April 3, 2025 • 22 mins
Ryan Flessner, What If I Don’t Understand Their Thinking?
ROUNDING UP: SEASON 3 | EPISODE 15
“What do I do if I don’t understand my student’s strategy?” This is a question teachers grapple with constantly, particularly when conferring with students during class. How educators respond in moments like these can have a profound impact on students’ learning and their mathematical identities.
In this episode, we talk with Ryan Flessner from Butler University about what educators can say or do when faced with this situation.
BIOGRAPHY
Ryan Flessner is a professor of teacher education in the College of Education at Butler University in Indianapolis, Indiana. He holds a PhD in curriculum and instruction with an emphasis in teacher education from the University of Wisconsin–Madison; a master of arts in curriculum and teaching from Teachers College, Columbia University; and a bachelor of science in elementary education from Butler University. Prior to his time at the university level, he taught grades 3–7 in Indianapolis; New York City; and Madison, Wisconsin.
RESOURCES
TRANSCRIPT
Mike Wallus: “What do I do if I don't understand my student’s strategy?” This is a question teachers grapple with constantly, particularly when conferring with students during class. How we respond in moments like these can have a profound impact on our students' learning and their mathematical identities. Today we'll talk with Ryan Flessner from Butler University about what educators can say or do when faced with this very common situation.
Welcome to the podcast, Ryan. Really excited to talk to you today.
Ryan Flessner: Thanks, Mike. I'm flattered to be here. Thank you so much for the invitation.
Mike: So, this experience of working with a student and not being able to make sense of their solution feels like something that almost every teacher has had. And I'll speak for myself and say that when it happens to me, I feel a lot of anxiety. And I just want to start by asking, what would you say to educators who are feeling apprehensive or unsure about what to do when they encounter a situation like this?
Ryan: Yeah, so I think that everybody has that experience. I think the problem that we have is that teachers often feel the need to have all of the answers and to know everything and to be the expert in the room. But as an educator, I learned really quickly that I didn't have all the answers. And to pretend like I did put a lot of pressure on me and made me feel a lot of stress and would leave me answering children by saying, “Let me get back to you on that.” And then I would scurry and try and find all the answers so I could come back with a knowledgeable idea. And it was just so much more work than to just simply say, “I don't know. Let's investigate that together.” Or to ask kids, “That's something interesting that I'm seeing you do. I've never seen a student do that before. Can you talk to me a little bit about that?”
And just having that ability to free myself from having to have all the answers and using that Reggio-inspired practice—for those who know early childhood education—to follow the child, to listen to what he or she or they say to us and try to see. I can usually keep up with a 7- or an 8-year-old as they're explaining math to me. I just may never have seen them notate something the way they did. So, trying to ask that question about, “Show me what you know. Teach me something ne
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Transcript
Episode Transcript
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(00:03):
What do I do if I don'tunderstand my student's strategy?
This is a question teachersgrapple with constantly,
particularly when conferringwith students during class.
How we respond in moments like these canhave a profound impact on our students'
learning and theirmathematical identities.
Today we'll talk with Ryan Lesner fromButler University about what educators
(00:27):
can say or do when faced withthis very common situation.
Welcome to the podcast, Ryan.Really excited to talk to you today.
Thanks, Mike. I'm flattered to be here.Thank you so much for the invitation.
So this experience of workingwith a student and not being able to make sense of
their solution feels like somethingthat almost every teacher has had.
(00:50):
And I'll speak for myself andsay that when it happens to me,
I feel a lot of anxiety. And Ijust want to start by asking,
what would you say to educators who arefeeling apprehensive or unsure about
what to do when they encountera situation like this?
Yeah, so I think thateverybody has that experience.
I think the problem that we have is thatteachers often feel the need to have
(01:11):
all of the answers and to know everythingand to be the expert in the room.
But as an educator,
I learned really quickly that I didn'thave all the answers and to pretend like
I did put a lot of pressure on me andmade me feel a lot of stress and would
leave me answering children by saying,let me get back to you on that,
and then I would scurry and try and findall the answers so I could come back
with a knowledgeable idea.
(01:31):
And it was just so much more workthan to just simply say, I don't know.
Let's investigate thattogether. Or to ask kids,
that's something interestingthat I'm seeing you do.
I've never seen a student do that before.
Can you talk to me alittle bit about that?
And just having that ability to freemyself from having to have all the answers
and using that Reggio inspired practicefor those who know early childhood
(01:52):
education to follow the child,
to listen to what he or she orthey say to us and try to see.
I can usually keep up with a seven oran 8-year-old as they're explaining math
to me. I just may never have seen themnotate something the way they did.
So trying to ask that question aboutshow me what, teach me something new.
The idea that a teacher could be a learnerat the same time I think is novel to
(02:14):
kids and I think they respondreally well to that idea.
So before we dig in a little bit moredeeply about how teachers respond to
student strategies ifthey don't understand,
I just want to linger and thinkabout the assumptions that many
educators, myself includedmight bring to this situation.
Assumptions about the role,
(02:35):
assumptions about what it would mean fora student if they don't know the answer
right away.
How do you think about some of theassumptions that are causing some of that
anxiety for us?
Yeah. When the new generationof standards came out,
especially in the field of math,
teachers were all of a sudden askedto teach in a way that they themselves
didn't learn.
And so if you have that idea that youhave to have all the answers and you have
(02:56):
to know everything,
that puts you in a really vulnerablespot because how are we supposed to just
magically teach things we'venever learned ourselves?
And so trying to figure out ways thatwe can back up and try and make sense of
the work that we're doing with kids.
