September 18, 2025 • 28 mins
Sue Looney, Same but Different: Encouraging Students to Think Flexibly
ROUNDING UP: SEASON 4 | EPISODE 2
Sometimes students struggle in math because they fail to make connections. For too many students, every concept feels like its own entity without any connection to the larger network of mathematical ideas.
On the podcast today, we’re talking with Dr. Sue Looney about the powerful same and different routine. We explore the ways that teachers can use this routine to help students identify connections and foster flexible reasoning.
BIOGRAPHY
Sue Looney holds a doctorate in curriculum and instruction with a specialty in mathematics from Boston University. Sue is particularly interested in our most vulnerable and underrepresented populations and supporting the teachers that, day in and day out, serve these students with compassion, enthusiasm, and kindness.
RESOURCES
TRANSCRIPT
Mike Wallus: Students sometimes struggle in math because they fail to make connections. For too many students, every concept feels like its own entity without any connection to the larger network of mathematical ideas.
Today we're talking with Sue Looney about a powerful routine called same but different and the ways teachers can use it to help students identify connections and foster flexible reasoning.
Well, hi, Sue. Welcome to the podcast. I'm so excited to be talking with you today.
Sue Looney: Hi Mike. Thank you so much. I am thrilled too. I've been really looking forward to this.
Mike: Well, for listeners who don't have prior knowledge, I'm wondering if we could start by having you offer a description of the same but different routine.
Sue: Absolutely. So the same but different routine is a classroom routine that takes two images or numbers or words and puts them next to each other and asks students to describe how they are the same but different. It's based in a language learning routine but applied to the math classroom.
Mike: I think that's a great segue because what I wanted to ask is: At the broadest level—regardless of the numbers or the content or the image or images that educators select—how would you explain what [the] same but different [routine] is good for? Maybe put another way: How should a teacher think about its purpose or its value?
Sue: Great question. I think a good analogy is to imagine you're in your ELA— your English language arts—classroom and you were asked to compare and contrast two characters in a novel. So the foundations of the routine really sit there. And what it's good for is to help our brains think categorically and relationally. So, in mathematics in particular, there's a lot of overlap between concepts and we're trying to develop this relational understanding of concepts so that they sort of build and grow on one another. And when we ask ourselves that question—“How are these two things the same but different?”—it helps us put things into categories and understand that sometimes there's overlap, so there's gray space. So it helps us move from black and white thinking into this understanding of grayscale thinking.
And if I just zoom out a little bit, if I could, Mike—when we zoom out into that grayscale area, we're developing flexibility of thought, which is so important in all aspects of our lives. We need to be nimble on our feet, we need to be ready for what's coming. And it might not be black or white, it might actually be a little bit of both.
So that's the power of the routine and its roots come in exploring executive functioning and language acquisition. And so we just layer that on top of mathematics and it's pure gold.
Mike: When we were preparing for this podcast, you shared several really lovely examples of how an educator might use same but different to draw out ideas that involve things like place value, geometry, equivalent fractions, and that's just a few. So I'm wondering if you might share a few examples from different grade levels with our listeners, perhaps at some different grade levels.
Sue: Sure. So starting out, we can start with place value. It really sort of pops when we look in that topic area. So when we think about place value, we have a base ten number system, and our numbers are based on this idea that 10 of one makes one group of the next. And so, using same but different, we can help young learners make sense of that system.
So, for example, we could look at an image that shows a 10-stick. So maybe that's made out of Unifix cubes. There's one 10-stick a
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Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:03):
Students sometimes struggle in mathbecause they fail to make connections for
too many students.
Every concept feels like its own entitywithout any connection to the larger
network of mathematical ideas.
Today we're talking with Sue Looneyabout a powerful routine called Same but
Different and the ways teachers canuse it to help students identify
(00:24):
connections and foster flexible reasoning.
Well, hi Sue. Welcome to the podcast.
I'm so excited to betalking with you today.
Hi Mike. Thank you somuch. I am thrilled too.
I've been really looking forward to this.
Well, for listeners whodon't have prior knowledge,
I'm wondering if we could start byhaving you offer a description of the
(00:47):
same but different routine.
Absolutely.
So the same but differentroutine is a classroom routine
that takes two images or
numbers or words and putsthem next to each other and
asks students to describe howthey are the same but different.
(01:10):
It's based in a language learningroutine but applied to the math
classroom.
I think that's a great segue becausewhat I wanted to ask is at the broadest
level,
regardless of the numbers orthe content or the image or
images that educators select,
how would you explain whatsame but different is good for?
(01:35):
Maybe put another way,
how should a teacher thinkabout its purpose or its value?
Great question.
I think a good analogy is toimagine you're in your ELA,
your English language arts classroom andyou were asked to compare and contrast
two characters in a novel.
So the foundations of the routinereally sit there and what it's good for
(01:56):
is to help our brains thinkcategorically and relationally.
So in mathematics in particular,
there's a lot of overlap betweenconcepts and we're trying to develop this
relational understanding of concepts sothat they sort of build and grow on one
another. And when we askourselves that question,
how are these two thingsthe same but different?
(02:19):
It helps us put things intocategories and understand that
sometimes there's overlap,so there's gray space.
So it helps us move from blackand white thinking into this
understanding of gray scale thinking.And if I just zoom out a little bit,
if I could, Mike, when we zoomout into that gray scale area,
(02:40):
we're developing flexibility of thought,
which is so important inall aspects of our lives.
We need to be nimble on our feet, weneed to be ready for what's coming.
And it might not be black or white, itmight actually be a little bit of both.
So that's the power of theroutine and its roots come
(03:00):
in exploring executive functioningand language acquisition.
And so we just layer that on topof mathematics and it's pure gold.
