May 13, 2025 • 39 mins
Welcome to Season 5 of the More Math for More People podcast!!!
What if high school mathematics could be truly transformed into something students find engaging, meaningful, and applicable to their lives? In this thought-provoking conversation with mathematics education experts Kris Cunningham and Kristi Martin, we dive deep into the possibilities presented in the NCTM publication "High School Mathematics Reimagined, Revitalized, and Relevant."
The discussion opens doors to a reimagined approach to high school mathematics that moves beyond the traditional curriculum model. Both guests highlight the importance of mathematical modeling as a pathway to authentic learning experiences where students tackle complex, multi-variable problems without predetermined solutions. This creates space for creative thinking and problem-solving skills that transcend the classroom.
However, transformation doesn't come without challenges. Kristi candidly shares her classroom experiences of struggling to surface the mathematical concepts within engaging modeling activities and the difficulty of finding relevant problems that align with required standards. Kris emphasizes the need for systemic support, including administrative understanding and professional development opportunities that give teachers space to experiment and grow.
Perhaps most powerfully, both educators stress the importance of persistence through inevitable frustrations. "If you believe in it and know it's great for students, just keep trying," Kristi encourages, reminding listeners that transformation is a journey rather than a destination. The conversation serves as both inspiration and practical roadmap for anyone interested in creating mathematics education that truly prepares students for their futures rather than simply repeating practices of the past.
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Episode Transcript
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Speaker 1 (00:17):
You are listening to the More Math for More People
podcast.
An outreach of CPM educationalprogram Boom.
An outreach of CPM EducationalProgram.
Speaker 2 (00:26):
Boom.
Okay, so here we are.
It's already the 13th of May.
We're here.
Wow, seems like May is justzooming by already, since it's
already the middle of the monthand it's our first podcast of
May.
Speaker 1 (00:42):
Isn't it bad luck on the 13th, or it's like a?
Speaker 2 (00:45):
well, that was a friday, oh friday it's tuesday
tuesday, it's tuesday and yeah,big deal yeah this is our first
episode of season five that isbig deal, five seasons five
seasons.
That's more than some netflixshows joel, I mean intentionally
(01:05):
or not intentionally, but likewell you get to season five on a
, on a streaming or any like anyyeah, thing that's a big deal
and I would argue that a seasonis not always 25 episodes and we
average around 25 episodes forsure, yeah, for sure.
We, uh, we could have gone withthe eight season or eight
(01:25):
episode season, and that wouldhave been much, much.
Well, I don't know if it wouldhave been easier or not.
Yeah, anyway, here we are.
Speaker 1 (01:34):
We'd have to make it an hour long instead of a half
hour long, just with all ourthoughts that build up, that
build up to a cliffhanger thatmakes people come back the next
time.
Speaker 2 (01:42):
Yeah, yeah, a cliffhanger that makes people
come back the next time.
Yeah yeah, I think that's oneof the interesting things a
total side note, but justinteresting things about shows
that are not on networktelevision, they're just
streaming.
They're random lengths Like.
Sometimes they're like 33minutes, 47 minutes, 54 minutes.
Yeah, because they don't haveto make it match the hour.
Half hour slot with commercials.
Speaker 1 (02:02):
Yes, so they can.
Just here's how long we'regoing to tell the story this
time.
The other thing I wonder, too,is Julius H has given us this
great music, but like when Ithink of, let's say, when I
watch Game of Thrones when Ihear that theme music I kind of
get like pumped up.
I wonder if when people hearthe Julius H music they kind of
(02:23):
get pumped up.
Speaker 2 (02:24):
They get pumped up for more and more people.
They might, they might.
I hope so, I hope so.
That's what I imagine yeah Well, that's good, that's good, it's
healthy, yeah.
So here we are, season five,it's May 13th, sure is.
And it's our National Day ofsegment, because we're still
doing that.
Yep, I don't think we've missedan episode.
Speaker 1 (02:45):
No, all right, it's important to celebrate.
Speaker 2 (02:47):
I think so.
Speaker 1 (02:48):
Yeah.
Speaker 2 (02:50):
So what are we celebrating today?
Speaker 1 (02:55):
National Tulip Day.
Speaker 2 (02:56):
Tulip Day.
Tulip Day, wow.
This must be for people who areat very northern latitudes.
My tulips are long gone.
Speaker 1 (03:03):
What do you mean?
Mean, oh, they've already comeand gone oh yeah, they're long
gone.
Speaker 2 (03:06):
They.
Speaker 1 (03:07):
They bloomed, peaked like three, four weeks ago oh my
gosh, we're in peak bloom rightnow.
Really yes yeah, well, that'swhat I'm saying more northern or
south or continental time zones, colder latitude, colder spaces
yeah more I'm trying to thinktilted towards the sun, tilted
away from the sun.
Speaker 2 (03:27):
If you're at a higher latitude, then you would be I
mean you're it's a sphere.
Speaker 1 (03:33):
You can't go up and down.
What?
Speaker 2 (03:37):
The earth is a sphere .
You go up and down, you goaround it, but anyway, if you're
in a colder space, for thereasons that it might be colder,
your tulips might be onlyblooming now.
Speaker 1 (03:48):
That's true.
Speaker 2 (03:49):
I think they've pretty much bloomed in the
Netherlands too, though, but itdoesn't matter, it's tulip day
today.
Speaker 1 (03:55):
It is.
And do you know?
Actually you brought up theNetherlands.
Speaker 2 (03:59):
Yes, I did.
Speaker 1 (04:00):
That's not where they started, that's not where they
were first cultivated.
Speaker 2 (04:03):
Where were they first cultivated?
I'm curious.
Speaker 1 (04:05):
Turkey Around the year 1000.
Speaker 2 (04:09):
Wow yeah.
Speaker 1 (04:11):
They didn't actually arrive in Holland until the 16th
century, so like 600 years.
Speaker 2 (04:19):
That makes sense.
I don't know how they arrived.
16th century is a lot of thatcolonialism, time and whatnot.
Speaker 1 (04:23):
It is yes.
Speaker 2 (04:25):
The Dutch were doing lots of moving things around
commercially.
Speaker 1 (04:30):
Well, and it was a biologist that took the tulips
to there.
Speaker 2 (04:37):
They grow really well in that climate.
Speaker 4 (04:39):
Yeah.
Speaker 2 (04:41):
And earth that reclaimed flood dirt.
Speaker 1 (04:46):
Hmm, I didn't know about that part.
Yeah, they grow really well,they grow really well.
Here in Utah we have a tulipfestival.
Speaker 2 (04:55):
And the other.
Speaker 1 (04:55):
Thing that grows well .
Here is lavender.
We have lavender days.
Oh yeah, it's not NationalLavender.
Speaker 2 (05:01):
Day.
But no, it's not.
Lavender grows pretty wellaround here too.
I used to live in Mount Vernonand Skagit County is a major
tulip bulb producer, I think,like next to Holland, michigan
and the Netherlands.
So we would have a big tulipfestival every year and people
would come out and see thefields and fields and fields of
tulips Interesting, of tulipsInteresting, and then to make
(05:24):
the tulips grow more bulbs.
When the tulips are in bloomthey go out and they pull all
the petals off.
So then people would come andyou'd just see all the petals in
the middle of the rows andgreen Interesting.
Speaker 1 (05:39):
Here's kind of a, I think, an interesting fact and
maybe even a little bit of amath fact.
But this says tulips are evenso.
Tulip flower buds are almostperfectly symmetrical to each
other.
Speaker 2 (05:51):
Tulip flower bulbs are almost perfectly symmetrical
.
Speaker 1 (05:53):
Flower buds.
Speaker 2 (05:54):
Buds are, oh Hmm.
Speaker 1 (05:57):
Interesting.
Speaker 2 (05:58):
They're even like and they have an even number of
petals.
Speaker 1 (06:01):
Well, they're symmetrical.
Speaker 2 (06:03):
Oh, okay.
Speaker 1 (06:04):
Is that?
Another term for even you thinkmaybe.
I mean I feel like there's.
Speaker 2 (06:08):
I feel like plants.
They're either like they haveeven numbers of petals and
leaves or they have odd numbersof petals and leaves.
There's monocots and dicotskind of a thing or something.
