September 17, 2024 • 30 mins
Ever wondered what makes a Monte Cristo sandwich so special? Join us on the More Math for More People podcast as we celebrate National Monte Cristo Day with a fun-filled exploration of this delectable sandwich and its (supposed) ties to Omaha (spoiler alert - not true). We reminisce about our own encounters with the Monte Cristo, including the sad demise of a local favorite, and even indulge in some playful speculation about its connection to Alexandre Dumas' "The Count of Monte Cristo."
Next, we're thrilled to welcome Dr. Jenny Bay-Williams, a distinguished professor from the University of Louisville, who joins us to unravel mathematical fluency. Jenny shares her wealth of experience in math education, emphasizing that fluency is much more than speed or automaticity—it’s about reasoning, making smart choices, and choosing efficient strategies for problem-solving. Through examples of fraction addition, she demonstrates how true mathematical fluency involves navigating multiple approaches to find the best solution. This is part 1 of our conversation with her.
You can connect with Dr Bay-Williams on X: @JBayWilliams
To wrap up, we introduce CPM Educational Program's "Instructional Coaching Toolkit," a must-have resource for instructional coaches and leaders. You can purchase your own at shop.cpm.org!!
Send Joel and Misty a message!
The More Math for More People Podcast is produced by CPM Educational Program.
Learn more at CPM.org
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Email: cpmpodcast@cpm.org
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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.
Speaker 2 (00:26):
Boom Okay.
17th of September.
Speaker 1 (00:33):
Yes.
Speaker 2 (00:34):
What's the national day today?
It is National Monte Cristo Day.
Monte Cristo Day like thesandwich, the sandwich.
Okay.
So this is going to be acallback to we were just talking
about bowling from the lastepisode, right, and you and I
(00:57):
were talking about how well wemight not be able to go bowling
because we'll be traveling toOmaha.
Mm-hmm, mm-hmm.
And I learned when I wasresearching places to eat in
Omaha that Omaha is supposedly,like the home, the birthplace of
the Monte Cristo sandwich no.
That's what I saw Are youserious right now.
I am serious right now.
Oh my gosh.
I love a Monte Cristo sandwichso much.
We have to also have a MonteCristo sandwich while we're in
(01:18):
Omaha.
Oh my gosh.
Speaker 1 (01:20):
That is going on the checklist for sure.
Speaker 2 (01:26):
I think this is irony .
I think this doesn't qualifyjust as coincidence.
I think this is actual irony.
I'm not very good at thosethings do you enjoy a monte
cristo?
I haven't had a monte cristo ina long time, since I don't eat
very much bread or gluten, but Ithe monte cristos as, as I
remember, them are prettydelicious.
Actually, I'm trying to decideif I've had one since university
(01:49):
.
Speaker 3 (01:54):
I feel like they were one of the things that would be
on the lunch menu.
Speaker 2 (01:55):
Cristo sandwich and I never had had one before that,
because Monte Cristo is the one.
Wait, I'm confused.
Is Monte Cristo the one wherethere's cheese and some kind of
meat, meat, and then they likeput it in like egg and fry it?
Is that the one?
Speaker 3 (02:10):
Yeah.
Speaker 2 (02:11):
What's the one where they have the pumpernickel and
the like Thousand Islanddressing?
Speaker 1 (02:15):
and sauerkraut on it.
That's the Reuben.
Oh Reuben, that's right.
Totally different sandwich.
Speaker 2 (02:21):
Yeah, well, I know, but they're also sandwiches I
never had until I was an adult,because they weren't ones we had
as I was a kid.
Speaker 1 (02:28):
I love a Monte Cristo and local establishment here in
Salt Lake served my favoriteMonte Cristo Like they fried it
so good and the fresh.
Like they made the berry jamthat went with it.
There's berry jam on it, ohyeah, and it was so delicious.
Speaker 2 (02:42):
I don't think they made it with berry jam.
In went with it.
There's berry jam on it, ohyeah, and it was so delicious I
don't think they made it withberry jam in Northwestern's tiny
halls.
Speaker 1 (02:50):
Well, I was so sad because last time I went I went
down to get the Monte Cristo andthey changed the menu.
What they said, we reduced ourmenu size and that did not make
the list.
We're only going to make it onspecial days.
And I said, well, what's thespecial day?
I hope like September 17th is aspecial day because it's Monte
(03:11):
Cristo day, but I was so bummedLike it ruined my whole weekend.
Speaker 2 (03:16):
Apparently you weren't going and ordering it
enough.
Speaker 1 (03:19):
I know it's my fault, yeah.
Speaker 2 (03:24):
I'm not sure I mean think about.
Yeah, I'm not sure I'veactually.
I mean think about it.
I'm not sure I've had one sinceuniversity, which is a long
time now, and clearly those werenot gourmet Monte Cristo
sandwiches, they were bulk madeCristo sandwiches.
So yeah, monte Cristo is on thelist for Omaha.
I think it should be by thetime everyone on our team hears
(03:45):
this, it'll be too late for themto have Monte be.
Speaker 1 (03:47):
That's why everyone on our team hears this.
Speaker 2 (03:48):
It'll be too late for them to have a Monte Cristo.
Let's hope they had it.
Yeah, exactly, or they couldjust have one now.
Yeah, wherever they are.
Speaker 1 (03:56):
Love that.
Delicious sandwich days arekind of like I know I'll be
celebrating, I know I'm going tohave a Monte Cristo sandwich
because it's a delicioussandwich and I can celebrate,
and I love delicious sandwiches.
Speaker 2 (04:11):
And Monte Cristo just has like regular bread.
There's no special.
Speaker 1 (04:14):
I don't know that it's a special bread, but it's
because you fry it and thingslike that, it's very similar to
the French toast when it comesout, you want a thicker bread.
Speaker 2 (04:26):
Yeah, it's your wonder bread, the French toast.
When it comes out.
Speaker 1 (04:28):
You want a thicker bread.
Yeah, it's your wonder bread,that's right, Well cool.
Yeah.
Speaker 2 (04:31):
All right.
Well, I don't know what else tosay about Monte Cristo sandwich
day.
Speaker 1 (04:34):
I can't even say anything because I'm thinking
about it.
Speaker 2 (04:36):
Why is it called the Monte Cristo?
Well, it has.
Speaker 1 (04:39):
French roots, and I think wasn't there like a count
of Monte Cristo.
Speaker 2 (04:43):
Well, yeah, but I don't think it's named after him
.
Speaker 1 (04:45):
That was like an Alexandre Dumas book Right, but
he had all that time in prison,right, like he had a lot of time
to think about stuff.
Speaker 2 (04:53):
He did spend a lot of time in prison, and so he
probably thought about thisdelicious sandwich that he
couldn't have.