For me that was reallyhelpful in understanding what I wanted from my students.
I wanted them to makesense of the learning.
So if I hadn't made sense of it yet,
(03:16):
how in the world could I teachthem to make sense of it?
And so we have to have that humilityto say, I don't know how to do this.
I need to continue my learning trajectoryand to keep going and trying to do a
little bit better thanthe day that I did before.
I think that teachers are uniquely andthey're always trying to do better,
but I don't know if we necessarilyare taught how to learn once
(03:39):
we become teachers. We've alreadylearned everything we have to do now.
We just have to learn howto teach it to other people.
But I don't think we have learnedeverything that we have to learn.
There's a lot of stuff in the math worldthat I don't think we actually learned.
We just memorized steps and kind ofregurgitated them to get our a plus on a
test or whatever we did. So I thinkhaving the ability to stop and say,
I don't know how to do this, andso I'm going to keep working at it,
(04:01):
and when I start to learn it,
I'm going to be able to ask myselfquestions that I should be asking my
students.
And just being really thoughtful aboutwhy is the child saying the thing that
she is? Why is she doing itthe way that she's doing it?
Why is she writing it theway that she's writing it?
And if I can't figure it out,
the expert on that piece ofpaper is the child himself,
so why wouldn't I go to herand say, talk to me about this.
(04:24):
I don't have to have all theanswers right off the cuff.
In some ways,
what you were describing just there isa real nice segue because I've heard you
say that our minds and our students'minds often work faster than we can write,
or even in some casesfaster than we can speak.
I'm wondering if you can unpackthat. Why do you think this matters,
particularly in the situationthat we're talking about?
(04:46):
Yeah, I think a lot ofus, especially in math,
have been conditioned to get an answer.
And nobody's reallyasked us why in the past.
And so we've done all of the thinking,
we give the answer and thenwe think the job is done.
But with a lot of the new standards, wehave to explain why we think that way.
And so all those ideas thatjust flurried through our head,
we have to now articulate those eitherin writing on paper or in speech,
(05:11):
trying to figure out howwe can communicate the mathematics behind the answer.
And so a lot of times I'll be in aclassroom and I'll ask a student for an
answer and I'll say, how'd you get that?
And the first inclination thata lot of kids have is, oh,
I must be wrong if a teacher is askingme why so they think they're wrong.
And so I say, no, no, no, it's notthat you're wrong. I'm just curious.
You came to that answer,
you stopped and you lookedup at the ceiling for a while and then you came to me
(05:34):
and you said the answer is68. How did you do that?
A child will say something like, well,I just thought about it in my head.
I say, what did you thinkabout in your head? Well,
my brain just told me the answer was 68.
We have to actually talk to kids andwe have to teach them how to talk to us
that we're not quizzing them or sayingthat they're wrong or they didn't do
something well enough that we just wantthem to communicate with us how they're
(05:55):
going about finding thesethings, what the strategies are.
Because if they cancommunicate with us in writing,
if they can communicate on paper,
if they can use gestures to explainwhat they're thinking about,
all of those tell us strengthsthat they bring to the table.
And if I can figure out thestrengths that you have,
that I can leverage those strengthsas I address needs that arise in my
classroom.
And so I really want to create thisbank of information about individual
(06:17):
students that will help me be thebest teacher that I can be for them.
And if I can't ask those questions andthey can't answer those questions for me,
how am I going to individualize myinstruction in meaningful ways for kids?
We've been talking a little bit aboutthe teacher experience in this moment and
we've been talking about some ofthe things that a person might say.
(06:37):
One of the things that I'm thinking aboutbefore we dig in a little bit deeper
is just what is my role?
How do you think about the role of ateacher in the moment when they encounter
thinking from a student that theydon't quite understand it yet?
Part of what I'm after is how can ateacher think about what they're trying to
accomplish in that moment for themselvesas a learner and also for the learner
(07:00):
in front of them? How wouldyou answer that question?
When I think about an interactionwith a kid in a moment like that,
I try to figure out, as the teacher,
my goal is to try and figure out whatthis child knows so that I can continue
their journey in a forward trajectory.
Instead of thinking about they need togo to page 34 because we're on page 33,
just thinking about what does thiskid need next from me as the teacher.
(07:24):
What I want them to get outof the situation is I want them to understand that
they are powerful individuals,
that they have something to offer theconversation and not just to prove it to
the adult in the room, but if I canhear them talk about these ideas,
sometimes the kids in the classroomcan answer each other's questions.
And so if I can ask these thingsaloud and other kids are listening in,
(07:44):
maybe because we're in close proximityor because we're in a small group
setting, if I can get thekids to verbalize those ideas.
Sometimes one kid talking strikes anidea and another kid or another kid will
say, I didn't know how to answer Ryanwhen he asked me that question before,
but now that I hear what it soundslike to answer that type of a question,
now I get it and I know how Iwould say it if it were my turn.
(08:04):
So we have to actually offer kids theopportunity to learn how to engage in
those moments and how to share theirexpertise so others can benefit from their
expertise and use that in a way that'shelpful in the mathematical process.
One of the most practical,
and I have to say freeing things thatI've heard you recommend when a teacher
encounters student work and they'restill trying to make sense of it,
(08:26):
is to just go ahead and name it.
What are some of the things you imaginethat a teacher might say that just
straight out name the fact that they'restill trying to understand a student's
thinking? Tell me a little bit about that.
Well,
I think the first thing is that we justhave to normalize the question why or
tell me how you know that ifwe normalize those things.
