Rethinking Math Education part 1: S2 E24

Speaker 4: Hey everybody!

Welcome to Tier 1 Interventions,
where we work on helping you

gain the core in your classroom.

I am Cheri Dotterer, your classroom coach.

That's Cheri with a C
and Dot with a stutter.

I'm here today with Jonily Zupancic,
your instructional coach on mathematics.

And we are here to help learn, help
you learn how to deliver your math

instruction in a very unique way.

Today we are going to talk
about the pain problem.

Jonily

Speaker 6: get us started!

Hey everybody.

I'm Jay-Z.

Jay-Z in the house, Jonily Zupancic and
Tier one Interventions is, as Cheri said,

strengthening your core regular classroom.

This is for specifically the
classroom teacher, partnering with the

intervention specialist, instructional
coach, curriculum leader, principal.

Special Service Provider, Occupational
Therapist, Speech Therapist.

How can kids get exactly what they need in
the Tier 1 Core Regular General Classroom?

Too often we have kids leaving the
room to be pulled out for small

group Tier 2 or Tier 3 intervention.

By today, in 2025, The amount of
pullout that is needed or necessary,

so to speak, is astronomical.

We need to either avoid or severely reduce
the need to pull students out of the

Tier 1 Regular Core General Classroom.

The strategy for doing this
is strengthening the core.

We must unlearn, relearn, and rethink
how we operate in the regular classroom.

How instruction is presented and
delivered so that kids, all kids,

regardless of disability, ability,
any type of spectrum, neurodiversity,

Neurodivergence, whatever students are
dealing with, internally or externally,

public, private, and any school should
be able to meet their needs in the

Tier 1 Regular General Core Classroom.

We can do this with Tier 1
Interventions Mathematics, Mastery

Math, based on 12 reference tasks.

Reference tasks are such that
they are presented, the same

dirty dozen, to students.

Every single year, the exact same
tasks from preschool through high

school, they are presented multi
times a year, and every year, and

the complexity increases over time.

These tasks are sensory based,
multi sensory, neuroscience,

cognitively science, strategized.

To help teachers and specialists as
well as support specialists and school

leaders create learning environments and
experiences in the regular classroom.

I know that's a long introduction, but
as we have been presenting each module

of tier 1 interventions, oftentimes
we jump right into the content and

I want to make sure that we review.

And restate and make
known what our purpose is.

And our purpose is for all students
to get exactly what they need in the

regular classroom so that we can.

Minimize the number of times and
the number of students that are

pulled from the regular classroom.

Basically, we need to reinvent education.

We are going to look at a
few different parts today.

At a few different

Today I'm going to back up because
although our reference task today

is the paint problem is not
about the paint problem at all.

We are going to break down today's
module into What is the most

essential concept for math learning?

Because the paint problem is a vehicle
to get to that most essential concept.

That's the first thing we're going to
talk about is the most essential concept.

If students just knew this math
content piece, They could do

almost anything mathematically.

And this essential concept is in the
standards subtly, not explicitly,

from preschool through high school.

Our first part today, and to launch
into that, I'm going to say part one

is looking at the essential standard.

What are the essential standards for math?

And then we're going to talk about how
the paint problem facilitates that.

Big part two are direct service providers.

At one point in this session
today, I'm going to say part two.

How do we meet students functional needs?

What are the most important functional
needs that kids have that we can

bring into the regular core classroom?

Because what benefits, what is
necessary for some, benefits all.

Math essentials.

Special Service Essentials, Functional
Essentials, Non Academic Essentials.

And then finally, we are going to
unpack the paint problem mathematically.

I'm going to write that down because I
want to keep track of our checklist today.

And I'm going to write this on the top
of here because this is just going to be

our, like, when we go back to this, I will
section this into Part 1, Part 2, Part 3.

Part one today, math essentials,

and actually there's just one essential.

That's it.

There's only one thing.

What's the one thing?

There was a movie with Billy Crystal.

The name has slipped me.

We'll think of it, but the premise is.

The idea is he's trying to
search for the one thing.

What makes humans happy?

What's the one thing?

Because I want, he goes on this
journey to find this one thing.

And it's the secret of happiness.

What he finds out in the end is it's not
as profound as what he originally thought.

And he also found out That,
City Slickers, thank you.

City Slickers.

He also found out that the one thing
may be slightly different for others.

In mathematics, there is a one thing.

There's a one thing and
it's not as profound as what

you think it's going to be.

I'm gonna say it and you're gonna
be like, that can't be the one

thing, that doesn't even make sense.

But also paralleling the movie.

That one thing looks different
at every grade level.