Monocots can have odd, I think,and dicots always have an even,
but I'm not I'm not a hundredpercent on that.
Speaker 1 (06:26):
So Okay, you fact checkers out there.
Speaker 2 (06:28):
Yeah.
Speaker 1 (06:29):
Let us know how many varieties.
Speaker 2 (06:32):
Bring in the random science fact that I can't
remember.
Speaker 1 (06:36):
How many varieties do you think there are?
Speaker 2 (06:38):
Varieties like, like different named colors, like I
can buy a bulb of that variety.
Speaker 1 (06:47):
I know that there are many varieties of tulips and I
know that number.
Yeah, how many do you thinkthere are?
Speaker 2 (06:54):
Well, I mean, I think it depends on how you term this
variety, right?
I think that, like tulips areone species, there's only one
thing that's a tulip.
Speaker 1 (07:04):
But we're not talking about species.
If you name the genus andspecies, there's only one thing,
that's a tulip.
But we're not talking aboutspecies If you name, the genus
and species.
Speaker 2 (07:07):
There's only one thing right.
But then if you have oh, like,what are the different varieties
Like, when I plant this one,it's going to come up and it's
going to look different than allthe other ones right.
I bet there are easilythousands.
Speaker 1 (07:20):
How many of thousands ?
Speaker 2 (07:23):
I'm going to go with the over under on five thousand.
Oh my gosh over three thousandfor sure.
Speaker 1 (07:29):
Yeah, now that I think it's, I think you're right
in there for sure yeah, yeah,no it's.
Speaker 2 (07:35):
There's a lot because I think about, like that brex
catalog or the spring hillcatalogs I might get and the
just the number of differentpages and pages of really cool
looking tulips.
So you know the ones likeyou've seen those tulips that
are like they have super frillyblooms, like the blooms that are
like straight and have allthese curly edges on them and
they might have like variegatedcolors to them yeah, yeah.
(07:57):
That's caused by viruses.
Speaker 1 (07:59):
Oh really.
Speaker 2 (08:05):
Yeah, mutations Like no viruses, oh viruses, not a
mutation Like some of them are.
Some of them are mutations inhow, like in the, or slight
differences in what genes areexpressed.
Speaker 1 (08:10):
Okay.
Speaker 2 (08:10):
Right, but this is the viruses actually causes
differences in the actual cellexpression itself.
Speaker 1 (08:16):
I like it.
Speaker 2 (08:18):
Yeah, super cool, did you know you can eat tulips.
And not die.
Mm-hmm, you can eat tulips andnot die.
Speaker 1 (08:25):
I can eat a lot of things.
That's true too once that'strue.
That's true.
This says that you can usetulip petals instead of onions
in some recipes oh, I wouldn't.
Speaker 2 (08:35):
I wouldn't do that no , because you don't like onions
I don't like onions anyway so Idon't want to replace them with
something else, I just don'twant to have them.
But that's interesting.
I did not know they could beused as a food, garnish or
additive.
Yeah, so that's interesting,cool, all right.
Well, so what are you going todo to celebrate Tulip Day?
Speaker 1 (08:57):
Well, I'm going to go outside and look at my tulips.
Speaker 2 (08:59):
Nice, nice, I don't have that option.
My tulips are long gone.
Yeah, nice, I don't have thatoption.
My tulips are long gone.
I have some really, reallylovely pictures.
I took a lot of pictures when Iwas in the Netherlands three
years ago, four years ago, threeyears ago, and we went to a
tulip farm factory, whatever,and took a lot of pictures, so I
might look at those.
Some of them sure are prettycool.
Speaker 1 (09:20):
Okay, I'll send you a picture of mine.
Speaker 2 (09:22):
Excellent, sounds good.
Yeah, all right Well enjoyTulip Day.
Speaker 1 (09:34):
Everyone Excited to be here for the first episode of
Season 5 for the More Math forMore People podcast, and we were
lucky enough to interview ChrisCunningham and Christy Martin,
who were part of the writingteam for the book High School
(09:55):
Mathematics Reimagined,revitalized and Relevant.
It's an NCTM publication.
I was lucky enough to be partof the book study in the
leadership thread and learned alot and had a lot of great
discussions, and we thought thiswould be great if we could have
a chat with Chris and Christy.
Chris Cunningham is amathematics content specialist
(10:19):
and leader in the PhoenixArizona area and has also served
as a board member for NCSM.
Christy Martin is a mathematicshigh school teacher from the
Tumwater area in WashingtonState and is also a recipient of
the Presidential Award forExcellence in Mathematics and
Science Teaching.
And so please enjoy thisinterview with Chris and Christy
(10:44):
as we dive into how high schoolmathematics can be reimagined,
revitalized and relevant.
So I feel like I'm taking thispart from Misty a little bit,
but today we're here with ChrisCunningham and Christy Martin
and we're going to have adiscussion about reimagining and
(11:07):
revitalizing and making highschool mathematics relevant
enough to be in a book studyaround a publication that NCTM
put out and Chris and Christyare a part of that.
And first of all, welcome,welcome, and please introduce
yourselves and tell us who youare.
Speaker 3 (11:27):
Christine, you go first, okay.
Speaker 4 (11:29):
I'm Chris Cunningham.
I am a math specialist for ahigh school district in Phoenix
Arizona.
Speaker 3 (11:37):
And I'm Christ, math specialist for a high school
district in Phoenix, arizona.
And I'm Christy Martin.
I am a high school mathematicseducator in Washington State.
Speaker 1 (11:44):
Okay, that's right, well welcome.
So, just to get started, couldyou tell us what maybe some of
the main ideas of this book wereand how did you feel?
Why was it written, written, orwhat was the inspiration for
making it?
Speaker 3 (11:59):
Well, I will share that.
The book is written in.
When I think of it there'sthree major parts to it, which
is in the title of the book,realistically speaking, and so
I'm unpacking.
What does it mean to reimaginemathematics education?
For so long mathematicseducation has kind of stayed
(12:21):
stagnant.
We've made great progress, butwe want to continue moving that
needle in a positive directionfor students.
And then also, what does itmean to revitalize the
educational experience for ourmathematics students?
And then also, how do we makemathematics more relevant in an
ever-changing world?
And unpacking some ways that wecan do that at the high school
(12:44):
level.
So that's kind of where thebook kind of lives in those
three spaces.
Speaker 1 (12:52):
Right on, Chris.
Anything to add?
Speaker 4 (13:11):
Right on, chris, anything to add seen in the past
.
So we definitely want torecognize that it's an extension
or a continuation of some bookslike Catalyzing Change and like
bringing some ideas, like tocontinue moving forward.
Speaker 1 (13:27):
So how does it kind of align with other math
initiatives that are out there?
Like you're saying, you want tocontinue this work, so how is
it the same or how is itdifferent from other math
initiatives that have been outthere?
Speaker 4 (13:40):
I think.
I mean you see in the bookconnections explicitly made to
catalyzing change.
There's the you know charts inthe back where it links some of
those cross-cutting concepts toideas from catalyzing change.
I think and Christy can alsoelaborate more like I think the
cross-cutting concepts aresomething that we haven't seen
(14:02):
addressed specifically in highschool.
There's a lot in the K-8 spacefor topics that really have to
be covered, but I feel like thisis the first place where
someone has tried to narrow thatdown for high school and
provide that focus.
Speaker 3 (14:18):
Going along with that there's also a new piece of it
is really allowing gettingpermissions to de-emphasize some
of the mathematics.
So we've been talking a lot fordecades now on how the
standards are so broad.
We have so many of them andreally now really thinking about
what do we want to de-emphasizeso that we have so many of them
and really now really thinkingabout what do we want to
(14:38):
de-emphasize so that we canemphasize what really matters.
So taking those next steps andtaking liberties to really
connect with our colleagues andothers in our mathematical
spheres of where do we want toreally emphasize the mathematics
?
What's the mathematics that allstudents are need in order to
(15:01):
be successful, whatever theirplans are post high school, and
what are the?
What's the mathematics?
That's kind of specialized forpeople going into different
spaces after high school, sothat that's something that's new
but also definitely is addingon to the conversation that's
been going on forever.
(15:24):
Some other things is we'vetalked about the processes.
We have the mathematical andthe statistical processes.
So with this publication wereally tried to bring in some
more statistics.
