Join us at the CPM 2025 Teacher Conference in sunny San Diego, featuring an inspiring keynote by Dr. Tyrone Howard. With sessions led by CPM authors, professional learning team members, and experienced teachers, this conference promises to equip you with practical classroom strategies and activities. Plus, don’t miss the pre-conference day with seven diverse options covering leadership, coaching, inclusion, and more.
Then Joel and Misty celebrate National Homemade Cookie Day, indulge in some light-hearted fun with us as we reminisce about our favorite cookie recipes.
And Part 2 of their conversation with Dr. Jenny Bay-Williams about math fluency. If you missed part 1 of the conversation, head back to Episode 4.10 (Sept 17, 2024) to give it a listen.
You can connect with Dr Bay-Williams on X: @JBayWilliams
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
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
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 Boom.
Speaker 2 (00:31):
Announcements, announcements.
It's time for someannouncements.
Doop, doo-doop.
All right, that's anannouncement song, it's not that
great, but I want to let youknow that registration is open
for CPM's 2025 TeacherConference.
This year, the TeacherConference will be on February
(00:53):
22nd and 23rd 2025, and it'sgoing to be in beautiful San
Diego, california, this year.
So remember, the CPM TeacherConference features all kinds of
classroom-ready ideas andstrategies and activities that
you can use right away.
There's sessions led by CPMauthors, professional learning
(01:15):
team members and teachers, and,additionally, you can also sign
up for the pre-conference ifyou'd like.
The pre conference is on Friday,february 21st.
It is a lovely lead-in to themain conference.
We're going to have sevendifferent options this year,
including leadership, coaching,inclusion, merging, multilingual
(01:38):
learners, equity and a sessionon the California math framework
.
Our keynote speaker this yearis Dr Tyrone Howard.
He is a Pritzker Family EndowedChair and Professor in the
School of Education andInformation Studies at UCLA, and
he is also the former AssociateDean for Equity, diversion and
(01:59):
Inclusion.
Dr Howard is one of the mostfrequently cited scholars in the
nation on issues tied to race,equity and educational
opportunity.
He has been listed by EducationWeek as one of the 200 most
influential scholars in thenation informing educational
policy practice and reform tocpmorg backslash conference.
Click register and you can getin on the early bird prices.
(02:30):
We're excited and we'll hope tosee you there.
Today is October 1st 2024.
(02:52):
True Good.
What is the national day of?
Speaker 1 (02:56):
It's National Homemade Cookie Day.
Speaker 2 (02:58):
Oh my goodness, after all of the difficulties we've
been having trying to get thisrecorded, I could use some
homemade cookies, right.
Speaker 1 (03:04):
I do like cookies.
I actually last night I wascleaning out cupboards and I
found two no three uneaten packsof Girl Scout cookies.
Not homemade cookies, Iunderstand, but just think of
the restraint that I've had toput on myself.
(03:25):
Just sitting in your cupboardJust sitting in the cupboard.
And now it's like a treasurethat I get to open and have it's
like how many months were theyin their cupboard?
Speaker 2 (03:32):
Are they still good?
Speaker 1 (03:33):
I bought them from our coworker, Jocelyn, her
daughter, about three or fouryears ago.
Oh wow, they're Girl Scoutcookies.
They got to be good.
Speaker 2 (03:46):
The fact that they can live in your cupboard for
several years and still be gooddoes not make them sound more
delicious.
Speaker 1 (03:48):
I think it's.
I think it's gonna be good.
Speaker 2 (03:50):
I'm excited to try all right, well, we'll report
back later.
Yeah you, the opposite ofhomemade, because homemade
cookies would never survive inyour cupboard.
Speaker 1 (03:59):
For three to four years.
The last homemade cookie that Imade was a peanut butter cookie
and it was flourless and it wasdelicious.
It was really good well, cool,yeah, I've.
Speaker 2 (04:11):
So my grandma, my favorite cookies.
I had two favorite cookiesgrowing up when I was a kid.
One was cowboy cookies, whichwere basically like fancy
oatmeal chocolate chip cookies,and my other favorite cookie was
this no-bake chocolate andoatmeal cookie which had peanut
butter also.
Speaker 1 (04:30):
That would be good too, yeah.
Speaker 2 (04:32):
I saw they actually sell those in the store too.
I always had them homemade.
I didn't know, they were likecookies that you could buy, but
I have seen them and I havebought them.
Speaker 1 (04:40):
That's awesome, I used to get tricked.
That's awesome, I used to gettricked.
I had a friend who would makechocolate like a chocolate
cookie and instead of chocolatechips would put raisins in it.
I was like, who puts a raisinin a chocolate cookie?
And it would trick me.
Speaker 2 (04:55):
They would have raisins and chocolate or just
like it was a chocolate, it wasa chocolate cookie, and then it
has-.
Like a chocolate flavoredcookie, like the whole cookie is
chocolate and then raisins werethe condiment.
Speaker 1 (05:08):
Do you call?
Speaker 2 (05:08):
it a condiment.
Well, that would be addition.
Speaker 1 (05:10):
We'll call it yes, it could be addition, huh
interesting.
Speaker 2 (05:15):
I mean, I like chocolate covered raisins, but
making it into a cookie seemsstrange it was odd.
Speaker 1 (05:19):
I didn't like it.
Speaker 2 (05:20):
That does seem it does seem I haven't made any
homemade cookies in a while.
Have you made any homemadecookies in a while, after a?
Speaker 1 (05:25):
while, but it is.
I just made my first soup ofthe season, so perhaps it's time
for cookies yeah, yeah, okay,you consider cookies as
seasonals.
I do.
I don't do a lot of summercookies.
Feels more wintery fall-ish tome, yeah.
Speaker 2 (05:46):
Those comfort foods for winter.
What Are you going to makecookies today?
Speaker 1 (05:51):
Absolutely.
Speaker 2 (05:53):
All right, what kind of cookies are you going to make
?
Speaker 1 (05:54):
I think I'm going to try.
I don't know what I'm going totry.
I was going to make somethingup right there, but I think I'll
just go into my recipe book Oneof my favorite cookies.
I used to be a sales person forPampered Chef and I got a lot
of good materials like bakingstones and stuff like that, and
(06:16):
two.
I got a lot of great recipes.
So I'll go into my PamperedChef Rolodex it's literally
index card Rolodex.
I'll pick one of those.
How about you?
Okay, Are you going tocelebrate?
Speaker 2 (06:28):
Probably not.
Speaker 1 (06:29):
All right.
Speaker 3 (06:30):
Well, I'm not going to have homemade cookies, that's
for sure.
Speaker 2 (06:32):
That'd be way, way too many cookies for me.