I don't think that is theactual.
I mean I'm very skeptical aboutthis story.
Oh well.
So we don't have a goodexplanation on your source.
Speaker 1 (05:09):
Well, it's got some French roots here, but this day
was initiated to commemorate thelong history of Monte Cristo
sandwiches that continue tobless our taste buds for decades
now.
So like in 1910 is when theMonte Cristo kind of made its
debut.
Speaker 2 (05:30):
Is it called Monte Cristo sandwich?
I can't even spell Monte Cristo, what, okay?
The AI overview says the MonteCristo sandwich is named after
the Count of Monte Cristo, anadventure novel by Alexander
Dumas.
Come on, I'm just saying thesandwich flavor profile pays
homage to its French origins andsome believe the name was Come
on, I knew it.
(06:02):
Oh, that's very vague.
Speaker 1 (06:05):
That is vague.
I can't believe.
Speaker 2 (06:07):
It also says that the Monte Cristo sandwich is a
variation of the Croque Monsieur, a French sandwich that was
lightly served in Paris cafes inthe 20s.
Apparently, it's all from the20s.
Speaker 1 (06:18):
There you go.
I'm trying to click on.
How was the Monte Cristosandwich created and it won't
open up, so I have no idea.
Speaker 2 (06:33):
But I think I just told the story that the Count
was in prison and that's how itwas created.
Yeah, it doesn't explain inthis AI overview why it would be
named after the Count, but itdoes say also in the 1960s the
sandwich was added to the menuat Disneyland's.
Speaker 3 (06:43):
Blue Bayou restaurant and became an American favorite
.
Speaker 2 (06:46):
Yes, which just cracks me up.
I mean, the AI overview ishelpful, but it doesn't really
tell me the why.
Anyway, all right.
Speaker 1 (06:58):
Well, there's some interesting tidbits of how the
Monte Cristo sandwich might benamed or not and I hope all of
you listening, we have not datachecked, are going to go out and
get a Monte Cristo sandwich.
Speaker 2 (07:06):
Might be named or not , and I hope all of you
listening.
Speaker 1 (07:06):
We have not data checked, are going to go out and
get a Monte Cristo sandwich.
Speaker 2 (07:10):
Yep, Enjoy your sandwich.
So as a side note, we do wantto clarify that Omaha is the
home of the Reuben sandwich andapparently my conflation of
Monte Cristo and Reubensandwiches is pretty severe.
So if you go to Omaha, don'task for Monte Cristo, Go get a
Reuben Any day, All right.
(07:46):
So today we're going to havepart one of a conversation with
Dr Jennifer Bay Williams.
Jenny Bay Williams has been aprofessor at the University of
Louisville since 2006.
She teaches courses related tomathematics teaching to
pre-service teachers andpracticing teachers and is
frequently working in elementaryschools to support mathematics
(08:08):
teaching.
Prior to coming to theUniversity of Louisville, she
taught in a variety of otherplaces, such as Kansas, Missouri
and Peru.
Dr Bae-Williams is aninternationally respected
mathematics educator.
She is a prolific author andpopular speaker on topics
related to effective mathematicsteaching.
Her work has focused on ways toensure that every student
(08:31):
understands mathematics anddevelops a positive mathematics
identity.
Her most recent work hasfocused on fluency and
mathematics, communicating thatit is more than learning facts
and algorithms, but rather thatit's about being able to reason
and choose appropriatestrategies.
Her books on fluency andmathematics coaching are
bestsellers.
(08:52):
We're excited to have Dr BaeWilliams here on the CPM podcast
today to talk with us about herviews on fluency.
All right, well, while Joel isfinishing figuring out how to
get himself connected to us,we're just going to start
because we can always we canalways use AI to insert Joel
later.
I'll just we'll replace myvoice with his voice asking one
of the questions.
That's pretty amazing.
(09:14):
So we're here today with JennyBay Williams and, Jenny, you are
a professor at the Universityof Louisville.
I have that right.
Excellent.
We have co-workers who are inLouisville.
I think one of them is at theUniversity of Kentucky.
Might done a lot of work withfluency.
(09:35):
You've written some books andmany articles, and fluency is
definitely a question that comesup, or a topic of concern, I
think, for a lot of teachers,and particularly teachers in CPM
, because of the mixed spacepractice that we have and
students are interacting withmaterial over time.
(09:56):
Then how do we figure out whatfluency is right?
And there's always theseconcerns around whether students
know their basic math facts andwhat to do if they don't know
them.
So we're going to talk aboutseveral of those things today.
So thanks for joining us on thepodcast today.
Speaker 3 (10:11):
I'm excited to talk about all of those things.
So thank you for inviting me.
Speaker 2 (10:15):
No, worries and Joel's just going to keep trying
to figure out if he can talk tous or not, and we're just going
to keep going.
So we appreciate your time.
The first thing I wanted tolaunch with is I think that a
lot of times when we talk aboutfluency and what is it?
What comes to mind is beingable to I think of oh, how fast
can you do your multiplicationfacts right?
(10:37):
You have kids doing speed testsand different things, and
that's this idea of fluency andI'm wondering what you think
about that.
I guess, or am I guessing, youdon't agree with that.
Speaker 3 (10:46):
Yeah, I don't agree with that.
But there is this need to beautomatic with something so that
you can recall things,information that you need, that
you're going to be using withoutusing a lot of thought.
But that's not fluency, that'sautomaticity being automatic.
So we want to be automatic withbasic facts.
And in middle and high schoolthere's other things where
(11:09):
automaticity supports the biggerreasoning.
For example, equivalencies witha one half, recognizing that 13
over 26,.
Hey, that's one half.
How do you know?
Without a lot of thought?
You just recognize fractionequivalencies of fourths, halves
and other things likerecognizing, I don't know,
pythagorean, triples or whatever.
But there's these things whereyou see them so much, you
(11:32):
recognize them and you just know.
So there are.
That's automaticity.
But fluency is about being ableto solve a problem using an
efficient method.
So I'm going to start withefficiency.
So let's just take a fraction.
We work on fraction fluency inmiddle school, right?
So let's take two andthree-fourths plus two and
(11:53):
three-fourths just the samenumbers.
So we don't have troubleremembering the problem Two and
three-fourths plus two andthree-fourths just the same
numbers.
So we don't have troubleremembering the problem Two and
three-fourths, two andthree-fourths.
So what you were saying, mistyis that somebody would be really
fast so they could go aboutdoing the algorithm really
really fast.
That's not fluency, that isbeing, I don't know adept at
(12:14):
using an algorithm.
A fluent person is going to gooh hey, I have some options here
for adding that problem.