So we're not just talking aboutmathematics.
We all know that statistics isbecoming increasingly more
important for our students, justto be data literate, and so we
(15:47):
made sure to have NCTM and NCSMand ASSM all made sure to have
some statistics specialists onthe writing team so that we also
had that perspective as well.
Speaker 1 (16:02):
Very cool.
Speaker 2 (16:04):
So what would be some of the challenges that you see
when educators read this bookand they're excited about these
ideas.
What are going to be some ofthe challenges that they're
going to face to implement thoseideas?
Speaker 3 (16:17):
I can start on that one, since I am in the classroom
yes totally.
Speaker 4 (16:21):
That's why I was waiting.
I'm like yeah, because I willtell you.
Speaker 3 (16:26):
So there's really great ideas.
Especially, I love the idea ofbringing more modeling into our
classrooms.
I think that that really doessupport kind of this relevancy
and I don't mean just some wordproblem that can like kind of
fit our situation.
It's more of having I like theidea of students having to
(16:48):
consider multiple variables fordifferent situations and having
different outcomes that are allvalid depending on what the
situation is and what lensyou're looking through.
I think that that's reallygreat problem solving that
students are going to need andit's a great skill for wherever
you're going in life when we geta little bogged down.
(17:08):
There's a couple of things thatare challenging for educators.
One is how do you find thesereally relevant modeling
problems that still fit inwithin your topic that you're
teaching your concept that'sstill aligned with our state
standards but then is alsomeeting requirements from what
our colleges are telling us weneed to have students prepared
(17:30):
for.
So that that's one thing that Ifind challenging is I can find
some of these modeling problems.
That's another thing like Ifind challenging is I can find
some of these modeling problemsthat's another thing Like
they're limited.
I use CoMap a lot because youknow they have really great
stuff.
So finding these resources,making sure that they're aligned
with what your outcomes are,your student outcomes, and what
(17:51):
they are required to know.
There's a lot of restrictionsthere.
You know there's a lot ofrestrictions there.
But then also the pedagogicalshift into teaching modeling
problems.
It's not, and we have beenshifting into student centered,
but I feel like this is like awhole new beast of student
centered, where recognizing thatall students are going to have
(18:14):
different ways of getting todifferent answers is something
that I think the support on howto teach those skill sets and
also, even if you find amodeling problem that you think
is going to be fantastic.
This happened to me.
I thought I spend this left outLike.
(18:35):
This is going to be great.
It's aligned, students had alot of fun with it.
I had a challenge on surfacingand elevating the mathematics
afterwards, like okay, so let'sstrip away all of that modeling
and let's focus on what was thecore mathematics.
I had a challenge in doing thatbecause I don't know how to do
(18:55):
it.
It was great, students wereengaged, they did fantastic.
But when it came down to, okay,how do systems work, or
whatever it was, it was like Idon't know that mathematics had
a showcase in what we were doingas a classroom.
So those are some challengesthat I have encountered.
(19:16):
So those are some challengesthat I have encountered.
Speaker 4 (19:17):
Thank you, and I would agree I'm not in the
classroom but I supportclassroom teachers and it is
difficult when you are in asystem with expectations of
curriculum and standards andwhat they want you to do every
single day.
So I do think that teachersclassroom teachers can see that
(19:39):
as a barrier.
But I definitely also see thatthis is a great place to start a
conversation right To bring thebook and the ideas to the
people that you work with.
You know start you got to startsomewhere.
So it might not be somethingthat you can directly change by
yourself, but you can definitelystart having conversations
(20:00):
about the things in the bookwith the people who can help
make that change.
Speaker 3 (20:06):
Yeah, I I will say and I think you might be getting
to this question later, soyou'll have to kind of recognize
.
So what I've started to do ispartner with some of our local
colleges to see what mathematicscourses they offer.
And one of our local communitycolleges offers credit to high
(20:29):
school students if they takewhat they call math and society,
which is like the math that anystudent getting an associate's
degree would would have, and inthat math course it's kind of
like you kind of get to choosewhat's in it.
And so for me I was like that'sfantastic, because then I can
(20:52):
really kind of choose themodeling.
I'm not in this box and I knowthat that's not an option for
everyone.
That's not an option foreveryone.
However, if there are peoplethat work in school districts
that offer college in the highschool credit or whatever that
may be, whatever that's calledin their district, they might be
able to reach out to thecolleges that just say like hey,
is this something that we canpartner with you, because then
(21:15):
you can start getting thatmodeling and have a modeling
class potentially.
And so that's kind of what I'mworking on in my district, so
that students do have anopportunity to engage in that
type of problem solving Nice.
Speaker 1 (21:32):
I know, and we kind of broke up during the book
study into our breakout rooms totalk about this, but you had
the two lenses of there's themathematical modeling and the
statistical modeling and I thinkthat is that kind of what
you're talking about bringingthe math out of it.
Or are they really just twoseparate ideas?
Speaker 3 (21:51):
Oh, I think that when I say bringing the math or it
could be statistics, it's it's.
We do all this engagement andthe problem solving and
sometimes students may notrecognize that they're doing
mathematics Right.
And mathematical thinking isreally like what's what's the
problem?
What's the variables that?
What's the problem we're tryingto solve?
(22:12):
What's the variables solve?
What's the variables?
It's all this mathematics andessentially there's some
mathematical concept kind ofhidden inside of the problem
that they're trying to solve.
And how do you support studentsin kind of teasing that piece
out and then thinking about okay, that mathematics, what other
types of problems could we usethat same mathematical thinking
(22:38):
to to solve, and things likethat.
And so, even though the wholeprocess might be mathematical or
statistical, what's what's thatlike grain of mathematics that
we're we're really trying tolearn within this problem, or
what and and how do you surfacethat out without making it
non-engaging?
Speaker 2 (22:59):
And that's a much harder thing to do right than to
teach the concept and now do anapplication Right, Because the
application can include so manydifferent other pieces and that
thread is in there.
But to go back to the threadand to decide which thread you
want to go back to or how youwant to go back to, it.
That is a much more challengingtask, for sure.
Speaker 3 (23:19):
But the learning is more authentic.
Speaker 2 (23:21):
Absolutely.
Speaker 3 (23:22):
So yes, and you are absolutely right, it is so much
more challenging to go to thatspace and I think there is going
to be a lot of professionaldevelopment opportunities around
how what are like bestpractices, around moving from
the that that problem solvingpiece, to the medical concept so
(23:45):
when you were talking aboutchallenges, you talked a little
bit about finding problems andthe sort of trying to find a
curriculum resource right thatyou can use.
Speaker 2 (23:54):
so if we assume that I have a curriculum resource
that will work for me, then whatam I focusing on in my
classroom?
What are the things I'm reallygoing to be focusing on doing In
your opinion?
Speaker 3 (24:10):
Chris, do you want to start off on this one or no?
Speaker 4 (24:14):
I can.
I'm like it's Like you're inthe classrooms.
Your perspective is so valuable, I know.
I do think like if you have, ifI had, the perfect trying to do
in there, which is what you seein a lot of traditional
(24:45):
mathematics.
You know, you see the, just theone math thing that you're
trying to learn and there's nota lot of context.
I also think that the contest,the context, has to be like
relevant and important to kids.
Right, it'd be no one's buyinga hundred watermelons and taking
them in their backpacksomewhere.
(25:06):
So I think, like deep problemsthat are like important to kids
and the lives that they have,and they live in a world that
has so much going on.
Right, we have so much going onin the world and our kids are
so much more connected to all ofthe things that are happening
in the world and it's importantto them.
So I think if we could findways to bring them content that
(25:31):
solves real problems but alsogets to the math, that would be
the perfect answer.
I don't know that that willever realistically exist, but
like those are things that Ithink kids would love and it
would do the like like Christywas talking about.
It would give them the problemsolving and the math and they
might not find the math at firstor realize that that's what
(25:53):
they're doing, but every problemwe solve in the world has some
kind of math involved in it.
Speaker 3 (26:00):
And I think, even if you do find those problems and
it depends on where everyone isin their math education journey
as far as teaching goes butreally focusing on releasing
control I think that if you'regoing to be teaching in this
modeling way, you have to bevery comfortable with not having
(26:21):
control and getting thatcontrol to students and then
also really focusing on thinkingthrough.
