chapter learning how to makeall of the ways to make 10. Not
one lesson. One chapter out oftheir 10 chapters. And then,
the next chapters are about howdo you use tens to work with
numbers? So, for instance,seven plus eight. Alot of
(33:32):
American teachers in the pasthave thought that, "Well, we
should teach kids to do sevenplus seven plus one." But,
that's not what I've read andseen in other countries'
approaches. They're constantlyand consistently building
making tens. So, seven pluseight, the most likely approach
(33:54):
of students from these othercountries would be to give two
to the eight and then have 10plus five is 15. I've been
really impressed by the factthat teachers understand more
strategies. Because theirinstructional materials are
emphasizing that. The thingthat I'd love for teachers to
(34:18):
think more about is why othercountries emphasize making tens
and de-emphasize doubles. I'vedone a little analysis. And
doubles, and doubles plus one,limit the number of facts you
can solve up within ... up to20. And they absolutely limit
(34:43):
what you can do within 100. Forinstance, how many problems
beyond 20 really work withdoubles plus one? If I ask,
"What's 38 plus 49?" Doublesplus one doesn't help me at
all, but making a 10 helps. SoI think that's one of the
things I've been reallyimpressed by is this shift
(35:03):
towards tens thinking.
Dan Meyer (35:05):
That's great to get your perspective there, Val. I
know that, as the Common Corefirst rolled out, a lot of
parents were very uncomfortablewith some of the changes,
especially around fluency. It'sreally been a generational
project, as the students whowere coming up in the Common
Core are slowly becomingteachers. It's just great to
have your perspective on thesetwo snapshots, before and
(35:25):
after, and what has changed.
And the value of 10. So, thankyou so much for coming on with
us again. Again, you inspiredthe whole season. It's j ust
been great to have a moment todive deeper into fluency with
you. And t r ade i deas. Thankyou so much.
Dr. Valerie Henry (35:40):
You're welcome. And I look forward to
hearing from teachers, as maybethey get a chance to think more
about assessment and fluency.
Bethany Lockhart Johnso (35:50):
Thanks so much, Val.
Dan Meyer (35:52):
Thanks so much for listening to our conversation
with Dr. Val Henry, creator ofFactsWise.
Bethany Lockhart Johnson (35:57):
Check out the show notes for more
information on Dr. Val Henryand FactsWise. Let us know what
you thought of this episode inour Facebook discussion group,
Math Teacher Lounge (36:06):
The Community. We're still early in
this new season, so let us knowwhat you'd like to hear about
when it comes to math fluency.
You can share your questions,your ideas, your thoughts, your
wonderings. And make sure youcatch all the episodes in this
new season by subscribing toMath Teacher Lounge wherever
you get your podcasts. Andwhile you're there, we'd really
(36:27):
appreciate it if you couldleave us a review. It helps
other listeners find the showand, if you're enjoying it, let
a friend know about it. You canfind more information on all of
Amplify's great shows at ourPodcast Hub. Go to
amplify.com/hub. Thanks againfor listening.
Popular Podcasts
Las Culturistas with Matt Rogers and Bowen Yang
Ding dong! Join your culture consultants, Matt Rogers and Bowen Yang, on an unforgettable journey into the beating heart of CULTURE. Alongside sizzling special guests, they GET INTO the hottest pop-culture moments of the day and the formative cultural experiences that turned them into Culturistas. Produced by the Big Money Players Network and iHeartRadio.
On Purpose with Jay Shetty
I’m Jay Shetty host of On Purpose the worlds #1 Mental Health podcast and I’m so grateful you found us. I started this podcast 5 years ago to invite you into conversations and workshops that are designed to help make you happier, healthier and more healed. I believe that when you (yes you) feel seen, heard and understood you’re able to deal with relationship struggles, work challenges and life’s ups and downs with more ease and grace. I interview experts, celebrities, thought leaders and athletes so that we can grow our mindset, build better habits and uncover a side of them we’ve never seen before. New episodes every Monday and Friday. Your support means the world to me and I don’t take it for granted — click the follow button and leave a review to help us spread the love with On Purpose. I can’t wait for you to listen to your first or 500th episode!
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com