(08:47):
A lot of times kids get askedthat question when they're wrong,
and so it's an immediately tipof the hat that you're wrong.
Now go back and fix it. There'ssomething wrong with you.
Haven't tried hard enough kids get thesemessages even if we don't intend for
them to get them. So if wecan normalize the question,
tell me why you think thator explain that to me,
if we can just get them to see thatevery time you give me an answer whether
it's right or wrong, I'm just goingto ask you to talk to me about it.
(09:10):
That takes care of half of the problem.
But I think sometimes teachers get stuckbecause, and myself being one of them,
we get stuck because we'll look at whata student is doing and they do something
that we don't anticipate or we say,
I've shown you three differentways to get at this problem,
different strategies you can use,and you're not using any of them.
And so instead of getting frustratedthat they're not listening to us,
(09:30):
how do we use that moment to inquireinto the things that we said obviously
aren't useful? So whatis useful to this kid?
How is he attacking this on his paper?So I often like to say to a kid,
huh, I noticed that you're doing somethingthat isn't up on our anchor chart.
Tell me about this. Ihaven't seen this before.
How can you help meunderstand what you're doing?
(09:51):
And sometimes it's the exact samethinking as other strategies that kids are
using. So I can pair kidstogether and say, huh,
you're both talkingabout it in the same way,
but you're writing itdifferently on paper.
And so I think about how I can get kidsjust to talk to me and tell me what's
happening so that I can help give thema notation that might be more acceptable
to other mathematicians or to just honorthe fact that they have something novel
(10:12):
and interesting to share with otherkids. Other questions I talk about are,
I will say, I don't understand what'shappening here, and that's not your fault,
that's my fault.
I just need you to keep explaining it tome until you say something that strikes
a chord.
Or sometimes I'll bring another kid inand I'll have the kids listen together
and I'll say, I think this is interesting,
but I don't understand what'sgoing on. Can you say it to her?
(10:35):
And then maybe she'll say it in away that will make more sense to me.
Or I'll say, can you show me onyour paper you just said that?
Can you show me on yourpaper where that idea is?
Because a lot of times kidswill fake things in their head,
but they don't translate it allonto the paper. And so on the paper,
it's missing a step that isn'tobvious to the viewer of the paper.
And so we'll say, oh,I see how you do that.
(10:58):
Maybe you could label your table sothat we know exactly what you're talking
about when you do this.
Or maybe you could show us how you gotto 56 by writing eight times seven in the
margin or something.
Just getting them to clarifyand try to help us understand
all of the amazing things that are intheir head. I will often tell them too,
I love what you're saying. Idon't see it on your paper,
(11:20):
so I just want you to say it again andI'm going to write it down on a piece of
paper that makes sense to me so that Idon't forget all of the cool things that
you said, and I'll just write itusing more of a standard notation,
whether that's a ratio table or astandard US algorithm or something.
I'll write it to show the kidthat thing that you're doing.
There's a way that people write that down.
(11:40):
And so then we can compare our notationsand try and figure out what's the thing
that you did? How does thatcompare to the thing that I did?
Do I understand you clearly nowto make sure that the kid has the
right to say the thing she wants to sayin the way that she wants to say it,
and then I can still makesense of it in my own way.
It's not a problem for me to write itdifferently as long as we're speaking the
(12:01):
same language.
I want to mark something really importantand I don't want it to get lost.
For folks,
one of the things that jumped out isthe moves that you were describing.
You could potentially take up thosemoves if you really were unsure of how a
student were thinking. Ifyou had a general notion,
but you had some questionsor if you totally already understood what the student
(12:23):
was doing,
those are questions that aren't justreserved for the point in time when you
don't understand they're actually goodquestions regardless of whether you fully
understand it or don't understandit at all. Did I get that right?
Yes. I think that's exactly the point.
One thing that I am carefulof is sometimes kids will ask me a question that I
know the answer to,
and there's this thing that we do asteachers where we're like, I'm not sure.
(12:45):
Why don't you help me figure that outwhen the kid knows full well that you know
the answer? And so try not topatronize kids with those questions,
but to really show that I'masking you these questions,
not because I'm patronizing you,
I'm asking these questions because I amtruly curious about what you're thinking
inside and all of the ideas that surroundthe things that you've written on your
paper or the things that you've saidto your partner to truly honor that.
(13:08):
The more I know about you, thebetter teacher I can be for you.
So in addition to naming the situation,
one of the things that jumped out for me,
particularly as you weretalking about the students,
is what do you think the impactis on a student's thinking,
but also their mathematical identityor even the set of classroom norms when
they experience this type ofquestioning or these type of questions?
(13:33):
So I think I talked a little bitabout normalizing the question,
why or how do you know that?
And so just letting that become aclassroom norm I think is a sea changing
moment for a lot of classrooms thatthe conversation is just different.
If the kids know they haveto justify their thinking,
whether they're right or wrong, halfthe time, if they are incorrect,
they'll be able to correct themselvesas they're talking it through with you.
(13:53):
So kids can be freed up whenthey're allowed to use their
expertise in ways that allow them tounderstand that the point of math is to
truly make sense of it so thatwhen you go out into the world,
you understand the situation and youhave different tools to attack it.
So what's the way that we can create anenvironment that allows them to truly
(14:14):
see themselves as mathematicalthinkers and to let them know that your
grades and other classes don't tellme much about you as a mathematician,
I want to learn what really works for you,
and I want to try and figureout where you struggle.