So making sure to think throughthose problems and do them in
all of the different ways thatyou can think of and that will
help be more prepared when somestudent does like the off the
wall thing and you could stillbe like oh yeah, it allows you
(26:43):
to be more flexible, but it alsoallows you to highlight and
support students who may notnecessarily have a positive
mathematical identity.
I think that this modelingallows for creativity and
freedom of thinking aboutdifferent things, and this is a
great way to make sure that thestudents are the ones whose
(27:07):
learning is kind of progressingthe class and showcasing them.
So I think it's a greatopportunity for that.
And a lot of these things arepedagogical, because if you have
your curriculum now, you reallyhave to focus on your pedagogy
and then also thinking about howare you going to change your
assessments, your paper pencilassessments.
(27:27):
They're not going to work inthis situation because students
aren't.
They're not learning in thatway, and so you're assessing
them in this totally foreign waythat they didn't learn.
And so what are you going to dowith your assessments that are
going to be an accurate versionof where your students can
demonstrate what they've learned.
That may not be what you'reused to, and that's also another
(27:51):
change of ensuring thatstudents can demonstrate what
they're learning through thisprocess through this process.
Speaker 1 (27:59):
So I'm hearing a lot of re-imagining in the classroom
right now.
But how would, how would aleadership support this or how,
how would how do we help thoseteachers?
Coach Like.
Speaker 4 (28:12):
We are re-imagining the classroom and that is so
important and it it, it might Idon't know that it's going to be
easy to reimagine it from, youknow, outside the classroom's
lens either, because we knowit's like this will take time.
You have to be able to supportteachers and help them think
(28:32):
through.
What does this look like?
How do I do it?
Classroom teachers will needsupport.
Even though these are thingswe've talked about for a really
long time, we're still notseeing those changes happening
in the classroom or even in, youknow, university, when people
go to become math teachers, likewe're not seeing that change
happening there all the timeeither.
(28:54):
So I do think teachers needsupport and professional
development.
They need time to practice.
They need time to be able to dothe math problems in a million
different ways so they cananticipate what teachers or what
students are going to do.
I know most teachers get likeplanning time, but it's not
(29:14):
enough and there's so manythings that teachers have to do
in that one hour every day orwhatever it might look like.
So I do think we have to thinkabout from a system you know,
like how do we also reimaginewhat does school look like?
What does a teacher's workday.
Look like I think there's.
I think this could open up thedoor to lots of possibilities,
(29:35):
but I do think you know like itis hard.
We are bound by state standardsand state assessments, so you
have to be a little creative.
But I think there aredefinitely places to start.
I think teachers can startthinking through this and, with
professional development andcoaching and support, I think
that they can try.
(29:56):
No-transcript.
Speaker 1 (30:19):
Absolutely.
Speaker 3 (30:20):
I think it's also really helpful if you have
administrators or whoever yourevaluator is, that comes in and
observes you for that, like oneperiod per year.
It would be really helpful ifthey knew about math education,
like if they knew like a onesheet, sheet, sheet I.
(30:41):
That would be really hard to do, but if they were able to
actually support rather thanjust looking at behavior or like
be in knowledgeable, so thatwhen, as as a teacher, you go
and you have your conversation,you can say, hey, I, you know,
this is my challenge.
Can you focus in on this for meand have confidence that that
(31:03):
person is going to be asoundboard and maybe have some
conversation about how toimprove?
So I think it's really importantfor your administrator or
whoever it is, to be, becausenot everyone has a coach and so
having other people or eventalking to administrators about
hey, can my colleague come, isthere anything that we can do so
(31:23):
that my colleague can come inand observe me Because we'd like
to work out some how to improve.
So there's ways to get aroundit if you don't have a coach.
But you also need a supportiveadmin team to do that.
But you can advocate for,advocate for the worst that
they're going to say is no,which is unfortunate.
But I mean realistically.
(31:44):
I think administrators want ourteachers to be successful and
if they can see value in thattype of collaboration to improve
the outcomes for students andexperiences for students, then I
think that that could be apossibility as well for students
then I think that that could bea possibility as well.
Speaker 2 (32:02):
It definitely feels like a combination of it's not
very easy and it's reallyimportant.
Speaker 4 (32:09):
Right Things that are really important aren't usually
easy, right, so you got tostart somewhere.
So I think, like we've saideverywhere, we just have to
start with advocating and havingconversations and finding the
right people whether that's theteacher next door or the
principal that evaluates you, orthe coach at the district
(32:29):
office Start dropping commentsfrom the book in their inbox and
saying let's talk about thissomething, just to get it on
their radar.
Speaker 1 (32:42):
That's such a good point to just start the
conversation Again with thebooks.
Today I feel really lucky.
I got to talk to some peopleabout it and that felt like an
outreach that you guys weredoing.
Do you plan to outreach more?
Do you plan to offer morevenues for conversation?
Speaker 4 (33:00):
Hopefully.
I know I'm on the board forNCSM and I know I did bring it
up this weekend at our boardmeeting.
I said NCTM did a book studyand we did it through them.
Maybe let's do it through NCSMthis time and offer a book study
to our membership and put itout there.
So hopefully that will happensoon.
(33:22):
I know I've also seen which wasa surprise, but the WestEd and
the Gates Foundation are workingon a project and the book is
something that they've sent outto their participants.
So that was exciting to seethat it was getting into.
And classroom teachers they'reclassroom teachers, so I'm
looking forward to see where theconversation goes from there.
(33:43):
So it's trickling out there.
So we definitely would love tosee more book studies happen.
It was a fun experience.
There was great ideas and lotsof good conversation.
Speaker 1 (33:56):
And I know as a participant a lot of things I
heard were we want more.
Do you have ideas for how totalk together, get support for
this and things like that?
So that's great you're thinkingabout it.
Speaker 2 (34:09):
We're getting close to our time, so we're wondering
if there's anything else that wedidn't ask you that you would
like to include.
Make sure that you have achance to say.
Speaker 4 (34:19):
I was thinking about the connection to like other
work that's happening, and Iknow the book talks a lot also
about like pathways and I thinkthat that is work that is
happening in a lot of placesright now.
I see a lot of states workingon those high school pathways.
We're seeing lots of standardsrevisions happening across the
(34:42):
United States in different areasand I think and I hope, like
there are some examples in here,there's some links on the
webpage at NCTM to differentstates and some of the work that
has been done there.
So I hope that, as people indifferent states are going
through that work, that thiscould also become a resource for
(35:03):
them to guide them in some ofthe decisions that they're
making.
Speaker 3 (35:09):
I also want to share that and this is true.
This has been true forever.
But I also just want tohighlight that if you're trying
to make a change or anadjustment, it's okay if it
doesn't work out at first.
That doesn't mean that it's afailure.
It doesn't mean to abandon it.
If you believe in it and youknow that it's great for
(35:31):
students, just keep on trying,Revise your thinking, get some
people that you can have someconversations with.
Hopefully you have colleaguesthat you can talk to and really
it's okay.
It's okay if it doesn't work.
I think that those that are themost successful in making those
changes have to be kind toourselves and also with our
(35:54):
students.
If you start something new, ourstudents are going to need a
little bit of adjustment, as wedo as adults.
And so really thinking abouthow to make improvements as
you're going along the process,and if you're starting at point
zero, you're at a wonderful spotbecause that just means that
you, you're going to make thatmuch more progress and so really
(36:16):
not giving up it.
But it is hard, it really ishard, and when you're doing that
reflection, don't get too hardon yourself, like you're doing
great things.
So highlight those great thingsand then think about what are
your next steps.
How are you going to makeimprovements and also getting
student feedback like, hey, whatworked, what didn't work, what
(36:37):
do you think we can do toimprove this?
You're not, even if you're at areally small school, you're not
alone, because you're workingwith students to support them
and getting feedback from themcould be a great spot to start
thinking about making thoseimprovements.
Speaker 2 (36:54):
It's well said.
Speaker 1 (36:55):
Yeah, well, thanks for being with us today.
Speaker 2 (36:59):
Thank you for coming on the podcast and sharing all
your wonderful insights andideas with us.
We really appreciate it.
Speaker 4 (37:05):
Thanks for having us, thanks for being part of our
(37:28):
book study, of course.