I'm not a big you know cookiefan to begin with, gotcha, but I
might have a cookie.
Okay, I like it.
I can find one that I like.
Speaker 1 (06:43):
Excellent.
Speaker 2 (06:45):
All right.
Well, hopefully everyone elseenjoys homemade cookie.
Please do, okay.
(07:12):
Okay.
So this week we have part twoof our conversation with Dr
Jenny Bay Williams from theUniversity of Louisville in
Kentucky, and if you missed partone, then please go back and
take a listen to our podcastfrom two weeks ago so that you
can hear part one of ourconversation with Dr Bae
Williams about fluency.
Here you go, part two.
Speaker 1 (07:32):
So do you think in like basic fact instruction then
?
So I'm hearing about the gamesand stuff like that.
Oh, I noticed my studentsaren't getting facts so I should
stop and take a day to playgames.
Or do you play a game in themiddle of the lesson?
Or what type of instructionstrategies would you say?
Speaker 3 (07:49):
So I like for strategy instruction, because
you're really trying to teachstrategy to address the facts
that they're working on.
So, as an example, let's gowith the doubling strategy so
you could show like images.
I had these images from thegrocery store of the little
cheeses that come in six packs,so six times seven, just by
(08:12):
coincidence, because we werealready talking about it but
they come in a six pack.
So so, if you have.
But I'm going to go to adifferent strategy.
Okay so, because now you have agroup of six, so you've.
So let's say, they know, theydon't know their fours facts,
but they know they're double.
So you have two bags.
So there's like maybe an imageon screen that has two of the
bags of six If you can picturetwo bags of six on a screen of
(08:34):
any objects, it doesn't matterand then they're like there's 12
.
And then the very next screenhas four bags of six.
And so you pause and you askhow many little rounds of cheese
?
Students say 24.
Well, how did you think aboutthat?
And they'll say, well, I skip,counted 6, 12, 18, 24.
(08:54):
And then somebody will say,well, I just doubled the last
one.
Oh, okay.
So then we do this again.
But now there's some otherobject.
The first screen has two of thegroups could be boxes of
crayons that come in eight.
So there's two of them.
And then the next screen hasfour of them, and so they're
learning the doubling, and thenwe can do the same thing.
Getting back to the threes andthe sixes, where there's three
(09:16):
on the screen and then there'ssix on the screen.
There's three on the screen andthere's six on the screen.
So they're saying oh hey, whatare you noticing?
Well, if I know my three facts,I can use them for my six facts
.
Are you following this?
It's hard to do without thevisuals, but I think, teach that
.
And then I like to play a gamethat actually is very focused on
that fact we're working onbefore we just do an all-out
(09:38):
game that uses all the facts.
So a game, for example, thatI've included in my book is
Trios, which is basicallyconnect four, but it takes too
long to get four in a row soit's just three in a row.
So the name is Trios and let'snot stop with one.
Let's just keep getting as manytrios as you can, as much as
the time allows.
So a teacher might have eightminutes for them to play the
(09:59):
game.
That's enough that everybody'splaying the whole eight minutes.
So trios, they can block theirpartner or not.
No-transcript.
So when they roll a dice,they're multiplying it by six.
But they're thinking, oh, I'mgoing to use that idea that I
know my three's fact and I'mgoing to double it.
You can give students sentenceframes to work on that, but
(10:22):
they're going to practice thatfact unless they just remember
it.
So then when they see six timesseven, they might say 42,
because I just saw somebody elserolled that two turns ago.
I remember it.
Or they might forget six timesseven and think oh, three times
seven, I'm going to double itbecause the game board is six
facts, right?
So they're just going to bepracticing their six facts by
using the doubling strategy.
(10:43):
So you're tearing up thestrategy of doubling with the
six facts and then, I don't know, in two weeks let's play that
game again.
Sure, and maybe a month laterwe'll play that game again.
Ooh, let's pull that game out,but this time it's got the seven
facts on it.
Now what strategy are you goingto use?
And so you're like justinterweaving.
They know how to play that game, they like that game, they got
(11:06):
beat the last time, they want towin the next time and then
you're just changing out thefacts.
So I think you help them see anidea, not memorize them.
Speaker 2 (11:13):
See an idea, not memorize, but see an idea
visually, throughrepresentations, and then they
practice it, talking through italoud, and just practice,
practice, practice through thatinterwoven gameplay over time
and and I could see thatconnecting to a couple of
different things that teachersmight be doing right, what you
were describing at the beginningis a lot like a form of number
(11:33):
talks or dot talks, right, right, where you're looking at
different things and makingthose connections and that you
could use as a classroom openerand then interweaving this,
games at different timesthroughout and not just stopping
.
Great, we're gonna spend twoweeks on math facts now and,
before we do anything else,making it a barrier to the rest
(11:54):
of what we're doing.
Speaker 3 (11:55):
Exactly when you just take that time out.
First of all, not everybodyneeds that time, but also it
feels like you're remediatingthem and what you're really
trying to do is help them justbring to automaticity the facts
that aren't there yet.
And so most of their facts arethere.
We got to get all of them therebecause we're going to be just
using these facts so often inour grade level work.
(12:17):
So we're just going to work onthis strategy and we're going to
practice it, and then we'regoing to keep coming back to it
and set a goal for how often youwant to check in on how they're
doing with their automaticityand which facts they're really
struggling with.
Speaker 2 (12:33):
Yeah, I wrote down one word here.
I wrote down confidence.
Right, that it's notnecessarily the speed at which
I'm doing it at this moment,it's also building that
confidence, which then not goingoh, three times six and then
(12:55):
doubling, that's just theprocess.
But I can do that more quicklyand with more confidence as I
practice it.
Speaker 3 (13:01):
That's right and when you can do it with competence
and you're efficient at doingthe doubling strategy so that it
doesn't distract you from theother thing you're doing.
If you have to go over here andreally think about four times
six, well then you've lost trackof this other thing that you're
really working on.
So you want to get to where theproduction of that strategy is
automated so that you can do itover time, which happens over
(13:23):
time.
You have to distribute thatpractice over time to get to
automaticity.
It's not going to happen quickand likely.
If there are students in middleand high school that are
struggling with facts, it isbecause that's been like the
September, September, Octoberpopular topic and so, honestly,
when they don't know what thenext year, it isn't that they
(13:43):
forgotten it since May.
They might not have beenworking on it since the year
before.
Speaker 1 (13:48):
So no wonder, right so for anything that we want.
Speaker 3 (13:51):
Automaticity, where we want students to be adept at
something, be able to revisit itover time through gameplay and
through just quick problems hereand there, just helps us
continue to have that, thatfluency with it, that we
recognize it, we know what ourchoices are, we can, we're adept
at what method we want to useto solve it.