So what we're going to unpack today is
the one math essential, and then how

that progresses through the grades.

What does that look like at first grade?

What does it look like at fourth grade?

What does it look like at seventh grade?

What does it look like
in tenth grade geometry?

Because what we're missing in
schools mathematically is a

progression of experiences.

That kids can build
upon the previous year.

Now we think we're doing that.

We think we're doing that because the
fourth grade teacher will say you guys,

I know you learned this last year.

It's not about the content and
the learning, it's about the

experiences they were engaged in.

And that's the pure
essence of reference tasks.

We're going to break down the essential,

but it's not always about the
math in the math classroom.

Now, secondary teachers, hear me out.

I'm going to pick on you for a minute
because I am 712 secondary certified.

I am one of you.

We have to be humbled.

We do not just teach mathematics.

We teach life and functionality.

And through that, mathematics evolves.

Because mathematics is thinking,
it's reasoning, it's sense making.

Mathematics is a training
and exercising of the mind.

Mathematics!

is how we start to think logically,
conceptually, contextually, and then we

use those skills to our advantage in life.

The second part of today is
going to be the non academic.

The functional and we have two of our
amazing experts here today, Cheri and

Teresa from the medical world, from the
occupational therapy world that are going

to be able to give us insight on what
some of these key functionalities are.

What are these subtle things that
we can teach that are going to help

our human beings in our classrooms?

Function and live life better because we
as the adults in the room have control

over doing that through our content
and not just through the math content.

We're going to talk about through
the math content specifically

with Tier 1 interventions, but
not just through the math content.

We could do this through phys ed, through
the arts, science, social studies.

And then Part 3 today is
unpacking the reference task.

The paint problem and referring
to how it relates to our academic

and non academic standards.

Now, in addition to that, in addition
to that, there are 4 questions that

we always like to answer, but our
session today is not going to be

broken down into these 4 parts.

I'm going to put the 4 questions that we.

Answer through this, like what's our why?

Like, why do we care about this?

I'm going to put that off to the
side because other modules have

been structured in that format.

But today we're just going to keep
those four things in mind as we

go through each of these parts.

Each of these parts will connect.

To these other structures and
one is how do we and I'll call

this a how do we increase focus
and engagement in the classroom.

Because we talk in each module about
how reference tasks do all 4 of

these things that I'm going to list
and then B, how do we individualize?

With one lesson, less prep
and less stress for the adult.

That's the key.

We all know ways of individualizing
that take 17 hours to plan.

No, we want to minimize the planning
time, prep time, and stress time,

and be able to do one lesson for an
entire group of all ability levels.

And be able to individualize this.

The third piece is, How do
we make math accessible?

This is why I don't write these because
I don't know how to spell accessible.

I think that's correct,
but chat me if not.

And we cannot make math
accessible by stripping the

complexity and simplifying it.

Because that's what we do.

And it's not working.

How do we increase the complexity and
rigor of mathematics, even for our most

struggling student, but also increase
the accessibility at the same time?

These are outcomes that we
want from Tier 1 interventions.

techniques.

And then finally, how do we improve
memory and retention of content?

Here are all of the pieces that if you
go back and watch any other module in

Tier 1 Interventions Level 1, Year 1,
different pieces of this are focused

on depending on the reference task.

There's our overview, and part
one, right now, part one, is what

are the math power standards.

And I'm gonna make that
singular and not plural.

What is the standard, the concept,
the content piece that if I had to

pick just one to teach at every grade
level, this would not only build fact

fluency, automaticity, improved number
sense, it would do everything that

we want kids to have mathematically.

In the chat right now, go
ahead and type what you think.

The one thing is.

One.

One concept.

That's it.

See, you all are well versed.

Counting and skip counting
is a part of the concept.

Yes.

Relationships.

What is the big math concept
that means relationships?

There's a math term for
understanding relationships.

Mathematically.

Function.

Good.

Okay.

There is one important concept that is
completely indirectly related to function,

but is actually more important than
function, and it's the pure essence.

Of counting, Natalie,

the only topic that we ever
need to teach to improve all

mathematical understanding is rate.

But here's where we argue with
ourselves and maybe our admin

and maybe our curriculum people.

This part one of this session is
essential for all stakeholders

in a school or district to hear.

Because you're not going to see the word
rate in a kindergarten set of standards.

What you will see in the kindergarten
standards is, we want kids to be able

to count to a certain number by ones.

10. Maybe it's to 100, maybe it's to 120.

Some states in the United States
have varied what that final

number is for kindergarten.

Doesn't matter.

Me, I like 120 for all kids.

And I like 120 charts.