Speaker 2 (37:31):
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 podcast wascreated by Julius H.
It can be found on pixabaycom.
So thank you very much, julius.
Join us in two weeks for thenext episode of More Math for
(37:54):
More People.
What day will that be, joel?
Speaker 1 (37:58):
It'll be May 27th, national Sunscreen Day, and
we'll be able to talk about somegreat stories surrounding
sunscreen and find out maybemore about what that beautiful
thing is.
But I know that I will havestories to share about when I
didn't use sunscreen and howthat affected my day.
(38:20):
But looking forward to having achat with Misty about sunscreen
May 27th.
Speaker 2 (39:17):
We'll see you there.
Thank you, bye.
You are listening to the More Math for More People
podcast.
An outreach of CPM educationalprogram Boom.
An outreach of CPM EducationalProgram.
Speaker 2 (00:26):
Boom.
Okay, so here we are.
It's already the 13th of May.
We're here.
Wow, seems like May is justzooming by already, since it's
already the middle of the monthand it's our first podcast of
May.
Speaker 1 (00:42):
Isn't it bad luck on the 13th, or it's like a?
Speaker 2 (00:45):
well, that was a friday, oh friday it's tuesday
tuesday, it's tuesday and yeah,big deal yeah this is our first
episode of season five that isbig deal, five seasons five
seasons.
That's more than some netflixshows joel, I mean intentionally
(01:05):
or not intentionally, but likewell you get to season five on a
, on a streaming or any like anyyeah, thing that's a big deal
and I would argue that a seasonis not always 25 episodes and we
average around 25 episodes forsure, yeah, for sure.
We, uh, we could have gone withthe eight season or eight
(01:25):
episode season, and that wouldhave been much, much.
Well, I don't know if it wouldhave been easier or not.
Yeah, anyway, here we are.
Speaker 1 (01:34):
We'd have to make it an hour long instead of a half
hour long, just with all ourthoughts that build up, that
build up to a cliffhanger thatmakes people come back the next
time.
Speaker 2 (01:42):
Yeah, yeah, a cliffhanger that makes people
come back the next time.
Yeah yeah, I think that's oneof the interesting things a
total side note, but justinteresting things about shows
that are not on networktelevision, they're just
streaming.
They're random lengths Like.
Sometimes they're like 33minutes, 47 minutes, 54 minutes.
Yeah, because they don't haveto make it match the hour.
Half hour slot with commercials.
Speaker 1 (02:02):
Yes, so they can.
Just here's how long we'regoing to tell the story this
time.
The other thing I wonder, too,is Julius H has given us this
great music, but like when Ithink of, let's say, when I
watch Game of Thrones when Ihear that theme music I kind of
get like pumped up.
I wonder if when people hearthe Julius H music they kind of
(02:23):
get pumped up.
Speaker 2 (02:24):
They get pumped up for more and more people.
They might, they might.
I hope so, I hope so.
That's what I imagine yeah Well, that's good, that's good, it's
healthy, yeah.
So here we are, season five,it's May 13th, sure is.
And it's our National Day ofsegment, because we're still
doing that.
Yep, I don't think we've missedan episode.
Speaker 1 (02:45):
No, all right, it's important to celebrate.
Speaker 2 (02:47):
I think so.
Speaker 1 (02:48):
Yeah.
Speaker 2 (02:50):
So what are we celebrating today?
Speaker 1 (02:55):
National Tulip Day.
Speaker 2 (02:56):
Tulip Day.
Tulip Day, wow.
This must be for people who areat very northern latitudes.
My tulips are long gone.
Speaker 1 (03:03):
What do you mean?
Mean, oh, they've already comeand gone oh yeah, they're long
gone.
Speaker 2 (03:06):
They.
Speaker 1 (03:07):
They bloomed, peaked like three, four weeks ago oh my
gosh, we're in peak bloom rightnow.
Really yes yeah, well, that'swhat I'm saying more northern or
south or continental time zones, colder latitude, colder spaces
yeah more I'm trying to thinktilted towards the sun, tilted
away from the sun.
Speaker 2 (03:27):
If you're at a higher latitude, then you would be I
mean you're it's a sphere.
Speaker 1 (03:33):
You can't go up and down.
What?
Speaker 2 (03:37):
The earth is a sphere .
You go up and down, you goaround it, but anyway, if you're
in a colder space, for thereasons that it might be colder,
your tulips might be onlyblooming now.
Speaker 1 (03:48):
That's true.
Speaker 2 (03:49):
I think they've pretty much bloomed in the
Netherlands too, though, but itdoesn't matter, it's tulip day
today.
Speaker 1 (03:55):
It is.
And do you know?
Actually you brought up theNetherlands.
Speaker 2 (03:59):
Yes, I did.
Speaker 1 (04:00):
That's not where they started, that's not where they
were first cultivated.
Speaker 2 (04:03):
Where were they first cultivated?
I'm curious.
Speaker 1 (04:05):
Turkey Around the year 1000.
Speaker 2 (04:09):
Wow yeah.
Speaker 1 (04:11):
They didn't actually arrive in Holland until the 16th
century, so like 600 years.
Speaker 2 (04:19):
That makes sense.
I don't know how they arrived.
16th century is a lot of thatcolonialism, time and whatnot.
Speaker 1 (04:23):
It is yes.
Speaker 2 (04:25):
The Dutch were doing lots of moving things around
commercially.
Speaker 1 (04:30):
Well, and it was a biologist that took the tulips
to there.
Speaker 2 (04:37):
They grow really well in that climate.
Speaker 4 (04:39):
Yeah.
Speaker 2 (04:41):
And earth that reclaimed flood dirt.
Speaker 1 (04:46):
Hmm, I didn't know about that part.
Yeah, they grow really well,they grow really well.
Here in Utah we have a tulipfestival.
Speaker 2 (04:55):
And the other.
Speaker 1 (04:55):
Thing that grows well .
Here is lavender.
We have lavender days.
Oh yeah, it's not NationalLavender.
Speaker 2 (05:01):
Day.
But no, it's not.
Lavender grows pretty wellaround here too.
I used to live in Mount Vernonand Skagit County is a major
tulip bulb producer, I think,like next to Holland, michigan
and the Netherlands.
So we would have a big tulipfestival every year and people
would come out and see thefields and fields and fields of
tulips Interesting, of tulipsInteresting, and then to make
(05:24):
the tulips grow more bulbs.
When the tulips are in bloomthey go out and they pull all
the petals off.
So then people would come andyou'd just see all the petals in
the middle of the rows andgreen Interesting.
Speaker 1 (05:39):
Here's kind of a, I think, an interesting fact and
maybe even a little bit of amath fact.
But this says tulips are evenso.
Tulip flower buds are almostperfectly symmetrical to each
other.
Speaker 2 (05:51):
Tulip flower bulbs are almost perfectly symmetrical
.
Speaker 1 (05:53):
Flower buds.
Speaker 2 (05:54):
Buds are, oh Hmm.
Speaker 1 (05:57):
Interesting.
Speaker 2 (05:58):
They're even like and they have an even number of
petals.
Speaker 1 (06:01):
Well, they're symmetrical.
Speaker 2 (06:03):
Oh, okay.
Speaker 1 (06:04):
Is that?
Another term for even you thinkmaybe.
I mean I feel like there's.
Speaker 2 (06:08):
I feel like plants.
They're either like they haveeven numbers of petals and
leaves or they have odd numbersof petals and leaves.
There's monocots and dicotskind of a thing or something.
Monocots can have odd, I think,and dicots always have an even,
but I'm not I'm not a hundredpercent on that.
Speaker 1 (06:26):
So Okay, you fact checkers out there.
Speaker 2 (06:28):
Yeah.
Speaker 1 (06:29):
Let us know how many varieties.
Speaker 2 (06:32):
Bring in the random science fact that I can't
remember.
Speaker 1 (06:36):
How many varieties do you think there are?
Speaker 2 (06:38):
Varieties like, like different named colors, like I
can buy a bulb of that variety.
Speaker 1 (06:47):
I know that there are many varieties of tulips and I
know that number.
Yeah, how many do you thinkthere are?
Speaker 2 (06:54):
Well, I mean, I think it depends on how you term this
variety, right?