What are my options?
And this way looks really fastfor this problem and so, and all
that happens like in it happensquickly.
So for two and three-fourthsplus two and three-fourths, what
they might recognize is theyknow three-fourths and
(12:36):
three-fourths is one andone-half and then add the
whole-fourths is one andone-half and then add the whole
numbers, add the one andone-half and they're done.
They might just move one-fourthover from one fraction to the
other and think, oh, that'sthree plus two and one-half.
Again, they got thatautomaticity with fractions
going.
Those are then ones they canadd in their head, and so the
(12:57):
fluent person goes about aproblem by looking at it, sizing
it up and making a decisionabout how they're going to solve
it.
That's what somebody withfluency does.
That's different than somebodyjust being really really fast.
It's about making good choices,what we like to talk to middle
and high school students about.
Speaker 1 (13:17):
Making good choices with math, you know so I have
some questions.
Speaker 2 (13:23):
So I see that as, like one, you talk about the
automaticity with fractions andthe numbers and making some
choices would rely upon areasonable number sense, right
that our ability to just I don'tknow know, it's just just to
know that a half and a half isone, or just to know like that,
(13:43):
and and so, which could becalled basic facts, but I think
it's also, it's that numbersense, like I know my tens, I
know how to group in fives.
I have these like lots ofdifferent abstract and more
representational ways ofthinking about numbers.
However, that is, is that?
Do you see that?
Speaker 3 (14:04):
or Definitely so.
There's more literature,research and discussion about
decomposing.
I'm just going to pick up onone of the things you were
talking about.
In, like kindergarten, can youbreak apart eight lots of
different ways, five plus threeand that sort of thing but just
take like a fraction, likethree-fourths right there.
To do that strategy that Italked through, you have to
(14:24):
think, oh, I could break thatthree-fourths apart into
two-fourths plus one-fourths orone-half plus one-fourths.
It's that flexibility and thatnumber sense that allows you to
be flexible in breaking numbersapart, putting them back
together, knowing that you couldapply the distributive property
but you don't have to apply thedistributive property as your
first step in solving algebraicequations, solving for X.
(14:46):
So there is this level oflooking at number relations and
seeing and using those numberrelations to efficiently solve a
problem.
So, which is harder tounderstand in the general and
easier to understand an example.
So if you want someclarification, just ask for an
example.
Speaker 2 (15:07):
Well, and the other piece of what I was thinking
about, as you were saying, thatis that we talk about building
procedural fluency fromconceptual understanding.
So when, in the example youwere talking about, how would
you and maybe you need adifferent example, that's okay
Like, how would you apply theidea of procedural fluency to
that?
Because I think of, when Ithink of procedural fluency, I
(15:28):
think, oh, you can do thiscalculation or this algorithm
very quickly or well, but and Ithink that that teachers often
get into that right, it meansyou can do the long division
algorithm, it means you can doall these algorithms.
And is that how you see it, ordo you see it a little
differently than that?
Speaker 3 (15:46):
I do see it that way.
I think that the there's thisimportant relationship where the
conceptual understandingsupports the fluency and the
fluency then strengthens theconceptual understanding.
So for example, with that twoand three-fourths plus two and
three-fourths, the more thatstudents are applying this
strategy of moving one-fourthover, the better they're getting
at the skill of breakingfractions apart.
(16:07):
But the more they're gettingthis idea of basically the
associative property that theycan take something from one
add-in and move it to the otheradd-in, they still have an
equivalent expression after athing.
Another great example is withsubtraction.
So if we had, let's just dofive and three-fourths minus two
(16:28):
and three minus I don't know,let's do no, I'm going to change
the problem.
Let's talk about subtractionand that relationship between
conceptual understanding andprocedural frequency.
So if you take something likefive and one-fourths minus I
don't know, four andthree-fourths, somebody with a
(16:50):
conceptual understanding ofsubtraction understands that it
is take away and it's also findthe difference or compare.
So they look at that problemand they say, oh, those
fractions are close together.
It's going to be easier to findthe difference between four and
three-fourths and five andone-fourth it's one-half.
(17:11):
Maybe they picture a ruler or anumber line.
And so, again, that conceptualunderstanding is coming in and
helping them visualize and solvethe problem.
A student with no conceptualunderstanding of fractions will
see those fractions and followan algorithm.
They'll regroup from the fiveto get four and five fourths and
subtract it and get theiranswer.
(17:32):
And that's not fluency, becauseit took them a much longer time
to do all of that work.
They have no idea of knowing iftheir answer makes sense, and
so that's the two supportingeach other.
The conceptual understandingallows for an efficient solution
strategy and also to understandif the answer makes sense.
And then just the very questionof are you going to find the
(17:52):
difference or use takeaway issupporting both their fluency
and their conceptualunderstanding.
Speaker 2 (17:58):
Right, right, joel, can I hear you?
Can you hear me?
Takeaway is supporting boththeir fluency and their
conceptual understanding.
Right, right, joel, can I hearyou?
Can you hear me?
Yes, can you hear us?
I can hear you.
Welcome to the program, joel.
Speaker 1 (18:11):
Thank you.
Speaker 2 (18:12):
Yeah, technical difficulties resolved.
Speaker 1 (18:15):
Okay.
Speaker 3 (18:49):
Cool, so I'm just fascinated by this, this whole
idea, because there's so many itthe way that I was supposed
mathematicians are.
As in research mathematiciansor engineers or people who are
using mathematics, they'retrying to be creative about how
they're putting things togetherin order to figure something out
(19:12):
, so they're not reallyfollowing like algorithmic stuff
as the way their brain isengaged right.
The algorithmic stuff is doneusually with technology, so that
decision making and creativityis oftentimes the insights into
a better way to engineersomething or create something or
whatever.
And so to squelch that in schoolis the exact opposite of what
(19:35):
we want to be doing withstudents.
We want to inspire them to takethis problem in and come up
with an efficient way to solveit, based on what you notice,
what the features of the problemare.
Speaker 2 (19:49):
I was going to move to thinking about.
So with that in mind, right, weCPM teachers are working with
6th through 12th graders.
Mostly, and often I mean Iencounter teachers, and they
particularly in middle schooland they have all this, or even
high school.
They're quite distressed thattheir students don't know their
(20:10):
basic math facts or whateverthat might mean.
So I'm wondering, if I'm comingto a teacher and they're saying
this to me, what are somethings that you might suggest or
how could I approach that?
How can I help those teachers?
Speaker 3 (20:25):
So what you're sharing is common.
I had an email as recently asyesterday where the message was
that the middle school teachersare I think the phrase was using
the common refrain of thestudents don't know their basic
facts.