Speaker 1 (14:11):
I like that, and it also makes me think about
flexibility and about so.
There's not just one way tolook at those patterns or the
solutions to that game, right,like they could think of it in a
variety of different groupingsor a variety of different ways.
Speaker 3 (14:57):
No-transcript.
And isn't the calculator,because they're just going to
encounter it too often and bothof those other things are too
distracting to what they'retrying to focus on.
Speaker 2 (15:12):
Whatever the problem is, yeah, yeah, and I see that
also helping build their own,their own ownership of their
ideas, and sharing mathauthority.
Right, if I get to choose how Iwant to do it, it's not just
memorize, it's not just know it.
Those parts haven't worked forme, for whatever, for this
particular one.
Oh, here's a way that I likeand I'm going to do it that way
(15:35):
and and then build myunderstanding around that.
Speaker 3 (15:39):
Exactly, it's their go-to way.
And then simultaneously they'rebuilding their confidence and
their competence.
So they're like all right, nowI have a way that I can multiply
this.
Now I'm not going to getnervous when I see six times
seven because I've got my way.
I got my way.
I might even have a second way.
That's like my backup, but Igot my way.
I might even have a second way.
That's like my backup, but Igot my way.
Now I don't have to sit herewith my fingers under the table
embarrassingly trying to skipcount.
(16:00):
That takes us back to thebigger problems, right?
So if you have four times twoand three-fourths, you could
double you could do.
(16:30):
That's not a great problem forthat strategy but you could use
a doubling strategy to solve itbecause the four you could do
two groups of two and a fourthand then double again.
Again, it depends on howflexible you are with your
fraction work, because wehaven't really done a lot of
flexibility work with fractions,but as soon as you said it, I
had to look left and think aboutthe three-fourths part like
that was right
Speaker 2 (16:47):
there, yeah, yeah, totally what are some of the
other things we said we weregoing to talk about.
Jenny, can we mention to youthat we haven't got.
Speaker 3 (17:01):
We've been all over the place how about what
flexibility looks like withsolving for x?
Speaker 2 (17:06):
oh, I love that, I love that this is one of my
least favorite things to eversee on it.
Well, I have many unfavoritethings to see on teachers walls,
but one of them is the rule ofalgebra that what you do on the
left you must do on the right.
And I'm like, unless you do the, the equation are the same
amount.
Speaker 3 (17:23):
Yeah, and so that helps us.
But where we go awry in termsof fluency is we think about
(17:44):
solving for X as sort of goingthrough the order of operations.
Now, like you've got toeliminate parentheses first
which, by the way, that isapplying the distributive
property, to call it the correctthing and then, after we do
that, the next thing we're goingto do is add and subtract on
both sides, and the last thingwe're going to do is we have the
sequence that we tell studentsto follow.
(18:05):
But that's not the fluencyapproach, that's sort of an
algorithmic approach.
So a fluency approach would beto let them know you have four
options of things you can do.
Actually, I'm going to say fivethings, five things that you
can do and you get to pick fromthat menu.
(18:26):
So the first thing on the menuis use relational understanding
like reason, think backwards.
So if you have like 2x plus 1equals 11, do you really need to
subtract 1 from both sides andthen divide by 2 to solve it?
You don't.
So could we just reason throughthat If 2x plus 1 equals 11, 2x
(18:48):
has to equal 10, x has to equal5.
And here we see back again theconceptual understanding and the
procedural fluency hand in hand, because you have to understand
that 2X that term means twogroups of X, right, that's the
meaning of it.
And so two fives is 10.
Can you use relationalunderstanding?
Do it in your head?
Great, go for it.
(19:09):
Do it that way.
That's the most efficient.
That doesn't work.
You got four actions you cantake, still on the menu.
So one of them is distribute isapply the distributed property,
which in the example I gavedoesn't apply, in fact the one
that I gave you.
Only one of them really makessense, which would be to
subtract from both sides.
But let's do a different one.
(19:30):
Let's say, parentheses, x plusone half equals 25.
Okay, I could solve that duringrelational understanding.
If I get any longer, nolistener is going to be able to
(19:51):
track the problem.
Let's just say you don't wantto do it relational
understanding.
So you have this thing inparentheses, it's multiplied by
five and you got 25 on the otherside.
So one option is to apply thedistributive property.
Then you had to multiply thatfive times that one half.
Speaker 2 (20:07):
So yeah, who wants to do that?
What middle or high schoolstudent?
Speaker 3 (20:14):
wants to end up with five halves after they've used
the distributive property.
So, if they would have noticedthat one of the things on the
menu is to divide both sides bythe same quantity.
They could divide both sides byfive.
Now they have x plus one halfequals five, at which point they
can go back to the menu and dorelational understanding or
(20:35):
decide to subtract one half fromboth sides.
So it's that sort of menuapproach.
That is again confidence andcompetence.
So you can choose.
If you love applying thedistributed properties, your
first step, you go for it.
But what happens is and theteacher can have students who
started the problem differentlyshare their way and compare.
(20:56):
That's where the flexibilitycomes in.
Which way worked out better forthis problem?
Why did it work out better?
What's your takeaway for thenext time you solve a problem?
That will help you decidewhether you want this to be your
first step or that to be yourfirst step.
So that is the flexibility thatis important to being fluent at
solving equations.
Speaker 2 (21:16):
And one of the things I loved about the way you said
that is having two students whodid it different ways, share
what they did, talk about whatthey did.
What do you like other students?
As opposed to the teacher goingup and saying, well, here's a
way you could have done itdifferently and showing them a
new way that now they take as oh, that's the way I was supposed
to do it.
Right.
It's sharing that authorityagain and really using the
(21:39):
student voice in the classroom.
Speaker 3 (21:41):
A hundred percent, and part of it is choice.
But there's also the point atwhich choice might not be
efficient, where we get to comein and say, all right, which of
these is more efficient?
Make a case right for whichone's efficient, and the answer
could be both.
Or they could make a case thatthis other way was two steps
(22:02):
shorter, so it's more efficient.
Right, so that we're havingthat as part of our own
development of fluency,recognizing that if this problem
can be solved in I don't know15 seconds using three steps,
that that is a quote-unquotebetter method than using seven
steps over here in two minutes.
That is sort of the norm in thefield.
(22:22):
Right, so that follows thenorms, without putting time
pressure on the students, butjust helping them weigh in on.
Oh yeah, this way is way tooclunky.
This way is morestraightforward, less prone to
error.
This is a quote-unquote bettermethod and the number one's
better than the other, andsometimes they're not.
So it's just a good dialogue toengage the students in, because
you're teaching them to thinklike a mathematician.
Speaker 1 (22:43):
Exactly.