And both of those things are importantto me because we can use them in concert
with each other. So if Iknow the things you do well,
I can use those to help me build aplan of instruction that will take you
(14:37):
further in your understandings.
I think that one of the things thatis really important is for kids to
understand that we don't do mathbecause we want a good grade.
I think a lot of people think that thepoint of math is to get a good grade or
to pass a test or to get into thecollege that you want to get into,
or because sixth gradeteachers want you to know this.
I really want kids to understand thatmath is a fantastic language to use out in
(15:02):
the world,
and there are ways that we can interpretthings around us if we understand some
pretty basic math.
And so how do we get them to stop thinkingthat math is about right answers and
next year and to get the job I want?Well, those things may be true.
That's not the real meaning of math.Math is a way that we can live life.
And so if we don't help them understandthe connections between the things that
(15:24):
they're doing on a worksheetor in a workbook page,
if we don't connect those things tothe real world, what's the meaning?
What's the point for them and how dowe keep them engaged in wanting to know
more mathematics?
So really getting kids to think aboutwho they are as people and how math can
help them live the lifethat they want to live.
Creating classroom environments thathave routines in place that support kids
(15:49):
in thinking in ways that will movethem forward in their mathematical
understanding,
trying to help them see that there'sno such thing as a math person or not a
math person that everybody has todo math. You do math all the time.
You just might not evenknow that you're doing math.
So I think all of thoseideas are really important.
And the more curious Ican be about students,
maybe the more curiousthey'll be about the math.
(16:12):
You're making me think thatthis experience of making sense of someone else's
reasoning has a lot of value for students.
And I'm wondering how you've seeneducators have students engage
and make sense of their peer strategies?
Yeah. One of the things that I love tosee teachers doing is using students'
(16:32):
work as the conversation starter.I often, in my classroom,
when I started doing this work,
I would bring children up to the overheadprojector or the document camera,
and they would kind of do ashow and tell and just say,
I did this and then I did this, and thenI did this thing next. And I would say,
that's really great, thank you.
And I'd bring up the next student andit kind of became a show and tell type
(16:52):
situation.
And I would look at the faces of theother kids in the room and they would kind
of just either be completely checkedout or sitting there like raising their
hand excitedly. I want to sharemine, I want to share mine.
And what I realized was that there wasreally only one person who was engaged in
that show and tell manner, and that wasthe person who was sharing their work.
And so I thought, how can I change that?
So I saw a lot of really amazingteachers across my career,
(17:15):
and the thing that I sawthat I appreciated the most is that when a piece of
student work is shared,
the person who really shouldn't talk isthe person who created the work because
they already know the work.
What we need to do as a group is we needto investigate what happened here on
this paper.
Why do you think they made the movesthat they made and how could that help us
understand math, our ownmath in a different way?
(17:36):
And so getting kids to look in at otherkids' work and not just saying, oh,
Mike, how do you understand Ryan'swork? It's Mike, can you get us started?
And then you say the first thing,and then I say, okay, let's stop.
Let's make sure that we've got this right.
And then we go to the kid whose work itis and say, are we on the right track?
Are we understanding what you're, sowe're always checking with that expert.
We're making sure they have the lastword, because it's not my strategy.
(17:59):
I didn't create it.
Just because I'm the teacher doesn't meanyou should come and ask me about this
because this is Mike's strategy. So goand ask the person who created that.
So trying to get them to understand thatwe all need to engage in each other's
work, we all need to see the connections.We can learn from each other,
and there's an expectationthat everyone shares, right?
So it's not just the firstkid who raises his hand.
(18:20):
It's all of you are goingto get a chance to share.
And I think the really powerful thingis I've done this work even with
in-service teachers. And so whenwe look at samples of student work,
what's fascinating is it just happensnaturally because the kid's not in the
room. We can't have thatkid do a show and tell.
We have to interpret their work.
And so trying to look at the kid's workand imagine what are the types of things
(18:40):
we think this child is doing? What do wethink the strengths are on this paper?
What questions would youask? What would you do next?
Is such an interesting thing to dowhen the child isn't in the room.
But when I'm with students,
it's just fascinating to watch the kidwhose work is on display just shine,
even though they're not saying a word,because they just say, huh, they get it.
(19:01):
They understand what Idid and why I did it.
I think that it's really important forus not just to have kids walk up to the
board and do board work and just solvea problem using the steps that they've
memorized or just go up and do a show andtell to really engage everyone in that
process so that we're all learning.
We're not just kind of checking outor waiting for our turn to talk.
(19:22):
Okay. You were talking about the waysthat an educator can see how a student was
thinking or the ways that an educatorcould place student work in front of
other students and have themtry to make sense of it.
I wonder if there are any educationaltechnology tools that you've seen that
might help an educator who's tryingto either understand their students'
thinking or put it out for their studentsto understand one another's thinking.
(19:47):
Yeah, there's so many different piecesof technology and things out there.
It's kind of overwhelming to try andfigure out which one is which. So I mean,
I've seen people use thingslike Nearpod or Pear Deck,
some of those kind of common technologiesthat you'll see when people do an
educational technology class or aworkshop at a conference or something.
I've seen a lot of people lately usingGeoGebra to create applets that they can
(20:08):
use with their kids. One that I've startedusing a lot recently is Magma Math.
Magma Math is great.
I've used this with teachersand professional development situations to look at
samples of student work because the thingthat Magma has that I haven't seen in
a lot of other technologies isthere's a playback function.
So I can look at a static piece offinished work, but I can also rewind.
(20:31):
And as the child works in this program,
it records it so I can watch inreal time what the child does.
