December 2, 2025 • 33 mins
A bag of popcorn, a few movie-theater secrets, and then the big pivot: what actually makes math materials high quality. We invited Bridget Gunn and Dan Henderson to help us pull HQIM out of acronym-land and into real classrooms, where teachers need time, students need voice, and everyone needs coherence. The result is a candid, practical tour of how curriculum design can elevate thinking without burying teachers in prep.
We break down five components that anchor equitable, engaging teaching—planning around big ideas, open and engaging tasks, student questions and conjectures, reasoning and justification, and teaching toward social justice—and show what they look like day to day. Bridget and Dan explain why “good” materials aren’t enough, how high quality design anticipates student strategies, and where author notes, sample questions, and team routines give you the support to listen, probe, and connect ideas. We dig into full-stack lesson arcs that start with experience and grow toward generalization, so students build concepts instead of memorizing steps.
You’ll hear how routines like rough draft talk shift authority to students, and why simple moves—like a quick door question—can spark belonging that pays off in mathematical risk-taking. We also share adoption advice: look past checklists and ask whether a program centers student thinking, connects concepts across units and grades, and gives practical facilitation cues that free your attention for what matters.
Come for the corn puns, stay for the concrete ways HQIM can transform your classroom culture. If this conversation resonates, follow the show, share it with a colleague, and leave a review telling us which “big idea” you want to see woven through your course next.
Send Joel and Misty a message!
The More Math for More People Podcast is produced by CPM Educational Program.
Learn more at CPM.org
X: @cpmmath
Facebook: CPMEducationalProgram
Email: cpmpodcast@cpm.org
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
SPEAKER_00 (00:17):
You are listening to the More Math for More People
podcast, an outreach of CPMeducational program.
Boom.
SPEAKER_02 (00:31):
December.
SPEAKER_03 (00:33):
I can't believe it's almost the end of 2025.
It's crazy.
SPEAKER_06 (00:38):
It is crazy.
SPEAKER_03 (00:39):
So it's 2nd of December.
SPEAKER_06 (00:42):
Yes.
SPEAKER_02 (00:43):
2nd of December?
It is 2nd of December.
And what's our national daytoday?
SPEAKER_00 (00:48):
Today is the business of popping corn day.
SPEAKER_03 (00:56):
That really sounds made up.
SPEAKER_00 (00:58):
No, they are.
They're all all things are justmade up.
SPEAKER_02 (01:01):
So you know that that wasn't much of a you know
qualification.
SPEAKER_00 (01:05):
No.
SPEAKER_02 (01:06):
The business of popping corn day.
SPEAKER_00 (01:08):
Everything about these days is made up.
It's totally true.
And and the business of poppingcorn day.
And I don't have the facts infront of me right now, but I can
tell you I like to pop corn.
SPEAKER_02 (01:19):
You like to pop corn?
You are you're gonna have factsabout popping corn?
I like so I remember whenpopping corn moved from you had
to put it in a pan with oil, andyou had to like shake and move
the pan, you know, and pop it toJiffy Pop, first of all, which I
(01:41):
don't sure I've actually hadJiffy Pop.
When I was a kid, we alwayswanted Jiffy Pop because it
looks so cool.
I mean, it looks so cool how itlike stands and blows the thing
up into a big bubble.
SPEAKER_00 (01:50):
It's all right there for you.
You don't even have to doanything.
SPEAKER_02 (01:52):
We were never we never got Jiffy Pop because you
know it was more expensive.
And they had the Jiffy Pop thatcame in different colors, I
think, even.
It was like rainbow jiffy pop.
And then it moved to the airpopper.
Like that was a big deal when itmoved to the air popper because
then you could put it in, itwould all spin around, it would
pop out into the bowl, and theninto microwave popcorn.
SPEAKER_00 (02:15):
Yep.
SPEAKER_02 (02:15):
Which pretty much feels like the only way I would
make popcorn now.
SPEAKER_00 (02:18):
Really?
I I still make it it it it's apan, but it has like a crank.
Oh so I I put the oil and then Ihave I have like three or four
bags of specialty corn that Ichoose from.
SPEAKER_02 (02:32):
So is the is the pan like a popping corn pan?
SPEAKER_00 (02:36):
It's a popping corn pan.
I I think it's actually calledlike the popping corn number two
or something like that.
unknown (02:43):
Oh.
SPEAKER_02 (02:43):
I don't know what the popping corn number is.
That makes sense.
And from then a third poppingcorn pan or any other third
popping corn pans.
SPEAKER_00 (02:51):
Definitely a hand crank situation, so you don't
have to shake the pan.
SPEAKER_02 (02:54):
You just burn.
SPEAKER_00 (02:57):
Yeah.
And I I remember the air popper.
And my folks still have an airpopper.
SPEAKER_02 (03:01):
Air popper was cool because you couldn't ever burn
the air popper pretty much.
SPEAKER_00 (03:06):
That was pretty cool.
It was fun to watch catchingyour mouth, like if you held it
over your head or whatever.
I don't I didn't really do that.
SPEAKER_02 (03:12):
I mean it was yeah.
SPEAKER_00 (03:14):
I don't like that.
I'm I made that up.
SPEAKER_02 (03:16):
That was I didn't like it that it you it was hard
to get the butter on it becauseyou had to like the butter was
on a little pan, the thing thatwas supposed to drip on, and
that didn't really work.
You just had to pour it onafterwards.
SPEAKER_00 (03:26):
We had we had one.
You know how I was talking aboutthe hand crank?
The crank would go by itself,like it was motorized.
And at the top of the dome wherethe it was gonna pop, you put
butter on it, and it was like afilter that dripped the butter
on as it heated up.
That was pretty good.
Did it work?
SPEAKER_02 (03:46):
Yeah.
SPEAKER_00 (03:48):
Yeah.
SPEAKER_02 (03:48):
Yeah.
I feel like the auto butterthings didn't work as
successfully.
Maybe they didn't make as muchbutter as I wanted.
When I I pretty much wanted likebutter, you know, popcorn dipped
in butter when I was a child.
SPEAKER_00 (03:58):
You know.
I think my second or third jobwas working in the movie
theater.
SPEAKER_02 (04:03):
At home.
SPEAKER_00 (04:04):
And just to put some context to it, Bill and Ted's
Excellent Adventure.
SPEAKER_02 (04:08):
Nice.
SPEAKER_00 (04:09):
Pet Cemetery, those kind of movies were coming out
at the time.
But I was an usher.
And it was actually one of thefirst public speakings I'd have
to do because I was collectingmoney for like the Will Rogers
Institute and stuff like that.
And with a popcorn, two things.
One, when they needed butter, Iwould have to go get this
(04:32):
five-gallon thing of butter-likesubstance.
unknown (04:36):
Right.
SPEAKER_00 (04:36):
And the butter-like substance, instantly my face
would break out in acne just byopening the can, right?
Like whatever I don't even knowwhat it was, but it was gross.
Second thing is, it's tricky ifyou go to the movie theater
during the morning becauseyou're getting last night's
popcorn.
You are not getting freshpopcorn because we had to save
(04:57):
it because it's so you know,popcorn's expensive and valid.
Oh, yeah.
Yeah, exactly.
You don't want to repop thatstuff.