When we were preparing for this podcast,
you shared several reallylovely examples of how an
educator might use same butdifferent to draw out ideas that
(03:23):
involve things like place value, geometry,
equivalent fractions,and that's just a few.
So I'm wondering if you might share afew examples from different grade levels
with our listeners perhaps atsome different grade levels.
Sure. So starting out, wecan start with place value.
It really sort of pops whenwe look in that topic area.
(03:45):
So when we think about place value,
we have a base 10 number system and ournumbers are based on this idea that 10
of one makes one group of the next.
And so using same but different,
we can help young learners makesense of that system. So for example,
we could look at an imagethat shows a 10 stick.
So maybe that's made out of Unix cubes.
(04:07):
There's one 10 stick a stick of10 with three extras next to it
and next to that are 13 separate cubes.
And then we ask how arethey the same but different?
And so helping children developthat idea that while I have one
10 in that collection,I also have 10 ones.
(04:29):
That is so amazing because I will sayas a former kindergarten and first grade
teacher,
that notion of somethingbeing a unit of one composed
of smaller units is such abig deal and we can talk about
that so much.
But the way that I can visualizethis in my mind with the
(04:50):
stick of 10 and the threeand then the 13 individuals,
what jumps out is that it invitesthe students to notice that as
opposed to me as the teacher feelinglike I need to offer some kind of perfect
description that suddenly thelight bulb goes off for kids.
Does that make sense?
It does. And I lovethat description of it.
(05:11):
So what we do is we invitethe students to add their own
understanding and their own languagearound a pretty complex idea.
And they're invited inbecause it seems so simple.
How are these the same butdifferent? What do you notice?
And so it's a pretty complexidea and we gloss over it.
Sometimes we think our studentsunderstand that and they really don't.
(05:35):
Is there another examplethat you want to share?
Yeah, I'd love the fractionexample. So equivalence,
when I learned about this routine,
the first thing that came to mind forme when I layered it from thinking about
language into mathematics was, ohmy gosh, it's equivalent fractions.
So if I were to asklisteners to think about,
put a picture in your head of one halfand imagine in your mind's eye what that
(05:59):
looks like. And thenif I said to you, okay,
well now I want you to imagine twofourths, what does that look like?
And chances are those pictures arenot the same. Mike, when you imagine,
did you picture the same thing ordid you picture different things?
They were actually fairly different.
Yeah. So when we think aboutone half is two fourth,
(06:21):
and we tell kids those arethe same, yes and no, right?
They have the same value that if we werelooking at a collection of m and ms or
Skittles or something, maybe half of themare green, and if we make four groups,
two fourths are green. Butcontextually it could really vary.
And so helping children makesense of equivalence is a perfect
(06:44):
example of how we can ask thequestion. Same but different.
So we just show two pictures.
One picture is one half andone picture is two fourths,
and we use the same colors, thesame shapes, sort of the same topic,
but we group them a little differentlyand we have that conversation with kids
to help make sense of equivalence.
So I want to shift because we'vespent a fair amount of time right now
(07:07):
describing two instances where youcould take a concept like equivalent
fractions or place value andyou could design a set of
images within the same but differentroutine and do some work around that.
But you also talked with me aswe were preparing about different
scenarios where same butdifferent could be a helpful tool.
(07:29):
So what I remember is youmentioned three discreet instances,
this notion of concepts that connect,
things learned in pairs andcommon misconceptions or as I've heard you describe
them, naive conceptions. Can youtalk about each of those briefly?
Sure. As I talked aboutthis routine to people,
I really want educators to be ableto find the opportunities on their
(07:53):
own authentically as opportunities arise.
So we should think about eachof these as an opportunity.
So I'll start with concepts that connectwhen you're teaching something new,
it's good practice to connectit to what do I already know?
So maybe I'm in a third grade classroomand I want to start thinking about
multiplication.
(08:14):
And so I might want toconnect repeated addition to
multiplication.
So we could look at two plustwo plus two next to two times
three. And it can be an expression,these don't always have to be images.
And a fun thing to look at mightbe to find out where do I see
three and two plus two plus two?
(08:37):
So what's happening here with factors,what is happening with the operations?
And then of course they bothyield the same answer of six.
So concepts that connect are particularlypowerful for helping children build
from where they know which is themost powerful place for us to be.
Love that.
Great. The next one is thingsthat are learned in pairs.
(09:00):
So there's all sorts of things thatcome in pairs and can be confusing.
And we teach kids all sorts ofweird tricks and poems to tell
themselves and whateverto keep stuff straight.
And another approach could be tolet's get right in there to where it's
confusing. So for example,
if we think about area and perimeter,
(09:23):
those are two ideas thatare frequently confusing for
children. And we often focus on,well, this is how they're different,
but what if we put up an image,let's say it's a rectangle,
but wouldn't have to be. And we'vegot some dimensions on there.
We're going to think about the area ofone and then the perimeter on the other.
(09:45):
What is the same though, right? Becausewhere the confusion is happening.
So just telling students, wellperimeters around the outside,
so think of P for pen or somethinglike that and areas on the
inside. What if we looked at, well,
what's the same about these two things?We're using those same dimensions,
(10:06):
we've got the same shape,
we're measuring in both of those andlet students tell you what is the same
and then focus on that criticalthing that's different,
which ultimately leads to understandingformula for finding both of those
things.
But we've got to start at that conceptlevel and link it to scenarios that make
sense for kids.
(10:28):
Before we move on to talking aboutmisconceptions or naive conceptions,
I want to mark that point,
this idea that confusion for childrenmight actually arise from the fact
that there are some things that are thesame as opposed to a misunderstanding of
what's different.
