How Cognitive Science Transforms Math Education: S2 E14

Jonily : Welcome everyone. This
is tier one interventions

podcast. I am one of your hosts.
Joni zupanczyk, math specialist,

and my co host is here, co
author, partner in crime, all of

those things. Cheri Dotterer, an
occupational therapist and

neuroscience expert. We're
getting ready to begin the

science of math.

Cheri Dotterer: Hey everybody.
It's Cheri Dotterer here. I just

wanted to give you an update on
today's episode. We have

recorded this at a Saturday
math, which is a free webinar

that we do monthly. We follow
that up with impact Wednesday on

a Wednesday night. So this past
Saturday, we recorded this

episode, and we want to share it
with you in its entirety. We're

not going to break it up for
you, because we think it is such

a powerful episode. But if you
want to come on Wednesday night

to hear the next segment of
this, join us on impact

Wednesday at the science of
math, non academic connections,

what happens in our brain. So
we're going to do a neuroscience

dive into what we talked about
here in the Math Episode at our

free Saturday math session. The
link for both of them will be in

the show notes, so you can sign
up next month at Joni Lee's

website on Eventbrite, or just
give me an email at Cheri, at

Cheri dotterer.com, and I will
let you know how to sign up

before we begin. Please
subscribe and comment on this

episode. Let's tune in to
Saturday math. Good

Jonily : morning everyone, and
welcome to this Saturday's

webinar all about the science of
math. Yes, that is what I said.

Good morning. Yes, good morning
to all of you. The Science of

math is coming, and I want to
give us some details, some

cautions, some warnings and also
some solutions. This morning,

very excited about today's
webinar. Thank you so much for

being here on in my part of the
world, in Ohio, in the United

States, snowy and cold part of
the world, but it is beautiful

this morning as I look out my
window and we are going to talk

all about the science of math
today, as the science of math

begins to roll out in definitely
in the state of Ohio, but also

in the United States, there will
be different phases of roll out.

And then, of course, Canada,
you'll have your own roll out,

and then in other parts of the
world, it's going to look a

little different. And the big
wave is coming for everyone, and

it's going to happen in
different ways. However, I want

us to be informed and not
misinformed. And some of you

might be saying, then, how do I
know that your information is

not the misinformation? And that
is the question, not only do you

need to be asking me, but also
people like me, also anyone in

your school district that is
narrating some of these changes

that are going to come. Now,
what typically happens in

education is we know that a wave
is coming. There's buzz about

it. There might be a few
professional developments about

it, and then it gets stagnant,
sometimes for 345, years, and

then it comes back around. A lot
of times it takes a while to get

traction. Other times, there are
mandates that come in and things

happen immediately. I think
we're still walking on thin, icy

water at this point, which is
which makes me thrilled to have

everybody here today, because I
want today to be a foundational

tool for you to use to assess
against everything else that

comes your way. The first
question you should ask when the

topic of science of math comes
around, or research based or

evidence based, as far as
mathematics is, are you

currently implementing in
classrooms, and what results are

you getting? And I think
oftentimes, even when we adopt

math textbooks, and the speaker
comes, whether it's the sales.

Rep or the trainer. Sometimes
it's one in the same it's even a

question we should ask them, Who
in your company is currently

implementing the textbook and
the ideas that you're presenting

in the training, and what
results are you getting, and we

need to see that in real time. I
think we take for face value,

what people are telling us and
what people are saying, and then

we're frustrated that we're not
seeing immense scaling results

in mathematics. Those are some
of my cautions, and I'm going to

be very direct and aggressive
today. However, I want to fill

your day with solutions again.
Welcome everyone. I am your

host, Jonily Zupancic, Jay Z in
the house this snowy Saturday

morning where I am to really
unveil science of math in its

early stages and early form.
Many times you'll hear me talk

about cognitive science of
learning, there are four

components, four strategies, not
necessarily in the education

world, but in the psychological
world, in the neuroscience

world, there are four strategies
of cognitive science that

promote highly effective
learning and retention of

content. So if I'm a college
student, let's say and I have to

learn information or relearn
information for a midterm or a

final exam. There are many
strategies, but in cognitive

science, I typically focus on
these four strategies to excel

learning memory and retention of
the content. These strategies

work short term as well as long
term. I'm going to show you them

on the screen, but right now I'm
going to just tell them to you

so you'll just hear them right
now, and I'll refer back to them

during this entire session, and
they are interleaving spaced

repetition, retrieval practice
and metacognitive feedback. And

what I'm going to do today is
I'm going to define each of

those. Then I'm going to show
you how they relate to teaching

and learning in general. Then I
will show you how they relate to

teaching and learning of
mathematics specifically. Then I

have then what I'm going to do
is share with you some resources

of the exact implementation of
these strategies in mathematics

classrooms. It is going to be
exciting this morning, and we

will interact in a moment, but
right now, I'm just going to

seminar it. I'm just going to
give you a lot of stuff, and

then we'll process and interact
later. So again, welcome.

Welcome to all of you that know
me. Welcome to all of you that

don't know me. Again, my name is
Jonily Zupancic, Jay Z right

here, bringing to you on the
front lines science science of

math. And again, I will
interchange science of math with

with cognitive science of math
with science of learning, and

I'll talk about the little
caveats of all of those things.

But the cognitive science of
math for us here at minds on

math is a model that provides
scalable math achievement

through explicit instructional
techniques. The explicit,

deliberate and intentional
training is much more for the

teacher and facilitator and
educator intervention specialist

rather than for the student. So
there are there, there are

certain explicit instructional
techniques for the teacher, but

then the explicit techniques and
strategies for the students are

different, and oftentimes during
professional development

trainings, we teach the explicit
and direct strategies that

benefit the students, which then
don't allow teachers to

implement in the appropriate.
Correct way for students to get

the full advantage of the
strategies. So the teaching

techniques and the learning
techniques are different. The

action steps, the moves that we
make as instructors are

different than the moves that we
ask students to make, and many

times we don't differentiate
between those two things. Just

an example. You probably since
you're here on your own time,

virtually whatever part of the
world you're from, whatever time

of day it is, you chose to be
here. You've probably been to

many trainings, seminars,
professional developments like

this. And in those trainings,
seminars, professional

developments. Oftentimes you get
really excited, and by the end,

you're like, that was really
amazing, or you might say that

was really awful, but in those
that you say that was really

amazing, so fantastic. I'm going
to go, I'm just going to go

change my entire classroom
tomorrow. You get back to your

classroom and you're like, I
just went through the most

amazing experience, but I don't
know how to do this in my

classroom, and there's this
disconnect between the

techniques that we learn in
trainings, the techniques that

we teach to our students, and
then the techniques that we

specifically and explicitly
learn as the educator on

actually facilitating these
transformations, and all of

those have their own names and
strategies. Bottom line, though,

we want we all want the same
outcomes for math. We want kids

to know their facts. We want
kids to be confident. We want

kids to be able to work
independently. We want kids to

be able to just do we want them
to have the prerequisites. We

want them to have number sense.
No matter who I interview or

survey anywhere in the world. We
all want the same outcomes, but

if I survey and narrow those
outcomes, if I survey math

teachers, instructional
specialists, interventionists.