And so if I can't understand the workbecause things are kind of sporadically
all over the page,
I can just rewatch the order that thechild put something onto the page.
And I think that's a really great,
there's just all these technologiesthat offer us opportunities to do things
that I couldn't do at the beginning ofmy career or I didn't know how to do.
(20:54):
And the technology facilitates that.
And it's not just putting kids on an iPadso they can shoot lasers at the alien
that's invading by saying eight timesfive is 40 and the alien magically blows
up. How does that teach us anything?
But some of these technologies reallyallow us to dig deeply into a sample of
work that students havefinished or inquire into,
(21:14):
how did that happen andwhy did that happen?
And the technologies are justgetting smarter and smarter,
and they're listening to teachers saying,
it would be really helpful if wecould do this or if we could do that.
And so I think there are a lot ofresources out there, sometimes too many,
almost an embarrassment of riches.
So trying to figure out which ones arethe ones that are actually worth our
time,
and how do we fund that in a schooldistrict or in a school so that teachers
(21:38):
aren't paying for thesepieces out of their pocket.
You know what? I think that'sa great place to stop. Brian,
thank you so much for joining us.
It has been an absolutepleasure talking with you.
It's always great to talk toyou, Mike. Thanks for all you do.
This podcast is brought to you by theMath Learning Center and the Meyer Math
Foundation dedicated to inspiring andenabling all individuals to discover
(22:02):
and develop their mathematicalconfidence and ability.
What do I do if I don'tunderstand my student's strategy?
This is a question teachersgrapple with constantly,
particularly when conferringwith students during class.
How we respond in moments like these canhave a profound impact on our students'
learning and theirmathematical identities.
Today we'll talk with Ryan Lesner fromButler University about what educators
(00:27):
can say or do when faced withthis very common situation.
Welcome to the podcast, Ryan.Really excited to talk to you today.
Thanks, Mike. I'm flattered to be here.Thank you so much for the invitation.
So this experience of workingwith a student and not being able to make sense of
their solution feels like somethingthat almost every teacher has had.
(00:50):
And I'll speak for myself andsay that when it happens to me,
I feel a lot of anxiety. And Ijust want to start by asking,
what would you say to educators who arefeeling apprehensive or unsure about
what to do when they encountera situation like this?
Yeah, so I think thateverybody has that experience.
I think the problem that we have is thatteachers often feel the need to have
(01:11):
all of the answers and to know everythingand to be the expert in the room.
But as an educator,
I learned really quickly that I didn'thave all the answers and to pretend like
I did put a lot of pressure on me andmade me feel a lot of stress and would
leave me answering children by saying,let me get back to you on that,
and then I would scurry and try and findall the answers so I could come back
with a knowledgeable idea.
(01:31):
And it was just so much more workthan to just simply say, I don't know.
Let's investigate thattogether. Or to ask kids,
that's something interestingthat I'm seeing you do.
I've never seen a student do that before.
Can you talk to me alittle bit about that?
And just having that ability to freemyself from having to have all the answers
and using that Reggio inspired practicefor those who know early childhood
(01:52):
education to follow the child,
to listen to what he or she orthey say to us and try to see.
I can usually keep up with a seven oran 8-year-old as they're explaining math
to me. I just may never have seen themnotate something the way they did.
So trying to ask that question aboutshow me what, teach me something new.
The idea that a teacher could be a learnerat the same time I think is novel to
(02:14):
kids and I think they respondreally well to that idea.
So before we dig in a little bit moredeeply about how teachers respond to
student strategies ifthey don't understand,
I just want to linger and thinkabout the assumptions that many
educators, myself includedmight bring to this situation.
Assumptions about the role,
(02:35):
assumptions about what it would mean fora student if they don't know the answer
right away.
How do you think about some of theassumptions that are causing some of that
anxiety for us?
Yeah. When the new generationof standards came out,
especially in the field of math,
teachers were all of a sudden askedto teach in a way that they themselves
didn't learn.
And so if you have that idea that youhave to have all the answers and you have
(02:56):
to know everything,
that puts you in a really vulnerablespot because how are we supposed to just
magically teach things we'venever learned ourselves?
And so trying to figure out ways thatwe can back up and try and make sense of
the work that we're doing with kids.
For me that was reallyhelpful in understanding what I wanted from my students.
I wanted them to makesense of the learning.
So if I hadn't made sense of it yet,
(03:16):
how in the world could I teachthem to make sense of it?
And so we have to have that humilityto say, I don't know how to do this.
I need to continue my learning trajectoryand to keep going and trying to do a
little bit better thanthe day that I did before.
I think that teachers are uniquely andthey're always trying to do better,
but I don't know if we necessarilyare taught how to learn once
(03:39):
we become teachers. We've alreadylearned everything we have to do now.
We just have to learn howto teach it to other people.
But I don't think we have learnedeverything that we have to learn.
There's a lot of stuff in the math worldthat I don't think we actually learned.
We just memorized steps and kind ofregurgitated them to get our a plus on a
test or whatever we did. So I thinkhaving the ability to stop and say,
I don't know how to do this, andso I'm going to keep working at it,
(04:01):
and when I start to learn it,
I'm going to be able to ask myselfquestions that I should be asking my
students.
And just being really thoughtful aboutwhy is the child saying the thing that
she is? Why is she doing itthe way that she's doing it?
Why is she writing it theway that she's writing it?
And if I can't figure it out,
the expert on that piece ofpaper is the child himself,
so why wouldn't I go to herand say, talk to me about this.
(04:24):
I don't have to have all theanswers right off the cuff.