It makes me think of likequadratics and we think about
the different forms and then gointo solving.
Do I want to have it instandard form or factored form
or text form or complete thesquare?
However, we want to do itQuadratic formula and having the
students think about that.
Speaker 3 (23:14):
Exactly, exactly, and so here we are, back up to the
higher math that goes all theway back to basic facts when
they're choosing.
How, then, you recognizecharacteristics that a fluent
person knows?
I see these characteristics, soI'm going to use this strategy.
Speaker 2 (23:31):
What does a problem look like?
Looking at different ways thatpeople solved it or did it and
thinking about, well, what makessense to me?
What do I like better?
Why do I like it better?
Yes, sometimes, oh, that wasmore efficient.
I didn't see that I still hadthe skills to do it this other
way or not, but having then beable to expand my toolbox and my
(23:53):
repertoire of things that I'veseen and understand to be able
to do, yeah, and on that note,when you say repertoire of
things I've seen and understand,we have to be super intentional
that they see and understandthe methods that are useful.
Speaker 3 (24:10):
So there can be students who never want to
divide by five on that problemthat I gave, because they are
comfortable with applying thedistributive property, because
that's what they were told toalways do first, if you see
parentheses.
So there's this discomfort withthe freedom of being able to
choose from a menu.
(24:31):
So they have to have enoughexperiences with the methods
that are possible so that theywill feel like choosing from
that menu.
They have to feel comfortablewith what's on the menu.
Speaker 2 (24:46):
A number of times I've seen students solving some.
Quadratic was like something inparentheses squared equals 36
and they're multiplying it out.
Speaker 3 (24:55):
I'm just like oh, what are you doing?
What are you doing?
Speaker 1 (25:00):
But this is what I'm supposed to do.
Speaker 2 (25:02):
Yeah.
Speaker 3 (25:02):
Notice the features of the problem Like just pause,
that's going back to this hurryup piece about fluency.
Fluency actually typicallystarts with a pause, like let's
pause and take in what we'renoticing.
What are we noticing about thisproblem Features?
Do we see any shortcuts?
Is there anything that gives mea hint into how I should
(25:23):
approach this?
It's those that pause at thestart that tend to be the really
have that strategic competence,you know.
So that's why we're not tryingto say hurry up, get busy, do
this.
That's sort of like a wholedifferent direction that was
maybe appropriate beforetechnology ever existed, if you
were training people to be Idon't know, accountants or
(25:44):
something where they werecompeting by hand.
But press to be fast nowdoesn't really play out in terms
of the discipline.
Speaker 2 (25:53):
Yeah, it's disappointing that there's so
much about being good at math asmeans being a quick calculator.
When I hear adults say I'm notvery good at math as means being
a quick calculator, you know,when I hear adults say I'm not
very good at math and I ask themwhy they're like I could never
memorize my math facts that muchand it's ah.
Speaker 3 (26:09):
Or they struggle with understanding fractions.
Speaker 2 (26:10):
I'm like that's because your brain was never
really designed to understandthings that aren't whole.
We like whole, number things.
So it is a stretch, it is achallenge.
Speaker 1 (26:19):
It is a stretch.
Speaker 3 (26:20):
I have sort of I build a case when I work with
teachers for why not?
Why should you not use timetests?
But one of them really is thatit sends a message that being
fast is being good at math, andthat's just so far from the
truth.
If you watch people doingmathematics in their careers,
(26:41):
they're making good choices.
That choice might be usingtechnology.
That choice might be solvingsomething mentally.
That choice might be pencil andpaper, getting away for hours,
but it isn't.
But it's very intentional.
It's this intentionality thatcomes in the discipline.
That is why the time test issuch a misdirect into what's
really important.
(27:01):
Automaticity is important.
I don't want to A hundredpercent.
Speaker 2 (27:04):
Yeah, yeah.
Speaker 3 (27:05):
They need the automaticity Right, but the
automaticity is something thatcan be better assessed in other
ways.
Speaker 2 (27:11):
Mm-hmm, mm-hmm.
Yeah, oh, my goodness, thankyou so much for this
conversation.
Speaker 3 (27:18):
I think we're probably going to wrap it up, I
think that we got to all thethings, at least that I know
(27:39):
that I remember we were going totalk about and we've talked
about so many more, so we reallyappreciate you coming and
having this conversation with us.
We're glad Joel was able to gethis volume and his microphone
working and thank you so much.
Thank you for having me.
I'm happy to talk about theseideas at the middle and
secondary level and how theyreally whether it's basic facts
or it's quadratics that thisfluency focus is critical to
students' competence.
Speaker 1 (28:03):
do at CPM is with our work.
We do some modules to helpteachers work through issues
with students withexceptionality, so strategies
and things like that.
And we got to listen to yourtalk and your research when you
spoke at Mead about your factsand fallacies around fluency, so
we'd love to talk to you againand continue the conversation.
One last thing, one thing thatwe've been starting this season
on our podcast is a math joke.
Speaker 2 (28:24):
I'm going to put you on the spot.
Speaker 1 (28:25):
I'm going to put you on the spot.
Do you have a math joke?
And if you don't, that's okay.
Math's not that funny.
Speaker 3 (28:34):
I don't have a math joke.
Speaker 2 (28:36):
And.
Speaker 3 (28:36):
I'm terrible when I'm being put on the spot.
Speaker 2 (28:39):
Sorry, we can end that part the.
Speaker 3 (28:41):
thing is my colleague that was in my office.
I had to shoo him out when youall came in.
He has an endless and I'mtalking infinite jokes.
He was a high school mathteacher and he literally, if you
just even specifically name atopic, he's got one.
Speaker 1 (29:03):
You're good.
I appreciate you playing along.
Speaker 3 (29:05):
I'll be ready for the next podcast.
Speaker 2 (29:09):
Awesome, all right, thank you so much.
So that is all we have time foron this episode of the More
Math for More People podcast.
If you are interested inconnecting with us on social
media, find our links in thepodcast description, and the
(29:30):
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
More People.
What day will that be, joel?
Speaker 1 (29:45):
It'll be October 15th , national Cheese Curd Day, and,
being from the Midwest myself,I do love me some cheese curds.
I know that my favorite is inmy memory anyway is probably
fried cheese curds at theMinnesota State Fair.
I've had them for breakfast,for lunch, for snacks, for
(30:06):
dinner.
They're so good there.
But even here now, living inUtah, there's many cheese places
.
Here you can buy curds localcurds in the store, in the
grocery stores, or you can go tothe dairy themselves.
Curds in the store, in thegrocery stores, or you can go to
the dairy themselves.