If I survey the people that are
currently teaching math students

and helping specifically
struggling students, everything

boils down into the same
categories. I'm going to rename

these categories as we go today,
but these categories are

different than outcomes, so to
speak, because as I survey

teachers, what ends up coming
out are the deficits kids have,

but yet in turn, they're the
outcomes that teachers wish they

did have. So the three major
categories of deficits and the

three major outcomes that we
want are computation. We want

efficient, accurate computation.
The other thing that comes up

most popular, no matter really
what grade level, what school

district, what area in the world
you're in, kids need to

understand. Kids struggle with
equations, equations,

equivalence, substitution,
solving for an unknown. And the

third category, nobody that I
survey really has the same name

for it. So what I've done is
I've named this category based

on all of the similarities of
this category, and that's why

it's a different color here. I
call it shape. So for some

teachers, they're like, I need
my kids to understand volume,

area, perimeter. I need my kids
to know how to measure with a

ruler. So there's lots of things
like that fall into this

category, but it's really all
about shape and utilizing shape

in mathematics, and really
computations with shape

measurement is a computation.
Now these are the words that we

as educators use, the words that
I use, and I'll I'm not going to

give you all of the reasons I
use these words today, but the

words that I use are factors,
meaning facts, but factors are

essential function and right and
fraction. So I call them the

three F's, factors, function and
fraction, and all of

mathematics, preschool through
high school, I'd say a good 95%

a. Our standards will fall into
one of those categories,

factors, fraction and function.
So at minds on math. We power

standard, we essentialize and
compartmentalize the major

concepts of mathematics and then
attach the dozens of standards

from every grade level to each
of those categories. What that

allows us to do is use the same
exercises and experiences, tasks

and lessons with every grade
level and every ability level of

students, but we use them and
facilitate them in a different

way. But it all comes down to
the same tasks, but I've gone

off into a different path with
our model. But the entire

justification of our model is
because kids do not remember

mathematics. Some do 10% 20%
some of those kids just remember

no matter how we teach, no
matter what we do, no matter

what we put them through.
Honestly, some of the kids,

they're not just remembering.
They knew it before we even

taught them. You have that. I'm
going to call it, I'm going to

call it, I'm going to be
generous, I'm going to call it a

30% group of students that are
going to get the math, that are

going to learn the math, that
are going to excel in math, no

matter what. So most school
districts, when they're given

any type of math achievement
test, at least 30% of the kids

are going to pass, and we cannot
attribute that to what we've

done. Ouch. So now we need to
start looking at percentages of

passing in a very different
light. How do we know that we've

contributed to the students that
are actually gaining the

achievement? So back to our
frustrations as educators. Why

don't kids remember it's because
if I go back to the idea of

cognitive science, of math, the
way we typically and

traditionally teach mathematics
is the exact opposite of the way

that the brain learns the way
that textbooks are written and

implemented are the exact
opposite of the way the brain

learns. So what do we do? Do we
give up textbooks? No, do we

stop doing most of the things
that we're doing? No, not

necessarily because textbooks
are necessary, but for a

different reason, not to
implement science of math

textbooks are necessary for a
different reason, not to scale

mathematics achievement, because
if we saw huge gains in

mathematics achievement in
certain pockets that are using

the same textbooks, then we
could contribute it to the

textbook. But really, these
scales that I'm talking about

today have nothing to do with
our textbook resources. They

have nothing to do with our
current curriculum pacing

guides. Kind of a downer, a
downer. At this point, you're

either going to hang up and walk
away and be like, then that's

too overwhelming. Jay Z or
you're going to be like, Okay, I

agree with you. Let's keep
going. Where's the rubber meet

the road? In order to increase
memory, we have to focus on

teaching through the four
strategies I've mentioned

earlier. I'm going to show you
those now, the four cognitive

science strategies. And this is
not me. This is not Jonily. This

is not Jay Z. I did not coin
these. These are from one of my

favorite resources. They're from
many resources, but one of my

favorite resources is the book
make it stick, The Science of

Successful Learning. Here's your
authors,

and the book make it stick is
not necessarily for educators.

So as a teacher, as a math
teacher, to pick it up and be

like, Okay, I'm going to read
this and then I'm going to go

implement these things. No,
there. It's not as streamlined

as that. So what I have done,
what my team has done over the

years, is from the research,
from make it stick. We have then

taken these strategies and
implemented in different. Their

explicit, deliberate,
intentional ways in math

classrooms of all levels, and
analyze the results. I have not

coined these. These four
strategies are from cognitive

psychology, interleaving, spaced
repetition, retrieval, practice

and metacognitive feedback. My
current work with two of the

school districts that I'm
working with right now is we are

mapping their textbook resource,
their curriculum resource, to

these strategies within our
lesson plans, and I'm going to

show you a few of those examples
today. But why should you listen

to me? Yeah, my family would ask
you the same thing. I'm going to

give you a couple of examples,
in 1000s at this point in the

last 15 years, in 1000s of
middle schools, I have done a

little experiment asking
students to tell me the decimal

equivalent for 1/8 typically I
do this in a year seven grade

seven grade eight, right before
kids go to high school. And just

randomly, I'll ask seventh and
eighth graders to put the

decimal equivalent for this
number. And this is one class

this year, but there have been
literally hundreds and 1000s of

classes and students over the
last 15 years that we've gotten

the same results. And the
majority of students in this

specific grade eight classroom
this year gave me a decimal that

had the number eight in it, and
then I had some other results.

And these results are fairly
typical. Now I have also run a

little action research project
for the past seven years. I

began with a group of
kindergarteners, so five year

olds about seven years ago, and
I have followed them every year,

and as they move from teacher to
teacher, I have coached their

current teacher while we're
implementing the model at their

new grade level. So I will come
in and actually model the model

and train and coach the teacher
during that school year that he

or she has these students. So
these current students that I've

been following are in grade
seven this year, and they've

been in this model since
kindergarten. Now we also have

transiency. So we have kids that
have moved out and moved in. We

have move ins. And so what I'm
going to show you are their

results from the beginning of
this year at seventh grade for

the decimal equivalent from 1/8
and they are this. You can

notice the amount of fewer
students who have an eight in

the decimal. By the way, if you
don't know the fraction, 1/8

doesn't have an eight in the
decimal at all. But the

significant number of students
that don't give me an eight in

the decimal is really extreme,
from the one group to the other.