In some ways,
what you were describing just there isa real nice segue because I've heard you
say that our minds and our students'minds often work faster than we can write,
or even in some casesfaster than we can speak.
I'm wondering if you can unpackthat. Why do you think this matters,
particularly in the situationthat we're talking about?
(04:46):
Yeah, I think a lot ofus, especially in math,
have been conditioned to get an answer.
And nobody's reallyasked us why in the past.
And so we've done all of the thinking,
we give the answer and thenwe think the job is done.
But with a lot of the new standards, wehave to explain why we think that way.
And so all those ideas thatjust flurried through our head,
we have to now articulate those eitherin writing on paper or in speech,
(05:11):
trying to figure out howwe can communicate the mathematics behind the answer.
And so a lot of times I'll be in aclassroom and I'll ask a student for an
answer and I'll say, how'd you get that?
And the first inclination thata lot of kids have is, oh,
I must be wrong if a teacher is askingme why so they think they're wrong.
And so I say, no, no, no, it's notthat you're wrong. I'm just curious.
You came to that answer,
you stopped and you lookedup at the ceiling for a while and then you came to me
(05:34):
and you said the answer is68. How did you do that?
A child will say something like, well,I just thought about it in my head.
I say, what did you thinkabout in your head? Well,
my brain just told me the answer was 68.
We have to actually talk to kids andwe have to teach them how to talk to us
that we're not quizzing them or sayingthat they're wrong or they didn't do
something well enough that we just wantthem to communicate with us how they're
(05:55):
going about finding thesethings, what the strategies are.
Because if they cancommunicate with us in writing,
if they can communicate on paper,
if they can use gestures to explainwhat they're thinking about,
all of those tell us strengthsthat they bring to the table.
And if I can figure out thestrengths that you have,
that I can leverage those strengthsas I address needs that arise in my
classroom.
And so I really want to create thisbank of information about individual
(06:17):
students that will help me be thebest teacher that I can be for them.
And if I can't ask those questions andthey can't answer those questions for me,
how am I going to individualize myinstruction in meaningful ways for kids?
We've been talking a little bit aboutthe teacher experience in this moment and
we've been talking about some ofthe things that a person might say.
(06:37):
One of the things that I'm thinking aboutbefore we dig in a little bit deeper
is just what is my role?
How do you think about the role of ateacher in the moment when they encounter
thinking from a student that theydon't quite understand it yet?
Part of what I'm after is how can ateacher think about what they're trying to
accomplish in that moment for themselvesas a learner and also for the learner
(07:00):
in front of them? How wouldyou answer that question?
When I think about an interactionwith a kid in a moment like that,
I try to figure out, as the teacher,
my goal is to try and figure out whatthis child knows so that I can continue
their journey in a forward trajectory.
Instead of thinking about they need togo to page 34 because we're on page 33,
just thinking about what does thiskid need next from me as the teacher.
(07:24):
What I want them to get outof the situation is I want them to understand that
they are powerful individuals,
that they have something to offer theconversation and not just to prove it to
the adult in the room, but if I canhear them talk about these ideas,
sometimes the kids in the classroomcan answer each other's questions.
And so if I can ask these thingsaloud and other kids are listening in,
(07:44):
maybe because we're in close proximityor because we're in a small group
setting, if I can get thekids to verbalize those ideas.
Sometimes one kid talking strikes anidea and another kid or another kid will
say, I didn't know how to answer Ryanwhen he asked me that question before,
but now that I hear what it soundslike to answer that type of a question,
now I get it and I know how Iwould say it if it were my turn.
(08:04):
So we have to actually offer kids theopportunity to learn how to engage in
those moments and how to share theirexpertise so others can benefit from their
expertise and use that in a way that'shelpful in the mathematical process.
One of the most practical,
and I have to say freeing things thatI've heard you recommend when a teacher
encounters student work and they'restill trying to make sense of it,
(08:26):
is to just go ahead and name it.
What are some of the things you imaginethat a teacher might say that just
straight out name the fact that they'restill trying to understand a student's
thinking? Tell me a little bit about that.
Well,
I think the first thing is that we justhave to normalize the question why or
tell me how you know that ifwe normalize those things.
(08:47):
A lot of times kids get askedthat question when they're wrong,
and so it's an immediately tipof the hat that you're wrong.
Now go back and fix it. There'ssomething wrong with you.
Haven't tried hard enough kids get thesemessages even if we don't intend for
them to get them. So if wecan normalize the question,
tell me why you think thator explain that to me,
if we can just get them to see thatevery time you give me an answer whether
it's right or wrong, I'm just goingto ask you to talk to me about it.
(09:10):
That takes care of half of the problem.
But I think sometimes teachers get stuckbecause, and myself being one of them,
we get stuck because we'll look at whata student is doing and they do something
that we don't anticipate or we say,
I've shown you three differentways to get at this problem,
different strategies you can use,and you're not using any of them.
And so instead of getting frustratedthat they're not listening to us,
(09:30):
how do we use that moment to inquireinto the things that we said obviously
aren't useful? So whatis useful to this kid?
How is he attacking this on his paper?So I often like to say to a kid,
huh, I noticed that you're doing somethingthat isn't up on our anchor chart.
Tell me about this. Ihaven't seen this before.
How can you help meunderstand what you're doing?
(09:51):
And sometimes it's the exact samethinking as other strategies that kids are
using. So I can pair kidstogether and say, huh,
you're both talkingabout it in the same way,
but you're writing itdifferently on paper.