I really think that's animportant question that an educator could consider when
(10:50):
they're thinking about makingthis bridging step between one concept or another
or the fact that kids have learnedhow whole numbers behave and also
how fractions might behave,
that there actually might be some thingsthat are similar about that that caused
the confusion,
particularly on the front end ofexploration as opposed to they just don't
(11:10):
understand the difference.
And what happens there is then weaid in memory because we've developed
these aha moments and painteda more detailed picture of our
understanding in our mind's eye.
And so it's going to really help childrento remember those things as opposed to
these mnemonic tricks thatwe give kids that may work,
(11:32):
but it doesn't mean they understand it.
Absolutely. Well,
let's talk about naive conceptions andthe ways that same and difference can
work with those.
So I want to kick it up to maybe middleschool and I was thinking about what
example might be good here andI want to talk about exponents.
So if we have two raised to the third,
(11:53):
the most common naive conception wouldbe like, oh, I just multiply that.
It's just two times three.So let's talk about that.
So if I am working on exponents,
I notice a lot of mystudents are doing that,
let's put it right up upon theboard, two rays to the third power,
two times three, how arethese the same but different?
(12:17):
And the conversations abit like that last example,
well let's pay attentionto what's the same here,
but noticing something that alot of children have not quite
developed clearly and then putting itup there against where we want them to
go and then helping them. I likethat you use the word bridge.
Helping them bridge their way over therethrough this conversation is especially
(12:40):
powerful.
I think the other thing that jumpsout for me as you were describing that
example with exponents is that in someways what's happening there when you have
an example,
two times three next to twoto the third power is you're
actually inviting kids to tell you, thisis what I know about multiplication.
So you're not just disregarding itor saying we're through with that.
(13:04):
It's in the exploration that thoseideas come out and you can say to
kids, you are right, that ishow multiplication functions,
and I can see why that wouldlead you to think this way.
And it's a flow that's different.
It doesn't disregard kids' thinkingit actually acknowledges it.
And that feels subtle,but really important.
(13:26):
I really love shining a light on that.
So it allows us to operatefrom a strength perspective.
So here's what I know andlet's build from there.
So it absolutely draws out inthe discussion what it is that
children know about the conceptsthat we put in front of them.
So I want to shift now and talkabout enacting same but different.
(13:48):
I know that you've developed a protocolfor facilitating the same but different
routine, and I'm wondering if you couldtalk us through the protocol, Sue,
how should a teacher think about theirrole during same but different and are
there particular teacher moves thatyou think are particular important?
Sure.
So the protocol I've workedout goes through five steps
(14:10):
and it's really nice to just kindof think about them succinctly.
And all of them have embedded withinthem particular teacher moves.
They are all based onresearch of how children learn
mathematics and engage in meaningfulconversation with one another.
So step one is to look.
(14:31):
So if I'm using this routine with threeand four year olds and I'm putting a
picture in front of them, learningthat to be a good observer,
we've got to have eyes onwhat it is we're looking at.
So I have examples of counting,
asking a 4-year-old how manythings do I have in front of me?
And they're counting away withouteven looking at the stuff.
So teaching the skill ofobservation, step one is look,
(14:55):
step two is silent think time.
And this is so critically important.So giving everybody the
time to get their thoughts together.
If we allow hands to goin the air right away,
it makes others that haven't hadthat processing time to figure it
out shut down quite often.
(15:16):
And we all think at different speedswith different tasks all the time,
all day long.
So we just honor that everyone's goingto have generally about 60 seconds
in which to silently think,
and we give students a sentence frameat that time to help them. Again,
this is a language-based learning routine.
So we would maybe put on theboard or practice saying out loud,
(15:40):
I'd like you to think aboutthey are the same because blank,
they are different because blank.
And that silent think time is justso important for allowing access
and equitable opportunitiesin the classrooms.
The way that you described theimportance of giving kids that space,
(16:01):
it seems like it's a littlebit of a two for one,
because we're also kind of pushing backon this notion that to be good at math,
you have to have yourhand in the air first,
and if you don't have your hand inthe air first or close to first,
your idea may be less valuable.
So I just wanted to shine a light on thedifferent ways that seems important for
(16:22):
children,
both in the task that they're engagingwith and also in the culture that you're
trying to build around mathematics.
I think it's really important. And ifwe even zoom out further just in life,
we should think before wespeak, we should take a moment.
We should get our thoughts together.
We should formulate what it is thatwe want to say and learning how to be
(16:42):
thoughtful and giving the luxuryof what we're just going to
all think for 60 seconds. And guesswhat? If you had an idea quickly,
maybe you have another one. How elseare they the same but different?
So we just keep that culture thatwe're fostering, like you mentioned,
we just sort of growthat within this routine.
I think it's very safe to say that theworld might be a better place if we all
(17:05):
took 60 seconds to think aboutwhat we wanted to say. Sometimes.
Yes. So as teachers,
we can start teaching that and wecan teach kids to advocate for that.
I just need a moment to get mythoughts together. All right,
so the third step is the turn and talk.
And it's so important andit's such an easy move.
(17:26):
It might be my favoritepart. So during that time,
we get to have both an experiencewith expressive language and receptive
language, every single person.
So as opposed to hands in the airand I'm playing ball with you, Mike,
and you raise your hand and you getto speak and we're having a good time.
When I do a turn and talk, everybodyhas an opportunity to speak.
(17:47):
And so taking the thoughts that are intheir head and expressing them is a big
deal. And if we think aboutour multilingual learners,
our young learners,even our older learners,
and it's just a brand new concept thatI've never talked about before. And then
on the other side, the receptive learning.