And for some other information,
all of these students have moved

in to this cohort after
kindergarten. At some point, two

of them are new to our school
this year. So just to put some

numbers to this, and these are
typical results, 26% of students

in that grade eight group give
me a decimal that doesn't have

an eight in it. But 75% of the
group that's been through the

model gives me a decimal that
doesn't have an eight in it. Now

I don't know if that seems
groundbreaking to you, but it is

to me, just with that one
example, and if we look at other

results, we have seen cohorts of
kids go from 27% passing the

year end assessment to 60%
passing in less than a year, and

92% showing growth. We also had
a really cool group of students

last year, typically And
historically, in grade four at

the end of. Year, eoy, end of
year, end of course, math exam

that the state provides,
typically fourth graders in that

district and surrounding
districts, there are usually 50

to 65% of those students that
pass after two years of

partially implementing this
model. Funny story. So I've

working with these teachers, the
fourth grade teachers for two

years at this school district,
and in the middle of last year,

they both, there's 2/4 grade
teachers, they both said to me,

Jonily, like we're really
trying, but we're not even doing

half of what you've taught us.
And boom, last year, 84% of the

entire fourth grade level. So
this is the entire fourth grade

so they have about 130 students
at that grade level. 84% of

those students passed that end
of course math exam. And we just

continuously show results after
results. It is very powerful,

and I share it not to be like,
so you guys are probably like,

just show us your strategy
strongly. You all that are here

today. You didn't come to be
convinced you're here because,

like, you want to know what to
do, but because we're recording

this and because I want the
science of math intro session to

be all wrapped in one bundle.
It's important that we have some

validity behind us, and it's
important that you all hear that

there's more where that came
from. But again, I don't want to

bore you. I want to get to what
do we do? But it's important

that when someone is bringing in
training, professional

development, a new initiative to
your district, based on what

I've said today, or how you
should formulate questions to

ask about the validity of the
strategies that they're bringing

in. We, at this point, need to
question everything as we so let

me back up for just a minute. So
this is Saturday math. We do a

once a month Saturday session.
It's completely free. You

register on Eventbrite. Here you
are today. You found us. We

typically focus on improving
number sense. That's our go to

on Saturday, maths, improving
number sense is the number one

thing that we need to do to swim
in this science of math area and

improve memory and achievement.
So we're still on that topic,

but for the rest of this year,
each month that we do Saturday

math, from here until June, not
only are we going to be focusing

on improving number sense each
Saturday, I'm going to share

with you a different strategy, a
different example, a different

implementation facilitation
technique that you can go back

and use right away in your
classroom, and you can use that

strategy or technique for 10
minutes one day and see really

impactful results. But it's not
anything that takes a lot of

time. As a matter of fact, I
don't want it to take a lot of

time. Spaced practice from
cognitive science says or spaced

repetition, I interchange that
space repetition means that we

need repetition over time, but
in very small chunks, with space

in between. What that means is,
if I give you a strategy today,

and you're like, Okay, I'm
taking that strategy to the

limit. The way that you
implement it is, next Tuesday,

you do 10 minutes of it and
that's it. Then a week later,

you do another 10 minutes, and
then two weeks later, you do 20

minutes of it, that is spaced
repetition, that is space

practice. And what that also
involves is that first strategy,

called interleaving.
Interleaving is just out of

context to learning. So if
you're in college and you're

studying for midterms

in the Make It Stick book, in
other research articles and

journals, it is said, if you
have four midterms, don't study

for one midterm at a time study
for 30 minutes one content, 30

minutes a second, content 30
minutes a third, content, 30

minutes a fourth, content, and
then repeat that cycle that is

interleaving in space practice,
because interleaving is out of

context. Switch tasking your
brain, which is necessary for

the muscle to strengthen and
remember more. Think about math

textbooks for a moment. Y'all,
I'm sorry to be the bearer of

bad news today. You think of
chapter one, all similar

concept. Chapter Two, all
similar. What happens is we're

doing the exact opposite of
interleaving in space. Practice.

Do you burn your textbooks in a
bonfire next weekend. Now, now,

especially if they're digital,
that would be it's a new

concept. What we at minds on
math do with schools and

teachers and districts is we
open up the table of contents of

the textbook and we pull nuggets
from each unit and chapter that

become our here's a new word
stimulus. This is a minds on

math word a stimulus is a
trigger that's going to

stimulate mathematical thinking,
reasoning and sense making, but

we pull these right from our
textbook. Now, I have some that

I've generated that are really
good stimulus that are

transferable from one grade
level to a next. And they come

from textbooks. They come from
release test questions. They

come from the A, C, T, they come
from. There are summit minds on

math that are our go tos, couple
dozen of them. But you can also

randomly pull from your
textbook. What we do is we help

teachers and school districts
look at your textbook and

implement it in a different way
that involves interleaving in

space practice that's some of
our structure, just as I'm

glancing at the content or at
the comments as well. It's

interesting you ask this
question, because one of the

schools that I work with is we
have gotten these results in

schools from urban, rural, large
schools, medium schools, small

schools, private schools,
Catholic schools, you name it.

We have the entire sampling. And
the one school district that I

work with right now, I work in
one of their schools, that is a

seven eight building, grade
seven, grade eight. The entire

building is seventh and eighth
graders. However, there's about

600 700 kids in the school. The
majority of these students have

either learning needs, brain
disconnects, special abilities,

so they're being served with
IEPs, and a number of these

students are ELLs or sels or
students as a second language.

Many of the students in this
particular school have come in

not speaking any English, and so
we also, alongside our regular

classroom teachers and
intervention specialists, we

train, and there's other models,
the SIOP model, there are other

trainings and other models that
when you bring the science of

math pieces into it, it just
enhances the other really good

models we're using for those
kids that have English language

disconnects and barriers. So
Great question, great question.

Keep those questions coming in
the comments. I may not answer

them right away, but I'll keep
glancing over and then I'll also

ask us to have some dialog
together today as well. So as we

are thinking about everything
that I've said in this session

so far. Where is your brain
right now? So let me ask it a

different way. What are your
current thoughts?

And I invite you, you don't need
to turn your video on, you don't

need to engage. You do not need
to interact. But I do invite you

to put anything that's swimming
in your brain right now in the

comments or right now just
unmute and give me your wise

words.

Unknown: I am liking your
construct of the interleaving in

the space repetition, because I
all the kids that I do work with

are kids with. Learning
diagnosed learning difficulties.

And the thing that I find the
hardest with the math concepts

is they can't switch from one
thing to the other. If you're

giving them something to do, it
has to all be the same thing,

because their mind can't go back
and forth between two different

things. So to me, to be able to
teach in that way where you're

not keeping them on the same
track over and over again, makes

sense, I think, to make those
connections work in the brain.

Absolutely

Jonily : Good point. And really,
if you think about end of year

exams, final exams, midterm
exams, state assessments.

Problem number one has nothing
to do with problem number two.

So what we're asking kids to do
on an assessment does not match

our day to day instruction, and
it actually doesn't match our

day to day lives, I have to
switch to we as human beings.

Have to switch tasks all day
long, from being the driver of a

car and Okay, so right now my
role as a human is to drive on

the road to get myself to work.
Then I have to switch my brain

from my road rage traffic
incident, and then I have to

start working, but then I get a
text from my kids school, then I

have to jump back into work, but
then I get a call from my boss

about another meeting. We are
setting kids up for failure by

not using this model.

Unknown: I want to hop on just a
second and oh, yes,

Jonily : Sarah, good, yes.

Unknown: I just wanted to first
validate what Kelly said,

because that is pretty big for
you to recognize that it's hard

for your students to go from one
thing to another, and I feel

like it's unnatural for you to
then think about what Jonily

saying and be like, Oh, I should
try to switch back and forth

more. Because what I tend to
hear from teachers who say the

same thing that you did, is that
then I have to keep them in the

same we have to just do this,
and I need to lay it all out for

them, because they they aren't
able to do this or that or

switch focus, whatever the case
may be. And we keep doing the

same thing, but we're also
getting the same results, which

then I also hear in our multi
grade level meetings what you

said earlier, Joni, that that
students aren't remembering from

one unit to another, or one
grade level to another, and

they're like, I know you've seen
this before. I know we did this

before, and why are we having
such a hard time remembering it.