SPEAKER_02 (05:05):
Waste all those things.
Oh man.
SPEAKER_00 (05:11):
I remember those days.
SPEAKER_02 (05:12):
Yeah.
Yeah.
Popcorn, I start with popcornthat has like sometimes it has
too much salt.
Like it has to have just theright amount of salt.
SPEAKER_00 (05:19):
Too much salt is a bad thing.
Too much salt is right.
SPEAKER_02 (05:22):
I remember I like I like that now, you know, I can
go to places and I can get like,you know, basically like cattle
corn or you know, fancierpopcorn.
They just make corn.
SPEAKER_00 (05:32):
I had a friend who asked me one time, do you want
some yeast on this popcorn?
And the the theater had likepopcorn yeast or whatever.
Yeah.
Sure.
But they mistaken the yeast fora for granulated sugar.
They were like in the samecontainer.
We ate it, but we still ate it.
I'm sure it was really it wasn'tit wasn't that good.
SPEAKER_02 (05:53):
It wasn't what you expected, but yeah, yeah,
interesting.
SPEAKER_00 (05:57):
Yeah.
SPEAKER_02 (05:57):
So just the other just the other night I went to a
Broadway show here in Portland,Shucked.
SPEAKER_06 (06:05):
Okay.
SPEAKER_02 (06:06):
Which it's not really about corn, but corn is
kind of the You Shuck a corn.
Yeah.
Well, uh yeah.
But it's not like it's not likea musical about corn.
It's a musical about thisreally, really small town that
you know grows corn, and corn iskind of the center of the theme.
But I would say more more thanthat, it's really about corny
jokes.
(06:27):
Like it is like just full ofpuns, non-stop, not like
continuous and like groaners,like so, and and and you know,
some very like you know,definitely not always in the
like mainstream, you know, likeclean jokes, but like it's you
know, it's along the lines ofyou know, Book of Mormon, or
(06:49):
some things that are pretty likethis.
But uh very, very it's so sofunny.
So, so funny.
I was sounds amazing.
It was far more hysterical thanI anticipated.
So yeah, very good.
Very cool.
I'll have to check it out.
Yeah, definitely.
If it's if it's in your area, Ihighly recommend it.
I would definitely either, andlike I say, it was very funny.
SPEAKER_00 (07:11):
Okay, very entertaining.
Excellent.
SPEAKER_02 (07:13):
So, what are you gonna do for the business of
popping corn?
SPEAKER_00 (07:18):
I am see you stress the business part.
I was just gonna pop some corn.
Well, I know.
SPEAKER_02 (07:25):
But if I'm celebrating, the business part
of it is apparently an importantpart of the day.
They wouldn't have labeled it,you know, the business of
popping corn.
SPEAKER_00 (07:32):
Maybe I'll actually read the label on the thing to
see what kind of businessproduces.
SPEAKER_02 (07:39):
Your business could be, you know, the the companies
that are making it, but it alsocould be the busyness of popping
corn.
SPEAKER_00 (07:46):
I'm gonna I'm gonna get busy and pop some corn.
How about you?
SPEAKER_02 (07:50):
I'm I think I'm definitely gonna eat some
popcorn today.
I might not pop it myself, butit will be popped corn.
SPEAKER_00 (07:55):
I love it.
SPEAKER_02 (07:56):
So there you go.
Enjoy your popped corn.
Indeed, so so we're here todaywith Bridget Gunn and Dan
(08:19):
Henderson.
Hi.
Bridget works on yeah, that'sDan.
Bridget works on the PL teamwith us, and Dan is on the
curriculum assessment team.
And we brought them here todaybecause we know they are people
who can answer our questionsabout HQIM.
SPEAKER_00 (08:36):
Yeah, what's that actually?
SPEAKER_02 (08:37):
Beginning with yeah, did you know what HQIM is, Joel?
SPEAKER_00 (08:40):
I had to look it up.
SPEAKER_02 (08:42):
Okay, what'd you find out?
SPEAKER_00 (08:44):
I think it's high quality instructional materials.
SPEAKER_02 (08:47):
I think I think that is targeted.
SPEAKER_00 (08:51):
But I I did have to look it up for sure.
Yeah.
And I saw that there was a verynice article about well,
actually, I it seems like thewhole publication was about
HQIM, but there was an articlein there.
And I and I'm not a big acronymfan, so I might start saying
high quality instructionalmaterials.
(09:13):
But Bridget and Dan were authorsof this article.
SPEAKER_02 (09:17):
They were.
They were amongst the authors ofthis article.
So we brought them here to helpanswer our questions about HQIM.
We already answered thequestion, what is it?
Well, what does it stand for?
Yes.
But my first question, beyondwhat it stands for, then, is
what is what what makessomething a high quality
instructional material like?
I feel like this is not justsomething you dub upon yourself.
(09:38):
Someone has to put some likecriteria on it.
So that's our first question,Bridget or Dan.
SPEAKER_03 (09:43):
What is an HQ?
What makes something an HQIM?
SPEAKER_01 (09:48):
Bridget, you want to try?
SPEAKER_03 (09:50):
Sure.
I'll try.
You're gonna have to nose goesor something.
SPEAKER_04 (09:58):
So we kind of took took the idea that like there
are a lot of good curriculummaterials or instructional
materials, I guess, that likefollow the standards and have
math problems in them.
But that high-qualityinstructional materials kind of
(10:20):
go one or a few steps furtherthan that.
And then we looked at um theCalifornia math framework.
They have a section on equitableand engaging teaching.
So we kind of looked athigh-quality instructional
materials through that lens.
And they have five components ofequitable and engaging teaching.
(10:43):
And we think that high-qualityinstructional materials do those
five things and really helpteachers on their journey to
equitable and engaging teaching.
SPEAKER_00 (10:56):
And what are the five things?
SPEAKER_04 (10:59):
The five things are perpleid teaching around big
ideas, to use open and engagingtasks, to invite student
questions and conjectures, toprioritize reasoning and
justification.
And this is also kind of ourinterpretation of these five
(11:21):
things, but that though doingthose four things can help you
teach towards social justice,which is the fifth component of
equitable and engaging teaching.
SPEAKER_02 (11:34):
And so are you suggesting or saying that if
something is a high qualityinstructional material, it does
those things automatically?
Or that would be included inlike if it meets the criteria of
being an HQIM, it's gonna dothose things?
Or are you suggesting that somedo that better than others?
Or like how connect those twofor me?
SPEAKER_01 (11:55):
So California just adopted a bunch of curricula,
and states across the countryare looking to adopt new
curricula, and schoolseverywhere are looking at
curricula and trying to decidewhat to pick.
We were thinking what do theyreally need to know in addition
to like checking your ed reportsor whatever, what do you really
want to look at?
Uh we identified some thingsthat good curriculum do that we
(12:17):
think high-quality curriculumcould do a little bit more.
One way to think about it islike like uh good material,
sorry, like a cookbook.
They give you good recipes andclear steps, you can follow all
those things.
But a high quality material ismore like a like a master chef
apprenticeship, where you getthe recipes, but you also learn
(12:38):
how to think about how things gotogether and how to rise given
what you've got.
That sort of thing.
SPEAKER_03 (12:45):
So I like that analogy.
SPEAKER_06 (12:47):
Yeah.
