Season 3 | Episode 12 – Inside Out: Examining the Meaning and Purpose of our Questions - Guest: Dr. Victoria Jacobs

Dr. Victoria Jacobs,
Examining the Meaning and Purpose of our Questions

ROUNDING UP: SEASON 3 | EPISODE 12

Mike (00:03):
The questions educators ask their students matter. They can have a profound impact on students' thinking and the shape of their mathematical identities. Today we're examining different types of questions, their purpose and the meaning students make of them. Joining us for this conversation is Dr. Vicki Jacobs from the University of North Carolina Greensboro. Welcome to the podcast, Vicki. I'm really excited to talk with you today.

Vicki (00:33):
Thanks so much for having me. I'm excited to be here.

Mike (00:36):
So you've been examining the ways that educators use questioning to explore the details of students' thinking. And I wonder if we could start by having you share what drew you to the topic.

Vicki (00:47):
For me, it all starts with children's thinking because it's absolutely fascinating, but it's also mathematically rich. And so a core part of good math instruction is when teachers elicit children's ideas and then build instruction based on that. And so questioning obviously plays a big role in that, but it's hard. It's hard to do that well in the moment. So I found questioning to explore children's thinking to be a worthwhile thing to spend time thinking about and working on.

Mike (01:17):
Well, let's dig into the ideas that have emerged from that work. How can teachers think about the types of questions that they might ask their students?

Vicki (01:24):
Happy to share. But before I talk about what I've learned about questioning, I really need to acknowledge some of the many people that have helped me learn about questioning over the years. And I want to give a particular shout out to the teachers and researchers in the wonderful cognitively guided instruction or CGI community as well as my long-term research collaborators at San Diego State University. And more recently, Susan Sen. This work isn't done alone, but what have we learned about teacher questioning across a variety of projects? I'll share two big ideas and the first relates to the goals of questioning and the second addresses more directly the types of questions teachers might ask. So let's start with the goals of questioning because there are lots of reasons teachers might ask questions in math classrooms. And one common way to think about the goal of questioning is that we need to direct children to particular strategies during problem solving.

(02:23):
So if children are stuck or they're headed down a wrong path, we can use questions to redirect them so that they can get to correct answers with particular strategies. Sometimes that may be okay, but when we only do that, we're missing a big opportunity to tap into children's sense-making. Another way to think about the goal of questioning is that we're trying to explore children's thinking during problem solving. So think about a math task where multiple strategies are encouraged and children can approach problem solving in any way that makes sense to. So we can then ask questions that are designed to reveal how children are thinking about the problem solving, not just how well they're executing our strategies. And we can ask these questions when children are stuck, but also when they solve problems correctly. So this shift in the purpose of questioning is huge. And I want to share a quote from a teacher that I think captures the enormity of this shift.

(03:26):
She's a fifth grade teacher, and what she said was the biggest thing I learned from the professional development was not asking questions to get them to the answers so that I could move them up a strategy, but to understand their thinking. That literally changed my world. It changed everything. So I love this quote because it shows how transformative this shift can be becau

Episode Transcript

(00:03):
The questions educatorsask their students matter.
They can have a profound impact onstudents' thinking and the shape of their
mathematical identities. Today we'reexamining different types of questions,
their purpose and the meaningstudents make of them.
Joining us for this conversation isDr. Vicki Jacobs from the University of

(00:24):
North Carolina Greensboro.
Welcome to the podcast, Vicki. I'mreally excited to talk with you today.
Thanks so much for havingme. I'm excited to be here.
So you've been examining the ways thateducators use questioning to explore the
details of students' thinking.
And I wonder if we could start by havingyou share what drew you to the topic.

(00:47):
For me,
it all starts with children's thinkingbecause it's absolutely fascinating,
but it's also mathematically rich.
And so a core part ofgood math instruction is
when teachers elicit children's ideasand then build instruction based on that.
And so questioning obviously playsa big role in that, but it's hard.