And so I think about how I can get kidsjust to talk to me and tell me what's
happening so that I can help give thema notation that might be more acceptable
to other mathematicians or to just honorthe fact that they have something novel
(10:12):
and interesting to share with otherkids. Other questions I talk about are,
I will say, I don't understand what'shappening here, and that's not your fault,
that's my fault.
I just need you to keep explaining it tome until you say something that strikes
a chord.
Or sometimes I'll bring another kid inand I'll have the kids listen together
and I'll say, I think this is interesting,
but I don't understand what'sgoing on. Can you say it to her?
(10:35):
And then maybe she'll say it in away that will make more sense to me.
Or I'll say, can you show me onyour paper you just said that?
Can you show me on yourpaper where that idea is?
Because a lot of times kidswill fake things in their head,
but they don't translate it allonto the paper. And so on the paper,
it's missing a step that isn'tobvious to the viewer of the paper.
And so we'll say, oh,I see how you do that.
(10:58):
Maybe you could label your table sothat we know exactly what you're talking
about when you do this.
Or maybe you could show us how you gotto 56 by writing eight times seven in the
margin or something.
Just getting them to clarifyand try to help us understand
all of the amazing things that are intheir head. I will often tell them too,
I love what you're saying. Idon't see it on your paper,
(11:20):
so I just want you to say it again andI'm going to write it down on a piece of
paper that makes sense to me so that Idon't forget all of the cool things that
you said, and I'll just write itusing more of a standard notation,
whether that's a ratio table or astandard US algorithm or something.
I'll write it to show the kidthat thing that you're doing.
There's a way that people write that down.
(11:40):
And so then we can compare our notationsand try and figure out what's the thing
that you did? How does thatcompare to the thing that I did?
Do I understand you clearly nowto make sure that the kid has the
right to say the thing she wants to sayin the way that she wants to say it,
and then I can still makesense of it in my own way.
It's not a problem for me to write itdifferently as long as we're speaking the
(12:01):
same language.
I want to mark something really importantand I don't want it to get lost.
For folks,
one of the things that jumped out isthe moves that you were describing.
You could potentially take up thosemoves if you really were unsure of how a
student were thinking. Ifyou had a general notion,
but you had some questionsor if you totally already understood what the student
(12:23):
was doing,
those are questions that aren't justreserved for the point in time when you
don't understand they're actually goodquestions regardless of whether you fully
understand it or don't understandit at all. Did I get that right?
Yes. I think that's exactly the point.
One thing that I am carefulof is sometimes kids will ask me a question that I
know the answer to,
and there's this thing that we do asteachers where we're like, I'm not sure.
(12:45):
Why don't you help me figure that outwhen the kid knows full well that you know
the answer? And so try not topatronize kids with those questions,
but to really show that I'masking you these questions,
not because I'm patronizing you,
I'm asking these questions because I amtruly curious about what you're thinking
inside and all of the ideas that surroundthe things that you've written on your
paper or the things that you've saidto your partner to truly honor that.
(13:08):
The more I know about you, thebetter teacher I can be for you.
So in addition to naming the situation,
one of the things that jumped out for me,
particularly as you weretalking about the students,
is what do you think the impactis on a student's thinking,
but also their mathematical identityor even the set of classroom norms when
they experience this type ofquestioning or these type of questions?
(13:33):
So I think I talked a little bitabout normalizing the question,
why or how do you know that?
And so just letting that become aclassroom norm I think is a sea changing
moment for a lot of classrooms thatthe conversation is just different.
If the kids know they haveto justify their thinking,
whether they're right or wrong, halfthe time, if they are incorrect,
they'll be able to correct themselvesas they're talking it through with you.
(13:53):
So kids can be freed up whenthey're allowed to use their
expertise in ways that allow them tounderstand that the point of math is to
truly make sense of it so thatwhen you go out into the world,
you understand the situation and youhave different tools to attack it.
So what's the way that we can create anenvironment that allows them to truly
(14:14):
see themselves as mathematicalthinkers and to let them know that your
grades and other classes don't tellme much about you as a mathematician,
I want to learn what really works for you,
and I want to try and figureout where you struggle.
And both of those things are importantto me because we can use them in concert
with each other. So if Iknow the things you do well,
I can use those to help me build aplan of instruction that will take you
(14:37):
further in your understandings.
I think that one of the things thatis really important is for kids to
understand that we don't do mathbecause we want a good grade.
I think a lot of people think that thepoint of math is to get a good grade or
to pass a test or to get into thecollege that you want to get into,
or because sixth gradeteachers want you to know this.
I really want kids to understand thatmath is a fantastic language to use out in
(15:02):
the world,
and there are ways that we can interpretthings around us if we understand some
pretty basic math.
And so how do we get them to stop thinkingthat math is about right answers and
next year and to get the job I want?Well, those things may be true.
That's not the real meaning of math.Math is a way that we can live life.
And so if we don't help them understandthe connections between the things that
(15:24):
they're doing on a worksheetor in a workbook page,
if we don't connect those things tothe real world, what's the meaning?
What's the point for them and how dowe keep them engaged in wanting to know
more mathematics?
So really getting kids to think aboutwho they are as people and how math can
help them live the lifethat they want to live.
Creating classroom environments thathave routines in place that support kids
(15:49):
in thinking in ways that will movethem forward in their mathematical
understanding,
trying to help them see that there'sno such thing as a math person or not a
math person that everybody has todo math. You do math all the time.
You just might not evenknow that you're doing math.
So I think all of thoseideas are really important.
And the more curious Ican be about students,
maybe the more curiousthey'll be about the math.