SPEAKER_03 (12:49):
So so what other things did you tell us?
Did you talk about then?
So how do those things gotogether?
SPEAKER_04 (12:57):
So one of the things we talked about is well, we kind
of think that all five of thesethings really work together.
So planning teaching around bigideas is this idea that math
concepts are interconnected.
And so instead of learning justlike your six times table, you
might talk about multiplicativethinking and reasoning, which is
(13:19):
like additive reasoning,subtractive, then moves into
proportional reasoning.
So like teaching around bigideas helps students connect
what they are currently learningto things that they already know
and sets them up for success infuture learning.
SPEAKER_01 (13:39):
Should we clarify that like so we think like good
materials uh do that?
They help you plan instructionaround big ideas.
We should not adopt materials,they don't do that.
On top of that, we thinkhigh-quality materials also
offer support for studentinteraction.
Like uh CPM uses those studyteam teaching strategies.
SPEAKER_06 (13:59):
That would be one of those supports efforts.
I mean quiet now.
SPEAKER_02 (14:08):
There's no there's no need to be quiet.
SPEAKER_00 (14:09):
I know.
SPEAKER_02 (14:10):
Well that's a podcast, someone has to be
talking.
SPEAKER_00 (14:13):
What when I was looking over the article, it it
seemed it seemed like, okay,there's five things.
Those five things seem prettybig to me.
Like, like it it's not a simpleone, two, three, four, five
checklist or something likethat.
Like it's it's a bigger ideathan that.
And what stood out to me, andI'm interested to hear what you
(14:35):
have to say about this, is thatit it's not just about the
students, it kind of frees upthe teacher to be in a
beneficial teaching mode almost.
SPEAKER_04 (14:49):
Yeah, I feel like the the kind of difference
between good materials and highquality instructional materials
is that high qualityinstructional materials do free
up the time.
So you're not sitting there as ateacher figuring out, okay,
where do I put this lesson sothat it connects to all these
things?
Because we're about to do this.
(15:09):
Like that's a lot of brain spacefor one person to do on their
own.
So high quality instructionalmaterials kind of free you of
that brain space.
They give you the open andengaging task that's already
connected through a storylinethat naturally invites questions
and conjectures so that you canstep in and figure out how to
(15:33):
facilitate those conversations.
SPEAKER_05 (15:35):
Right.
SPEAKER_04 (15:35):
And it might even help you facilitate those
conversations by providing, youknow, an author's vision that
says, hey, when we wrote this,this is what we were thinking.
These are questions we might askin our classroom.
Um, consider doing thisactivity, consider doing this
exhibit visit and asking thesequestions as your closure for
(15:56):
the day.
SPEAKER_00 (15:57):
And again, what made me think about that too is your
conclusion.
I kept thinking I kept goingback to that teacher lens of
that your thinking matters, yourvoice matters, you matter, and
reflect and revise.
And with a high qualityinstructional material, it's
just seemed like that was ableto happen in a more what's the
(16:22):
right word, like a conducivespace, a free space, or like a
I'm saying, I'm probably sayingthis all wrong, but like a
visionary space of like as ateacher, I appreciate that that
what I bring to the tablematters as much as what I'm
trying to let students bring tothe table.
SPEAKER_04 (16:41):
I completely agree with that.
I feel like I feel like that'swhy so in that framework, they
talk about teaching towardssocial justice as like not
necessarily bringing justbringing in like social justice
topics or topics that you mightthink of when you think of that
phrase, but that there's an ideathat we are trying to develop
(17:07):
students into students withpositive math identity and
agency.
You're right, Joel, likehigh-quality instructional
materials kind of create theenvironment where teachers can
then have some breathing room tostep back and really observe
what's happening in theirclassrooms, really like try to
(17:28):
understand how their studentsare understanding these concepts
and then facilitate discussionsaround them.
So you're kind of gaining backthat agency of like, as a
teacher, what's going on in yourown classroom.
Because you're kind of likeputting the pieces together to
create this, this environment.
SPEAKER_02 (17:48):
I can see how I can see how this would also be.
So I'm like what I'm seeing andhearing is like that the
high-quality instructionalmaterials and those five things,
right, are really kind ofcreating the conducive
environment for the studentcentered classroom and bringing
kids into the conversation andthose pieces and changing the
(18:10):
teacher role, right?
Is what I hear you saying.
Like the teacher role shifts andchanges.
And it and at the same time, theteacher role needs to shift and
change, right?
You couldn't just bring ahigh-quality instructional
material into your classroom andthen just teach the way you were
always teaching.
Does that feel accurate?
SPEAKER_01 (18:29):
Yes.
If I was just I'm sitting overhere kind of being quiet and
thinking about the differencebetween my master's degrees in
curriculum and instruction, andthat's the sort of reality
that's playing in my head rightnow.
Instructional part obviouslybeing instruction and the
curriculum part being thematerials part.
Well I'm trying to think throughparsing out what your question
(18:52):
is about like how does theinstructional material shift
your instruction and vice versa.
That's why I'm being quiet.
You can edit that whole thingout if you want to, but no
worries.
SPEAKER_02 (19:07):
It feels like I was gonna say, what is your brain
putting together with it?
SPEAKER_01 (19:11):
Well, it sort of feels like the thinking about
the instructional shifts, right?
Like the center of student voiceand putting equity in the center
of the the conversation is twobig things that kind of have to
happen.
If you're not gonna listen towhat students say and take
(19:33):
seriously their ideas, thenthere's nothing the materials
can do for you.
But if you are willing to takethat leap and listen to
students, then instructionalmaterials can guide you with the
kinds of questions that will beopen and engaging for them
that'll help change theirperspective of the world and of
(19:55):
math and of themselves.
So that's the kind ofinstructional piece.
I feel like we have likespecific pieces embedded in the
CPM curriculum that do that,right?
Like we build in rough drafttalk and all the siding team
strategies like SWAT meets andthings like that.
And those routines shift theauthority of the classroom.
SPEAKER_06 (20:19):
Which make it more equitable just from the job.
That's uh instructional piece.
The materials piece, I'mthinking like the focus on the
big ideas.
SPEAKER_01 (20:35):
Super traditional instruction is organized around
like the very small day-to-day,can I do this skill?
Can I remember to carry the onewhen I'm adding multi-digit
numbers or whatever?
Big idea just keeps happeningover and over and over and over
again.
And this like within the theseventh grade curriculum, right?
(20:56):
We just have this idea ofproportional reasoning just
keeps happening, right?
It starts on that first datewith the pencil topic, and it
just keeps going.
And you just encounter it overand over and over again in these
different ways.
And that helps students connectit to the world and wrap their
heads around a really big shift.
Right.
When you think about it, like inelementary school, the only way
(21:16):
to think about differencebetween numbers is like six is
one more than five.
Right.
Like that's the extent of yourability to think about
difference.
That's super advanced if you'rein second grade.
It's not so advanced when you'rein seventh grade.
Because then you learn to thinkproportionally, you think okay,
(21:38):
six is twenty percent more thanfive.
Right.
It's like that kind ofrelationship.
What else is like what's what's20% bigger than than an old 20?
It's not just one more again.
It's a different thinking.
So it's a big idea, and it takessome time to wrap your head
around and it just keepshappening over and over and over
(21:59):
again.