How can they do fill in theblank, and so basic facts become
(20:45):
like a barrier to doing highermath or other math.
So they shouldn't be.
And so what I want to say aboutbasic facts is it's never too
late for a student to learn thefacts that they're struggling
with.
So that means if you'reteaching middle school or high
school, then don't give up onthe fact that the student can
(21:07):
learn that fact, because fortheir life, regardless of what
profession they're picking, it'sgoing to be a constant problem
for them to not know eight timesseven or six times nine or
whatever.
So that's the first thing isjust commit to helping the
student to learn those facts,because the facts are going to
help solving systems ofequations.
Think of all the.
(21:27):
If you're setting up a systemof equations, you're looking for
like a common factor orwhatever, like they're just
there all the time everywhere.
So it's an investment of timethat, even though it's listed as
a third grade topic, it's worththe investment of time to come
up with a way to teach it.
The thing not to do is whatwe've always done, which is have
them retry to memorize.
Obviously, that didn't work forthem in third grade, fourth
(21:50):
grade, fifth grade it's not.
It's a weak learning strategyin general, so that's not the
way to go about it.
So, and when teachers say thisis a long answer.
Speaker 2 (22:01):
No, this is a great long answer.
Speaker 3 (22:03):
So the thing is is we have to become diagnosticians.
So when we say a seventh graderdoesn't know their facts, they
do know facts.
They know a lot of the facts.
There's 100 of them.
They likely know 80 of them, 85of them, they might know 95 of
them.
There's just some that aregetting in the way, but all it
takes is a few facts that theydon't know to all of a sudden
(22:27):
really trip them up with theother work that they're doing.
So we have to really figure outwhat facts they know and go
from there.
So that's my wisdom.
And so, like using a test, abasic facts test, isn't
insulting to an older child,it's really distasteful to
anyone.
But you can play a game of anysort.
(22:48):
So that involves basic factsand you can observe the students
and start to notice.
With that age student they cando like flashcard sorts where
they're going through and likeself-identifying which facts
they know and which facts theydon't know, so that then you can
engage them in their ownstrategic planning.
For oh, six times seven tripsme up, but I always know three
(23:10):
times seven, aha.
Speaker 2 (23:12):
Mm-hmm.
Speaker 3 (23:13):
Aha, what's the relationship between three times
seven and six times seven?
Speaker 2 (23:18):
Right.
Speaker 3 (23:18):
And if that becomes, is that what you want to use as
your go-to, Joel?
Is that is, that you're goingto be your go-to.
Right, great.
So when you see six times sevenand you're stuck, don't try.
Skip counting, that's going toyou're going to hurt your brain.
Skip counting by sevens or six,Think oh, I know.
my three times seven, I candouble it.
So I think we have to be reallyintentional with helping the
(23:39):
student realize that they reallycan learn the facts that they
don't figure out, what factsthey don't really really know.
And they come up with a goodstrategy to get them down, and
then they'll be glad.
And there's so many games I'vewritten about.
I have many of them in my basicfact book, which and many of
those are available on thecompanion website free download
(24:00):
in English and in Spanish.
Yeah yeah, those games give anopportunity for ongoing practice
.
So, again, with this idea ofthe program of the practice over
time, these games come in to dothat.
So if you're working with themto try to help them with their
facts that they're strugglingwith and they come up with these
ideas for their method they'regoing to use when they get stuck
(24:22):
on one of their facts that isnot automatic for them, then
playing those games areenjoyable for the students.
Some of them have a lot ofstrategy to them where they're
blocking their partner orthey're going to bump them off
of the game board or whatever.
But in the meantime they'regetting a lot of.
Every time they roll a six anda seven they're like what's six
(24:47):
times seven?
I forgot?
Oh, yeah, but I know threetimes seven.
So then that's where you get tothat automaticity and they
could for life always thinkthree times seven when they see
six times seven.
But it becomes automatic.
And that's basically.
I mean that's me for a coupleof facts like six times eight, I
think, five, eights and onemore, and I can do that in a
split second.
So I think that's what we haveto do because we'll see the
(25:11):
benefits in their fraction,fluency, they're solving
equations, all that.
It's worth that additional timeto help them.
Help the students sort out whatfacts are, you know, getting in
their way and helping them sortit out.
Speaker 1 (25:25):
So do you think in some 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 toplay games.
Or do you play a game in themiddle of the lesson?
Or what type of instructionstrategies would you say?
Speaker 2 (25:42):
That's all we'll have time for today, on part one of
our conversation with DrJennifer Bay-Williams, and you
can tune in in two weeks to hearthe rest of our conversation,
and we'll see you then.
Today I have a very excitingannouncement cpm.
(26:16):
As you know, cpm educationalprogram.
We are a mathematics publishingcompany as well as a
professional learning company,and this month we have our
inaugural professional learningpublication, our first
publication designed solely forprofessional learning that you
can purchase.
It is the InstructionalCoaching Toolkit.
(26:39):
So I'll tell you a little bitabout it here.
The Instructional CoachingToolkit is the launchpad for any
instructional coach who wantsto strengthen teacher's practice
and students' learning whilefocusing on their own growth.
This book is written with you,the instructional coach, as the
protagonist.
You will learn how to usecoaching tools and coaching
(27:00):
skills as you journey through acoaching cycle.
Using the framework and toolsin this book, you can help
foster the cognitive dissonancenecessary for teachers to
challenge their practices, theirbeliefs and their ways of being
.
With your guidance and support,teachers can prioritize equity
while setting rigorous goalsaligned with NCTM's eight
(27:22):
effective teaching practices andCPM's three pillars.
This, in turn, will supportstudents in embracing learning
through the standards formathematical practice.
This essential resourcerepresents the culmination of
almost a decade's worth ofthought and planning, started by
a team of collaborative,visionary educators who
recognize the positive impactthat job-embedded coaching has
(27:45):
on how mathematics is taught andlearned.
You can find the InstructionalCoaching Toolkit in the CPM web
store, which is at shopcpmorg,and you can purchase one for
yourself.
Cheers.
Speaker 1 (28:16):
Hello, it's Joel here .
If you listened all the way tothe end of the podcast hoping to
hear this week's math joke,well, you will be disappointed.
We've run out of submitted mathjokes, so if you love this
segment, then please send us arecording of your favorite math
joke to cpmpodcast at cpmorg.
(28:36):
Just give us your name, whereyou live and your math joke Easy
peasy.
We can't wait to hear them.
Speaker 2 (28:49):
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 and can be
found on pixabaycom.
So thank you very much, julius.
Join us in two weeks for thenext episode of More Math for
(29:12):
More People.
What day will that be, joel?
Speaker 1 (29:16):
It'll be October 1st, national Homemade Cookie Day,
and I'm excited for this one too.