So you are hearing from someone elseand you're getting that opportunity of
(18:11):
perspective taking. Maybe theynotice something you hadn't noticed,
which is likely to happen tosomebody within that discussion. Wow,
I never thought about it that way. Sothe turn and talk is really critical.
And the teacher's role duringthis is so much fun because we are
walking around and we're listening and Istarted walking around with a notebook.
(18:33):
So I tell students while you are talking,I'm going to collect your thinking.
And so I'm already imaginingwhere this is going next.
And so I'm on the ground if we'resitting on the rug, I'm leaning over,
I'm collecting thoughts,I'm noticing patterns,
I'm noticing where I want to gonext as the facilitator of the
(18:54):
conversation that's going to happen, wholegroup. So that's the third component,
turn and talk.The fourth component is the share.
So if I've walked around andgathered student thinking,
I could say who would like to share theirthinking and just throw it out there.
But I could instead say,
let's say we're doing the same butdifferent with squares and rectangles.
(19:15):
And I could say,
I noticed a lot of you talkingabout the length of the sides.
Is there anyone that was talking aboutthe lengths of the sides that would like
to share what either youor your partner said?
So I know that I want tosteer it in that direction.
I know a lot of people talked aboutthat, so let's get that in the air.
(19:35):
But the share is really important becausethese little conversations have been
happening now. We want tomake it public for everybody,
and we're calling on maybethree or four students.
We're not trying to getaround to everybody.
We're probably hopefully not going todrawing Popsicle sticks and going random
at this point. Studentshave had the opportunity to talk, to listen, to prepare.
(19:58):
They've had a sentence stem.
So let's see who would like to shareand get those important ideas out.
I think what strikes me is there'ssome subtlety to what's happening there
because you are namingsome themes that you heard.
And as you do that, and you namethat, kids can say, that's me,
(20:18):
or I thought about that or mypartner thought about that.
You're also clearly actingwith intention as an educator.
There are probably some ideas thatyou either heard that you want to
amplify or that youwant kids to attend to,
and yet you're not doing it in a way thattakes away from the conversations that
they had.
(20:39):
You're still connecting towhat they said along the way,
and you're not suddenly saying,great, you had your turn and talk,
but now let's listen to David over herebecause we want to hear what he has to
share.
Yes. And I don't have to be afraidof calling out a naive conception.
Maybe a lot of people were saying, well,I think the rectangles have too long,
(21:02):
too short, and they're not seeingthat the square is also a rectangle.
And so maybe I'm going to use thatlanguage in the conversation too,
so that yeah, theintentionality is exactly it.
Building off of that turnand talk to the share,
the last step is the summary.So after we've shared,
we have to have put a bow on that,right? So we've had this experience.
(21:25):
They generally are under 15minutes, could be five minutes,
could be 10 minutes, but we've donesomething important altogether.
And so the teacher's rolehere is to summarize,
to bring that all togetherand to sort of say, okay,
so we looked at this picture here andwe noticed I'll stick with the square
rectangle example thatboth shapes have four
(21:49):
sides and four square corners.They're both
rectangles, but this oneover here is a special one.
It's a square and all four sidesare equal and that's what makes it
special or something like that.
But we want to succinctlynail that down in a
summary.
(22:10):
If you do a same but differentand nobody gets there,
and so you chose thiswith intention, you said,
this is what we need to talk abouttoday. And all of a sudden you're like,
oh boy. Then your summarymight not sound like that.
It might sound like some of you noticethis and some of you notice that,
and we're going to come back to thisafter we do an activity where we're going
(22:31):
to be sorting some shapes.
So it's an opportunityfor formative assessment.
So summary isn't say what Ireally wanted to say all along,
even though I do havesomething I want to say,
it's a connection to whathappened in that conversation.
And so almost always itcomes around to that.
But there are those instanceswhere you learn that we need to
(22:55):
do some more work here. Before Ican just nicely put that bow on it.
You're making me think about what oneof my longtime mentors used to say,
and the analogy he would use is youcan definitely lead the horse to water,
but it is not your job to shovethe horse's face in the water.
And I think what you're really gettingat is I can have a set of mathematical
(23:17):
goals that I'm thinking about asI'm going into a same and different.
I can act with intention,
but there is still kind of this elementof I don't quite know what's going to
emerge. And if that happens,
don't shove the metaphoricalhorse's head in the water.
Meaning don't force that there.
(23:39):
If the kids haven't made the connectionyet or they haven't explored the gray
space, that's important. Acknowledgethat that's still in process.
Exactly. There is one last optionalstep which relates to summary.
So if you have time andyou're up for an exploration,
you can now ask your studentsto make one of their own.
(24:01):
And that's a whole otherlevel of sophistication of
thought for students to recognize, oh,
this is how those twowere same but different.
I'm going to make another set that arethe same but different in the same way.
It's actually a very complex task.
We could scaffold it by givingstudents, if this was my first image,
(24:23):
what would the other one be?
That would be like what wejust did very worthwhile.
Obviously now we're not within the 10minute timeframe. It's a lot bigger.
What I found myself thinking about,the more that we talk through intent,
purpose, examples, the protocolsteps is the importance of language.
(24:43):
And it seemed like part of what'shappening is that the descriptive language
that's accessed over the course ofthe routine that comes from students,
it really paves the way fordeeper conceptual understanding.
Is that an accurate understanding ofthe way that same and different can
function?
A hundred percent.
So it's really the way that wethink as we're looking at something,
(25:07):
we might be thinking inmental pictures of things,
but we might also be thinking in thewords and if we're going to function
in a classroom and in society,
we have to have the language for whatit is that we're doing. And so yes,
we're playing in that space of languageacquisition, expressive language,
receptive language,
all of it to help us developthis map of what that is really
(25:31):
deeply all about so thatwhen I see that concept
in another context,
I have this rich database inmy head that involves language
that I can draw on to nowdo the next thing with it.