There's even a program whereyou can learn to be a
(30:26):
cheesemaker and I've beenthinking that I might apply for
that as another thing to put onmy recipe be a cheesemaker,
(31:07):
no-transcript.
You are listening to the More Math for More People
podcast.
An outreach of CPM educationalprogram Boom.
An outreach of CPM educationalprogram Boom.
Speaker 2 (00:31):
Announcements, announcements.
It's time for someannouncements.
Doop, doo-doop.
All right, that's anannouncement song, it's not that
great, but I want to let youknow that registration is open
for CPM's 2025 TeacherConference.
This year, the TeacherConference will be on February
(00:53):
22nd and 23rd 2025, and it'sgoing to be in beautiful San
Diego, california, this year.
So remember, the CPM TeacherConference features all kinds of
classroom-ready ideas andstrategies and activities that
you can use right away.
There's sessions led by CPMauthors, professional learning
(01:15):
team members and teachers, and,additionally, you can also sign
up for the pre-conference ifyou'd like.
The pre conference is on Friday,february 21st.
It is a lovely lead-in to themain conference.
We're going to have sevendifferent options this year,
including leadership, coaching,inclusion, merging, multilingual
(01:38):
learners, equity and a sessionon the California math framework
.
Our keynote speaker this yearis Dr Tyrone Howard.
He is a Pritzker Family EndowedChair and Professor in the
School of Education andInformation Studies at UCLA, and
he is also the former AssociateDean for Equity, diversion and
(01:59):
Inclusion.
Dr Howard is one of the mostfrequently cited scholars in the
nation on issues tied to race,equity and educational
opportunity.
He has been listed by EducationWeek as one of the 200 most
influential scholars in thenation informing educational
policy practice and reform tocpmorg backslash conference.
Click register and you can getin on the early bird prices.
(02:30):
We're excited and we'll hope tosee you there.
Today is October 1st 2024.
(02:52):
True Good.
What is the national day of?
Speaker 1 (02:56):
It's National Homemade Cookie Day.
Speaker 2 (02:58):
Oh my goodness, after all of the difficulties we've
been having trying to get thisrecorded, I could use some
homemade cookies, right.
Speaker 1 (03:04):
I do like cookies.
I actually last night I wascleaning out cupboards and I
found two no three uneaten packsof Girl Scout cookies.
Not homemade cookies, Iunderstand, but just think of
the restraint that I've had toput on myself.
(03:25):
Just sitting in your cupboardJust sitting in the cupboard.
And now it's like a treasurethat I get to open and have it's
like how many months were theyin their cupboard?
Speaker 2 (03:32):
Are they still good?
Speaker 1 (03:33):
I bought them from our coworker, Jocelyn, her
daughter, about three or fouryears ago.
Oh wow, they're Girl Scoutcookies.
They got to be good.
Speaker 2 (03:46):
The fact that they can live in your cupboard for
several years and still be gooddoes not make them sound more
delicious.
Speaker 1 (03:48):
I think it's.
I think it's gonna be good.
Speaker 2 (03:50):
I'm excited to try all right, well, we'll report
back later.
Yeah you, the opposite ofhomemade, because homemade
cookies would never survive inyour cupboard.
Speaker 1 (03:59):
For three to four years.
The last homemade cookie that Imade was a peanut butter cookie
and it was flourless and it wasdelicious.
It was really good well, cool,yeah, I've.
Speaker 2 (04:11):
So my grandma, my favorite cookies.
I had two favorite cookiesgrowing up when I was a kid.
One was cowboy cookies, whichwere basically like fancy
oatmeal chocolate chip cookies,and my other favorite cookie was
this no-bake chocolate andoatmeal cookie which had peanut
butter also.
Speaker 1 (04:30):
That would be good too, yeah.
Speaker 2 (04:32):
I saw they actually sell those in the store too.
I always had them homemade.
I didn't know, they were likecookies that you could buy, but
I have seen them and I havebought them.
Speaker 1 (04:40):
That's awesome, I used to get tricked.
That's awesome, I used to gettricked.
I had a friend who would makechocolate like a chocolate
cookie and instead of chocolatechips would put raisins in it.
I was like, who puts a raisinin a chocolate cookie?
And it would trick me.
Speaker 2 (04:55):
They would have raisins and chocolate or just
like it was a chocolate, it wasa chocolate cookie, and then it
has-.
Like a chocolate flavoredcookie, like the whole cookie is
chocolate and then raisins werethe condiment.
Speaker 1 (05:08):
Do you call?
Speaker 2 (05:08):
it a condiment.
Well, that would be addition.
Speaker 1 (05:10):
We'll call it yes, it could be addition, huh
interesting.
Speaker 2 (05:15):
I mean, I like chocolate covered raisins, but
making it into a cookie seemsstrange it was odd.
Speaker 1 (05:19):
I didn't like it.
Speaker 2 (05:20):
That does seem it does seem I haven't made any
homemade cookies in a while.
Have you made any homemadecookies in a while, after a?
Speaker 1 (05:25):
while, but it is.
I just made my first soup ofthe season, so perhaps it's time
for cookies yeah, yeah, okay,you consider cookies as
seasonals.
I do.
I don't do a lot of summercookies.
Feels more wintery fall-ish tome, yeah.
Speaker 2 (05:46):
Those comfort foods for winter.
What Are you going to makecookies today?
Speaker 1 (05:51):
Absolutely.
Speaker 2 (05:53):
All right, what kind of cookies are you going to make
?
Speaker 1 (05:54):
I think I'm going to try.
I don't know what I'm going totry.
I was going to make somethingup right there, but I think I'll
just go into my recipe book Oneof my favorite cookies.
I used to be a sales person forPampered Chef and I got a lot
of good materials like bakingstones and stuff like that, and
(06:16):
two.
I got a lot of great recipes.
So I'll go into my PamperedChef Rolodex it's literally
index card Rolodex.
I'll pick one of those.
How about you?
Okay, Are you going tocelebrate?
Speaker 2 (06:28):
Probably not.
Speaker 1 (06:29):
All right.
Speaker 3 (06:30):
Well, I'm not going to have homemade cookies, that's
for sure.
Speaker 2 (06:32):
That'd be way, way too many cookies for me.
I'm not a big you know cookiefan to begin with, gotcha, but I
might have a cookie.
Okay, I like it.
I can find one that I like.
Speaker 1 (06:43):
Excellent.
Speaker 2 (06:45):
All right.
Well, hopefully everyone elseenjoys homemade cookie.
Please do, okay.
(07:12):
Okay.
So this week we have part twoof our conversation with Dr
Jenny Bay Williams from theUniversity of Louisville in
Kentucky, and if you missed partone, then please go back and
take a listen to our podcastfrom two weeks ago so that you
can hear part one of ourconversation with Dr Bae
Williams about fluency.