And I just appreciate the
conversation about, like, how

the brain learns what we know
now, and how do we keep pushing

forward to kind of change things
so that we get the results that

that we really want to see.

Jonily : Well, Said, said, other
thoughts.

Cheri Dotterer: Yeah, Habits.
Habits drive our day. 90% of it.

Our brain wants to do automatic
activities. It doesn't want to

think

Jonily : Amen. We

Cheri Dotterer: tend to do what
is automatic, what those

pathways are that we've
developed that are currently

working like in this circular
loop. And if we try to take that

loop and put a little fringe in
it, our brains go, Wait a

minute, confusion. And so we're
looking at it from this so

looking at it from that
perspective, where anytime you

put a little blip in in the
brain, it's going, Daniel, now I

want safety. I'm

Jonily : going to be real for
just a minute. From what I hear,

I'm in dozens and dozens of
schools every year, sometimes

every month I get around. When I
first started teaching in 1999

I'm a secondary math teacher by
trade. I was not going to be a

teacher. I actually have a math
degree. I have a Bachelor of

Science in pure mathematics,
knowing that you can really

understand my disconnect when I
started teaching eighth graders

mathematics with a Bachelor of
Science in mathematics, who

knows more than me, and I would
teach my kids brilliant lessons,

and they would not get it talk
about a personal struggle, and

to have that background that
really set me off on a journey

of I have a degree in
mathematics, and I don't know

any mathematics. Now, I say a
lot of that to just give you a

little more background. But if
I. Go back to Theresa's question

in the comments, what holds
districts back from applying

these techniques when I'm in
dozens and dozens of schools,

because I had my own classroom.
I was in one school district for

15 years, and then I went on
this journey which I had to

branch away from that district
because sample size. I've got to

go out and try these things with
lots of other places. So I've

done that for for the past at
least 12, 1314, years, to see if

it happens everywhere. And what
I hear from teachers is, but we

have to use our textbook. We
have to use it page by page. But

then I talk to their
administrator and their

principal will say that is not
what I told them. They need to

use it as a so everybody's
blaming each other because of

what Cheri said. Nobody wants to
change their habits, so because

they're resisting so much, it's
very difficult to say as a human

being, I know I need to do this
change. It makes complete sense.

And this is all rationally,
subconsciously, I know I need to

make this change. I know it
makes sense. I don't know how to

do it. I don't even know where
to start. It's overwhelming. And

then what comes out of their
mouth is, yep, my principal

says, No, I have to do it. I
have to go page by page. There's

a lot of disconnecting
communication. Now the other

answer to your question,
Theresa, which is why I'm pretty

aggressive today, and I want all
of you to hear me today and stay

connected as the science of math
emerges, whether it's in a year

or in five years, or 15 years or
30 years, at some point, this

recording will be public. This
recording is what we need to

point the fingers to, not
because I'm all that I am and a

bag of chips. No, y'all. I'm a
lot. I'm a lot. Stop it. Jay Z

anywho, not because I'm all
that, but because we need to

begin questioning everything.
Because another answer to your

question, Theresa, is what
dictates what happens in

schools. Oh, I'm really going to
get blasted here is driven by

government and money. I have no
affiliation with the government

and I have no affiliation with
big money business and kickbacks

from any textbook company or
anything. I have no connection

at all. My company is minds on
math. We are a service provider

that consults and coaches to
support school districts with

the materials that they have
with the mandates that are in

place. We're not asking you to
break the rules. We're just

saying you can implement the
rules differently. So what we do

at minds on math is we support
school districts with their

current model, their current
resources, their current

mandates, we ask a lot of
questions to say, okay, is this

one really true? And then we
start to rethink how we deliver

what's being told that we have
to do, thoughts, comments,

questions, go ahead and unmute
if you have any.

Unknown: Think there's also a
fear that teachers have that

especially if you're mathy,
whether you're mathy or not, if

you're mathy, we learned this
way. We were able to do it this

way, and so we think that's the
way math teachers more than any

other specialty in in education,
tend to teach as we were taught.

So it's hard to break away. It's
hard to have to sell it to your

administrator. It's hard to have
to sell it to parents, and we

don't want them to come at us
and say, Why are they learning

three different ways to
subtract? I learned one, and I

got by just fine. So why are
they wasting time? So it's this

fear that we have that if we
break away from the mold, even

though we know in our hearts and
in our heads that it's probably

the best thing to do, because,
again, definition of insanity,

doing the same thing over and
over, and getting and expecting

different results, it just
doesn't happen, so we need to

break away. But it's fearful.
It's very scary. Fear,

Jonily : amen. It's

Unknown: interesting you say
that Cathy, because I literally

had this huge, long discussion
last year with my principal,

particularly about a particular
student. Right? She's like, why

are you teaching them five
different ways to do division?

And I'm like, because that's
what the requirement is, and

that's what they're going to
look at on the testing. When

they see testing, it's going to
get they're going to get hit

with it five different ways. And
every kid doesn't learn it the

same way. And there is more than
one way to do math, and they

should be exposed to all of them
and then pick what works for

them. And she goes, I think one
way is just perfectly fine. And

I'm like, I think that too, but
I don't know. I don't know what

y'all think about that, but I
think they do need to be exposed

to all the different ways so
that if they can figure out what

works for their brain.

Jonily : And Kelly, your next
follow up question for that

person is, how does that relate
to how the brain learns

information? It all has to come
back to the science of learning.

Right now in a few of our
states, we're having this really

large battle and controversy
with science of reading. And I

get it, and I'm not a literacy
person. I'm not going to get

into it. I'm not dying on that
hill. I don't really care,

honestly, to but as I sit back
and watch from an outsider, and

I watch the debates like Kelly,
you're talking about these two

different opinions, two
different views. It's still not

grounded in cognitive science,
the science of reading. I just I

think we need to really question
you guys should question me. You

don't take what I'm saying today
at face value. Please don't.

Please don't you all should
question me. You should question

anyone that comes and says, how
does that relate to how the

brain learns? That's the bottom
line. That's the bottom line.