That's really powerful. Listenershave heard me say this before,
(25:52):
but we've just had a really insightfulconversation about the structure,
the design, the implementation, andthe impact of same and different.
And yet we're coming tothe end of the podcast.
So I want to offer an opportunityfor you to share any resources,
any websites,
any tools that you think a listener whowanted to continue learning about same
(26:14):
but different, where might theygo? What might you recommend Sue?
Sure. So there's two mainplaces to find things,
and they actually do exist in both. Butthe easiest way to think about this,
there is the website,
which is same but different math.com,
and it's important to getthe word math in there.
(26:34):
And that is full of imagesfrom early learning,
really even up through highschool. So that's the first place,
and they are there with acreative common licensing.
And then you mentioned tools.
So there are some tools and ifwe wanted to do deeper learning,
and I think the easiest way toaccess those is my other website,
which is just loony math.com.
(26:56):
And if you go up at the top under books,
there's a children's book that youcan have kids reading and enjoying it
with a friend.
There's a teacher book that talks aboutin more detail some of the things we
talked about today.
And then there are some cards wherestudents can sit in a learning
center and turn over a card thatpresents them with an opportunity to sit
(27:19):
shoulder to shoulder.
And so those are all easily accessedreally on either one of those websites,
but probably easiest to findunder the loony math.com.
One for listeners,
we'll put a link to those resources inthe show notes to this episode. Sue,
I think this is probablya good place to stop,
but I just want to say thank you again.
It really has been a pleasuretalking with you today.
(27:40):
You're welcome, Mike. It's one ofmy favorite things to talk about,
so I really appreciate the opportunity.
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.
Students sometimes struggle in mathbecause they fail to make connections for
too many students.
Every concept feels like its own entitywithout any connection to the larger
network of mathematical ideas.
Today we're talking with Sue Looneyabout a powerful routine called Same but
Different and the ways teachers canuse it to help students identify
(00:24):
connections and foster flexible reasoning.
Well, hi Sue. Welcome to the podcast.
I'm so excited to betalking with you today.
Hi Mike. Thank you somuch. I am thrilled too.
I've been really looking forward to this.
Well, for listeners whodon't have prior knowledge,
I'm wondering if we could start byhaving you offer a description of the
(00:47):
same but different routine.
Absolutely.
So the same but differentroutine is a classroom routine
that takes two images or
numbers or words and putsthem next to each other and
asks students to describe howthey are the same but different.
(01:10):
It's based in a language learningroutine but applied to the math
classroom.
I think that's a great segue becausewhat I wanted to ask is at the broadest
level,
regardless of the numbers orthe content or the image or
images that educators select,
how would you explain whatsame but different is good for?
(01:35):
Maybe put another way,
how should a teacher thinkabout its purpose or its value?
Great question.
I think a good analogy is toimagine you're in your ELA,
your English language arts classroom andyou were asked to compare and contrast
two characters in a novel.
So the foundations of the routinereally sit there and what it's good for
(01:56):
is to help our brains thinkcategorically and relationally.
So in mathematics in particular,
there's a lot of overlap betweenconcepts and we're trying to develop this
relational understanding of concepts sothat they sort of build and grow on one
another. And when we askourselves that question,
how are these two thingsthe same but different?
(02:19):
It helps us put things intocategories and understand that
sometimes there's overlap,so there's gray space.
So it helps us move from blackand white thinking into this
understanding of gray scale thinking.And if I just zoom out a little bit,
if I could, Mike, when we zoomout into that gray scale area,
(02:40):
we're developing flexibility of thought,
which is so important inall aspects of our lives.
We need to be nimble on our feet, weneed to be ready for what's coming.
And it might not be black or white, itmight actually be a little bit of both.
So that's the power of theroutine and its roots come
(03:00):
in exploring executive functioningand language acquisition.
And so we just layer that on topof mathematics and it's pure gold.
When we were preparing for this podcast,
you shared several reallylovely examples of how an
educator might use same butdifferent to draw out ideas that
(03:23):
involve things like place value, geometry,
equivalent fractions,and that's just a few.
So I'm wondering if you might share afew examples from different grade levels
with our listeners perhaps atsome different grade levels.
Sure. So starting out, wecan start with place value.
It really sort of pops whenwe look in that topic area.
(03:45):
So when we think about place value,
we have a base 10 number system and ournumbers are based on this idea that 10
of one makes one group of the next.
And so using same but different,
we can help young learners makesense of that system. So for example,
we could look at an imagethat shows a 10 stick.
So maybe that's made out of Unix cubes.
(04:07):
There's one 10 stick a stick of10 with three extras next to it
and next to that are 13 separate cubes.
And then we ask how arethey the same but different?
And so helping children developthat idea that while I have one
10 in that collection,I also have 10 ones.
(04:29):
That is so amazing because I will sayas a former kindergarten and first grade
teacher,
that notion of somethingbeing a unit of one composed
of smaller units is such abig deal and we can talk about
that so much.
But the way that I can visualizethis in my mind with the
(04:50):
stick of 10 and the threeand then the 13 individuals,
what jumps out is that it invitesthe students to notice that as
opposed to me as the teacher feelinglike I need to offer some kind of perfect
description that suddenly thelight bulb goes off for kids.
Does that make sense?
It does. And I lovethat description of it.
(05:11):
So what we do is we invitethe students to add their own
understanding and their own languagearound a pretty complex idea.
And they're invited inbecause it seems so simple.
How are these the same butdifferent? What do you notice?
And so it's a pretty complexidea and we gloss over it.
Sometimes we think our studentsunderstand that and they really don't.