Here you go, part two.
Speaker 1 (07:32):
So do you think in like basic fact instruction then
?
So I'm hearing about the gamesand stuff like that.
Oh, I noticed my studentsaren't getting facts so I should
stop and take a day to playgames.
Or do you play a game in themiddle of the lesson?
Or what type of instructionstrategies would you say?
Speaker 3 (07:49):
So I like for strategy instruction, because
you're really trying to teachstrategy to address the facts
that they're working on.
So, as an example, let's gowith the doubling strategy so
you could show like images.
I had these images from thegrocery store of the little
cheeses that come in six packs,so six times seven, just by
(08:12):
coincidence, because we werealready talking about it but
they come in a six pack.
So so, if you have.
But I'm going to go to adifferent strategy.
Okay so, because now you have agroup of six, so you've.
So let's say, they know, theydon't know their fours facts,
but they know they're double.
So you have two bags.
So there's like maybe an imageon screen that has two of the
bags of six If you can picturetwo bags of six on a screen of
(08:34):
any objects, it doesn't matterand then they're like there's 12
.
And then the very next screenhas four bags of six.
And so you pause and you askhow many little rounds of cheese
?
Students say 24.
Well, how did you think aboutthat?
And they'll say, well, I skip,counted 6, 12, 18, 24.
(08:54):
And then somebody will say,well, I just doubled the last
one.
Oh, okay.
So then we do this again.
But now there's some otherobject.
The first screen has two of thegroups could be boxes of
crayons that come in eight.
So there's two of them.
And then the next screen hasfour of them, and so they're
learning the doubling, and thenwe can do the same thing.
Getting back to the threes andthe sixes, where there's three
(09:16):
on the screen and then there'ssix on the screen.
There's three on the screen andthere's six on the screen.
So they're saying oh hey, whatare you noticing?
Well, if I know my three facts,I can use them for my six facts
.
Are you following this?
It's hard to do without thevisuals, but I think, teach that
.
And then I like to play a gamethat actually is very focused on
that fact we're working onbefore we just do an all-out
(09:38):
game that uses all the facts.
So a game, for example, thatI've included in my book is
Trios, which is basicallyconnect four, but it takes too
long to get four in a row soit's just three in a row.
So the name is Trios and let'snot stop with one.
Let's just keep getting as manytrios as you can, as much as
the time allows.
So a teacher might have eightminutes for them to play the
(09:59):
game.
That's enough that everybody'splaying the whole eight minutes.
So trios, they can block theirpartner or not.
No-transcript.
So when they roll a dice,they're multiplying it by six.
But they're thinking, oh, I'mgoing to use that idea that I
know my three's fact and I'mgoing to double it.
You can give students sentenceframes to work on that, but
(10:22):
they're going to practice thatfact unless they just remember
it.
So then when they see six timesseven, they might say 42,
because I just saw somebody elserolled that two turns ago.
I remember it.
Or they might forget six timesseven and think oh, three times
seven, I'm going to double itbecause the game board is six
facts, right?
So they're just going to bepracticing their six facts by
using the doubling strategy.
(10:43):
So you're tearing up thestrategy of doubling with the
six facts and then, I don't know, in two weeks let's play that
game again.
Sure, and maybe a month laterwe'll play that game again.
Ooh, let's pull that game out,but this time it's got the seven
facts on it.
Now what strategy are you goingto use?
And so you're like justinterweaving.
They know how to play that game, they like that game, they got
(11:06):
beat the last time, they want towin the next time and then
you're just changing out thefacts.
So I think you help them see anidea, not memorize them.
Speaker 2 (11:13):
See an idea, not memorize, but see an idea
visually, throughrepresentations, and then they
practice it, talking through italoud, and just practice,
practice, practice through thatinterwoven gameplay over time
and and I could see thatconnecting to a couple of
different things that teachersmight be doing right, what you
were describing at the beginningis a lot like a form of number
(11:33):
talks or dot talks, right, right, where you're looking at
different things and makingthose connections and that you
could use as a classroom openerand then interweaving this,
games at different timesthroughout and not just stopping
.
Great, we're gonna spend twoweeks on math facts now and,
before we do anything else,making it a barrier to the rest
(11:54):
of what we're doing.
Speaker 3 (11:55):
Exactly when you just take that time out.
First of all, not everybodyneeds that time, but also it
feels like you're remediatingthem and what you're really
trying to do is help them justbring to automaticity the facts
that aren't there yet.
And so most of their facts arethere.
We got to get all of them therebecause we're going to be just
using these facts so often inour grade level work.
(12:17):
So we're just going to work onthis strategy and we're going to
practice it, and then we'regoing to keep coming back to it
and set a goal for how often youwant to check in on how they're
doing with their automaticityand which facts they're really
struggling with.
Speaker 2 (12:33):
Yeah, I wrote down one word here.
I wrote down confidence.
Right, that it's notnecessarily the speed at which
I'm doing it at this moment,it's also building that
confidence, which then not goingoh, three times six and then
(12:55):
doubling, that's just theprocess.
But I can do that more quicklyand with more confidence as I
practice it.
Speaker 3 (13:01):
That's right and when you can do it with competence
and you're efficient at doingthe doubling strategy so that it
doesn't distract you from theother thing you're doing.
If you have to go over here andreally think about four times
six, well then you've lost trackof this other thing that you're
really working on.
So you want to get to where theproduction of that strategy is
automated so that you can do itover time, which happens over
(13:23):
time.
You have to distribute thatpractice over time to get to
automaticity.
It's not going to happen quickand likely.
If there are students in middleand high school that are
struggling with facts, it isbecause that's been like the
September, September, Octoberpopular topic and so, honestly,
when they don't know what thenext year, it isn't that they
(13:43):
forgotten it since May.
They might not have beenworking on it since the year
before.
Speaker 1 (13:48):
So no wonder, right so for anything that we want.
Speaker 3 (13:51):
Automaticity, where we want students to be adept at
something, be able to revisit itover time through gameplay and
through just quick problems hereand there, just helps us
continue to have that, thatfluency with it, that we
recognize it, we know what ourchoices are, we can, we're adept
at what method we want to useto solve it.
Speaker 1 (14:11):
I like that, and it also makes me think about
flexibility and about so.
There's not just one way tolook at those patterns or the
solutions to that game, right,like they could think of it in a
variety of different groupingsor a variety of different ways.
Speaker 3 (14:57):
No-transcript.
And isn't the calculator,because they're just going to
encounter it too often and bothof those other things are too
distracting to what they'retrying to focus on.
Speaker 2 (15:12):
Whatever the problem is, yeah, yeah, and I see that
also helping build their own,their own ownership of their
ideas, and sharing mathauthority.