(01:07):
It's hard to do that well in the moment.
So I found questioning toexplore children's thinking to be a worthwhile thing
to spend time thinkingabout and working on.
Well, let's dig into the ideasthat have emerged from that work.
How can teachers think about the typesof questions that they might ask their
students?
Happy to share. But before I talk aboutwhat I've learned about questioning,

(01:28):
I really need to acknowledge some of themany people that have helped me learn
about questioning over the years.
And I want to give a particular shout outto the teachers and researchers in the
wonderful cognitively guided instructionor CGI community as well as my
long-term research collaboratorsat San Diego State University.
And more recently, Susan Sen.This work isn't done alone,

(01:51):
but what have we learned about teacherquestioning across a variety of projects?
I'll share two big ideas and thefirst relates to the goals of
questioning and the second addressesmore directly the types of questions
teachers might ask.
So let's start with thegoals of questioning because there are lots of reasons

(02:12):
teachers might ask questionsin math classrooms.
And one common way to think about thegoal of questioning is that we need to
direct children to particularstrategies during problem solving. So if
children are stuck or they'reheaded down a wrong path,
we can use questions to redirect themso that they can get to correct answers
with particular strategies.Sometimes that may be okay,

(02:36):
but when we only do that,
we're missing a big opportunity totap into children's sense-making.
Another way to think about the goalof questioning is that we're trying to
explore children's thinkingduring problem solving.
So think about a math task wheremultiple strategies are encouraged and
children can approach problem solvingin any way that makes sense to.

(02:59):
So we can then ask questions that aredesigned to reveal how children are
thinking about the problem solving,
not just how well they'reexecuting our strategies.
And we can ask these questionswhen children are stuck,
but also when they solveproblems correctly.
So this shift in the purposeof questioning is huge.

(03:20):
And I want to share a quote from ateacher that I think captures the
enormity of this shift.She's a fifth grade teacher,
and what she said was the biggestthing I learned from the professional
development was not asking questionsto get them to the answers so that I
could move them up a strategy,but to understand their thinking.

(03:41):
That literally changed myworld. It changed everything.
So I love this quote because itshows how transformative this shift
can be because when teachers becomecurious about how children are thinking
about problem solving,
they give children more space toproblem solve in multiple ways,

(04:01):
and then they can question tounderstand and support children's ideas.
And these types of questions aregreat because they increase learning
opportunities for bothchildren and teachers.
So children get more opportunitiesto learn how to talk math
in a way that's meaningful to them becausethey're talking about their own ideas

(04:23):
and they also get to clarify whatthey did think more about important
math that's embedded in their strategiesand sometimes to even self-correct.
And then as teachers,
these types of questions give us awindow into children's understandings,
and that helps usdetermine our next steps.
Questioning can have a different andpowerful purpose when we shift from

(04:47):
directing children toward particularstrategies to exploring their
mathematical thinking.
I keep going back to thequote that you shared,
and I think the details of the whyand kind of the difference in the
experience for students really jump out.
But I'm really compelled by what thatteacher said to you about how it changes

(05:10):
everything.
And I wonder if we could just linger therefor a moment and you could talk about
some of the things that you've seenhappen for educators who have that kind of
aha moment in the sameway that that teacher did,
how that impacts the work that they'redoing with children or how they see
themselves as an educator.
That's a great question.
I think it's freeing in some way

(05:34):
because it changes how educators
think about what their next steps are.
Every teacher has lots of pressuresfrom standards and sometimes
pacing guides and grade level teamsthat are working on the same page,
all sorts of things thatare a big part of teaching.
But it puts the focus back onchildren and children's thinking and

(05:59):
that my next steps shouldthen come from there.
And so in some ways,
I think it gives aclearer direction for how
to navigate all those variouspressures that teachers have.
I love that. Let's talk about part two.
Sure.
So if we have the goal of questioningto explore children's thinking,

(06:23):
how do we decide what questionsto ask? So first of all,
there's never a best question.
There are many questioning frameworksout there that can provide lots of ideas,
but what we've found is that the mostproductive questions always start with
what children say and do.
So that means I can't planall my questions in advance,

(06:43):
and instead I have to pay closeattention to what children are saying and
doing during problem solving.And to help us with that,
we found a distinction between insidequestions and outside questions.
And that distinction has been reallyuseful to us and also usable even during
instruction.