(05:35):
Is there another examplethat you want to share?
Yeah, I'd love the fractionexample. So equivalence,
when I learned about this routine,
the first thing that came to mind forme when I layered it from thinking about
language into mathematics was, ohmy gosh, it's equivalent fractions.
So if I were to asklisteners to think about,
put a picture in your head of one halfand imagine in your mind's eye what that
(05:59):
looks like. And thenif I said to you, okay,
well now I want you to imagine twofourths, what does that look like?
And chances are those pictures arenot the same. Mike, when you imagine,
did you picture the same thing ordid you picture different things?
They were actually fairly different.
Yeah. So when we think aboutone half is two fourth,
(06:21):
and we tell kids those arethe same, yes and no, right?
They have the same value that if we werelooking at a collection of m and ms or
Skittles or something, maybe half of themare green, and if we make four groups,
two fourths are green. Butcontextually it could really vary.
And so helping children makesense of equivalence is a perfect
(06:44):
example of how we can ask thequestion. Same but different.
So we just show two pictures.
One picture is one half andone picture is two fourths,
and we use the same colors, thesame shapes, sort of the same topic,
but we group them a little differentlyand we have that conversation with kids
to help make sense of equivalence.
So I want to shift because we'vespent a fair amount of time right now
(07:07):
describing two instances where youcould take a concept like equivalent
fractions or place value andyou could design a set of
images within the same but differentroutine and do some work around that.
But you also talked with me aswe were preparing about different
scenarios where same butdifferent could be a helpful tool.
(07:29):
So what I remember is youmentioned three discreet instances,
this notion of concepts that connect,
things learned in pairs andcommon misconceptions or as I've heard you describe
them, naive conceptions. Can youtalk about each of those briefly?
Sure. As I talked aboutthis routine to people,
I really want educators to be ableto find the opportunities on their
(07:53):
own authentically as opportunities arise.
So we should think about eachof these as an opportunity.
So I'll start with concepts that connectwhen you're teaching something new,
it's good practice to connectit to what do I already know?
So maybe I'm in a third grade classroomand I want to start thinking about
multiplication.
(08:14):
And so I might want toconnect repeated addition to
multiplication.
So we could look at two plustwo plus two next to two times
three. And it can be an expression,these don't always have to be images.
And a fun thing to look at mightbe to find out where do I see
three and two plus two plus two?
(08:37):
So what's happening here with factors,what is happening with the operations?
And then of course they bothyield the same answer of six.
So concepts that connect are particularlypowerful for helping children build
from where they know which is themost powerful place for us to be.
Love that.
Great. The next one is thingsthat are learned in pairs.
(09:00):
So there's all sorts of things thatcome in pairs and can be confusing.
And we teach kids all sorts ofweird tricks and poems to tell
themselves and whateverto keep stuff straight.
And another approach could be tolet's get right in there to where it's
confusing. So for example,
if we think about area and perimeter,
(09:23):
those are two ideas thatare frequently confusing for
children. And we often focus on,well, this is how they're different,
but what if we put up an image,let's say it's a rectangle,
but wouldn't have to be. And we'vegot some dimensions on there.
We're going to think about the area ofone and then the perimeter on the other.
(09:45):
What is the same though, right? Becausewhere the confusion is happening.
So just telling students, wellperimeters around the outside,
so think of P for pen or somethinglike that and areas on the
inside. What if we looked at, well,
what's the same about these two things?We're using those same dimensions,
(10:06):
we've got the same shape,
we're measuring in both of those andlet students tell you what is the same
and then focus on that criticalthing that's different,
which ultimately leads to understandingformula for finding both of those
things.
But we've got to start at that conceptlevel and link it to scenarios that make
sense for kids.
(10:28):
Before we move on to talking aboutmisconceptions or naive conceptions,
I want to mark that point,
this idea that confusion for childrenmight actually arise from the fact
that there are some things that are thesame as opposed to a misunderstanding of
what's different.
I really think that's animportant question that an educator could consider when
(10:50):
they're thinking about makingthis bridging step between one concept or another
or the fact that kids have learnedhow whole numbers behave and also
how fractions might behave,
that there actually might be some thingsthat are similar about that that caused
the confusion,
particularly on the front end ofexploration as opposed to they just don't
(11:10):
understand the difference.
And what happens there is then weaid in memory because we've developed
these aha moments and painteda more detailed picture of our
understanding in our mind's eye.
And so it's going to really help childrento remember those things as opposed to
these mnemonic tricks thatwe give kids that may work,
(11:32):
but it doesn't mean they understand it.
Absolutely. Well,
let's talk about naive conceptions andthe ways that same and difference can
work with those.
So I want to kick it up to maybe middleschool and I was thinking about what
example might be good here andI want to talk about exponents.
So if we have two raised to the third,
(11:53):
the most common naive conception wouldbe like, oh, I just multiply that.
It's just two times three.So let's talk about that.
So if I am working on exponents,
I notice a lot of mystudents are doing that,
let's put it right up upon theboard, two rays to the third power,
two times three, how arethese the same but different?
(12:17):
And the conversations abit like that last example,
well let's pay attentionto what's the same here,
but noticing something that alot of children have not quite
developed clearly and then putting itup there against where we want them to
go and then helping them. I likethat you use the word bridge.
Helping them bridge their way over therethrough this conversation is especially
(12:40):
powerful.
I think the other thing that jumpsout for me as you were describing that
example with exponents is that in someways what's happening there when you have
an example,
two times three next to twoto the third power is you're
actually inviting kids to tell you, thisis what I know about multiplication.
So you're not just disregarding itor saying we're through with that.