It happens in a ton of differentcontexts and all that stuff, but
it's just a bigger thing thatyou have to think about a time.
SPEAKER_06 (22:09):
I'm angling, I'm sorry.
No, you're fine.
No.
SPEAKER_02 (22:13):
Well, and what I'm hearing you say is that like
like the material, the thecurriculum materials themselves
can have to lend themselves tothis different, these different
shifts in these ways ofthinking, right?
And shifting what's happening.
And the teacher also shifts whatthey're doing.
(22:33):
And these two things will happentogether, right?
Like you can't really it's hardto do one without the other
either way, right?
It's it's hard to move and dothe do these, make these five
changes, right?
Without a highly qualityinstructional material.
And it would be challengedactually to like stand and
deliver with a high qualityinstructional material.
They don't, they don't, they'renot, they're like co-compatible
(22:54):
in that way.
SPEAKER_01 (22:55):
Yeah.
Is that co-compatible is aninteresting phrase.
But I know I think they'rethey're almost codependent,
right?
Like you can't really have onewithout the other.
Yeah.
Think about like the we we madea point, I think, in the article
about full stack lessons.
(23:18):
Because she's the one that mostrecently actually read the
article again.
We did we did say that, right?
Uh Excel.
Yeah, so like the that fullstack idea is is the idea that
like you start with someexperience and then you describe
it linguistically, and then youstart to ask questions about it,
(23:39):
or then estimate and error, andthen you finally calculate
something, and then you canreveal what the answer is, and
then you can flip it around andchange the given and the little
yeah or the question uh or helpsyou get like a full range of
like exploration on a question.
(23:59):
Um and you can't if uh if thematerials aren't aren't there to
support it, then you're notgonna successfully do that in
your lesson.
But if you're not trying to dothat in your lesson, high
quality materials are gonna feelreally weird.
There's gonna be a whole bunchof stuff that's kind of left on
the table.
SPEAKER_00 (24:18):
So they're back to that codependent phrase.
SPEAKER_06 (24:22):
Mm-hmm.
SPEAKER_00 (24:23):
Yeah.
SPEAKER_06 (24:24):
Mm-hmm.
SPEAKER_00 (24:24):
I and I I I I like what you're saying there too
about so the the material thehigh quality material of what
I'm hearing you say is it'sgonna back you up.
So it's a shift.
Like when we're talking about ashift, sometimes I think, oh,
uh, as a teacher, I must bedoing something wrong because I
(24:45):
need to shift this way.
But maybe what you're doing isokay and it's promoting, but
what a high-quality materialwould do is back you up in
opening multiple avenues,opening discussions, opening
different thought processes.
SPEAKER_01 (25:03):
Yeah, exactly.
It would it would back you up init uh in a couple of specific
ways that we sort of try andhighlight or like we'll point
out in our in our teacher notesor in our author's vision uh
what we think students willprobably say based on our
experience with students andfield testing and all that.
And then we highlight what kindof responses you might give to
(25:26):
those things.
And we also highlight likeextension questions, we call
them encourage deeper thinkingquestions.
So there for everybody to like,hey, you had this thought, you
may as well explore thelandscape of math that's around
this problem.
Um when I was a when I was ageometry teacher, we were
playing around with Pythagoreantriples just because we had a
(25:46):
day before Thanksgiving, so thisis well timed.
Um playing around withPythagorean triples, and uh had
a group of students just be likescrewing around and were like,
well, what about A to the third,B to the third equals C to the
third?
And I was like, that'sinteresting.
See if you can find it, right?
Like, does it work?
Try some numbers.
(26:06):
They couldn't find any.
And I asked them, like, why?
Why do you think that is?
Like, can you give me anargument for why that's not
working at all?
Um they thought about it for acouple minutes and they decided
that instead of that they wouldtry another even number.
They'd try A to the fourthpower, B to the fourth power,
and C to the fourth power.
And I was happy with that.
They were fine, they werecontinuing their thinking,
right?
(26:26):
It's a nice big openexploration.
I didn't have the heart to tellthem, but or you'll hear the
podcast.
You get that that openness isthere for them to explore, and
you want to encourage it as longas they're thinking mission
accomplished.
SPEAKER_02 (26:49):
So you're good.
You're good.
As we so as we get toward it,kind of the end of the time that
we have here, like what are thebig things, the big takeaways
that you would want someone toremember as they're thinking
about high quality instructionalmaterials and good teaching?
SPEAKER_01 (27:05):
Well, my short and sweet answer is by CPM
curriculum.
Well, shouldn't say that on yourpodcast.
Yeah.
What's my what's my longeranswer to that, Bridget?
SPEAKER_04 (27:17):
Well, my longer answer.
I'm really encouraged by again,I live in California, so I guess
I'll say the Californiaframework matters out here.
And I'm really encouraged by thefocus on I think developing an
(27:42):
environment where students feellike they matter in a math
classroom more than theiranswers matter.
So I feel like a high-qualityinstructional material is going
to give you the space as ateacher to kind of find those
moments when your students arehaving really brilliant ideas
(28:05):
and allow you to dive into thatconversation with them.
We talk about um a lesson that'sin our eighth grade curriculum
about like finding as manyequations that have a solution
of four as you can, and the ideathat a student could kind of in
their middle school way writedown x equals four and say that
(28:29):
I'm done is like the best startto a conversation.
Is that a correct answer is whatdoes it mean to be, you know,
have a solution of four.
So I think finding instructionalmaterials that help you say
you're right, or yeah, explainthat to me more so that your
(28:52):
students start to really feel asthough they're a part of this
math classroom community andlearning community as as you
can.
SPEAKER_00 (29:01):
Yeah.
I'm I'm excited.
You know, that again, thispublication is the CMC
communicator.
So I to hear districts, states,schools talk about this kind of
thing, it'll be interesting forme to follow what unfolds from
these discussions.
SPEAKER_01 (29:24):
One of the things we didn't highlight in our article
that I think I would look for ifI was looking for a curriculum
for my own uh school or my ownstudents, is sort of the care
with which students' ideas arecentered the whole way through.
And then we highlighted someways that it's centered uh
(29:45):
within a lesson.
But uh we've also included doorquestions in our in our latest
core connection courses and inthe inspiring connection
courses.
And I heard the greatest thing.
At the conference this year.
Richard, I think you were therefor that conversation, actually.
So tell me if I got this wrong.
(30:07):
It starts with that doorquestion.
You ask a question at the door,it's just getting the kid's
opinion on random stuff.
Right.
It's intentionally not relatedto the lesson.
It's intentionally just out ofthe blue.
Like every day.
And you get this moment with thekid or with your your students.
(30:30):
It's like they feel like theiranswer matters to you in some
way.
What they have to say matters toyou.
And then that translates likeeventually like, oh, maybe they
care what I think in English.
And then that translates you,like, oh, maybe they care about
me.
SPEAKER_06 (30:52):
I love that.
SPEAKER_03 (30:54):
That's awesome.
SPEAKER_02 (30:57):
Thank you so much for coming on the podcast today
and talking about high-qualityinstructional materials and the
California math framework andhow teachers can be better
teachers with the materialsthey're using.
So we appreciate that.
SPEAKER_04 (31:11):
Thank you for having us.