(07:04):
So inside questions arequestions that explore
details that are part ofinside children's current
strategies.
And outside questions arequestions that focus on strategies
or representations that are not whatchildren have done and may even be linked
to how we as teachers are thinkingabout problem solving. So I promised an

(07:27):
example,
and this is from our recent researchproject on teaching and learning about
fractions.
And we asked teachers to think about achild's written strategy for a fraction
story problem.
And the problem was that there aresix children equally sharing four
pancakes, and they need to figure outhow much pancake each child can get.

(07:47):
So we're going to talk about Joy'sstrategy for solving this problem.
She is a fourth grader whosolved the problem successfully,
but in a complex andrather unconventional way.
So I'm going to describeher strategy as a reminder.
We have six childrensharing four pancakes.
So she drew the four pancakes.
She split the first three pancakes intofourths and distributed the pieces to

(08:11):
the six children, and that worksout to two fourths for each child.
But now she has a problem because shehas one pancake left and fourths aren't
going to work anymore because that's notenough pieces for her six children. So
she split the pancake first intoeighths and then into 20 fourths
and distributed those pieces.
So each child ends upreceiving two fourths,

(08:34):
one eighth and one 24th. And whenyou put all those amounts together,
they equal the correct amountof two thirds pancake per child.
But Joy left her answerin pieces as two fourths,
one eighth and one 24th,
and she wrote those fractions inwords rather than using symbols.
Okay, so there's a lotgoing on in this strategy.

(08:56):
And the specific strategydoesn't matter so much for our
conversation, but the situation does.
Here we have a child who hassuccessfully solved the problem,
but how she solved it and howshe represented her answer are
different than what weas adults typically do.

(09:17):
So we ask teachers to think about whatkind of follow-up conversation would you
want to have with joy? What types ofquestions would you want to ask her?
And there were these twomain questioning approaches,
what we call inside questioningand outside questioning.
So let's start with outside questioning.
These teachers focused onimproving Joy's strategy.

(09:40):
So they ask follow-up questions like,
is there another way you can sharethe four pancakes with six children?
Or is your strategy the most efficientway you could share the pancakes?
Or is there a way to cut biggerservings that would be more efficient?
So given the complexity of Joy's strategy,
we can appreciate these teachers' goalsof helping joy move to a more efficient

(10:03):
strategy.
But all of these questions are pushingher to use a different strategy.
So we considered them outside questionsbecause they were outside of her current
strategy. And outside questionscan sometimes be productive,
but they tend to get overused.And when we use them a lot,
they can communicate to kids that whatthey're actually doing was wrong and that

(10:26):
it needs fixing. So let's thinkabout the other approach of inside
questioning.
These teachers started by exploring whatJoy had done in all of its complexity.
And they ask a variety ofquestions. Usually it started with a general question,
can you tell me what you did?
But then they zoomed in on some ofthe many details. So for examples,

(10:48):
they've asked how she split thepancakes. They offered questions like,
why did you split the firstthree pancakes into four pieces?
Or Tell me about the last pancake.
That was the one that she splitinto eights and 20 fourths.
Or they might ask about how she knew howto name each of the fractional amounts,
especially the one 24th,
because that's something that manychildren might've struggled with.

(11:10):
And then there were questionsabout a variety of other details.
Some of them are hard to explain withoutshowing you a picture of the strategy,
but the point is that the teacherstook seriously what Joy had done and
elevated it to the focusof the conversation.
So Joy had a chance to shareher reasoning and reflect on it,
and the teachers could better understandJoy's approach to problem solving.

(11:35):
So we found this distinctionbetween inside and outside questioning to be useful
to teachers and even in the midst ofinstruction because teachers can quickly
check in with themselves. Am I asking aninside question or an outside question?
Well, I have so many questionsabout inside and outside questions,
but I want to linger on inside questions.