(16:12):
You're making me think thatthis experience of making sense of someone else's
reasoning has a lot of value for students.
And I'm wondering how you've seeneducators have students engage
and make sense of their peer strategies?
Yeah. One of the things that I love tosee teachers doing is using students'
(16:32):
work as the conversation starter.I often, in my classroom,
when I started doing this work,
I would bring children up to the overheadprojector or the document camera,
and they would kind of do ashow and tell and just say,
I did this and then I did this, and thenI did this thing next. And I would say,
that's really great, thank you.
And I'd bring up the next student andit kind of became a show and tell type
(16:52):
situation.
And I would look at the faces of theother kids in the room and they would kind
of just either be completely checkedout or sitting there like raising their
hand excitedly. I want to sharemine, I want to share mine.
And what I realized was that there wasreally only one person who was engaged in
that show and tell manner, and that wasthe person who was sharing their work.
And so I thought, how can I change that?
So I saw a lot of really amazingteachers across my career,
(17:15):
and the thing that I sawthat I appreciated the most is that when a piece of
student work is shared,
the person who really shouldn't talk isthe person who created the work because
they already know the work.
What we need to do as a group is we needto investigate what happened here on
this paper.
Why do you think they made the movesthat they made and how could that help us
understand math, our ownmath in a different way?
(17:36):
And so getting kids to look in at otherkids' work and not just saying, oh,
Mike, how do you understand Ryan'swork? It's Mike, can you get us started?
And then you say the first thing,and then I say, okay, let's stop.
Let's make sure that we've got this right.
And then we go to the kid whose work itis and say, are we on the right track?
Are we understanding what you're, sowe're always checking with that expert.
We're making sure they have the lastword, because it's not my strategy.
(17:59):
I didn't create it.
Just because I'm the teacher doesn't meanyou should come and ask me about this
because this is Mike's strategy. So goand ask the person who created that.
So trying to get them to understand thatwe all need to engage in each other's
work, we all need to see the connections.We can learn from each other,
and there's an expectationthat everyone shares, right?
So it's not just the firstkid who raises his hand.
(18:20):
It's all of you are goingto get a chance to share.
And I think the really powerful thingis I've done this work even with
in-service teachers. And so whenwe look at samples of student work,
what's fascinating is it just happensnaturally because the kid's not in the
room. We can't have thatkid do a show and tell.
We have to interpret their work.
And so trying to look at the kid's workand imagine what are the types of things
(18:40):
we think this child is doing? What do wethink the strengths are on this paper?
What questions would youask? What would you do next?
Is such an interesting thing to dowhen the child isn't in the room.
But when I'm with students,
it's just fascinating to watch the kidwhose work is on display just shine,
even though they're not saying a word,because they just say, huh, they get it.
(19:01):
They understand what Idid and why I did it.
I think that it's really important forus not just to have kids walk up to the
board and do board work and just solvea problem using the steps that they've
memorized or just go up and do a show andtell to really engage everyone in that
process so that we're all learning.
We're not just kind of checking outor waiting for our turn to talk.
(19:22):
Okay. You were talking about the waysthat an educator can see how a student was
thinking or the ways that an educatorcould place student work in front of
other students and have themtry to make sense of it.
I wonder if there are any educationaltechnology tools that you've seen that
might help an educator who's tryingto either understand their students'
thinking or put it out for their studentsto understand one another's thinking.
(19:47):
Yeah, there's so many different piecesof technology and things out there.
It's kind of overwhelming to try andfigure out which one is which. So I mean,
I've seen people use thingslike Nearpod or Pear Deck,
some of those kind of common technologiesthat you'll see when people do an
educational technology class or aworkshop at a conference or something.
I've seen a lot of people lately usingGeoGebra to create applets that they can
(20:08):
use with their kids. One that I've startedusing a lot recently is Magma Math.
Magma Math is great.
I've used this with teachersand professional development situations to look at
samples of student work because the thingthat Magma has that I haven't seen in
a lot of other technologies isthere's a playback function.
So I can look at a static piece offinished work, but I can also rewind.
(20:31):
And as the child works in this program,
it records it so I can watch inreal time what the child does.
And so if I can't understand the workbecause things are kind of sporadically
all over the page,
I can just rewatch the order that thechild put something onto the page.
And I think that's a really great,
there's just all these technologiesthat offer us opportunities to do things
that I couldn't do at the beginning ofmy career or I didn't know how to do.
(20:54):
And the technology facilitates that.
And it's not just putting kids on an iPadso they can shoot lasers at the alien
that's invading by saying eight timesfive is 40 and the alien magically blows
up. How does that teach us anything?
But some of these technologies reallyallow us to dig deeply into a sample of
work that students havefinished or inquire into,
(21:14):
how did that happen andwhy did that happen?
And the technologies are justgetting smarter and smarter,
and they're listening to teachers saying,
it would be really helpful if wecould do this or if we could do that.
And so I think there are a lot ofresources out there, sometimes too many,
almost an embarrassment of riches.
So trying to figure out which ones arethe ones that are actually worth our
time,
and how do we fund that in a schooldistrict or in a school so that teachers
(21:38):
aren't paying for thesepieces out of their pocket.
You know what? I think that'sa great place to stop. Brian,
thank you so much for joining us.
It has been an absolutepleasure talking with you.
It's always great to talk toyou, Mike. Thanks for all you do.
This podcast is brought to you by theMath Learning Center and the Meyer Math
Foundation dedicated to inspiring andenabling all individuals to discover
(22:02):
and develop their mathematicalconfidence and ability.
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