The other thing that I want to mention
today is when I said the paint problem

is not about the paint problem, Today is
going to be a combination and connection

of a few different reference tasks.

And the reason I say that is because
when you listen to this podcast or

you're listening to this recording in
this module of Tier 1 Interventions,

I'm going to refer you back to some
other podcasts and some other modules

that you can get the connections.

To rate and the 1st 1 is
the module or any podcast.

that has anything to do with 120 chart.

I was in a kindergarten
classroom yesterday.

I had never met these kids.

It was in a high poverty building and it
was absolutely a beautiful experience.

I walk in and I knew in my head I
had four things, four reference tasks

that I wanted to do in 35 minutes with
kindergartners that I had never met.

In a high poverty school
with very high needs.

I audio taped this and in tier
one interventions on this module.

If you are a member, I will put
this kindergarten audio and it will

be named kindergarten multitask.

And rate you will have
access to that audio.

I just recorded it yesterday,
it's not been uploaded anywhere

before the four stimulations experiences.

I wanted kids to have.

were quick dots, fact based quick dots.

There are two types of quick dots,
fact based and function based.

Fact

based, and I'm going to show you
right now the quick dot that I gave.

Fact based is when each stage of the
quick dot has the same number of dots.

Each chunk of the quick dot
has the same number of dots.

This was the quick dot, and this will
be uploaded into this module as well.

For those of you that are listening to the
podcast and not watching, there are seven

chunks, and each chunk is a rectangle
of eight dots, so two by four arrays.

with eight dots each.

This is a quick dot fact.

This is to build fact fluency.

This is to build single digit
multiplication automaticity.

A quick dot is, I show this to the
kinders for a few seconds, I take it

away, I have them raise their hands
and tell me how many dots they see, and

then how did they see the dots arranged.

That is the one experience
I wanted kids to have.

Now because Each of these chunks,
each of these stages, have the

same exact number of dots, 8.

The goal was to skip count by 8.

We were at carpet, and we were just
having conversations about this.

What do you see?

What do you notice?

I show them the dots again,
and I have kids talk about what

they see and what they notice.

What do they know about 8?

How much is 1 8?

How much are 2 8s?

And then we practice a technique
called whisper counting.

Whisper counting helps toddlers, primary
school kiddos, How to skip count by

numbers that we would typically not have
them skip count by like the number eight.

At carpet, we started learning
this whisper counting technique.

We point to each dot in one
chunk and we whisper two, three,

four, five, six, seven, eight.

When we get to the final dot in
that chunk, that's our loud number.

That's how many dots were in that chunk.

Then I say to students,
how much is one eight?

Eight.

And that's a phrase I want kids to know.

Because this is what function is.

One eighth is eight.

Then how much are a hundred eighths?

Do you see?

That jump,

that efficient counting, that
explicit rule is all about function.

Being able to figure out what the explicit
rule is to be able to do higher numbers.

with a certain pattern.

Then we say, okay, what
was our loud number?

Eight.

Let's whisper again.

Nine, ten, eleven, twelve, thirteen,
fourteen, fifteen, sixteen.

Sixteen is our loud number.

How much are two eights?

Sixteen.

Then we whisper count.

And then I say to students, I
wonder how much four eights are.

I had never met these kids.

They had never done this before.

They'd never done a quick dot.

They'd never done a whisper counting.

And right away, I release them
to go back to their seats.

I give them a 120 chart
that I'm going to show you

a visual of right now.

There are many adaptations.

Cheri, I want you to talk about
this when we get to the function.

Oh, talk about, let's talk about it now.

She's got it right there.

This girl is on.

This is why she's our brain boss, okay?

This is why Cheri is our classroom
coach, brain boss, partner in crime.

You name it, the girl's got it all.

I like four 120 charts on a
sheet, and my kinders didn't

have too much trouble with this.

But, an adaptation when we start utilizing
the 120 chart for other exercises.

Cheri has taken the 120
chart where I put 4 on an 8.

8. 5 by 11 sheet, and she has
enlarged one 120 chart to put on two

sheets.

Cheri, talk to

Speaker 6: us a little bit about
this adaptation, which these are

the things we're going to talk to
you about in part two of today,

which is some of those adaptations
and functionalities, non academic

things that we can support kids with.

Cheri, tell us about what you did here.

Speaker 4: How simple.

I used Canva.

I just took the image.

of a 120 chart, not a PDF.

I took an image of a 120 chart
and I grew it to fit on the 8.

5 by 11 and then took another page
and moved the 120 chart to the other

side and put the rest of the 120
chart on a second sheet of paper in

Canva and then taped them together.