I can remember as a kid my momwould leave me to my own devices
a lot.
So I remember I got a hold ofmy Mickey Mouse cookbook and I
wanted to make some sugarcookies for when she got home.
(29:37):
So I remember I made this sugarcookie.
I wanted it to be the size of abaking sheet so I put it out on
the baking sheet.
I added green food coloringsbecause I thought that would
look good, and it did.
It looked beautiful and whenshe came home to have some of
the cookies and my mom's thebest she tried it.
(29:57):
She said it was delicious, butI bet she lost three teeth at
least because it was so rockhard that cookie.
I thought in my early days ofmaking homemade cookies.
I can't wait to talk more,thank you.
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.
17th of September.
Speaker 1 (00:33):
Yes.
Speaker 2 (00:34):
What's the national day today?
It is National Monte Cristo Day.
Monte Cristo Day like thesandwich, the sandwich.
Okay.
So this is going to be acallback to we were just talking
about bowling from the lastepisode, right, and you and I
(00:57):
were talking about how well wemight not be able to go bowling
because we'll be traveling toOmaha.
Mm-hmm, mm-hmm.
And I learned when I wasresearching places to eat in
Omaha that Omaha is supposedly,like the home, the birthplace of
the Monte Cristo sandwich no.
That's what I saw Are youserious right now.
I am serious right now.
Oh my gosh.
I love a Monte Cristo sandwichso much.
We have to also have a MonteCristo sandwich while we're in
(01:18):
Omaha.
Oh my gosh.
Speaker 1 (01:20):
That is going on the checklist for sure.
Speaker 2 (01:26):
I think this is irony .
I think this doesn't qualifyjust as coincidence.
I think this is actual irony.
I'm not very good at thosethings do you enjoy a monte
cristo?
I haven't had a monte cristo ina long time, since I don't eat
very much bread or gluten, but Ithe monte cristos as, as I
remember, them are prettydelicious.
Actually, I'm trying to decideif I've had one since university
(01:49):
.
Speaker 3 (01:54):
I feel like they were one of the things that would be
on the lunch menu.
Speaker 2 (01:55):
Cristo sandwich and I never had had one before that,
because Monte Cristo is the one.
Wait, I'm confused.
Is Monte Cristo the one wherethere's cheese and some kind of
meat, meat, and then they likeput it in like egg and fry it?
Is that the one?
Speaker 3 (02:10):
Yeah.
Speaker 2 (02:11):
What's the one where they have the pumpernickel and
the like Thousand Islanddressing?
Speaker 1 (02:15):
and sauerkraut on it.
That's the Reuben.
Oh Reuben, that's right.
Totally different sandwich.
Speaker 2 (02:21):
Yeah, well, I know, but they're also sandwiches I
never had until I was an adult,because they weren't ones we had
as I was a kid.
Speaker 1 (02:28):
I love a Monte Cristo and local establishment here in
Salt Lake served my favoriteMonte Cristo Like they fried it
so good and the fresh.
Like they made the berry jamthat went with it.
There's berry jam on it, ohyeah, and it was so delicious.
Speaker 2 (02:42):
I don't think they made it with berry jam.
In went with it.
There's berry jam on it, ohyeah, and it was so delicious I
don't think they made it withberry jam in Northwestern's tiny
halls.
Speaker 1 (02:50):
Well, I was so sad because last time I went I went
down to get the Monte Cristo andthey changed the menu.
What they said, we reduced ourmenu size and that did not make
the list.
We're only going to make it onspecial days.
And I said, well, what's thespecial day?
I hope like September 17th is aspecial day because it's Monte
(03:11):
Cristo day, but I was so bummedLike it ruined my whole weekend.
Speaker 2 (03:16):
Apparently you weren't going and ordering it
enough.
Speaker 1 (03:19):
I know it's my fault, yeah.
Speaker 2 (03:24):
I'm not sure I mean think about.
Yeah, I'm not sure I'veactually.
I mean think about it.
I'm not sure I've had one sinceuniversity, which is a long
time now, and clearly those werenot gourmet Monte Cristo
sandwiches, they were bulk madeCristo sandwiches.
So yeah, monte Cristo is on thelist for Omaha.
I think it should be by thetime everyone on our team hears
(03:45):
this, it'll be too late for themto have Monte be.
Speaker 1 (03:47):
That's why everyone on our team hears this.
Speaker 2 (03:48):
It'll be too late for them to have a Monte Cristo.
Let's hope they had it.
Yeah, exactly, or they couldjust have one now.
Yeah, wherever they are.
Speaker 1 (03:56):
Love that.
Delicious sandwich days arekind of like I know I'll be
celebrating, I know I'm going tohave a Monte Cristo sandwich
because it's a delicioussandwich and I can celebrate,
and I love delicious sandwiches.
Speaker 2 (04:11):
And Monte Cristo just has like regular bread.
There's no special.
Speaker 1 (04:14):
I don't know that it's a special bread, but it's
because you fry it and thingslike that, it's very similar to
the French toast when it comesout, you want a thicker bread.
Speaker 2 (04:26):
Yeah, it's your wonder bread, the French toast.
When it comes out.
Speaker 1 (04:28):
You want a thicker bread.
Yeah, it's your wonder bread,that's right, Well cool.
Yeah.
Speaker 2 (04:31):
All right.
Well, I don't know what else tosay about Monte Cristo sandwich
day.
Speaker 1 (04:34):
I can't even say anything because I'm thinking
about it.
Speaker 2 (04:36):
Why is it called the Monte Cristo?
Well, it has.
Speaker 1 (04:39):
French roots, and I think wasn't there like a count
of Monte Cristo.
Speaker 2 (04:43):
Well, yeah, but I don't think it's named after him
.
Speaker 1 (04:45):
That was like an Alexandre Dumas book Right, but
he had all that time in prison,right, like he had a lot of time
to think about stuff.
Speaker 2 (04:53):
He did spend a lot of time in prison, and so he
probably thought about thisdelicious sandwich that he
couldn't have.
I don't think that is theactual.
I mean I'm very skeptical aboutthis story.
Oh well.
So we don't have a goodexplanation on your source.
Speaker 1 (05:09):
Well, it's got some French roots here, but this day
was initiated to commemorate thelong history of Monte Cristo
sandwiches that continue tobless our taste buds for decades
now.
So like in 1910 is when theMonte Cristo kind of made its
debut.
Speaker 2 (05:30):
Is it called Monte Cristo sandwich?
I can't even spell Monte Cristo, what, okay?
The AI overview says the MonteCristo sandwich is named after
the Count of Monte Cristo, anadventure novel by Alexander
Dumas.