Now, okay, we can swim in this
for a while, but I had started

something a while ago. I am so
non linear. Look, if any of you

have ADHD students, or you've
met an ADHD student, or you are

ADHD Okay, when Kelly, when you
talked about that before, about

the kids sticking with one
thing, blah, blah, blah, who

thrives the most on interleaving
and space repetition are ADHD

kids. They don't want to stick
with one thing when school

before has ousted our ADHD kids,
because we're trying to get that

square peg in a round hole,
we're trying to change the kid

to focus better when, in all
reality, ADHD humans have the

best focus. Actually, they're
hyper focused, but they're hyper

focused in switch tasking, which
is the way the world works. So

we should actually cater our
instruction and our environments

in our classrooms to the ADHD
brain and train others how to be

able to do this. We're doing the
opposite. We're trying to

conform everyone else to the non
ADHD brain, when really what we

should be doing is embracing the
ADHD brain. I was a very type, a

linear, structured girl. I
followed the rules. I did what I

was told. Give me one example,
I'll do the rest. I went into

teaching. I had my day, I had my
structure. I taught my kids in

that way. Then I realized I was
teaching them nothing. It wasn't

working. Always thought I was
going to be a girl mom going to

dance competitions, having
having my cheerleader following

my steps. Then I had two boys.
Boys are not typically type A,

yeah. So this mama was like,
everything I do in my life works

against everything I do in my
life. So I am no longer

actually, I am so far type A now
that I need to reel it in. I

need to reel it in because,
like, it's like, you can't walk

through my dining room right
now. Have you seen like those

episodes of orders? Anyway?
That's besides the point. Let me

back up for a minute, because my
point is I can't teach now in a

linear way. It's just not in my
nature anymore. When I said to

you what I'm bringing to you
today each Saturday, from now

until June, I'm going to be
bringing you snippets of the

same stuff, but I want to unveil
for you now this year's June

event. If you guys have been
around for a while, if you're

new, then this is new for you
anyway. But if you guys have

been around for a while, you.
Know that every year, annually,

we do a June event, and before
COVID, all of them were in

person, and it was a room tons
of people, all math educators,

administrators, just the whole
thing. It was a whole big one

day party of mathematics with
lots of learning and lots of

networking and lots of
collaborating, and since COVID,

our June events have always been
virtual. They're still great,

not the same flair. Our June
event this year, my friends, is

back to in person, so get your
plane tickets. Get them right

now. Alright, what I'm going to
be doing on Saturday, maths for

free. From now until June, is
little samples of the cognitive

science of math. The June event
is going to be a full day. Bring

your team. Okay, we've got we're
going to be in Grandville, Ohio,

that's close to Newark, Ohio,
very close to Central Ohio in

the States. So you're going to
want to travel for this. We're

going to have a full day on this
topic. You will walk away with

all of the materials, the
audios, the resources, the

worksheets, the lessons, the
slides, everything you need to

support your implementation of
the cognitive science of math in

now, at the bottom of the flyer,
it says, in person, Granville,

Ohio, we have not, uh, finished
our contract with the location,

so it's not in writing, but it's
98% we we literally have to tie

up the loose ends. It's whole
thing. But the event will be

held at the Cheri Valley Lodge.
And I'm not sure if their

address is Granville or Newark.
It doesn't matter. They're right

beside each other, but the Cheri
Valley lodge in licking County,

Ohio, it is a hotel and Event
Center. Oftentimes they'll have

weddings there. They have a
beautiful courtyard, they've got

a pool. They have a two
beautiful living room areas in

the lobby, fireplaces. Not that
in June, we're going to be

sitting around the fire drinking
hot cocoa, but it's a an amazing

event center, and we have as big
of a ballroom as we need to have

based on our registrations, and
it's a full day on everything

I'm teaching you now, we are not
going to go back to what I did

this morning. We are not going
to go back to all of the

convincing and the why and the
data and all of that anyone who

registers will get this
recording, that we will say you

need to preview this before you
come so that you have all of

this information so we don't
have to repeat it on that day.

We want to jump right into the
structure of the solution. We

don't want to massage the
problem all day on this day, so

I put this flyer in the chat,
download it, print it out, make

copies. Email it to people,
share it. You can actually scan

this QR code right now, if you
want to register right now and

jump into it. But I now even my
certified coaches here, we've

got Amy Garrison, give us a
wave. Krista Ewing, give us a

wave. We've got Teresa. Give us
a wave. Cheri, we've already

heard from Sherry, Sherry. Give
us a wave. Even our certified

coaches have not heard this yet.
This is the unveiling for

everybody. This is this year's
June event. We're super excited

about this annual event. What's
not on this flyer, which is also

coming, is that evening, for a
small extra fee, we are going to

have another micro event dinner
for alumni. So anybody that

comes to the June event has also
an option to purchase the two

and a half hour dinner training
for alumni of minds on math.

From the 15 years that we've
been in existence, we've reached

out and surfaced old school
districts and teachers that

we've worked with, and we're
going to continue to do that up

from now until June, but we're
going to have an alumni dinner

training, which is separate from
the day training, so you can

either attend both, or you can
attend one or the other. And

during that alumni training,
we're going to talk about.

Really the evolution of
mathematics, teaching and

learning and where we are now
and the best next steps. So

we're going to really streamline
the whole path of where we've

been, where we are and where
we're going, and then just have

an opportunity to maybe meet
people that you've been in

trainings with, and it's been
years. And so it's just going to

be a nice dinner party,
networking, collaborating,

event, and it'll be that same
evening at the same location. So

I'm very excited today to unveil
that, and I am just thrilled to

bring that to all of you today.
Let's see. I'm going to catch up

on the chat here, and you're
leaving while you're

Cheri Dotterer: doing that. I
just want to say, anybody in

eastern Pennsylvania, Sarah, I
know Theresa is not technically

there, but you have to come
through Pennsylvania. We can all

carpool together.

Jonily : There you go. Look at
that

through this model that includes
interleaving and space practice.

Yes, it doesn't matter if kids
are absent. I could have kids

missing 40 days a year, and
they're going to get exactly

what they need. As a matter of
fact, when I partner with

classrooms, because I'm in
classrooms every day, every

week, when I partner with
classrooms, and it's my

classroom like I'm not the
teacher of record, but the

teacher has agreed to partner
and collaborate with me, and

then I am infused in that
classroom all year, on certain

days, at certain times or
certain parts of the year. I am

never in the same classroom more
than two days a week for 30

minutes each day. So the way
that I plan a year of math now

for any grade level and any
classroom, I plan it so that you

can teach all of your standards
in two days a week, in 30

minutes each of those days for
mastery, and the results that we

get come from that model.
Because a lot of times, if I'm

with a teacher one day a week,
I'm with certain teachers one

day a week, every Wednesday at
the same time, I teach that

teacher's class every single
Wednesday at the same time,

depending on the comfort level
of the teacher, he or she either

tries to replicate what I do the
other days or just says, Look, I

love the one day. Focus on this.
But just for my sanity, Joni,

I've just gotta do my other four
days the way that I do math,

which may not be the model. As a
coach, I've gotta give that

teacher the the flexibility and
autonomy that they're

comfortable with. My chameleon
coach, meaning I change my

color, I change my outcome, I
change my goal, depending on the

teacher that I'm working with,
because the last thing we want

we already have a teacher
shortage. Last thing I want is

to overwhelm a teacher and have
them drive their car off a

cliff. Come on. We've got to
customize this for each we've

gotta differentiate the level of
implementation for each teacher

and as a service provider and
instructional coach, that's what

I do when I go into schools and
I customize the model that

matches the teacher's comfort
level and personality, because

everybody is different, and it's
not fair to dictate that

everybody does The exact same
thing. I have a question, yes

question

Unknown: in your model where
you're doing all the standards

in two days, 30 minutes,
whatever, yep. How does that

work for the kids in the
classroom who are on different

levels? Beautiful.

Jonily : All right. Here we go.
Kelly, are you ready? Kelly, are

you ready to rock and roll? I am
ready. Kelly, I love you. All

right, so here is in the last 30
minutes. Here are the goods.