(13:04):
It's in the exploration that thoseideas come out and you can say to
kids, you are right, that ishow multiplication functions,
and I can see why that wouldlead you to think this way.
And it's a flow that's different.
It doesn't disregard kids' thinkingit actually acknowledges it.
And that feels subtle,but really important.
(13:26):
I really love shining a light on that.
So it allows us to operatefrom a strength perspective.
So here's what I know andlet's build from there.
So it absolutely draws out inthe discussion what it is that
children know about the conceptsthat we put in front of them.
So I want to shift now and talkabout enacting same but different.
(13:48):
I know that you've developed a protocolfor facilitating the same but different
routine, and I'm wondering if you couldtalk us through the protocol, Sue,
how should a teacher think about theirrole during same but different and are
there particular teacher moves thatyou think are particular important?
Sure.
So the protocol I've workedout goes through five steps
(14:10):
and it's really nice to just kindof think about them succinctly.
And all of them have embedded withinthem particular teacher moves.
They are all based onresearch of how children learn
mathematics and engage in meaningfulconversation with one another.
So step one is to look.
(14:31):
So if I'm using this routine with threeand four year olds and I'm putting a
picture in front of them, learningthat to be a good observer,
we've got to have eyes onwhat it is we're looking at.
So I have examples of counting,
asking a 4-year-old how manythings do I have in front of me?
And they're counting away withouteven looking at the stuff.
So teaching the skill ofobservation, step one is look,
(14:55):
step two is silent think time.
And this is so critically important.So giving everybody the
time to get their thoughts together.
If we allow hands to goin the air right away,
it makes others that haven't hadthat processing time to figure it
out shut down quite often.
(15:16):
And we all think at different speedswith different tasks all the time,
all day long.
So we just honor that everyone's goingto have generally about 60 seconds
in which to silently think,
and we give students a sentence frameat that time to help them. Again,
this is a language-based learning routine.
So we would maybe put on theboard or practice saying out loud,
(15:40):
I'd like you to think aboutthey are the same because blank,
they are different because blank.
And that silent think time is justso important for allowing access
and equitable opportunitiesin the classrooms.
The way that you described theimportance of giving kids that space,
(16:01):
it seems like it's a littlebit of a two for one,
because we're also kind of pushing backon this notion that to be good at math,
you have to have yourhand in the air first,
and if you don't have your hand inthe air first or close to first,
your idea may be less valuable.
So I just wanted to shine a light on thedifferent ways that seems important for
(16:22):
children,
both in the task that they're engagingwith and also in the culture that you're
trying to build around mathematics.
I think it's really important. And ifwe even zoom out further just in life,
we should think before wespeak, we should take a moment.
We should get our thoughts together.
We should formulate what it is thatwe want to say and learning how to be
(16:42):
thoughtful and giving the luxuryof what we're just going to
all think for 60 seconds. And guesswhat? If you had an idea quickly,
maybe you have another one. How elseare they the same but different?
So we just keep that culture thatwe're fostering, like you mentioned,
we just sort of growthat within this routine.
I think it's very safe to say that theworld might be a better place if we all
(17:05):
took 60 seconds to think aboutwhat we wanted to say. Sometimes.
Yes. So as teachers,
we can start teaching that and wecan teach kids to advocate for that.
I just need a moment to get mythoughts together. All right,
so the third step is the turn and talk.
And it's so important andit's such an easy move.
(17:26):
It might be my favoritepart. So during that time,
we get to have both an experiencewith expressive language and receptive
language, every single person.
So as opposed to hands in the airand I'm playing ball with you, Mike,
and you raise your hand and you getto speak and we're having a good time.
When I do a turn and talk, everybodyhas an opportunity to speak.
(17:47):
And so taking the thoughts that are intheir head and expressing them is a big
deal. And if we think aboutour multilingual learners,
our young learners,even our older learners,
and it's just a brand new concept thatI've never talked about before. And then
on the other side, the receptive learning.
So you are hearing from someone elseand you're getting that opportunity of
(18:11):
perspective taking. Maybe theynotice something you hadn't noticed,
which is likely to happen tosomebody within that discussion. Wow,
I never thought about it that way. Sothe turn and talk is really critical.
And the teacher's role duringthis is so much fun because we are
walking around and we're listening and Istarted walking around with a notebook.
(18:33):
So I tell students while you are talking,I'm going to collect your thinking.
And so I'm already imaginingwhere this is going next.
And so I'm on the ground if we'resitting on the rug, I'm leaning over,
I'm collecting thoughts,I'm noticing patterns,
I'm noticing where I want to gonext as the facilitator of the
(18:54):
conversation that's going to happen, wholegroup. So that's the third component,
turn and talk.The fourth component is the share.
So if I've walked around andgathered student thinking,
I could say who would like to share theirthinking and just throw it out there.
But I could instead say,
let's say we're doing the same butdifferent with squares and rectangles.
(19:15):
And I could say,
I noticed a lot of you talkingabout the length of the sides.
Is there anyone that was talking aboutthe lengths of the sides that would like
to share what either youor your partner said?
So I know that I want tosteer it in that direction.
I know a lot of people talked aboutthat, so let's get that in the air.
(19:35):
But the share is really important becausethese little conversations have been
happening now. We want tomake it public for everybody,
and we're calling on maybethree or four students.
We're not trying to getaround to everybody.
We're probably hopefully not going todrawing Popsicle sticks and going random
at this point. Studentshave had the opportunity to talk, to listen, to prepare.
(19:58):
They've had a sentence stem.
So let's see who would like to shareand get those important ideas out.
I think what strikes me is there'ssome subtlety to what's happening there
because you are namingsome themes that you heard.
And as you do that, and you namethat, kids can say, that's me,
(20:18):
or I thought about that or mypartner thought about that.