Come on, I'm just saying thesandwich flavor profile pays
homage to its French origins andsome believe the name was Come
on, I knew it.
(06:02):
Oh, that's very vague.
Speaker 1 (06:05):
That is vague.
I can't believe.
Speaker 2 (06:07):
It also says that the Monte Cristo sandwich is a
variation of the Croque Monsieur, a French sandwich that was
lightly served in Paris cafes inthe 20s.
Apparently, it's all from the20s.
Speaker 1 (06:18):
There you go.
I'm trying to click on.
How was the Monte Cristosandwich created and it won't
open up, so I have no idea.
Speaker 2 (06:33):
But I think I just told the story that the Count
was in prison and that's how itwas created.
Yeah, it doesn't explain inthis AI overview why it would be
named after the Count, but itdoes say also in the 1960s the
sandwich was added to the menuat Disneyland's.
Speaker 3 (06:43):
Blue Bayou restaurant and became an American favorite
.
Speaker 2 (06:46):
Yes, which just cracks me up.
I mean, the AI overview ishelpful, but it doesn't really
tell me the why.
Anyway, all right.
Speaker 1 (06:58):
Well, there's some interesting tidbits of how the
Monte Cristo sandwich might benamed or not and I hope all of
you listening, we have not datachecked, are going to go out and
get a Monte Cristo sandwich.
Speaker 2 (07:06):
Might be named or not , and I hope all of you
listening.
Speaker 1 (07:06):
We have not data checked, are going to go out and
get a Monte Cristo sandwich.
Speaker 2 (07:10):
Yep, Enjoy your sandwich.
So as a side note, we do wantto clarify that Omaha is the
home of the Reuben sandwich andapparently my conflation of
Monte Cristo and Reubensandwiches is pretty severe.
So if you go to Omaha, don'task for Monte Cristo, Go get a
Reuben Any day, All right.
(07:46):
So today we're going to havepart one of a conversation with
Dr Jennifer Bay Williams.
Jenny Bay Williams has been aprofessor at the University of
Louisville since 2006.
She teaches courses related tomathematics teaching to
pre-service teachers andpracticing teachers and is
frequently working in elementaryschools to support mathematics
(08:08):
teaching.
Prior to coming to theUniversity of Louisville, she
taught in a variety of otherplaces, such as Kansas, Missouri
and Peru.
Dr Bae-Williams is aninternationally respected
mathematics educator.
She is a prolific author andpopular speaker on topics
related to effective mathematicsteaching.
Her work has focused on ways toensure that every student
(08:31):
understands mathematics anddevelops a positive mathematics
identity.
Her most recent work hasfocused on fluency and
mathematics, communicating thatit is more than learning facts
and algorithms, but rather thatit's about being able to reason
and choose appropriatestrategies.
Her books on fluency andmathematics coaching are
bestsellers.
(08:52):
We're excited to have Dr BaeWilliams here on the CPM podcast
today to talk with us about herviews on fluency.
All right, well, while Joel isfinishing figuring out how to
get himself connected to us,we're just going to start
because we can always we canalways use AI to insert Joel
later.
I'll just we'll replace myvoice with his voice asking one
of the questions.
That's pretty amazing.
(09:14):
So we're here today with JennyBay Williams and, Jenny, you are
a professor at the Universityof Louisville.
I have that right.
Excellent.
We have co-workers who are inLouisville.
I think one of them is at theUniversity of Kentucky.
Might done a lot of work withfluency.
(09:35):
You've written some books andmany articles, and fluency is
definitely a question that comesup, or a topic of concern, I
think, for a lot of teachers,and particularly teachers in CPM
, because of the mixed spacepractice that we have and
students are interacting withmaterial over time.
(09:56):
Then how do we figure out whatfluency is right?
And there's always theseconcerns around whether students
know their basic math facts andwhat to do if they don't know
them.
So we're going to talk aboutseveral of those things today.
So thanks for joining us on thepodcast today.
Speaker 3 (10:11):
I'm excited to talk about all of those things.
So thank you for inviting me.
Speaker 2 (10:15):
No, worries and Joel's just going to keep trying
to figure out if he can talk tous or not, and we're just going
to keep going.
So we appreciate your time.
The first thing I wanted tolaunch with is I think that a
lot of times when we talk aboutfluency and what is it?
What comes to mind is beingable to I think of oh, how fast
can you do your multiplicationfacts right?
(10:37):
You have kids doing speed testsand different things, and
that's this idea of fluency andI'm wondering what you think
about that.
I guess, or am I guessing, youdon't agree with that.
Speaker 3 (10:46):
Yeah, I don't agree with that.
But there is this need to beautomatic with something so that
you can recall things,information that you need, that
you're going to be using withoutusing a lot of thought.
But that's not fluency, that'sautomaticity being automatic.
So we want to be automatic withbasic facts.
And in middle and high schoolthere's other things where
(11:09):
automaticity supports the biggerreasoning.
For example, equivalencies witha one half, recognizing that 13
over 26,.
Hey, that's one half.
How do you know?
Without a lot of thought?
You just recognize fractionequivalencies of fourths, halves
and other things likerecognizing, I don't know,
pythagorean, triples or whatever.
But there's these things whereyou see them so much, you
(11:32):
recognize them and you just know.
So there are.
That's automaticity.
But fluency is about being ableto solve a problem using an
efficient method.
So I'm going to start withefficiency.
So let's just take a fraction.
We work on fraction fluency inmiddle school, right?
So let's take two andthree-fourths plus two and
(11:53):
three-fourths just the samenumbers.
So we don't have troubleremembering the problem Two and
three-fourths plus two andthree-fourths just the same
numbers.
So we don't have troubleremembering the problem Two and
three-fourths, two andthree-fourths.
So what you were saying, mistyis that somebody would be really
fast so they could go aboutdoing the algorithm really
really fast.
That's not fluency, that isbeing, I don't know adept at
(12:14):
using an algorithm.
A fluent person is going to gooh hey, I have some options here
for adding that problem.
What are my options?
And this way looks really fastfor this problem and so, and all
that happens like in it happensquickly.
So for two and three-fourthsplus two and three-fourths, what
they might recognize is theyknow three-fourths and
(12:36):
three-fourths is one andone-half and then add the
whole-fourths is one andone-half and then add the whole
numbers, add the one andone-half and they're done.
They might just move one-fourthover from one fraction to the
other and think, oh, that'sthree plus two and one-half.
Again, they got thatautomaticity with fractions
going.
Those are then ones they canadd in their head, and so the
(12:57):
fluent person goes about aproblem by looking at it, sizing
it up and making a decisionabout how they're going to solve
it.
That's what somebody withfluency does.