SPEAKER_01 (31:12):
Yeah.
Yeah.
Come back again.
I can hang up and Bridget cananswer all the questions, and
I'll be quiet this time.
SPEAKER_02 (31:26):
So that is all we have time for on this episode of
the More Math for More Peoplepodcast.
If you are interested inconnecting with us on social
media, find our links in thepodcast description.
And the music for the podcastwas created by Julius H and can
be found on pixabay.com.
So thank you very much, Julius.
Join us in two weeks for thenext episode of More Math for
(31:49):
More People.
What day will that be, Joel?
SPEAKER_00 (31:53):
It'll be December 16th, National Underdog Day.
So looking at all the underdogs.
Typically, I think of underdogsin a sports context, but there's
underdogs everywhere that we cantake a look at and talk about,
and I know that Misty will havesome stories as well.
You are listening to the More Math for More People
podcast, an outreach of CPMeducational program.
Boom.
SPEAKER_02 (00:31):
December.
SPEAKER_03 (00:33):
I can't believe it's almost the end of 2025.
It's crazy.
SPEAKER_06 (00:38):
It is crazy.
SPEAKER_03 (00:39):
So it's 2nd of December.
SPEAKER_06 (00:42):
Yes.
SPEAKER_02 (00:43):
2nd of December?
It is 2nd of December.
And what's our national daytoday?
SPEAKER_00 (00:48):
Today is the business of popping corn day.
SPEAKER_03 (00:56):
That really sounds made up.
SPEAKER_00 (00:58):
No, they are.
They're all all things are justmade up.
SPEAKER_02 (01:01):
So you know that that wasn't much of a you know
qualification.
SPEAKER_00 (01:05):
No.
SPEAKER_02 (01:06):
The business of popping corn day.
SPEAKER_00 (01:08):
Everything about these days is made up.
It's totally true.
And and the business of poppingcorn day.
And I don't have the facts infront of me right now, but I can
tell you I like to pop corn.
SPEAKER_02 (01:19):
You like to pop corn?
You are you're gonna have factsabout popping corn?
I like so I remember whenpopping corn moved from you had
to put it in a pan with oil, andyou had to like shake and move
the pan, you know, and pop it toJiffy Pop, first of all, which I
(01:41):
don't sure I've actually hadJiffy Pop.
When I was a kid, we alwayswanted Jiffy Pop because it
looks so cool.
I mean, it looks so cool how itlike stands and blows the thing
up into a big bubble.
SPEAKER_00 (01:50):
It's all right there for you.
You don't even have to doanything.
SPEAKER_02 (01:52):
We were never we never got Jiffy Pop because you
know it was more expensive.
And they had the Jiffy Pop thatcame in different colors, I
think, even.
It was like rainbow jiffy pop.
And then it moved to the airpopper.
Like that was a big deal when itmoved to the air popper because
then you could put it in, itwould all spin around, it would
pop out into the bowl, and theninto microwave popcorn.
SPEAKER_00 (02:15):
Yep.
SPEAKER_02 (02:15):
Which pretty much feels like the only way I would
make popcorn now.
SPEAKER_00 (02:18):
Really?
I I still make it it it it's apan, but it has like a crank.
Oh so I I put the oil and then Ihave I have like three or four
bags of specialty corn that Ichoose from.
SPEAKER_02 (02:32):
So is the is the pan like a popping corn pan?
SPEAKER_00 (02:36):
It's a popping corn pan.
I I think it's actually calledlike the popping corn number two
or something like that.
unknown (02:43):
Oh.
SPEAKER_02 (02:43):
I don't know what the popping corn number is.
That makes sense.
And from then a third poppingcorn pan or any other third
popping corn pans.
SPEAKER_00 (02:51):
Definitely a hand crank situation, so you don't
have to shake the pan.
SPEAKER_02 (02:54):
You just burn.
SPEAKER_00 (02:57):
Yeah.
And I I remember the air popper.
And my folks still have an airpopper.
SPEAKER_02 (03:01):
Air popper was cool because you couldn't ever burn
the air popper pretty much.
SPEAKER_00 (03:06):
That was pretty cool.
It was fun to watch catchingyour mouth, like if you held it
over your head or whatever.
I don't I didn't really do that.
SPEAKER_02 (03:12):
I mean it was yeah.
SPEAKER_00 (03:14):
I don't like that.
I'm I made that up.
SPEAKER_02 (03:16):
That was I didn't like it that it you it was hard
to get the butter on it becauseyou had to like the butter was
on a little pan, the thing thatwas supposed to drip on, and
that didn't really work.
You just had to pour it onafterwards.
SPEAKER_00 (03:26):
We had we had one.
You know how I was talking aboutthe hand crank?
The crank would go by itself,like it was motorized.
And at the top of the dome wherethe it was gonna pop, you put
butter on it, and it was like afilter that dripped the butter
on as it heated up.
That was pretty good.
Did it work?
SPEAKER_02 (03:46):
Yeah.
SPEAKER_00 (03:48):
Yeah.
SPEAKER_02 (03:48):
Yeah.
I feel like the auto butterthings didn't work as
successfully.
Maybe they didn't make as muchbutter as I wanted.
When I I pretty much wanted likebutter, you know, popcorn dipped
in butter when I was a child.
SPEAKER_00 (03:58):
You know.
I think my second or third jobwas working in the movie
theater.
SPEAKER_02 (04:03):
At home.
SPEAKER_00 (04:04):
And just to put some context to it, Bill and Ted's
Excellent Adventure.
SPEAKER_02 (04:08):
Nice.
SPEAKER_00 (04:09):
Pet Cemetery, those kind of movies were coming out
at the time.
But I was an usher.
And it was actually one of thefirst public speakings I'd have
to do because I was collectingmoney for like the Will Rogers
Institute and stuff like that.
And with a popcorn, two things.
One, when they needed butter, Iwould have to go get this
(04:32):
five-gallon thing of butter-likesubstance.
unknown (04:36):
Right.
SPEAKER_00 (04:36):
And the butter-like substance, instantly my face
would break out in acne just byopening the can, right?
Like whatever I don't even knowwhat it was, but it was gross.
Second thing is, it's tricky ifyou go to the movie theater
during the morning becauseyou're getting last night's
popcorn.
You are not getting freshpopcorn because we had to save
(04:57):
it because it's so you know,popcorn's expensive and valid.
Oh, yeah.
Yeah, exactly.
You don't want to repop thatstuff.
SPEAKER_02 (05:05):
Waste all those things.
Oh man.
SPEAKER_00 (05:11):
I remember those days.
SPEAKER_02 (05:12):
Yeah.
Yeah.
Popcorn, I start with popcornthat has like sometimes it has
too much salt.
Like it has to have just theright amount of salt.
SPEAKER_00 (05:19):
Too much salt is a bad thing.
Too much salt is right.
SPEAKER_02 (05:22):
I remember I like I like that now, you know, I can
go to places and I can get like,you know, basically like cattle
corn or you know, fancierpopcorn.
They just make corn.
SPEAKER_00 (05:32):
I had a friend who asked me one time, do you want
some yeast on this popcorn?
And the the theater had likepopcorn yeast or whatever.
Yeah.
Sure.
But they mistaken the yeast fora for granulated sugar.
They were like in the samecontainer.