I think that, like tulips areone species, there's only one
thing that's a tulip.
Speaker 1 (07:04):
But we're not talking about species.
If you name the genus andspecies, there's only one thing,
that's a tulip.
But we're not talking aboutspecies If you name, the genus
and species.
Speaker 2 (07:07):
There's only one thing right.
But then if you have oh, like,what are the different varieties
Like, when I plant this one,it's going to come up and it's
going to look different than allthe other ones right.
I bet there are easilythousands.
Speaker 1 (07:20):
How many of thousands ?
Speaker 2 (07:23):
I'm going to go with the over under on five thousand.
Oh my gosh over three thousandfor sure.
Speaker 1 (07:29):
Yeah, now that I think it's, I think you're right
in there for sure yeah, yeah,no it's.
Speaker 2 (07:35):
There's a lot because I think about, like that brex
catalog or the spring hillcatalogs I might get and the
just the number of differentpages and pages of really cool
looking tulips.
So you know the ones likeyou've seen those tulips that
are like they have super frillyblooms, like the blooms that are
like straight and have allthese curly edges on them and
they might have like variegatedcolors to them yeah, yeah.
(07:57):
That's caused by viruses.
Speaker 1 (07:59):
Oh really.
Speaker 2 (08:05):
Yeah, mutations Like no viruses, oh viruses, not a
mutation Like some of them are.
Some of them are mutations inhow, like in the, or slight
differences in what genes areexpressed.
Speaker 1 (08:10):
Okay.
Speaker 2 (08:10):
Right, but this is the viruses actually causes
differences in the actual cellexpression itself.
Speaker 1 (08:16):
I like it.
Speaker 2 (08:18):
Yeah, super cool, did you know you can eat tulips.
And not die.
Mm-hmm, you can eat tulips andnot die.
Speaker 1 (08:25):
I can eat a lot of things.
That's true too once that'strue.
That's true.
This says that you can usetulip petals instead of onions
in some recipes oh, I wouldn't.
Speaker 2 (08:35):
I wouldn't do that no , because you don't like onions
I don't like onions anyway so Idon't want to replace them with
something else, I just don'twant to have them.
But that's interesting.
I did not know they could beused as a food, garnish or
additive.
Yeah, so that's interesting,cool, all right.
Well, so what are you going todo to celebrate Tulip Day?
Speaker 1 (08:57):
Well, I'm going to go outside and look at my tulips.
Speaker 2 (08:59):
Nice, nice, I don't have that option.
My tulips are long gone.
Yeah, nice, I don't have thatoption.
My tulips are long gone.
I have some really, reallylovely pictures.
I took a lot of pictures when Iwas in the Netherlands three
years ago, four years ago, threeyears ago, and we went to a
tulip farm factory, whatever,and took a lot of pictures, so I
might look at those.
Some of them sure are prettycool.
Speaker 1 (09:20):
Okay, I'll send you a picture of mine.
Speaker 2 (09:22):
Excellent, sounds good.
Yeah, all right Well enjoyTulip Day.
Speaker 1 (09:34):
Everyone Excited to be here for the first episode of
Season 5 for the More Math forMore People podcast, and we were
lucky enough to interview ChrisCunningham and Christy Martin,
who were part of the writingteam for the book High School
(09:55):
Mathematics Reimagined,revitalized and Relevant.
It's an NCTM publication.
I was lucky enough to be partof the book study in the
leadership thread and learned alot and had a lot of great
discussions, and we thought thiswould be great if we could have
a chat with Chris and Christy.
Chris Cunningham is amathematics content specialist
(10:19):
and leader in the PhoenixArizona area and has also served
as a board member for NCSM.
Christy Martin is a mathematicshigh school teacher from the
Tumwater area in WashingtonState and is also a recipient of
the Presidential Award forExcellence in Mathematics and
Science Teaching.
And so please enjoy thisinterview with Chris and Christy
(10:44):
as we dive into how high schoolmathematics can be reimagined,
revitalized and relevant.
So I feel like I'm taking thispart from Misty a little bit,
but today we're here with ChrisCunningham and Christy Martin
and we're going to have adiscussion about reimagining and
(11:07):
revitalizing and making highschool mathematics relevant
enough to be in a book studyaround a publication that NCTM
put out and Chris and Christyare a part of that.
And first of all, welcome,welcome, and please introduce
yourselves and tell us who youare.
Speaker 3 (11:27):
Christine, you go first, okay.
Speaker 4 (11:29):
I'm Chris Cunningham.
I am a math specialist for ahigh school district in Phoenix
Arizona.
Speaker 3 (11:37):
And I'm Christ, math specialist for a high school
district in Phoenix, arizona.
And I'm Christy Martin.
I am a high school mathematicseducator in Washington State.
Speaker 1 (11:44):
Okay, that's right, well welcome.
So, just to get started, couldyou tell us what maybe some of
the main ideas of this book wereand how did you feel?
Why was it written, written, orwhat was the inspiration for
making it?
Speaker 3 (11:59):
Well, I will share that.
The book is written in.
When I think of it there'sthree major parts to it, which
is in the title of the book,realistically speaking, and so
I'm unpacking.
What does it mean to reimaginemathematics education?
For so long mathematicseducation has kind of stayed
(12:21):
stagnant.
We've made great progress, butwe want to continue moving that
needle in a positive directionfor students.
And then also, what does itmean to revitalize the
educational experience for ourmathematics students?
And then also, how do we makemathematics more relevant in an
ever-changing world?
And unpacking some ways that wecan do that at the high school
(12:44):
level.
So that's kind of where thebook kind of lives in those
three spaces.
Speaker 1 (12:52):
Right on, Chris.
Anything to add?
Speaker 4 (13:11):
Right on, chris, anything to add seen in the past
.
So we definitely want torecognize that it's an extension
or a continuation of some bookslike Catalyzing Change and like
bringing some ideas, like tocontinue moving forward.
Speaker 1 (13:27):
So how does it kind of align with other math
initiatives that are out there?
Like you're saying, you want tocontinue this work, so how is
it the same or how is itdifferent from other math
initiatives that have been outthere?
Speaker 4 (13:40):
I think.
I mean you see in the bookconnections explicitly made to
catalyzing change.
There's the you know charts inthe back where it links some of
those cross-cutting concepts toideas from catalyzing change.
I think and Christy can alsoelaborate more like I think the
cross-cutting concepts aresomething that we haven't seen
(14:02):
addressed specifically in highschool.
There's a lot in the K-8 spacefor topics that really have to
be covered, but I feel like thisis the first place where
someone has tried to narrow thatdown for high school and
provide that focus.
Speaker 3 (14:18):
Going along with that there's also a new piece of it
is really allowing gettingpermissions to de-emphasize some
of the mathematics.
So we've been talking a lot fordecades now on how the
standards are so broad.
We have so many of them andreally now really thinking about
what do we want to de-emphasizeso that we have so many of them
and really now really thinkingabout what do we want to
(14:38):
de-emphasize so that we canemphasize what really matters.
So taking those next steps andtaking liberties to really
connect with our colleagues andothers in our mathematical
spheres of where do we want toreally emphasize the mathematics
?
What's the mathematics that allstudents are need in order to
(15:01):
be successful, whatever theirplans are post high school, and
what are the?
What's the mathematics?
That's kind of specialized forpeople going into different
spaces after high school, sothat that's something that's new
but also definitely is addingon to the conversation that's
been going on forever.
(15:24):
Some other things is we'vetalked about the processes.
We have the mathematical andthe statistical processes.
So with this publication wereally tried to bring in some
more statistics.
So we're not just talking aboutmathematics.
We all know that statistics isbecoming increasingly more
important for our students, justto be data literate, and so we
(15:47):
made sure to have NCTM and NCSMand ASSM all made sure to have
some statistics specialists onthe writing team so that we also
had that perspective as well.
Speaker 1 (16:02):
Very cool.
Speaker 2 (16:04):
So what would be some of the challenges that you see
when educators read this bookand they're excited about these
ideas.
What are going to be some ofthe challenges that they're
going to face to implement thoseideas?
Speaker 3 (16:17):
I can start on that one, since I am in the classroom
yes totally.
Speaker 4 (16:21):
That's why I was waiting.
I'm like yeah, because I willtell you.