That's different than somebodyjust being really really fast.
It's about making good choices,what we like to talk to middle
and high school students about.
Speaker 1 (13:17):
Making good choices with math, you know so I have
some questions.
Speaker 2 (13:23):
So I see that as, like one, you talk about the
automaticity with fractions andthe numbers and making some
choices would rely upon areasonable number sense, right
that our ability to just I don'tknow know, it's just just to
know that a half and a half isone, or just to know like that,
(13:43):
and and so, which could becalled basic facts, but I think
it's also, it's that numbersense, like I know my tens, I
know how to group in fives.
I have these like lots ofdifferent abstract and more
representational ways ofthinking about numbers.
However, that is, is that?
Do you see that?
Speaker 3 (14:04):
or Definitely so.
There's more literature,research and discussion about
decomposing.
I'm just going to pick up onone of the things you were
talking about.
In, like kindergarten, can youbreak apart eight lots of
different ways, five plus threeand that sort of thing but just
take like a fraction, likethree-fourths right there.
To do that strategy that Italked through, you have to
(14:24):
think, oh, I could break thatthree-fourths apart into
two-fourths plus one-fourths orone-half plus one-fourths.
It's that flexibility and thatnumber sense that allows you to
be flexible in breaking numbersapart, putting them back
together, knowing that you couldapply the distributive property
but you don't have to apply thedistributive property as your
first step in solving algebraicequations, solving for X.
(14:46):
So there is this level oflooking at number relations and
seeing and using those numberrelations to efficiently solve a
problem.
So, which is harder tounderstand in the general and
easier to understand an example.
So if you want someclarification, just ask for an
example.
Speaker 2 (15:07):
Well, and the other piece of what I was thinking
about, as you were saying, thatis that we talk about building
procedural fluency fromconceptual understanding.
So when, in the example youwere talking about, how would
you and maybe you need adifferent example, that's okay
Like, how would you apply theidea of procedural fluency to
that?
Because I think of, when Ithink of procedural fluency, I
(15:28):
think, oh, you can do thiscalculation or this algorithm
very quickly or well, but and Ithink that that teachers often
get into that right, it meansyou can do the long division
algorithm, it means you can doall these algorithms.
And is that how you see it, ordo you see it a little
differently than that?
Speaker 3 (15:46):
I do see it that way.
I think that the there's thisimportant relationship where the
conceptual understandingsupports the fluency and the
fluency then strengthens theconceptual understanding.
So for example, with that twoand three-fourths plus two and
three-fourths, the more thatstudents are applying this
strategy of moving one-fourthover, the better they're getting
at the skill of breakingfractions apart.
(16:07):
But the more they're gettingthis idea of basically the
associative property that theycan take something from one
add-in and move it to the otheradd-in, they still have an
equivalent expression after athing.
Another great example is withsubtraction.
So if we had, let's just dofive and three-fourths minus two
(16:28):
and three minus I don't know,let's do no, I'm going to change
the problem.
Let's talk about subtractionand that relationship between
conceptual understanding andprocedural frequency.
So if you take something likefive and one-fourths minus I
don't know, four andthree-fourths, somebody with a
(16:50):
conceptual understanding ofsubtraction understands that it
is take away and it's also findthe difference or compare.
So they look at that problemand they say, oh, those
fractions are close together.
It's going to be easier to findthe difference between four and
three-fourths and five andone-fourth it's one-half.
(17:11):
Maybe they picture a ruler or anumber line.
And so, again, that conceptualunderstanding is coming in and
helping them visualize and solvethe problem.
A student with no conceptualunderstanding of fractions will
see those fractions and followan algorithm.
They'll regroup from the fiveto get four and five fourths and
subtract it and get theiranswer.
(17:32):
And that's not fluency, becauseit took them a much longer time
to do all of that work.
They have no idea of knowing iftheir answer makes sense, and
so that's the two supportingeach other.
The conceptual understandingallows for an efficient solution
strategy and also to understandif the answer makes sense.
And then just the very questionof are you going to find the
(17:52):
difference or use takeaway issupporting both their fluency
and their conceptualunderstanding.
Speaker 2 (17:58):
Right, right, joel, can I hear you?
Can you hear me?
Takeaway is supporting boththeir fluency and their
conceptual understanding.
Right, right, joel, can I hearyou?
Can you hear me?
Yes, can you hear us?
I can hear you.
Welcome to the program, joel.
Speaker 1 (18:11):
Thank you.
Speaker 2 (18:12):
Yeah, technical difficulties resolved.
Speaker 1 (18:15):
Okay.
Speaker 3 (18:49):
Cool, so I'm just fascinated by this, this whole
idea, because there's so many itthe way that I was supposed
mathematicians are.
As in research mathematiciansor engineers or people who are
using mathematics, they'retrying to be creative about how
they're putting things togetherin order to figure something out
(19:12):
, so they're not reallyfollowing like algorithmic stuff
as the way their brain isengaged right.
The algorithmic stuff is doneusually with technology, so that
decision making and creativityis oftentimes the insights into
a better way to engineersomething or create something or
whatever.
And so to squelch that in schoolis the exact opposite of what
(19:35):
we want to be doing withstudents.
We want to inspire them to takethis problem in and come up
with an efficient way to solveit, based on what you notice,
what the features of the problemare.
Speaker 2 (19:49):
I was going to move to thinking about.
So with that in mind, right, weCPM teachers are working with
6th through 12th graders.
Mostly, and often I mean Iencounter teachers, and they
particularly in middle schooland they have all this, or even
high school.
They're quite distressed thattheir students don't know their
(20:10):
basic math facts or whateverthat might mean.
So I'm wondering, if I'm comingto a teacher and they're saying
this to me, what are somethings that you might suggest or
how could I approach that?
How can I help those teachers?
Speaker 3 (20:25):
So what you're sharing is common.
I had an email as recently asyesterday where the message was
that the middle school teachersare I think the phrase was using
the common refrain of thestudents don't know their basic
facts.
How can they do fill in theblank, and so basic facts become
(20:45):
like a barrier to doing highermath or other math.
So they shouldn't be.
And so what I want to say aboutbasic facts is it's never too
late for a student to learn thefacts that they're struggling
with.
So that means if you'reteaching middle school or high
school, then don't give up onthe fact that the student can
(21:07):
learn that fact, because fortheir life, regardless of what
profession they're picking, it'sgoing to be a constant problem
for them to not know eight timesseven or six times nine or
whatever.
So that's the first thing isjust commit to helping the
student to learn those facts,because the facts are going to
help solving systems ofequations.
Think of all the.
(21:27):
If you're setting up a systemof equations, you're looking for
like a common factor orwhatever, like they're just
there all the time everywhere.