We ate it, but we still ate it.
I'm sure it was really it wasn'tit wasn't that good.
SPEAKER_02 (05:53):
It wasn't what you expected, but yeah, yeah,
interesting.
SPEAKER_00 (05:57):
Yeah.
SPEAKER_02 (05:57):
So just the other just the other night I went to a
Broadway show here in Portland,Shucked.
SPEAKER_06 (06:05):
Okay.
SPEAKER_02 (06:06):
Which it's not really about corn, but corn is
kind of the You Shuck a corn.
Yeah.
Well, uh yeah.
But it's not like it's not likea musical about corn.
It's a musical about thisreally, really small town that
you know grows corn, and corn iskind of the center of the theme.
But I would say more more thanthat, it's really about corny
jokes.
(06:27):
Like it is like just full ofpuns, non-stop, not like
continuous and like groaners,like so, and and and you know,
some very like you know,definitely not always in the
like mainstream, you know, likeclean jokes, but like it's you
know, it's along the lines ofyou know, Book of Mormon, or
(06:49):
some things that are pretty likethis.
But uh very, very it's so sofunny.
So, so funny.
I was sounds amazing.
It was far more hysterical thanI anticipated.
So yeah, very good.
Very cool.
I'll have to check it out.
Yeah, definitely.
If it's if it's in your area, Ihighly recommend it.
I would definitely either, andlike I say, it was very funny.
SPEAKER_00 (07:11):
Okay, very entertaining.
Excellent.
SPEAKER_02 (07:13):
So, what are you gonna do for the business of
popping corn?
SPEAKER_00 (07:18):
I am see you stress the business part.
I was just gonna pop some corn.
Well, I know.
SPEAKER_02 (07:25):
But if I'm celebrating, the business part
of it is apparently an importantpart of the day.
They wouldn't have labeled it,you know, the business of
popping corn.
SPEAKER_00 (07:32):
Maybe I'll actually read the label on the thing to
see what kind of businessproduces.
SPEAKER_02 (07:39):
Your business could be, you know, the the companies
that are making it, but it alsocould be the busyness of popping
corn.
SPEAKER_00 (07:46):
I'm gonna I'm gonna get busy and pop some corn.
How about you?
SPEAKER_02 (07:50):
I'm I think I'm definitely gonna eat some
popcorn today.
I might not pop it myself, butit will be popped corn.
SPEAKER_00 (07:55):
I love it.
SPEAKER_02 (07:56):
So there you go.
Enjoy your popped corn.
Indeed, so so we're here todaywith Bridget Gunn and Dan
(08:19):
Henderson.
Hi.
Bridget works on yeah, that'sDan.
Bridget works on the PL teamwith us, and Dan is on the
curriculum assessment team.
And we brought them here todaybecause we know they are people
who can answer our questionsabout HQIM.
SPEAKER_00 (08:36):
Yeah, what's that actually?
SPEAKER_02 (08:37):
Beginning with yeah, did you know what HQIM is, Joel?
SPEAKER_00 (08:40):
I had to look it up.
SPEAKER_02 (08:42):
Okay, what'd you find out?
SPEAKER_00 (08:44):
I think it's high quality instructional materials.
SPEAKER_02 (08:47):
I think I think that is targeted.
SPEAKER_00 (08:51):
But I I did have to look it up for sure.
Yeah.
And I saw that there was a verynice article about well,
actually, I it seems like thewhole publication was about
HQIM, but there was an articlein there.
And I and I'm not a big acronymfan, so I might start saying
high quality instructionalmaterials.
(09:13):
But Bridget and Dan were authorsof this article.
SPEAKER_02 (09:17):
They were.
They were amongst the authors ofthis article.
So we brought them here to helpanswer our questions about HQIM.
We already answered thequestion, what is it?
Well, what does it stand for?
Yes.
But my first question, beyondwhat it stands for, then, is
what is what what makessomething a high quality
instructional material like?
I feel like this is not justsomething you dub upon yourself.
(09:38):
Someone has to put some likecriteria on it.
So that's our first question,Bridget or Dan.
SPEAKER_03 (09:43):
What is an HQ?
What makes something an HQIM?
SPEAKER_01 (09:48):
Bridget, you want to try?
SPEAKER_03 (09:50):
Sure.
I'll try.
You're gonna have to nose goesor something.
SPEAKER_04 (09:58):
So we kind of took took the idea that like there
are a lot of good curriculummaterials or instructional
materials, I guess, that likefollow the standards and have
math problems in them.
But that high-qualityinstructional materials kind of
(10:20):
go one or a few steps furtherthan that.
And then we looked at um theCalifornia math framework.
They have a section on equitableand engaging teaching.
So we kind of looked athigh-quality instructional
materials through that lens.
And they have five components ofequitable and engaging teaching.
(10:43):
And we think that high-qualityinstructional materials do those
five things and really helpteachers on their journey to
equitable and engaging teaching.
SPEAKER_00 (10:56):
And what are the five things?
SPEAKER_04 (10:59):
The five things are perpleid teaching around big
ideas, to use open and engagingtasks, to invite student
questions and conjectures, toprioritize reasoning and
justification.
And this is also kind of ourinterpretation of these five
(11:21):
things, but that though doingthose four things can help you
teach towards social justice,which is the fifth component of
equitable and engaging teaching.
SPEAKER_02 (11:34):
And so are you suggesting or saying that if
something is a high qualityinstructional material, it does
those things automatically?
Or that would be included inlike if it meets the criteria of
being an HQIM, it's gonna dothose things?
Or are you suggesting that somedo that better than others?
Or like how connect those twofor me?
SPEAKER_01 (11:55):
So California just adopted a bunch of curricula,
and states across the countryare looking to adopt new
curricula, and schoolseverywhere are looking at
curricula and trying to decidewhat to pick.
We were thinking what do theyreally need to know in addition
to like checking your ed reportsor whatever, what do you really
want to look at?
Uh we identified some thingsthat good curriculum do that we
(12:17):
think high-quality curriculumcould do a little bit more.
One way to think about it islike like uh good material,
sorry, like a cookbook.
They give you good recipes andclear steps, you can follow all
those things.
But a high quality material ismore like a like a master chef
apprenticeship, where you getthe recipes, but you also learn
(12:38):
how to think about how things gotogether and how to rise given
what you've got.
That sort of thing.
SPEAKER_03 (12:45):
So I like that analogy.
SPEAKER_06 (12:47):
Yeah.
SPEAKER_03 (12:49):
So so what other things did you tell us?
Did you talk about then?
So how do those things gotogether?
SPEAKER_04 (12:57):
So one of the things we talked about is well, we kind
of think that all five of thesethings really work together.
So planning teaching around bigideas is this idea that math
concepts are interconnected.
And so instead of learning justlike your six times table, you
might talk about multiplicativethinking and reasoning, which is
(13:19):
like additive reasoning,subtractive, then moves into
proportional reasoning.
So like teaching around bigideas helps students connect
what they are currently learningto things that they already know
and sets them up for success infuture learning.
SPEAKER_01 (13:39):
Should we clarify that like so we think like good
materials uh do that?
They help you plan instructionaround big ideas.
We should not adopt materials,they don't do that.
On top of that, we thinkhigh-quality materials also
offer support for studentinteraction.