Okay, here are the goods. Okay,
oh my gosh, there's so many

answers to your question. Okay,
we have the entire model mapped

out. We have everything. We have
the whole course. We have

everything that you can follow
scripted. I am not giving you

everything today. I'm going to
give you one example. What I'm

also going to give you today is
you can actually purchase a

bundle for $40 today. Don't do
it now, because I haven't even

told you what's in it. Don't
just blindly do this. You can

purchase a bundle today for $40
that shows you the exact first

five days of implementation. Not
only. Is it the first five days?

Let me show you what you're
going to get. You're going to

get a link to this Google Drive,
because what we actually have at

one level is called the 15 day
formula. So we actually venture

to say in 15 days, and they
don't have to be consecutive

days. In 15 days you can do
this. So we have a 15 day

formula, then we have the 15 day
formula cycles we create, then a

60 day formula, and then we have
what your question is, Kelly,

that is like, how do you make
this all fit in your whole year,

okay, but that's too much to
answer today. What I'm going to

share with you today is day one.
I'm going to share with you what

one day looks like, and if you
and I'm going to share that

right now for free, but if you
want to purchase the bundle, you

can click on that link, pay the
$40 it's not an automatic

download. You'll get it within
24 hours, but you'll get this

Google link that has audio
lessons of me, yours truly,

teaching day one in a second,
third and seventh grade

classroom. Now there are more
audios than this, but these are

the ones that I literally just
did last week, because I always

like to stay fresh, relevant and
current. Now, if you are a sixth

grade teacher and you're like,
Oh, I'm out, there's nothing for

me. No, you don't understand.
It's the same it's the same

task. It's the same task. If
you're a sixth grade teacher,

listen to all three. If you're a
high school teacher, listen to

all three. Okay, you're also
going to get day two in the

third and the seventh grade
classroom. And also, I'm going

to add this in. I didn't, but
you're also going to get day

three for the seventh grade
classroom. You're also going to

get some additional audio
lessons that are from other days

that are just really good models
of this. You'll get three or

four of those audio lessons.
You're going to get fourth

grade, fifth grade and high
school there, since you don't

have those here, what you're
also going to get are the slide

decks that I'm going to show you
right now, that I'm going to

teach on. So this that I'm
showing you right now, that

you'll get in that bundle is the
first five days of what we call

the 15 day formula. And if I
want all standards to happen all

at once, interleaving space,
practice everything that I've

mentioned. The other thing that
I didn't mention is we have to

boil math. I did mention at the
beginning, we have to boil math

down into the essentials. You
remember my three F's, love me

some F words, factors, function,
fraction. So what we've done is

we've analyzed all the math
standards, preschool through

high school, and we've said
these ones are essential. We've

also done surveys with teachers.
You don't care about all that

boring stuff, but I need you to
trust me that what is selected

here is the most essential, most
important that leverages all

other content. So on day one,
here's what I did on day one.

And this is in January. So on
day one, I showed this to my

second graders, third graders,
seventh graders. Now let me give

you some context. The second
third graders I've been working

with since the beginning of the
year, one of those classes I've

been working with for a couple
years now, the seventh graders I

just met four days ago. This is
a brand new group in a brand new

school that I just started this
model randomly on Wednesday. So

my second graders had never seen
this symbol, and the seventh

graders, I didn't know if they
would have ever seen this symbol

or not. Now, the square root
symbol doesn't really explicitly

state in the standards until
grade eight. First of all,

that's our biggest problem with
deficits in mathematics about

the standards. But don't let me
get on that box right now. So so

don't dismiss this. If you have
a group of kids in fourth grade

and you're like, Okay, I need a
different stimulus, because I

can't show them that. Yeah, no,
you have to trust the system.

Trust the system. You show this
randomly out of context that is

part of interleaving, and you
propose to them to tell you

about what they see. So what I
did in the second grade, third

grade, seventh grade, and you'll
hear this on the audios. If you

purchase the bundle, you'll get
the audios, and you'll hear me

do this, and you'll hear me do
it different ways with different

grade level. That's why you need
to listen to all of them. And

I'll say to them, tell me about
this. Tell me about now, the

kids that I've been working
with, you're going to hear third

graders, and they're going to be
like, that square root, and

you're going to be like, how the
flip do they know that? And what

is she doing to possess these
kids? My third graders are

they're a group that I've worked
with for two years now, so

they're very comfortable with
square root. Okay. Now my second

graders, they were, like,
freaked. Okay, you'll hear in

the second grade audios how I
handle that and then what I

relate it to. My second graders
have done a problem this year

called the pizza problem. A
pizza company makes square

pizzas. Let's make squares. I
give them blocks. They make

squares. They draw squares on
paper. What math questions can

we create? What numbers make
squares? If you purchase the

bundle, you must listen to the
second grade class, and we and

us talking about square roots,
because they are relating this

to Pizza problem, and they're
talking about pizza problem and

numbers make squares. And a
couple of the second graders on

audio, as we were just exploring
and playing and having

conversation, a couple of the
second graders said, I think all

of the even numbers that makes
I'm sorry she's she said, I

think that all numbers that are
even make squares. She created a

conjecture. So we took her
statement. We've got her

statement. We did not prove or
disprove it. I just brought it

to the class and said, Hey guys,
we have this statement. We don't

know if it's true. In math, I
like to play a game called

always, sometimes never. This
could always be true. It could

never be true? It could
sometimes be true, but ally says

that all even numbers can make
squares, and then we didn't

really explore it. It was about
the end of class, but I want you

to listen to that in that second
grade audio, because my second

graders had an advantage. They
had never seen this symbol or

anything, but they have had
experience with the pizza

problem just making squares. So
if you decide you know what,

before I do day one, I want my
kids to play with the square

pizza problem and make squares.
You could do that. Then, when we

say, Okay, tell me about this
thing, I will then explicitly

and directly say to them, this
symbol is called a square root

symbol. You don't need to
remember that. You don't need to

remember it at all. But what it
means is, there's this check

mark, and then this line here
that is a side length of a

square okay, friends, there. We
want to check the side length of

a square. And that's how I talk
through this symbol. We want to

check the side length of this
square, because if this is the

side length of a square, and I
make a square, if I make a

square and I can actually draw a
square over top of this, what

this symbol tells me is that my
square pizza has 50 pieces

inside.

Now, kids, let's make that
square pizza, because the square

root says, What is the side
length of a square pizza with 50

pieces of pizza? So then I give
them grid paper, I give them

blocks. I give them exactly 50
blocks, and we the goal is to

make a square my kindergartners
can do this. My high schoolers

can do this. It is appropriate
and necessary for everyone.

Cheri Dotterer: Generally, I put
the link to the pizza problem

ebook in the chat,

Jonily : fantastic. Hey, we're
just upselling you everything

today. What

Cheri Dotterer: is the pizza
problem? Ebook, it has the first

seven interactions of the pizza
problem that you can do with

kids.