You're also clearly actingwith intention as an educator.
There are probably some ideas thatyou either heard that you want to
amplify or that youwant kids to attend to,
and yet you're not doing it in a way thattakes away from the conversations that
they had.
(20:39):
You're still connecting towhat they said along the way,
and you're not suddenly saying,great, you had your turn and talk,
but now let's listen to David over herebecause we want to hear what he has to
share.
Yes. And I don't have to be afraidof calling out a naive conception.
Maybe a lot of people were saying, well,I think the rectangles have too long,
(21:02):
too short, and they're not seeingthat the square is also a rectangle.
And so maybe I'm going to use thatlanguage in the conversation too,
so that yeah, theintentionality is exactly it.
Building off of that turnand talk to the share,
the last step is the summary.So after we've shared,
we have to have put a bow on that,right? So we've had this experience.
(21:25):
They generally are under 15minutes, could be five minutes,
could be 10 minutes, but we've donesomething important altogether.
And so the teacher's rolehere is to summarize,
to bring that all togetherand to sort of say, okay,
so we looked at this picture here andwe noticed I'll stick with the square
rectangle example thatboth shapes have four
(21:49):
sides and four square corners.They're both
rectangles, but this oneover here is a special one.
It's a square and all four sidesare equal and that's what makes it
special or something like that.
But we want to succinctlynail that down in a
summary.
(22:10):
If you do a same but differentand nobody gets there,
and so you chose thiswith intention, you said,
this is what we need to talk abouttoday. And all of a sudden you're like,
oh boy. Then your summarymight not sound like that.
It might sound like some of you noticethis and some of you notice that,
and we're going to come back to thisafter we do an activity where we're going
(22:31):
to be sorting some shapes.
So it's an opportunityfor formative assessment.
So summary isn't say what Ireally wanted to say all along,
even though I do havesomething I want to say,
it's a connection to whathappened in that conversation.
And so almost always itcomes around to that.
But there are those instanceswhere you learn that we need to
(22:55):
do some more work here. Before Ican just nicely put that bow on it.
You're making me think about what oneof my longtime mentors used to say,
and the analogy he would use is youcan definitely lead the horse to water,
but it is not your job to shovethe horse's face in the water.
And I think what you're really gettingat is I can have a set of mathematical
(23:17):
goals that I'm thinking about asI'm going into a same and different.
I can act with intention,
but there is still kind of this elementof I don't quite know what's going to
emerge. And if that happens,
don't shove the metaphoricalhorse's head in the water.
Meaning don't force that there.
(23:39):
If the kids haven't made the connectionyet or they haven't explored the gray
space, that's important. Acknowledgethat that's still in process.
Exactly. There is one last optionalstep which relates to summary.
So if you have time andyou're up for an exploration,
you can now ask your studentsto make one of their own.
(24:01):
And that's a whole otherlevel of sophistication of
thought for students to recognize, oh,
this is how those twowere same but different.
I'm going to make another set that arethe same but different in the same way.
It's actually a very complex task.
We could scaffold it by givingstudents, if this was my first image,
(24:23):
what would the other one be?
That would be like what wejust did very worthwhile.
Obviously now we're not within the 10minute timeframe. It's a lot bigger.
What I found myself thinking about,the more that we talk through intent,
purpose, examples, the protocolsteps is the importance of language.
(24:43):
And it seemed like part of what'shappening is that the descriptive language
that's accessed over the course ofthe routine that comes from students,
it really paves the way fordeeper conceptual understanding.
Is that an accurate understanding ofthe way that same and different can
function?
A hundred percent.
So it's really the way that wethink as we're looking at something,
(25:07):
we might be thinking inmental pictures of things,
but we might also be thinking in thewords and if we're going to function
in a classroom and in society,
we have to have the language for whatit is that we're doing. And so yes,
we're playing in that space of languageacquisition, expressive language,
receptive language,
all of it to help us developthis map of what that is really
(25:31):
deeply all about so thatwhen I see that concept
in another context,
I have this rich database inmy head that involves language
that I can draw on to nowdo the next thing with it.
That's really powerful. Listenershave heard me say this before,
(25:52):
but we've just had a really insightfulconversation about the structure,
the design, the implementation, andthe impact of same and different.
And yet we're coming tothe end of the podcast.
So I want to offer an opportunityfor you to share any resources,
any websites,
any tools that you think a listener whowanted to continue learning about same
(26:14):
but different, where might theygo? What might you recommend Sue?
Sure. So there's two mainplaces to find things,
and they actually do exist in both. Butthe easiest way to think about this,
there is the website,
which is same but different math.com,
and it's important to getthe word math in there.
(26:34):
And that is full of imagesfrom early learning,
really even up through highschool. So that's the first place,
and they are there with acreative common licensing.
And then you mentioned tools.
So there are some tools and ifwe wanted to do deeper learning,
and I think the easiest way toaccess those is my other website,
which is just loony math.com.
(26:56):
And if you go up at the top under books,
there's a children's book that youcan have kids reading and enjoying it
with a friend.
There's a teacher book that talks aboutin more detail some of the things we
talked about today.
And then there are some cards wherestudents can sit in a learning
center and turn over a card thatpresents them with an opportunity to sit
(27:19):
shoulder to shoulder.
And so those are all easily accessedreally on either one of those websites,
but probably easiest to findunder the loony math.com.
One for listeners,
we'll put a link to those resources inthe show notes to this episode. Sue,
I think this is probablya good place to stop,
but I just want to say thank you again.
It really has been a pleasuretalking with you today.
(27:40):
You're welcome, Mike. It's one ofmy favorite things to talk about,
so I really appreciate the opportunity.
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.
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