Speaker 3 (16:26):
So there's really great ideas.
Especially, I love the idea ofbringing more modeling into our
classrooms.
I think that that really doessupport kind of this relevancy
and I don't mean just some wordproblem that can like kind of
fit our situation.
It's more of having I like theidea of students having to
(16:48):
consider multiple variables fordifferent situations and having
different outcomes that are allvalid depending on what the
situation is and what lensyou're looking through.
I think that that's reallygreat problem solving that
students are going to need andit's a great skill for wherever
you're going in life when we geta little bogged down.
(17:08):
There's a couple of things thatare challenging for educators.
One is how do you find thesereally relevant modeling
problems that still fit inwithin your topic that you're
teaching your concept that'sstill aligned with our state
standards but then is alsomeeting requirements from what
our colleges are telling us weneed to have students prepared
(17:30):
for.
So that that's one thing that Ifind challenging is I can find
some of these modeling problems.
That's another thing like Ifind challenging is I can find
some of these modeling problemsthat's another thing Like
they're limited.
I use CoMap a lot because youknow they have really great
stuff.
So finding these resources,making sure that they're aligned
with what your outcomes are,your student outcomes, and what
(17:51):
they are required to know.
There's a lot of restrictionsthere.
You know there's a lot ofrestrictions there.
But then also the pedagogicalshift into teaching modeling
problems.
It's not, and we have beenshifting into student centered,
but I feel like this is like awhole new beast of student
centered, where recognizing thatall students are going to have
(18:14):
different ways of getting todifferent answers is something
that I think the support on howto teach those skill sets and
also, even if you find amodeling problem that you think
is going to be fantastic.
This happened to me.
I thought I spend this left outLike.
(18:35):
This is going to be great.
It's aligned, students had alot of fun with it.
I had a challenge on surfacingand elevating the mathematics
afterwards, like okay, so let'sstrip away all of that modeling
and let's focus on what was thecore mathematics.
I had a challenge in doing thatbecause I don't know how to do
(18:55):
it.
It was great, students wereengaged, they did fantastic.
But when it came down to, okay,how do systems work, or
whatever it was, it was like Idon't know that mathematics had
a showcase in what we were doingas a classroom.
So those are some challengesthat I have encountered.
(19:16):
So those are some challengesthat I have encountered.
Speaker 4 (19:17):
Thank you, and I would agree I'm not in the
classroom but I supportclassroom teachers and it is
difficult when you are in asystem with expectations of
curriculum and standards andwhat they want you to do every
single day.
So I do think that teachersclassroom teachers can see that
(19:39):
as a barrier.
But I definitely also see thatthis is a great place to start a
conversation right To bring thebook and the ideas to the
people that you work with.
You know start you got to startsomewhere.
So it might not be somethingthat you can directly change by
yourself, but you can definitelystart having conversations
(20:00):
about the things in the bookwith the people who can help
make that change.
Speaker 3 (20:06):
Yeah, I I will say and I think you might be getting
to this question later, soyou'll have to kind of recognize
.
So what I've started to do ispartner with some of our local
colleges to see what mathematicscourses they offer.
And one of our local communitycolleges offers credit to high
(20:29):
school students if they takewhat they call math and society,
which is like the math that anystudent getting an associate's
degree would would have, and inthat math course it's kind of
like you kind of get to choosewhat's in it.
And so for me I was like that'sfantastic, because then I can
(20:52):
really kind of choose themodeling.
I'm not in this box and I knowthat that's not an option for
everyone.
That's not an option foreveryone.
However, if there are peoplethat work in school districts
that offer college in the highschool credit or whatever that
may be, whatever that's calledin their district, they might be
able to reach out to thecolleges that just say like hey,
is this something that we canpartner with you, because then
(21:15):
you can start getting thatmodeling and have a modeling
class potentially.
And so that's kind of what I'mworking on in my district, so
that students do have anopportunity to engage in that
type of problem solving Nice.
Speaker 1 (21:32):
I know, and we kind of broke up during the book
study into our breakout rooms totalk about this, but you had
the two lenses of there's themathematical modeling and the
statistical modeling and I thinkthat is that kind of what
you're talking about bringingthe math out of it.
Or are they really just twoseparate ideas?
Speaker 3 (21:51):
Oh, I think that when I say bringing the math or it
could be statistics, it's it's.
We do all this engagement andthe problem solving and
sometimes students may notrecognize that they're doing
mathematics Right.
And mathematical thinking isreally like what's what's the
problem?
What's the variables that?
What's the problem we're tryingto solve?
(22:12):
What's the variables solve?
What's the variables?
It's all this mathematics andessentially there's some
mathematical concept kind ofhidden inside of the problem
that they're trying to solve.
And how do you support studentsin kind of teasing that piece
out and then thinking about okay, that mathematics, what other
types of problems could we usethat same mathematical thinking
(22:38):
to to solve, and things likethat.
And so, even though the wholeprocess might be mathematical or
statistical, what's what's thatlike grain of mathematics that
we're we're really trying tolearn within this problem, or
what and and how do you surfacethat out without making it
non-engaging?
Speaker 2 (22:59):
And that's a much harder thing to do right than to
teach the concept and now do anapplication Right, Because the
application can include so manydifferent other pieces and that
thread is in there.
But to go back to the threadand to decide which thread you
want to go back to or how youwant to go back to, it.
That is a much more challengingtask, for sure.
Speaker 3 (23:19):
But the learning is more authentic.
Speaker 2 (23:21):
Absolutely.
Speaker 3 (23:22):
So yes, and you are absolutely right, it is so much
more challenging to go to thatspace and I think there is going
to be a lot of professionaldevelopment opportunities around
how what are like bestpractices, around moving from
the that that problem solvingpiece, to the medical concept so
(23:45):
when you were talking aboutchallenges, you talked a little
bit about finding problems andthe sort of trying to find a
curriculum resource right thatyou can use.
Speaker 2 (23:54):
so if we assume that I have a curriculum resource
that will work for me, then whatam I focusing on in my
classroom?
What are the things I'm reallygoing to be focusing on doing In
your opinion?
Speaker 3 (24:10):
Chris, do you want to start off on this one or no?
Speaker 4 (24:14):
I can.
I'm like it's Like you're inthe classrooms.
Your perspective is so valuable, I know.
I do think like if you have, ifI had, the perfect trying to do
in there, which is what you seein a lot of traditional
(24:45):
mathematics.
You know, you see the, just theone math thing that you're
trying to learn and there's nota lot of context.
I also think that the contest,the context, has to be like
relevant and important to kids.
Right, it'd be no one's buyinga hundred watermelons and taking
them in their backpacksomewhere.
(25:06):
So I think, like deep problemsthat are like important to kids
and the lives that they have,and they live in a world that
has so much going on.
Right, we have so much going onin the world and our kids are
so much more connected to all ofthe things that are happening
in the world and it's importantto them.
So I think if we could findways to bring them content that
(25:31):
solves real problems but alsogets to the math, that would be
the perfect answer.
I don't know that that willever realistically exist, but
like those are things that Ithink kids would love and it
would do the like like Christywas talking about.
It would give them the problemsolving and the math and they
might not find the math at firstor realize that that's what
(25:53):
they're doing, but every problemwe solve in the world has some
kind of math involved in it.
Speaker 3 (26:00):
And I think, even if you do find those problems and
it depends on where everyone isin their math education journey
as far as teaching goes butreally focusing on releasing
control I think that if you'regoing to be teaching in this
modeling way, you have to bevery comfortable with not having
(26:21):
control and getting thatcontrol to students and then
also really focusing on thinkingthrough.
So making sure to think throughthose problems and do them in
all of the different ways thatyou can think of and that will
help be more prepared when somestudent does like the off the
wall thing and you could stillbe like oh yeah, it allows you
(26:43):
to be more flexible, but it alsoallows you to highlight and
support students who may notnecessarily have a positive
mathematical identity.
I think that this modelingallows for creativity and
freedom of thinking aboutdifferent things, and this is a
great way to make sure that thestudents are the ones whose
(27:07):
learning is kind of progressingthe class and showcasing them.
So I think it's a greatopportunity for that.
And a lot of these things arepedagogical, because if you have
your curriculum now, you reallyhave to focus on your pedagogy
and then also thinking about howare you going to change your
assessments, your paper pencilassessments.