Right, if I get to choose how Iwant to do it, it's not just
memorize, it's not just know it.
Those parts haven't worked forme, for whatever, for this
particular one.
Oh, here's a way that I likeand I'm going to do it that way
(15:35):
and and then build myunderstanding around that.
Speaker 3 (15:39):
Exactly, it's their go-to way.
And then simultaneously they'rebuilding their confidence and
their competence.
So they're like all right, nowI have a way that I can multiply
this.
Now I'm not going to getnervous when I see six times
seven because I've got my way.
I got my way.
I might even have a second way.
That's like my backup, but Igot my way.
I might even have a second way.
That's like my backup, but Igot my way.
Now I don't have to sit herewith my fingers under the table
embarrassingly trying to skipcount.
(16:00):
That takes us back to thebigger problems, right?
So if you have four times twoand three-fourths, you could
double you could do.
(16:30):
That's not a great problem forthat strategy but you could use
a doubling strategy to solve itbecause the four you could do
two groups of two and a fourthand then double again.
Again, it depends on howflexible you are with your
fraction work, because wehaven't really done a lot of
flexibility work with fractions,but as soon as you said it, I
had to look left and think aboutthe three-fourths part like
that was right
Speaker 2 (16:47):
there, yeah, yeah, totally what are some of the
other things we said we weregoing to talk about.
Jenny, can we mention to youthat we haven't got.
Speaker 3 (17:01):
We've been all over the place how about what
flexibility looks like withsolving for x?
Speaker 2 (17:06):
oh, I love that, I love that this is one of my
least favorite things to eversee on it.
Well, I have many unfavoritethings to see on teachers walls,
but one of them is the rule ofalgebra that what you do on the
left you must do on the right.
And I'm like, unless you do the, the equation are the same
amount.
Speaker 3 (17:23):
Yeah, and so that helps us.
But where we go awry in termsof fluency is we think about
(17:44):
solving for X as sort of goingthrough the order of operations.
Now, like you've got toeliminate parentheses first
which, by the way, that isapplying the distributive
property, to call it the correctthing and then, after we do
that, the next thing we're goingto do is add and subtract on
both sides, and the last thingwe're going to do is we have the
sequence that we tell studentsto follow.
(18:05):
But that's not the fluencyapproach, that's sort of an
algorithmic approach.
So a fluency approach would beto let them know you have four
options of things you can do.
Actually, I'm going to say fivethings, five things that you
can do and you get to pick fromthat menu.
(18:26):
So the first thing on the menuis use relational understanding
like reason, think backwards.
So if you have like 2x plus 1equals 11, do you really need to
subtract 1 from both sides andthen divide by 2 to solve it?
You don't.
So could we just reason throughthat If 2x plus 1 equals 11, 2x
(18:48):
has to equal 10, x has to equal5.
And here we see back again theconceptual understanding and the
procedural fluency hand in hand, because you have to understand
that 2X that term means twogroups of X, right, that's the
meaning of it.
And so two fives is 10.
Can you use relationalunderstanding?
Do it in your head?
Great, go for it.
(19:09):
Do it that way.
That's the most efficient.
That doesn't work.
You got four actions you cantake, still on the menu.
So one of them is distribute isapply the distributed property,
which in the example I gavedoesn't apply, in fact the one
that I gave you.
Only one of them really makessense, which would be to
subtract from both sides.
But let's do a different one.
(19:30):
Let's say, parentheses, x plusone half equals 25.
Okay, I could solve that duringrelational understanding.
If I get any longer, nolistener is going to be able to
(19:51):
track the problem.
Let's just say you don't wantto do it relational
understanding.
So you have this thing inparentheses, it's multiplied by
five and you got 25 on the otherside.
So one option is to apply thedistributive property.
Then you had to multiply thatfive times that one half.
Speaker 2 (20:07):
So yeah, who wants to do that?
What middle or high schoolstudent?
Speaker 3 (20:14):
wants to end up with five halves after they've used
the distributive property.
So, if they would have noticedthat one of the things on the
menu is to divide both sides bythe same quantity.
They could divide both sides byfive.
Now they have x plus one halfequals five, at which point they
can go back to the menu and dorelational understanding or
(20:35):
decide to subtract one half fromboth sides.
So it's that sort of menuapproach.
That is again confidence andcompetence.
So you can choose.
If you love applying thedistributed properties, your
first step, you go for it.
But what happens is and theteacher can have students who
started the problem differentlyshare their way and compare.
(20:56):
That's where the flexibilitycomes in.
Which way worked out better forthis problem?
Why did it work out better?
What's your takeaway for thenext time you solve a problem?
That will help you decidewhether you want this to be your
first step or that to be yourfirst step.
So that is the flexibility thatis important to being fluent at
solving equations.
Speaker 2 (21:16):
And one of the things I loved about the way you said
that is having two students whodid it different ways, share
what they did, talk about whatthey did.
What do you like other students?
As opposed to the teacher goingup and saying, well, here's a
way you could have done itdifferently and showing them a
new way that now they take as oh, that's the way I was supposed
to do it.
Right.
It's sharing that authorityagain and really using the
(21:39):
student voice in the classroom.
Speaker 3 (21:41):
A hundred percent, and part of it is choice.
But there's also the point atwhich choice might not be
efficient, where we get to comein and say, all right, which of
these is more efficient?
Make a case right for whichone's efficient, and the answer
could be both.
Or they could make a case thatthis other way was two steps
(22:02):
shorter, so it's more efficient.
Right, so that we're havingthat as part of our own
development of fluency,recognizing that if this problem
can be solved in I don't know15 seconds using three steps,
that that is a quote-unquotebetter method than using seven
steps over here in two minutes.
That is sort of the norm in thefield.
(22:22):
Right, so that follows thenorms, without putting time
pressure on the students, butjust helping them weigh in on.
Oh yeah, this way is way tooclunky.
This way is morestraightforward, less prone to
error.
This is a quote-unquote bettermethod and the number one's
better than the other, andsometimes they're not.
So it's just a good dialogue toengage the students in, because
you're teaching them to thinklike a mathematician.
Speaker 1 (22:43):
Exactly.
It makes me think of likequadratics and we think about
the different forms and then gointo solving.
Do I want to have it instandard form or factored form
or text form or complete thesquare?
However, we want to do itQuadratic formula and having the
students think about that.
Speaker 3 (23:14):
Exactly, exactly, and so here we are, back up to the
higher math that goes all theway back to basic facts when
they're choosing.
How, then, you recognizecharacteristics that a fluent
person knows?
I see these characteristics, soI'm going to use this strategy.
Speaker 2 (23:31):
What does a problem look like?