Jonily : I know you all are
like, Oh my gosh, I could go

next week and totally just, if
you told me what to do every

single day, I would just do it.
And that's not the best first

step. Okay, ease into this bad
boy. We do have the program now

Cheri. Could put an Cheri put
the link in the chat. I'm going

to tell you guys to ignore it,
but put the link in the chat for

tier one interventions, because
we do have the entire course the

tasks that we use. Issues boil
down to our Dirty Dozen. There

are 12 tasks. If everyone
preschool through high school

uses these same 12 tasks, that's
it. There's 12 of them. You can

teach all of your standards and
more, and be able to teach all

of your content in 60 days or
less each school year. So this

works very nicely. If you have a
textbook resource that you

guarantee your principal told
you you have to teach every page

of, okay, you can still do that
and this. So if Cheri, if you

put in so you put in the pizza
problem ebook, that's another

little upsell there. Now we do
have the entire course. It's a

year long process. When you
purchase this course, you get

once a month, live training.
Next Saturday is actually our

first of this 12 month process.
If your school district has

money, and you can go back this
week and be like, I want the

entire course, the mere sorry,
the mastery, math method, entire

course, tier one interventions,
is, I can't remember how much

it's like, 1400 and some
dollars, but what that will get

you is we actually launch our
new cohort group next Saturday.

We do a once a month, two and a
half hour live session. If you

can't go, everything's recorded.
It's uploaded into that module.

You get all of the previous
modules. So you get all of the

recordings. You get the entire
course, plus for 12 months and

an entire year. You get a live
training with Cheri and I as

well. Cheri I Cheri by trade,
occupational therapist,

neuroscience expert. So when
Cheri and I collided, I as the

math expert, education expert,
Cheri as the occupational

therapist, neuroscience, brain
based expert, medical expert,

Cheri worked with stroke
victims, so she worked in adult

therapy early in her career, and
then school based therapy,

occupational therapy, the second
half of her career. And when our

worlds collided, my model for
mathematics exploded, because

now it's it was directed to
cognitive science before, but

now it's grounded in
neuroscience. So Cheri and I

partner on a lot of this, and
Cheri and I partner on the tier

one interventions, the mastery
math. So if your school district

has an extra 1400s to drop, you
can start with us next Saturday.

It's a 12 month membership. If
you've got five or more people,

email me, we'll get you a
discount on it. If you want to

bring five or more people, we'll
get you a discount on that for

generally.

Cheri Dotterer: Just so
everybody is aware, I put two

links in the chat underneath the
pizza problem ebook. The reason

for that is the course is you'll
get lifetime access to it, so as

long as we have this platform up
and moving, you will have access

to it. The coaching is a
separate fee. Just logistically

in the system, we had to break
it down and make it a separate

fee. You will see two prices
there. If you want the

conversations with Joni and I
that one time a month that Joni

just talked about, you need to
get the coaching part as well as

the courses themselves. Just it
was a technical thing to create

the bundle. The question, if you
look at the courses, if you just

go on to the all the courses for
disability labs, and you see all

the dark parts to it, all the
dark things with the squares on

it. There's a question there.
How does automaticity and

pattern recognition support?
Answered by the locker problem.

I didn't say it exactly
correctly, but so we've gone

through, and we've analyzed each
one of those tasks that Jonily

talks about, and we've aligned
them with what it means

neurologically and how it that
particular problem fits The math

standards. Joni has taken a lot
of time to identify which math

standards are from K through
12th grade go with every single

one of those problems. The
reason I talk about the locker

problem is because my personal
opinion is it helps OTS

understand the math situations
much better than starting out

with the pizza problem. For you
as math teachers, you need to

start at the pizza problem and
work your way out. So I talk

about the locker problem a lot
more because I'm talking to OTS.

Jonily : Michelle. I love you.
Your comment in here, my

favorite quote from science of
reading you guys, beneficial for

all, essential for some. We've
not ever done that in

mathematics. We've we've tried,
and we've made some transition,

and we've made some gains, but
if we want significant scale,

this is the way to do it. So let
me go back to sharing my screen.

I'm going to share with you a
little more than than this,

because I ended up skipping this
with all three of the levels.

This is in day one, but I
skipped it because I'm I do a

lot of responsive teaching. And
day one after the square root

problem, I decided it was better
to go to a quick dot, because

the square root was a little
intense, especially for my new

group of seventh graders, and I
didn't want to freak them out. I

wanted to get them back to a
little bit of a comfort level

and an access point. So what
happened was, I said, I'm going

to show you a quick dot. A
quick.is I show you for quickly,

for a few seconds, take it away.
I show them this quick dot for

about four seconds, I take it
away. How many dots? Kids love

quick dots. Love, love. Then we
analyze. How were the dots

arranged. How did you see them?
Tell me about this. And then, if

that quick dot was stage three
of a pattern. Tell me about the

pattern. What you're going to
hear on the audio recordings

that I do this purple X is
you're going to hear all of

these math standards come out,
we're going to start to talk

about linear, non linear
function. We're going to start

to talk about chunks versus
overlaps versus dots, how the

stage number relates. We're
going to talk about how to

figure out how many chunks or
dots in the 100th stage. And

then what you're also going to
hear. And then I skipped around,

so you'll have this information
in your slide deck. But I

skipped around, and what I did
was responsively. I went to

Penny jar, which is similar to a
quick dot, but Penny jar is a

little easier to see the pattern
for kids. So we connected. We

made a lot of connections.
There. You'll see that I skipped

around a little bit in my days,
but then when I went back on day

two, boom, we got right back
into the slide deck. Now let me

show you what I did on day two
this okay, if you are not

implementing division in the way
that I'm about to tell you, you

are missing out on a deep
opportunity. Here we go. You

ready for this teaching? You
ready? Kelly,

Cheri Dotterer: that's okay.
Jonily, just before you go on

when you're talking about
division, yeah, I put in the

link to tier one interventions
podcast episode that went out

this week on division. So it's
also in the chat.

Unknown: Cheri, oh my gosh,

awesome, because I'm getting
ready to do division with my

kids next week. See,

Jonily : this is why I need
Cheri, I am a highly functional

adult. Don't get me wrong, I
make a lot of stuff happen

better than most people, but I
do not attend to detail

whatsoever. Cheri, you are so
brilliant. Because yes, Cheri,

How can I forget on the seventh,
the podcast dropped, watch it on

YouTube. Can subscribe, guys,
but I totally forgot that on the

seventh, what I'm about to tell
you right now is an entire

podcast for free. Watch it on
YouTube. Can subscribe. Actually

click that link, that YouTube
link, copy that link, send it to

20 people this weekend, tell
them to watch and listen to this

podcast on YouTube and
subscribe. Come on, do it. We'll

pay you. No, I'm just kidding.
We won't pay you. Okay. Oh, I

forgot to tell you, if you
really do want to jump into the

entire tier one interventions
course next Saturday, and drop

that boatload of money, and you
even want to bring your team and

get a discount, and we can work
with you this week to get it all

situated. And I know POS
purchase orders and everything

take time. So if you get
approval, but you don't have

your purchase order yet, you can
come in and start to join,

because we know that that
process takes time. We'll work

with you on it. But if you sign
up for the $1,400.12 month

bundle, we'll give you your
registration for the June event

for free. Mm. $450 registration
to the June event that I put the

flyer. We'll just add that in.
Included registration for the

June event, absolutely free if
you purchase the today's tier

one intervention bundle.
Alright, what's happening here?