The other thing I did was created 1, 1
20 chart on four pieces of paper because

Amy, one of the teachers we have in the
classroom today had a, has a student who

was had difficulty, I can get the words
out, who has had difficulty with his

vision and needed things even bigger.

One of the adaptations that you can do for
the one 20 chart is in making it bigger.

I won't know if I'd go
much smaller than what.

Jonily has there.

Agreed.

But one of the things that I am working
with, I have a student that I'm tutoring

right now in mathematics, and one of
the things that we have been talking

about is taking the four on one page,
but she wanted the full size, so

she's using full size one 20 chart.

And she's highlighting her multiplication
tables, and then we are laminating

them so that she has them available.

And because they're full size, as
she's having to struggle with being

able to see the smaller Smaller ones.

It had, we've been working on that
and trying to link that back to what

it looks like when she has a problem
in front of her in the classroom.

Mom tells me that she is starting to use
the 120 chart in her digital math program.

It is, she is starting to carry
it over into other instruction.

Speaker 6: This is beautiful
because if you are aware of

Hattie's research, visible learning,
it's not the same as visual.

We're not talking about visual here.

Visible learning is understanding
as the instructor or facilitator.

What the student is thinking
and what their brain is doing.

It's a instructional technique, a
facilitation act technique that extracts

student perspective, which we talk
about all the time in Minds on Math,

our achievement formula, our first
component is what's called stimulus.

A stimulus, and when we prompt
it, we say, tell me about this.

What do you see?

What do you notice?

Just like I did with the quick dots.

When we do that.

Our goal is to extract student
perspective and extract student thinking

so that we then can help them apply.

And what Hattie says in his
research is we need techniques and

strategies that are transferable.

If we have instructional facilitation
strategies that allow students

to transfer that experience.

Just like Cheri said, this child
now is using the 120 chart from math

tutoring session, but applying it,
transferring that strategy and technique.

to her digital program.

So when we can get transfer of
knowledge, that is the highest

level of learning and understanding.

And that's what we want
students to be able to do.

Transfer of knowledge does not happen
when we teach algorithms and procedures.

I'm not saying don't teach
algorithms and procedures.

We need to teach
algorithms and procedures.

But just understand that is not going
to elevate understanding of number.

It's not going to elevate number sense.

It's not going to
elevate math achievement.

It's not going to increase thinking,
reasoning, and sensemaking.

And it's definitely not going
to create a transfer knowledge

application opportunity.

So just keep those in mind,
depending on what your goals are.

The other reason I like what Cheri said
about the much larger spaces is, then we

have room to put a physical manipulative.

I like cubes.

I like block cubes.

Those are one of my favorites.

Don't like the teddy bear.

The teddy bear has no
mathematical structure.

I'm not in love with teddy
bears as manipulatives.

I'm in love with blocks as manipulatives
because we can transfer the block to a

lot of other math concepts and skills.

That comes back to that
transfer technique.

What I also like about what Cheri
said is, Now, one of the reasons

that Cheri actually enlarged the 120
chart is another one of our reference

tasks and another one of our tier one
interventions modules is locker problem.

So in the locker problem, we use a
good solving problem solving strategy.

Use a smaller number.

So a locker problem.

We have 100 students in 100 lockers
and they go through and play this game.

Through this problem, we want to
generalize patterns with a smaller number.

So we make a game board with 24 lockers.

But if you want to extend that and look
at the complexity of what happens in

the phenomenon mathematically of the
locker problem, Cheri's I want to look

at the 1 20 chart and I want to use.

Pieces that are TR two color and she has
purple on one side, white on the other,

and she's gonna show that to us right now.

She actually took the whole one 20 chart
and she's acting out locker problem,

not with the game board of 24 lockers.

Now that.

that we've had a lot of
interaction with 24 lockers.

What if we have 100 or 120 lockers?

We can do the same repeated reasoning.

We can do the same iterations, but now
we need the chart to be bigger to include

more numbers so that we can see how
that experience, how that locker problem

creates this natural math phenomenon.

So the point of all this is that We have
in tier one interventions, not only the

answers to all of your math troubles,
but we also provide the adaptations so

that all students can be successful.

That's the accessibility piece.

We want to continue to increase
the rigor and complexity, but we

want to make it accessible for all
students, all levels, all ability

levels, all of all functional levels.

Even our most struggling students,
but you can also see how this one

lesson can enhance and stimulate our
most gifted student, which oftentimes

they get shortchanged because
we're trying to keep everyone up.

They never get as far as
the gifted child's thinking.

And so the gifted child never
gets to go above and beyond.

But with reference tasks and
our instructional delivery

strategy, we're able to do that.

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