Like uh CPM uses those studyteam teaching strategies.
SPEAKER_06 (13:59):
That would be one of those supports efforts.
I mean quiet now.
SPEAKER_02 (14:08):
There's no there's no need to be quiet.
SPEAKER_00 (14:09):
I know.
SPEAKER_02 (14:10):
Well that's a podcast, someone has to be
talking.
SPEAKER_00 (14:13):
What when I was looking over the article, it it
seemed it seemed like, okay,there's five things.
Those five things seem prettybig to me.
Like, like it it's not a simpleone, two, three, four, five
checklist or something likethat.
Like it's it's a bigger ideathan that.
And what stood out to me, andI'm interested to hear what you
(14:35):
have to say about this, is thatit it's not just about the
students, it kind of frees upthe teacher to be in a
beneficial teaching mode almost.
SPEAKER_04 (14:49):
Yeah, I feel like the the kind of difference
between good materials and highquality instructional materials
is that high qualityinstructional materials do free
up the time.
So you're not sitting there as ateacher figuring out, okay,
where do I put this lesson sothat it connects to all these
things?
Because we're about to do this.
(15:09):
Like that's a lot of brain spacefor one person to do on their
own.
So high quality instructionalmaterials kind of free you of
that brain space.
They give you the open andengaging task that's already
connected through a storylinethat naturally invites questions
and conjectures so that you canstep in and figure out how to
(15:33):
facilitate those conversations.
SPEAKER_05 (15:35):
Right.
SPEAKER_04 (15:35):
And it might even help you facilitate those
conversations by providing, youknow, an author's vision that
says, hey, when we wrote this,this is what we were thinking.
These are questions we might askin our classroom.
Um, consider doing thisactivity, consider doing this
exhibit visit and asking thesequestions as your closure for
(15:56):
the day.
SPEAKER_00 (15:57):
And again, what made me think about that too is your
conclusion.
I kept thinking I kept goingback to that teacher lens of
that your thinking matters, yourvoice matters, you matter, and
reflect and revise.
And with a high qualityinstructional material, it's
just seemed like that was ableto happen in a more what's the
(16:22):
right word, like a conducivespace, a free space, or like a
I'm saying, I'm probably sayingthis all wrong, but like a
visionary space of like as ateacher, I appreciate that that
what I bring to the tablematters as much as what I'm
trying to let students bring tothe table.
SPEAKER_04 (16:41):
I completely agree with that.
I feel like I feel like that'swhy so in that framework, they
talk about teaching towardssocial justice as like not
necessarily bringing justbringing in like social justice
topics or topics that you mightthink of when you think of that
phrase, but that there's an ideathat we are trying to develop
(17:07):
students into students withpositive math identity and
agency.
You're right, Joel, likehigh-quality instructional
materials kind of create theenvironment where teachers can
then have some breathing room tostep back and really observe
what's happening in theirclassrooms, really like try to
(17:28):
understand how their studentsare understanding these concepts
and then facilitate discussionsaround them.
So you're kind of gaining backthat agency of like, as a
teacher, what's going on in yourown classroom.
Because you're kind of likeputting the pieces together to
create this, this environment.
SPEAKER_02 (17:48):
I can see how I can see how this would also be.
So I'm like what I'm seeing andhearing is like that the
high-quality instructionalmaterials and those five things,
right, are really kind ofcreating the conducive
environment for the studentcentered classroom and bringing
kids into the conversation andthose pieces and changing the
(18:10):
teacher role, right?
Is what I hear you saying.
Like the teacher role shifts andchanges.
And it and at the same time, theteacher role needs to shift and
change, right?
You couldn't just bring ahigh-quality instructional
material into your classroom andthen just teach the way you were
always teaching.
Does that feel accurate?
SPEAKER_01 (18:29):
Yes.
If I was just I'm sitting overhere kind of being quiet and
thinking about the differencebetween my master's degrees in
curriculum and instruction, andthat's the sort of reality
that's playing in my head rightnow.
Instructional part obviouslybeing instruction and the
curriculum part being thematerials part.
Well I'm trying to think throughparsing out what your question
(18:52):
is about like how does theinstructional material shift
your instruction and vice versa.
That's why I'm being quiet.
You can edit that whole thingout if you want to, but no
worries.
SPEAKER_02 (19:07):
It feels like I was gonna say, what is your brain
putting together with it?
SPEAKER_01 (19:11):
Well, it sort of feels like the thinking about
the instructional shifts, right?
Like the center of student voiceand putting equity in the center
of the the conversation is twobig things that kind of have to
happen.
If you're not gonna listen towhat students say and take
(19:33):
seriously their ideas, thenthere's nothing the materials
can do for you.
But if you are willing to takethat leap and listen to
students, then instructionalmaterials can guide you with the
kinds of questions that will beopen and engaging for them
that'll help change theirperspective of the world and of
(19:55):
math and of themselves.
So that's the kind ofinstructional piece.
I feel like we have likespecific pieces embedded in the
CPM curriculum that do that,right?
Like we build in rough drafttalk and all the siding team
strategies like SWAT meets andthings like that.
And those routines shift theauthority of the classroom.
SPEAKER_06 (20:19):
Which make it more equitable just from the job.
That's uh instructional piece.
The materials piece, I'mthinking like the focus on the
big ideas.
SPEAKER_01 (20:35):
Super traditional instruction is organized around
like the very small day-to-day,can I do this skill?
Can I remember to carry the onewhen I'm adding multi-digit
numbers or whatever?
Big idea just keeps happeningover and over and over and over
again.
And this like within the theseventh grade curriculum, right?
(20:56):
We just have this idea ofproportional reasoning just
keeps happening, right?
It starts on that first datewith the pencil topic, and it
just keeps going.
And you just encounter it overand over and over again in these
different ways.
And that helps students connectit to the world and wrap their
heads around a really big shift.
Right.
When you think about it, like inelementary school, the only way
(21:16):
to think about differencebetween numbers is like six is
one more than five.
Right.
Like that's the extent of yourability to think about
difference.
That's super advanced if you'rein second grade.
It's not so advanced when you'rein seventh grade.
Because then you learn to thinkproportionally, you think okay,
(21:38):
six is twenty percent more thanfive.
Right.
It's like that kind ofrelationship.
What else is like what's what's20% bigger than than an old 20?
It's not just one more again.
It's a different thinking.
So it's a big idea, and it takessome time to wrap your head
around and it just keepshappening over and over and over
(21:59):
again.
It happens in a ton of differentcontexts and all that stuff, but
it's just a bigger thing thatyou have to think about a time.
SPEAKER_06 (22:09):
I'm angling, I'm sorry.
No, you're fine.
No.
SPEAKER_02 (22:13):
Well, and what I'm hearing you say is that like
like the material, the thecurriculum materials themselves
can have to lend themselves tothis different, these different
shifts in these ways ofthinking, right?
And shifting what's happening.
And the teacher also shifts whatthey're doing.
(22:33):
And these two things will happentogether, right?
Like you can't really it's hardto do one without the other
either way, right?
It's it's hard to move and dothe do these, make these five
changes, right?
Without a highly qualityinstructional material.
And it would be challengedactually to like stand and
deliver with a high qualityinstructional material.