I'm teaching you, I get caught
up. Okay? The pure essence of

division is skip counting.
Division is skip counting. This

division symbol says I'm going
to skip count. I'm going to

divide up my counts into equal
parts. I'm going to skip count

by the second number, zero,
decimal five. I'm going to skip

count by zero, decimal five, to
land on eight. Decimal five,

decimal 511, decimal 522,
decimal five. Okay, so I'm skip

counting by 50 cents. I'm skip
counting by one half. However,

whatever, how many of those skip
counts? Does it take to land on

eight decimal five? This works
with every division problem,

with every type of number. Now
Kelly and Kathy, I'm going to go

back to what you had mentioned
earlier about having kids

exposed to lots of different
strategies. I agree with that,

but there's a more powerful
level. The more powerful level

is a transitional level, meaning
there are certain strategies for

operations that transfer easier
into different number systems.

For example, with division,
there's lots of different ways

to do division. There's the way
that you make division fraction,

or the way that you do groups of
or number in each group, or all

of those strategies are
important, but the transferable

way has the most impact. There's
always one strategy that

transfers for all kids, and
they're always triggered by that

one strategy in a good way, and
that is the bottom line.

Division is skip counting. Now
how they skip count can be

differentiated, but the bottom
line is, division is skip you

start with this number and you
skip count to this number. If I

have six divided by a half, I
skip count by halves to land on

six. Now, if I have 231 divided
by seven, I'll put that in the

chat. 231 divided by seven, same
thing. You skip count by sevens

to land on 231 and what some of
you are going to say is, yeah,

that's not efficient. My goal is
not efficiency. My goal right

now is for kids to just
understand, Oh, crap, that's a

lot of skip counts. That's all I
want them to care about. I don't

even care that they know exactly
how many, because then what I'm

going to do is I'm going to say,
okay, then how can we

efficiently skip count? Gosh,
with seven, if I could get to

70, I could skip count by 70s.
Oh gosh, that gets me to 210,

then I have 21 left over, which
happens to be a multiple of

seven. I'm not facilitating this
very well at all, but the bottom

line is, every time we see
division, it's a skip counting

to land on a number, and that
you needs to be universal, as

we're teaching as the
transferable strategy. Same goes

with subtraction. I won't get
into subtraction. That podcast

will come out next week. Now,
the reason I say that is my

third graders, if you listen to
the third grade audio, day two,

if you purchase the bundle for
$40 and you listen to the third

grade audio. What we were doing
at the third grade level on day

two was we were creating a
square, because we went back to

square pizza, and we were
creating a square, that's a 50

by 50. And we were trying to
figure out how many pieces of

pizza were in that and so I so
they know also that

multiplication is rectangle.
They know when they look at the

square pizza 50 by 50, they know
they're doing the multiplication

problem 50 times 50. They know
they're finding the area of that

square. Now third graders, we
only focus on single digit

multiplication. My third
graders, they don't know double

digit multiplication, but they
can access it because they know

multiplication is rectangle.
When I said to my kids, okay

with 50 times 50, what's my skip
counting number? My skip

counting number is 50, and then
I said, How many times? And

they're like, oh, 50. And my one
little guy, the oh my gosh, the

cutest little, chunkiest fellow
ever said, Yeah, I'm not doing

that. I think you hear him on
the audio saying that, but I

love about what he said was, and
I had him say it to the whole

class. I said, I love that you
said that, Dylan, because here's

why, because you have the
concept that skip counting by

5050, times is not worth your
time right now. That is a

mathematical understanding that
you can't teach and you can

facilitate it. You can ground
kids in experiences where

they're going to refuse to do it
because they know it's too many

skip counts, then the point
becomes but we still have to

figure out how many pieces of
pizza. So how can we do it more

efficiently than skip counting
by 5050, times? And then we

don't have to answer that
question, but I just want kids

to know that there is a more
efficient way to do it. We're

just not going to do it today.
But then I have kids like skip

counting by 50, because they
want to know there's no harm in

that. What's the harm in kids
skip counting by 50 if they want

to. That gives you a little
glimpse of part of one of the

models, and if you get the
bundle, you'll get the audio

recordings for the first two
days. I need to add in day three

for seventh grade, because it
was actually really good. I want

you guys to have it, and then
you'll get day four and five.

Also, you won't get the audios
for those, but you'll get the

slide decks for day four and
five so that you can see the

other tasks and stimulus. But if
we go back to where we started

today, the science of math is
coming. It's going to be

presented to you by either some
someone that has no idea about

being in a classroom with
children, or it's going to come

to you from somebody that has no
idea the science behind how the

brain learns. And this is going
to be uncomfortable, because

those people might be from a big
company or corporation that's

going to try to convince you
because they're good. They've

been trained in sales and not
neuroscience. Don't let them

fool you,

or the government is going to
make expectations about the

science of math, and obviously
we can't change that I used to

think my purpose here is to
change the system. Yeah, that's

never going to happen. I get I
gave up on that years ago. My

purpose here is to take whatever
mandates come to us and

manipulate the implementation so
that we're still covering the

mandate, but we're doing it
grounded in the science of

learning model that I've talked
about today. It's coming. How

are we going to react to it? I
do have a few minutes to stay

on. Today, I am going to
formally close us out for those

of you that need to leave. So
don't feel bad about jumping

off. The training is done. Thank
you for coming. Look for in

about a week for the
registration for next month,

February, Saturday, math on
Eventbrite. Follow minds on math

on Eventbrite, don't forget to
save all of these links here in

the comments, because you can
save the chat right now, or you

can copy and paste all of those
links in the comments to a Word

document or a Google document.
Have all of the links, even if

you don't click to purchase. I
want you to have all of them,

because these are special links
for today's session, and

although they will continue to
work over the next two months,

they won't be necessarily re
advertised, and especially at

the same price. So even if you
don't purchase anything today,

if you have the link at the
price today, and you've saved

that and you have it in a file,
and you can click on it, you can

always purchase at today's
price, today or like in the

coming months. So save the chat
or copy and paste all of those

links that Cheri and I put in
from today. Go back and spread

the word. Start listening to the
tier one and. Inventions,

podcast on YouTube and
subscribe. And subscribe is what

is most important for us right
now on YouTube, so and comments

and comments and this is just
selfishly. This has nothing to

do with your growth and your
professional learning.

Selfishly, for Cheri and I, so
that we can become the go to

experts. If you want us to
become the go to experts.

Selfishly, for Cheri and I, you
must go to YouTube, tier one.

Interventions podcast at YouTube
search tier one. Interventions

podcast, like and subscribe and
comment. And if you can do that

and get 20 others to do that,
we're totally lying right now.

Thanks all for coming. If you
gotta jump, I'm going to pause

for a moment, and then I can
I've got about another 10

minutes. I can hang on for
questions and comments. But this

was Saturday math brought to you
by minds on math and focused on

the science of math. And we hope
to see you in February. Bye,

everybody's asking

Cheri Dotterer: how to save the
chat. If you go up to the three

dots up next, January, 2025
click on that, it'll open a

thing that says, Save chat.
Hopefully that if you're not on

your phone, it makes it much
easier.

Jonily : If you can't save the
chat and you're having trouble,

email me and just say, Hey, can
you send me the chat and I'll

send you the PDF of it.

Cheri Dotterer: I put just a
summary of what's happening in

the next week, of how to see us
live. Free event on january 15,

paid event on january 18.
There's the link for tier one

interventions podcast. Thank
you. Alexa, thank you, Paula,

Jonily : hey, you're welcome.
You're welcome. Lots of thank

yous in the chat. You're
welcome, everybody.