(11:57):
What I found myself thinkingis that for the learner,
there are benefits for building numbersense or conceptual understanding.
The other thing that strikes me is thatinside questions are also an opportunity
to support students' math identity.
And I wonder if that's something thatyou've seen in your work with teachers and
with students.
Absolutely. I love your question.
One of my favorite things about insidequestions is that children see that their

(12:21):
ideas are being taken seriously.And that's so empowering.
It helps children believe that they cando math and that they are in charge of
their mathematical thinking. I'll sharea short story that was memorable for me,
and this was from a while agowhen I was in graduate school.
So I was working on a research projectand we were conducting problem solving

(12:43):
interviews with young children. And ourjob was to document their strategies.
So if we could see exactly what they did,
we were told to write downthe strategy and move on.
But if we needed to clarify something,we could ask follow up questions.
I was working with a first grader whohad just spent a really long time solving
a story problem. He hadsolved it successfully,

(13:03):
and he had done thatby joining many, many,
many unifix cubes into a very long train.And then he had
counted them by ones multiple times.
So he had been successful. I couldtell exactly what he had done.
So I started to moveon to the next problem.
So this young child looked at me alittle incredulous and simply asked,

(13:25):
don't you want to know how I did it?
And he had come from a class wherehis math thinking was valued,
and talking about children's thinkingwas a regular part of what they did.
So he couldn't quite understand why thisadult was not interested in how he had
thought about the problem. Well,
I was a little embarrassed and of coursebacktracked and listened to his full

(13:47):
explanation.
But the interaction stuck with me becauseit showed me how empowering it was for
children to truly belistened to as math thinkers.
And I think that's somethingwe want for all children.
The other thing that's hitting me inthat story and in the story of joy is mea
culpa. I am a person who has lived in thecult of efficiency where I looked at a

(14:09):
student's work and my initial thought was,
how do I nip the edges of thisto get to more efficiency?
But I really am struck by it how differentthe idea of asking the student to
explain their thinking or the why behindit. I find myself thinking about joy,
and it appears that she was intent onmaking sure that there were equal shares
for each person.

(14:30):
So there's ways that she couldbuild to a different level of
efficiency.
But I think recognizing that there'ssomething here that is really important to
note about how and why she chose that,
that would feel reallymeaningful as a learner.
I agree.
I think what I like about insidequestions is that they encourage us

(14:50):
to, that children's thinking makes sense,
even if it's differentthan how we think about it.
It's our job to figure out how it makessense. And then to build from there.
Can you just say more about that?That feels like kind of a revelation.
Well,
if we start with how kidsare thinking and we take that

(15:14):
seriously and we make that thecenter of the conversation,
then we're acknowledgingto the student and to
ourselves that the child hassomething meaningful to bring to
this conversation.
And so we need to figure outhow the child is thinking all
the kind of kernels ofmathematical strength in that

(15:38):
thinking. And then yes,we can build from there,
but we start with where theyare as opposed to how we
might solve the problem.
If you were to offer educators a universalinside question or a few sentence
frames for inside questions,
is it possible to construct somethinglike that that's generic or do you have

(16:00):
other advice for us?
So that's a nice trick question.I wish it were that easy.
I don't really think thereare any universal inside
questions. Perhaps the only universalone I can think of is something like,
how did you solve this problem? It'sa great general open-ended question.
That's a good starterquestion in most situations.

(16:23):
But the really powerfulquestions generally come from noticing mathematically
important details inchildren's strategies.
So a sentence stem that hasbeen helpful in our work is,
I noticed blank, so I wonder blank.
Obviously questions don't haveto be phrased exactly like this,

(16:43):
but the idea is that we pick somethingthat the child has done in their strategy
and ask a question about the child'sthinking behind that strategy
detail.
And that keeps us honest because thequestion absolutely has to begin with
something in the child's strategy ratherthan inadvertently kind of slipping
into our strategy.

(17:04):
Vicki, what do you think aboutthe purpose of outside questions?
Are there circumstances where we wouldwant to ask our students an outside
question?
Absolutely.
Sometimes we need to push children'sthinking or share particular ideas,
and that's okay. It's not thatall outside questions are bad,
it's just that we tend to overuse themand we could use them at more productive

(17:26):
times.
And by that I mean that we generallywant to understand children's thinking
before nudging their thinkingforward with outside questions.
So let's go back to theearlier example of Joy.
Who was solving that problem aboutsix children sharing four pancakes.
And we had the two groups of teachersthat had the different approaches to

(17:47):
follow up questioning.
There was the outside questioning thatimmediately zeroed in on improving Joy's
strategy and the inside questioning thatspent time exploring Joy's reasoning
behind her strategy. So I'm thinkingof two specific teachers right now.
One generally took the outsidequestioning approach and the other inside
questioning approach.