They don't, they don't, they'renot, they're like co-compatible
(22:54):
in that way.
SPEAKER_01 (22:55):
Yeah.
Is that co-compatible is aninteresting phrase.
But I know I think they'rethey're almost codependent,
right?
Like you can't really have onewithout the other.
Yeah.
Think about like the we we madea point, I think, in the article
about full stack lessons.
(23:18):
Because she's the one that mostrecently actually read the
article again.
We did we did say that, right?
Uh Excel.
Yeah, so like the that fullstack idea is is the idea that
like you start with someexperience and then you describe
it linguistically, and then youstart to ask questions about it,
(23:39):
or then estimate and error, andthen you finally calculate
something, and then you canreveal what the answer is, and
then you can flip it around andchange the given and the little
yeah or the question uh or helpsyou get like a full range of
like exploration on a question.
(23:59):
Um and you can't if uh if thematerials aren't aren't there to
support it, then you're notgonna successfully do that in
your lesson.
But if you're not trying to dothat in your lesson, high
quality materials are gonna feelreally weird.
There's gonna be a whole bunchof stuff that's kind of left on
the table.
SPEAKER_00 (24:18):
So they're back to that codependent phrase.
SPEAKER_06 (24:22):
Mm-hmm.
SPEAKER_00 (24:23):
Yeah.
SPEAKER_06 (24:24):
Mm-hmm.
SPEAKER_00 (24:24):
I and I I I I like what you're saying there too
about so the the material thehigh quality material of what
I'm hearing you say is it'sgonna back you up.
So it's a shift.
Like when we're talking about ashift, sometimes I think, oh,
uh, as a teacher, I must bedoing something wrong because I
(24:45):
need to shift this way.
But maybe what you're doing isokay and it's promoting, but
what a high-quality materialwould do is back you up in
opening multiple avenues,opening discussions, opening
different thought processes.
SPEAKER_01 (25:03):
Yeah, exactly.
It would it would back you up init uh in a couple of specific
ways that we sort of try andhighlight or like we'll point
out in our in our teacher notesor in our author's vision uh
what we think students willprobably say based on our
experience with students andfield testing and all that.
And then we highlight what kindof responses you might give to
(25:26):
those things.
And we also highlight likeextension questions, we call
them encourage deeper thinkingquestions.
So there for everybody to like,hey, you had this thought, you
may as well explore thelandscape of math that's around
this problem.
Um when I was a when I was ageometry teacher, we were
playing around with Pythagoreantriples just because we had a
(25:46):
day before Thanksgiving, so thisis well timed.
Um playing around withPythagorean triples, and uh had
a group of students just be likescrewing around and were like,
well, what about A to the third,B to the third equals C to the
third?
And I was like, that'sinteresting.
See if you can find it, right?
Like, does it work?
Try some numbers.
(26:06):
They couldn't find any.
And I asked them, like, why?
Why do you think that is?
Like, can you give me anargument for why that's not
working at all?
Um they thought about it for acouple minutes and they decided
that instead of that they wouldtry another even number.
They'd try A to the fourthpower, B to the fourth power,
and C to the fourth power.
And I was happy with that.
They were fine, they werecontinuing their thinking,
right?
(26:26):
It's a nice big openexploration.
I didn't have the heart to tellthem, but or you'll hear the
podcast.
You get that that openness isthere for them to explore, and
you want to encourage it as longas they're thinking mission
accomplished.
SPEAKER_02 (26:49):
So you're good.
You're good.
As we so as we get toward it,kind of the end of the time that
we have here, like what are thebig things, the big takeaways
that you would want someone toremember as they're thinking
about high quality instructionalmaterials and good teaching?
SPEAKER_01 (27:05):
Well, my short and sweet answer is by CPM
curriculum.
Well, shouldn't say that on yourpodcast.
Yeah.
What's my what's my longeranswer to that, Bridget?
SPEAKER_04 (27:17):
Well, my longer answer.
I'm really encouraged by again,I live in California, so I guess
I'll say the Californiaframework matters out here.
And I'm really encouraged by thefocus on I think developing an
(27:42):
environment where students feellike they matter in a math
classroom more than theiranswers matter.
So I feel like a high-qualityinstructional material is going
to give you the space as ateacher to kind of find those
moments when your students arehaving really brilliant ideas
(28:05):
and allow you to dive into thatconversation with them.
We talk about um a lesson that'sin our eighth grade curriculum
about like finding as manyequations that have a solution
of four as you can, and the ideathat a student could kind of in
their middle school way writedown x equals four and say that
(28:29):
I'm done is like the best startto a conversation.
Is that a correct answer is whatdoes it mean to be, you know,
have a solution of four.
So I think finding instructionalmaterials that help you say
you're right, or yeah, explainthat to me more so that your
(28:52):
students start to really feel asthough they're a part of this
math classroom community andlearning community as as you
can.
SPEAKER_00 (29:01):
Yeah.
I'm I'm excited.
You know, that again, thispublication is the CMC
communicator.
So I to hear districts, states,schools talk about this kind of
thing, it'll be interesting forme to follow what unfolds from
these discussions.
SPEAKER_01 (29:24):
One of the things we didn't highlight in our article
that I think I would look for ifI was looking for a curriculum
for my own uh school or my ownstudents, is sort of the care
with which students' ideas arecentered the whole way through.
And then we highlighted someways that it's centered uh
(29:45):
within a lesson.
But uh we've also included doorquestions in our in our latest
core connection courses and inthe inspiring connection
courses.
And I heard the greatest thing.
At the conference this year.
Richard, I think you were therefor that conversation, actually.
So tell me if I got this wrong.
(30:07):
It starts with that doorquestion.
You ask a question at the door,it's just getting the kid's
opinion on random stuff.
Right.
It's intentionally not relatedto the lesson.
It's intentionally just out ofthe blue.
Like every day.
And you get this moment with thekid or with your your students.
(30:30):
It's like they feel like theiranswer matters to you in some
way.
What they have to say matters toyou.
And then that translates likeeventually like, oh, maybe they
care what I think in English.
And then that translates you,like, oh, maybe they care about
me.
SPEAKER_06 (30:52):
I love that.
SPEAKER_03 (30:54):
That's awesome.
SPEAKER_02 (30:57):
Thank you so much for coming on the podcast today
and talking about high-qualityinstructional materials and the
California math framework andhow teachers can be better
teachers with the materialsthey're using.
So we appreciate that.
SPEAKER_04 (31:11):
Thank you for having us.
SPEAKER_01 (31:12):
Yeah.
Yeah.
Come back again.
I can hang up and Bridget cananswer all the questions, and
I'll be quiet this time.
SPEAKER_02 (31:26):
So that is all we have time for on this episode of
the More Math for More Peoplepodcast.
If you are interested inconnecting with us on social
media, find our links in thepodcast description.
And the music for the podcastwas created by Julius H and can
be found on pixabay.com.
So thank you very much, Julius.
Join us in two weeks for thenext episode of More Math for
(31:49):
More People.
What day will that be, Joel?
SPEAKER_00 (31:53):
It'll be December 16th, National Underdog Day.
So looking at all the underdogs.
Typically, I think of underdogsin a sports context, but there's
underdogs everywhere that we cantake a look at and talk about,
and I know that Misty will havesome stories as well.
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