Looking at different ways thatpeople solved it or did it and
thinking about, well, what makessense to me?
What do I like better?
Why do I like it better?
Yes, sometimes, oh, that wasmore efficient.
I didn't see that I still hadthe skills to do it this other
way or not, but having then beable to expand my toolbox and my
(23:53):
repertoire of things that I'veseen and understand to be able
to do, yeah, and on that note,when you say repertoire of
things I've seen and understand,we have to be super intentional
that they see and understandthe methods that are useful.
Speaker 3 (24:10):
So there can be students who never want to
divide by five on that problemthat I gave, because they are
comfortable with applying thedistributive property, because
that's what they were told toalways do first, if you see
parentheses.
So there's this discomfort withthe freedom of being able to
choose from a menu.
(24:31):
So they have to have enoughexperiences with the methods
that are possible so that theywill feel like choosing from
that menu.
They have to feel comfortablewith what's on the menu.
Speaker 2 (24:46):
A number of times I've seen students solving some.
Quadratic was like something inparentheses squared equals 36
and they're multiplying it out.
Speaker 3 (24:55):
I'm just like oh, what are you doing?
What are you doing?
Speaker 1 (25:00):
But this is what I'm supposed to do.
Speaker 2 (25:02):
Yeah.
Speaker 3 (25:02):
Notice the features of the problem Like just pause,
that's going back to this hurryup piece about fluency.
Fluency actually typicallystarts with a pause, like let's
pause and take in what we'renoticing.
What are we noticing about thisproblem Features?
Do we see any shortcuts?
Is there anything that gives mea hint into how I should
(25:23):
approach this?
It's those that pause at thestart that tend to be the really
have that strategic competence,you know.
So that's why we're not tryingto say hurry up, get busy, do
this.
That's sort of like a wholedifferent direction that was
maybe appropriate beforetechnology ever existed, if you
were training people to be Idon't know, accountants or
(25:44):
something where they werecompeting by hand.
But press to be fast nowdoesn't really play out in terms
of the discipline.
Speaker 2 (25:53):
Yeah, it's disappointing that there's so
much about being good at math asmeans being a quick calculator.
When I hear adults say I'm notvery good at math as means being
a quick calculator, you know,when I hear adults say I'm not
very good at math and I ask themwhy they're like I could never
memorize my math facts that muchand it's ah.
Speaker 3 (26:09):
Or they struggle with understanding fractions.
Speaker 2 (26:10):
I'm like that's because your brain was never
really designed to understandthings that aren't whole.
We like whole, number things.
So it is a stretch, it is achallenge.
Speaker 1 (26:19):
It is a stretch.
Speaker 3 (26:20):
I have sort of I build a case when I work with
teachers for why not?
Why should you not use timetests?
But one of them really is thatit sends a message that being
fast is being good at math, andthat's just so far from the
truth.
If you watch people doingmathematics in their careers,
(26:41):
they're making good choices.
That choice might be usingtechnology.
That choice might be solvingsomething mentally.
That choice might be pencil andpaper, getting away for hours,
but it isn't.
But it's very intentional.
It's this intentionality thatcomes in the discipline.
That is why the time test issuch a misdirect into what's
really important.
(27:01):
Automaticity is important.
I don't want to A hundredpercent.
Speaker 2 (27:04):
Yeah, yeah.
Speaker 3 (27:05):
They need the automaticity Right, but the
automaticity is something thatcan be better assessed in other
ways.
Speaker 2 (27:11):
Mm-hmm, mm-hmm.
Yeah, oh, my goodness, thankyou so much for this
conversation.
Speaker 3 (27:18):
I think we're probably going to wrap it up, I
think that we got to all thethings, at least that I know
(27:39):
that I remember we were going totalk about and we've talked
about so many more, so we reallyappreciate you coming and
having this conversation with us.
We're glad Joel was able to gethis volume and his microphone
working and thank you so much.
Thank you for having me.
I'm happy to talk about theseideas at the middle and
secondary level and how theyreally whether it's basic facts
or it's quadratics that thisfluency focus is critical to
students' competence.
Speaker 1 (28:03):
do at CPM is with our work.
We do some modules to helpteachers work through issues
with students withexceptionality, so strategies
and things like that.
And we got to listen to yourtalk and your research when you
spoke at Mead about your factsand fallacies around fluency, so
we'd love to talk to you againand continue the conversation.
One last thing, one thing thatwe've been starting this season
on our podcast is a math joke.
Speaker 2 (28:24):
I'm going to put you on the spot.
Speaker 1 (28:25):
I'm going to put you on the spot.
Do you have a math joke?
And if you don't, that's okay.
Math's not that funny.
Speaker 3 (28:34):
I don't have a math joke.
Speaker 2 (28:36):
And.
Speaker 3 (28:36):
I'm terrible when I'm being put on the spot.
Speaker 2 (28:39):
Sorry, we can end that part the.
Speaker 3 (28:41):
thing is my colleague that was in my office.
I had to shoo him out when youall came in.
He has an endless and I'mtalking infinite jokes.
He was a high school mathteacher and he literally, if you
just even specifically name atopic, he's got one.
Speaker 1 (29:03):
You're good.
I appreciate you playing along.
Speaker 3 (29:05):
I'll be ready for the next podcast.
Speaker 2 (29:09):
Awesome, all right, thank you so much.
So that is all we have time foron this episode of the More
Math for More People podcast.
If you are interested inconnecting with us on social
media, find our links in thepodcast description, and the
(29:30):
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
More People.
What day will that be, joel?
Speaker 1 (29:45):
It'll be October 15th , national Cheese Curd Day, and,
being from the Midwest myself,I do love me some cheese curds.
I know that my favorite is inmy memory anyway is probably
fried cheese curds at theMinnesota State Fair.
I've had them for breakfast,for lunch, for snacks, for
(30:06):
dinner.
They're so good there.
But even here now, living inUtah, there's many cheese places
.
Here you can buy curds localcurds in the store, in the
grocery stores, or you can go tothe dairy themselves.
Curds in the store, in thegrocery stores, or you can go to
the dairy themselves.
There's even a program whereyou can learn to be a
(30:26):
cheesemaker and I've beenthinking that I might apply for
that as another thing to put onmy recipe be a cheesemaker,
(31:07):
no-transcript.
Popular Podcasts
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com
24/7 News: The Latest
The latest news in 4 minutes updated every hour, every day.
Therapy Gecko
An unlicensed lizard psychologist travels the universe talking to strangers about absolutely nothing. TO CALL THE GECKO: follow me on https://www.twitch.tv/lyleforever to get a notification for when I am taking calls. I am usually live Mondays, Wednesdays, and Fridays but lately a lot of other times too. I am a gecko.