(18:08):
And what was interesting about thispair was that they both asked the
same outside question,
could Joy partition the pancakes ina different way? But they asked this
question at different timesand the timing really matters.
So the teacher who took an outsidequestioning approach wanted to begin her
conversation that way.She wanted to ask Joy,

(18:30):
could she partition in adifferent way? But in contrast,
the teacher who took an inside questioningapproach wanted to ask Joy lots of
questions about the detailsof her existing strategy,
and then posed this very samequestion at the end to see if Joy
had some new ideas for partitioningafter their conversation about her

(18:52):
existing strategy. And that feelsreally different to children.
So the exact same question can sendchildren different messages when
outside questions are posed.
First they communicate to childrenthat what they did was wrong and needs
fixing.
But when outside questions are posedafter a conversation about their thinking,

(19:13):
it communicates a puzzle ora problem to be solved. And
children often are betterequipped to consider this new
problem having thoroughlydiscussed their own strategy.
So I guess when I thinkabout outside questions,
I think of timing and amount.
We generally want to startwith inside questions,

(19:35):
and we want most of ourquestions to be inside questions,
but some outside questionscan be productive. It's just that we overuse them.
I want to mention one otherthing about outside questions,
and I think we often need feweroutside questions than we think we do,
as long as we have space for childrento learn from other children's thinking.

(19:57):
So think about a typical lessonstructure like launch, explore,
discuss where children solveproblems independently.
And then the lesson concludes with a wholeclass discussion where children share
their strategies and reflecton their problem solving.
Will these sharing sessions serveas natural outside questions?
Because children get to think aboutstrategies that are outside of their own,

(20:21):
but in a way that doesn't point to theirown strategy as lacking in some way.
So outside questions definitely have aplace we just need to think about when we
ask them and how many ofthem are really necessary.
That is really helpful.
I find myself thinking about my ownprocess when I'm working on a problem,
be it mathematical ororganizational or what have you.

(20:43):
When someone asks me to talkabout how I've thought about it,
engaging in that process insome ways primes me, right?
Because I've gottenclearer on my own thinking.
I suspect that the person who's askingme the question is also clearer on that,
which allows them to ask a differentkind of outside question if and when they
get to the point.
So there's the benefit for the learnerin that their clarifying their own

(21:03):
thinking.
There's the benefit in the educator who'sengaging with the learner and getting
just a much clearer sense ofhow that thinking was happening.
And I suspect that leads to an outsidequestion that's much more productive.
It's a win-win situation.
Absolutely. This conversationhas been wonderful.
The challenge of havinga podcast, of course,

(21:25):
is that we've got about 20 to 25minutes to talk about a really big idea
that has profoundimplications for teachers.
If someone wanted to pick up on thethings we've been talking about today,
where would you start, Vicki?
I would encourage themto go talk to children.
Children's thinking is so mathematicallyrich and it's so fascinating.

(21:47):
So be curious about theirthinking. Ask questions,
ask those inside questions. Don'tworry about asking the best question.
It doesn't exist,
but ask questions and thenchildren will be your guides.
They'll help you know where to go next.
The other thing I would suggest is thesejourneys are always best done with your

(22:07):
colleagues.
And so get a colleague together andthink about questioning together what we
were talking about earlierwith joy strategy teachers.
We're looking at students' writtenwork. That's a great place to practice.
You can look at children's written workand talk together to figure out what
types of conversations do you wantto have with this child afterwards.

(22:28):
I think that's a great place to stop.
I want to thank you so muchfor joining us today, Vicki,
it has really been apleasure talking with you.
That was fun. Thanks for having me.
This podcast is brought to you by theMath Learning Center and the Meyer Math
Foundation dedicated to inspiringand enabling all individuals to
discover and develop theirmathematical confidence and ability.