So it's an investment of timethat, even though it's listed as
a third grade topic, it's worththe investment of time to come
up with a way to teach it.
The thing not to do is whatwe've always done, which is have
them retry to memorize.
Obviously, that didn't work forthem in third grade, fourth
(21:50):
grade, fifth grade it's not.
It's a weak learning strategyin general, so that's not the
way to go about it.
So, and when teachers say thisis a long answer.
Speaker 2 (22:01):
No, this is a great long answer.
Speaker 3 (22:03):
So the thing is is we have to become diagnosticians.
So when we say a seventh graderdoesn't know their facts, they
do know facts.
They know a lot of the facts.
There's 100 of them.
They likely know 80 of them, 85of them, they might know 95 of
them.
There's just some that aregetting in the way, but all it
takes is a few facts that theydon't know to all of a sudden
(22:27):
really trip them up with theother work that they're doing.
So we have to really figure outwhat facts they know and go
from there.
So that's my wisdom.
And so, like using a test, abasic facts test, isn't
insulting to an older child,it's really distasteful to
anyone.
But you can play a game of anysort.
(22:48):
So that involves basic factsand you can observe the students
and start to notice.
With that age student they cando like flashcard sorts where
they're going through and likeself-identifying which facts
they know and which facts theydon't know, so that then you can
engage them in their ownstrategic planning.
For oh, six times seven tripsme up, but I always know three
(23:10):
times seven, aha.
Speaker 2 (23:12):
Mm-hmm.
Speaker 3 (23:13):
Aha, what's the relationship between three times
seven and six times seven?
Speaker 2 (23:18):
Right.
Speaker 3 (23:18):
And if that becomes, is that what you want to use as
your go-to, Joel?
Is that is, that you're goingto be your go-to.
Right, great.
So when you see six times sevenand you're stuck, don't try.
Skip counting, that's going toyou're going to hurt your brain.
Skip counting by sevens or six,Think oh, I know.
my three times seven, I candouble it.
So I think we have to be reallyintentional with helping the
(23:39):
student realize that they reallycan learn the facts that they
don't figure out, what factsthey don't really really know.
And they come up with a goodstrategy to get them down, and
then they'll be glad.
And there's so many games I'vewritten about.
I have many of them in my basicfact book, which and many of
those are available on thecompanion website free download
(24:00):
in English and in Spanish.
Yeah yeah, those games give anopportunity for ongoing practice
.
So, again, with this idea ofthe program of the practice over
time, these games come in to dothat.
So if you're working with themto try to help them with their
facts that they're strugglingwith and they come up with these
ideas for their method they'regoing to use when they get stuck
(24:22):
on one of their facts that isnot automatic for them, then
playing those games areenjoyable for the students.
Some of them have a lot ofstrategy to them where they're
blocking their partner orthey're going to bump them off
of the game board or whatever.
But in the meantime they'regetting a lot of.
Every time they roll a six anda seven they're like what's six
(24:47):
times seven?
I forgot?
Oh, yeah, but I know threetimes seven.
So then that's where you get tothat automaticity and they
could for life always thinkthree times seven when they see
six times seven.
But it becomes automatic.
And that's basically.
I mean that's me for a coupleof facts like six times eight, I
think, five, eights and onemore, and I can do that in a
split second.
So I think that's what we haveto do because we'll see the
(25:11):
benefits in their fraction,fluency, they're solving
equations, all that.
It's worth that additional timeto help them.
Help the students sort out whatfacts are, you know, getting in
their way and helping them sortit out.
Speaker 1 (25:25):
So do you think in some 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 toplay games.
Or do you play a game in themiddle of the lesson?
Or what type of instructionstrategies would you say?
Speaker 2 (25:42):
That's all we'll have time for today, on part one of
our conversation with DrJennifer Bay-Williams, and you
can tune in in two weeks to hearthe rest of our conversation,
and we'll see you then.
Today I have a very excitingannouncement cpm.
(26:16):
As you know, cpm educationalprogram.
We are a mathematics publishingcompany as well as a
professional learning company,and this month we have our
inaugural professional learningpublication, our first
publication designed solely forprofessional learning that you
can purchase.
It is the InstructionalCoaching Toolkit.
(26:39):
So I'll tell you a little bitabout it here.
The Instructional CoachingToolkit is the launchpad for any
instructional coach who wantsto strengthen teacher's practice
and students' learning whilefocusing on their own growth.
This book is written with you,the instructional coach, as the
protagonist.
You will learn how to usecoaching tools and coaching
(27:00):
skills as you journey through acoaching cycle.
Using the framework and toolsin this book, you can help
foster the cognitive dissonancenecessary for teachers to
challenge their practices, theirbeliefs and their ways of being
.
With your guidance and support,teachers can prioritize equity
while setting rigorous goalsaligned with NCTM's eight
(27:22):
effective teaching practices andCPM's three pillars.
This, in turn, will supportstudents in embracing learning
through the standards formathematical practice.
This essential resourcerepresents the culmination of
almost a decade's worth ofthought and planning, started by
a team of collaborative,visionary educators who
recognize the positive impactthat job-embedded coaching has
(27:45):
on how mathematics is taught andlearned.
You can find the InstructionalCoaching Toolkit in the CPM web
store, which is at shopcpmorg,and you can purchase one for
yourself.
Cheers.
Speaker 1 (28:16):
Hello, it's Joel here .
If you listened all the way tothe end of the podcast hoping to
hear this week's math joke,well, you will be disappointed.
We've run out of submitted mathjokes, so if you love this
segment, then please send us arecording of your favorite math
joke to cpmpodcast at cpmorg.
(28:36):
Just give us your name, whereyou live and your math joke Easy
peasy.
We can't wait to hear them.
Speaker 2 (28:49):
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 and can be
found on pixabaycom.
So thank you very much, julius.
Join us in two weeks for thenext episode of More Math for
(29:12):
More People.
What day will that be, joel?
Speaker 1 (29:16):
It'll be October 1st, national Homemade Cookie Day,
and I'm excited for this one too.
I can remember as a kid my momwould leave me to my own devices
a lot.
So I remember I got a hold ofmy Mickey Mouse cookbook and I
wanted to make some sugarcookies for when she got home.
(29:37):
So I remember I made this sugarcookie.
I wanted it to be the size of abaking sheet so I put it out on
the baking sheet.
I added green food coloringsbecause I thought that would
look good, and it did.
It looked beautiful and whenshe came home to have some of
the cookies and my mom's thebest she tried it.
(29:57):
She said it was delicious, butI bet she lost three teeth at
least because it was so rockhard that cookie.
I thought in my early days ofmaking homemade cookies.
I can't wait to talk more,thank you.
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