(27:27):
They're not going to work inthis situation because students
aren't.
They're not learning in thatway, and so you're assessing
them in this totally foreign waythat they didn't learn.
And so what are you going to dowith your assessments that are
going to be an accurate versionof where your students can
demonstrate what they've learned.
That may not be what you'reused to, and that's also another
(27:51):
change of ensuring thatstudents can demonstrate what
they're learning through thisprocess through this process.
Speaker 1 (27:59):
So I'm hearing a lot of re-imagining in the classroom
right now.
But how would, how would aleadership support this or how,
how would how do we help thoseteachers?
Coach Like.
Speaker 4 (28:12):
We are re-imagining the classroom and that is so
important and it it, it might Idon't know that it's going to be
easy to reimagine it from, youknow, outside the classroom's
lens either, because we knowit's like this will take time.
You have to be able to supportteachers and help them think
(28:32):
through.
What does this look like?
How do I do it?
Classroom teachers will needsupport.
Even though these are thingswe've talked about for a really
long time, we're still notseeing those changes happening
in the classroom or even in, youknow, university, when people
go to become math teachers, likewe're not seeing that change
happening there all the timeeither.
(28:54):
So I do think teachers needsupport and professional
development.
They need time to practice.
They need time to be able to dothe math problems in a million
different ways so they cananticipate what teachers or what
students are going to do.
I know most teachers get likeplanning time, but it's not
(29:14):
enough and there's so manythings that teachers have to do
in that one hour every day orwhatever it might look like.
So I do think we have to thinkabout from a system you know,
like how do we also reimaginewhat does school look like?
What does a teacher's workday.
Look like I think there's.
I think this could open up thedoor to lots of possibilities,
(29:35):
but I do think you know like itis hard.
We are bound by state standardsand state assessments, so you
have to be a little creative.
But I think there aredefinitely places to start.
I think teachers can startthinking through this and, with
professional development andcoaching and support, I think
that they can try.
(29:56):
No-transcript.
Speaker 1 (30:19):
Absolutely.
Speaker 3 (30:20):
I think it's also really helpful if you have
administrators or whoever yourevaluator is, that comes in and
observes you for that, like oneperiod per year.
It would be really helpful ifthey knew about math education,
like if they knew like a onesheet, sheet, sheet I.
(30:41):
That would be really hard to do, but if they were able to
actually support rather thanjust looking at behavior or like
be in knowledgeable, so thatwhen, as as a teacher, you go
and you have your conversation,you can say, hey, I, you know,
this is my challenge.
Can you focus in on this for meand have confidence that that
(31:03):
person is going to be asoundboard and maybe have some
conversation about how toimprove?
So I think it's really importantfor your administrator or
whoever it is, to be, becausenot everyone has a coach and so
having other people or eventalking to administrators about
hey, can my colleague come, isthere anything that we can do so
(31:23):
that my colleague can come inand observe me Because we'd like
to work out some how to improve.
So there's ways to get aroundit if you don't have a coach.
But you also need a supportiveadmin team to do that.
But you can advocate for,advocate for the worst that
they're going to say is no,which is unfortunate.
But I mean realistically.
(31:44):
I think administrators want ourteachers to be successful and
if they can see value in thattype of collaboration to improve
the outcomes for students andexperiences for students, then I
think that that could be apossibility as well for students
then I think that that could bea possibility as well.
Speaker 2 (32:02):
It definitely feels like a combination of it's not
very easy and it's reallyimportant.
Speaker 4 (32:09):
Right Things that are really important aren't usually
easy, right, so you got tostart somewhere.
So I think, like we've saideverywhere, we just have to
start with advocating and havingconversations and finding the
right people whether that's theteacher next door or the
principal that evaluates you, orthe coach at the district
(32:29):
office Start dropping commentsfrom the book in their inbox and
saying let's talk about thissomething, just to get it on
their radar.
Speaker 1 (32:42):
That's such a good point to just start the
conversation Again with thebooks.
Today I feel really lucky.
I got to talk to some peopleabout it and that felt like an
outreach that you guys weredoing.
Do you plan to outreach more?
Do you plan to offer morevenues for conversation?
Speaker 4 (33:00):
Hopefully.
I know I'm on the board forNCSM and I know I did bring it
up this weekend at our boardmeeting.
I said NCTM did a book studyand we did it through them.
Maybe let's do it through NCSMthis time and offer a book study
to our membership and put itout there.
So hopefully that will happensoon.
(33:22):
I know I've also seen which wasa surprise, but the WestEd and
the Gates Foundation are workingon a project and the book is
something that they've sent outto their participants.
So that was exciting to seethat it was getting into.
And classroom teachers they'reclassroom teachers, so I'm
looking forward to see where theconversation goes from there.
(33:43):
So it's trickling out there.
So we definitely would love tosee more book studies happen.
It was a fun experience.
There was great ideas and lotsof good conversation.
Speaker 1 (33:56):
And I know as a participant a lot of things I
heard were we want more.
Do you have ideas for how totalk together, get support for
this and things like that?
So that's great you're thinkingabout it.
Speaker 2 (34:09):
We're getting close to our time, so we're wondering
if there's anything else that wedidn't ask you that you would
like to include.
Make sure that you have achance to say.
Speaker 4 (34:19):
I was thinking about the connection to like other
work that's happening, and Iknow the book talks a lot also
about like pathways and I thinkthat that is work that is
happening in a lot of placesright now.
I see a lot of states workingon those high school pathways.
We're seeing lots of standardsrevisions happening across the
(34:42):
United States in different areasand I think and I hope, like
there are some examples in here,there's some links on the
webpage at NCTM to differentstates and some of the work that
has been done there.
So I hope that, as people indifferent states are going
through that work, that thiscould also become a resource for
(35:03):
them to guide them in some ofthe decisions that they're
making.
Speaker 3 (35:09):
I also want to share that and this is true.
This has been true forever.
But I also just want tohighlight that if you're trying
to make a change or anadjustment, it's okay if it
doesn't work out at first.
That doesn't mean that it's afailure.
It doesn't mean to abandon it.
If you believe in it and youknow that it's great for
(35:31):
students, just keep on trying,Revise your thinking, get some
people that you can have someconversations with.
Hopefully you have colleaguesthat you can talk to and really
it's okay.
It's okay if it doesn't work.
I think that those that are themost successful in making those
changes have to be kind toourselves and also with our
(35:54):
students.
If you start something new, ourstudents are going to need a
little bit of adjustment, as wedo as adults.
And so really thinking abouthow to make improvements as
you're going along the process,and if you're starting at point
zero, you're at a wonderful spotbecause that just means that
you, you're going to make thatmuch more progress and so really
(36:16):
not giving up it.
But it is hard, it really ishard, and when you're doing that
reflection, don't get too hardon yourself, like you're doing
great things.
So highlight those great thingsand then think about what are
your next steps.
How are you going to makeimprovements and also getting
student feedback like, hey, whatworked, what didn't work, what
(36:37):
do you think we can do toimprove this?
You're not, even if you're at areally small school, you're not
alone, because you're workingwith students to support them
and getting feedback from themcould be a great spot to start
thinking about making thoseimprovements.
Speaker 2 (36:54):
It's well said.
Speaker 1 (36:55):
Yeah, well, thanks for being with us today.
Speaker 2 (36:59):
Thank you for coming on the podcast and sharing all
your wonderful insights andideas with us.
We really appreciate it.
Speaker 4 (37:05):
Thanks for having us, thanks for being part of our
(37:28):
book study, of course.
Speaker 2 (37:31):
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 podcast wascreated by Julius H.
It can be found on pixabaycom.
So thank you very much, julius.
Join us in two weeks for thenext episode of More Math for
(37:54):
More People.
What day will that be, joel?
Speaker 1 (37:58):
It'll be May 27th, national Sunscreen Day, and
we'll be able to talk about somegreat stories surrounding
sunscreen and find out maybemore about what that beautiful
thing is.
But I know that I will havestories to share about when I
didn't use sunscreen and howthat affected my day.
(38:20):
But looking forward to having achat with Misty about sunscreen
May 27th.
Speaker 2 (39:17):
We'll see you there.
Thank you, bye.
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