Changing Perceptions of Math: Sean Briel & Daniel Nash at TEDxHonolulu

Sean Briel & Daniel Nash team up to reshape the very perceptions of how people learn by reshaping the way Math is learned and taught.

SB: Welcome. Hello everyone.
Today Dan and I are going to be ...

– let's see if we can get this presentation going...
all right, all right, cool! Ha, ha ... –

So, above all welcome. Today we're going to
be talking to you guys about

changing perceptions, motivation,
students, efficiency, effectiveness

DN: Whoa, whoa, whoa, Sean!
SB: What?

DN: Do you have any idea how many words
you just put in the audience...?

SB: Yeah! Oh!

DN: Let's clear things up a little bit.

What are the main ideas
we're going to be talking about today?

SB: OK, all right, fair enough.

How about perceptions, students,
math, themselves...

Yeah, something like that.
DN: Ok, that clears things [up] a little bit better.

But can you organise the ideas

so it is perfectly clear to the audience
what we are talking about?

SB: Ok, I'll take care of that. (Laughter)
Sorry, so, I get a little excited.

Talk about changing perceptions of math
by teaching students to teach themselves.

DN: All right, here we go! Much better.
So, as our title screen just showed you,

how we organise words affects
how we understand

the very meaning those words
are meant to convey.

So if we don't take the time
to organise words,

we can be very overwhelmed and confused

by something like this, instead of having...

yeah, that's overwhelming and confusing.

Instead of having something clear
and understandable, like this.

So the next thing we want to talk to you about,

is how prior organisation of words

can affect how we understand
and perceive new words

and the ideas those words
are supposed to represent. So...

SB: Ok, all right, so you know
what I want to say?

Did I tell you that Marcy
and I are getting a dog?

DN: Yeah, I don't think this is the proper time
to talk about that!

SB: We got the time!
DN: But I guess we... (Laughter)

Actually, this is kind of embarrassing,
but I don't really know what a dog is,

er, can you explain?

SB: Dan you're a high-school teacher
and you don't know what a dog is?

DN: Hopefully none of our students
are watching. (Laughter)

SB: Alright. I mean, you guys,
stay with me on this.

A dog is, you know, four legs,
has a head, furry and can lie down.

I mean we all agree, right?
That's what a dog is. Dan?

DN : Don't you guys already have
already one of those things?

SB: Oh my, Dan!
You're blowing this presentation, bud!

Come on, man, let's get it together.

What do you think, can you draw a picture
for this people of what you think it is?

DN: this.. ugly table with a '70's shag cloth,

in the middle of you guys' living room,
that's a dog, right?

SB: Dan! How can you confuse four legs..?
I.. You know ... I don't even..

This is a dog, Dan. It's got four legs,
it barks, it goes woof...

DN: Aw! I've seen one of those before.

SB: All right. Dan you've got
to fix it for these people!

They.. you got it.
How did you confuse a dog into a table?

DN: Ok, well, you said four legs.
Furniture has four legs,

... lies down, folding table, OK?

Furry, '70s shag carpet,
you can put that on a table,

Clearly that's a dog, Sean.
That's a dog!

SB: Dan, I'm actually not...
I'm not even mad, I'm actually impressed.

How you did that is beyond me.

Four legs: How about an animal?
Dan, did you stop to think about that?

Furry, lies down... THAT is a dog, Dan!

OK? Got it? All right! So, what this is meant
to illustrate is dog vs. table.

This idea is, schema is the very ways
we organise words in our brain,

especially the organization of prior words
affects how we perceive new words.

in the case of math, where it's even more abstract,
this gets challenging.

You know, in this case I could show
a picture to Dan and be like,

"Oh this is a dog, got it?" All right!
But how about in math?

where we're like,
"Ok, hey, come here, quadratic formula!

Come on kids, pet the quadratic formula!"

Or, "Did you see that pesky quadratic formula
running across the street yesterday?"

I didn't think so. All right?
As ideas get more abstract,

we ourselves need more set
and firm schemas.

Dan's going to talk a little bit
about how that looks in math.

DN: So, based on dog vs. table,

what is the key component to correctly
perceiving and learning mathematics?

Developing proficiency with number use
seems pretty important,

memorization of processes
seems pretty important,

cognitive organization of math words
seems pretty important,

but Sean, I realize you didn't know
what I put in D there.

I'm sure the entire audience wants
to talk about spaceships. So...

SB: Don't... Just stop!
He's going to try to show you

through a schema how
he can connect perceiving and learning

all the way to spaceships
and now you're gonna let him do it.

DN : All right, all right!
SB: Dan please, let's get to the point.

DN: Ok. So the real answer's actually C.

Based on this, Sean and I wondered:

what are the math words
that students actually have to organise

as they're going through their education?

Well, what we did is we went through
the common core standards.

Now if you're not familiar with them,
these are a set of standards

that are sweeping across
the entire United States,

almost every state has begun
adopting them in some way.

These are the words that a kindergartener
is expected to know,

at least to have in their vocabulary
based on the concepts in those standards.

OK? Then we move on to first grade.
Now we realize you'll never

be able to read all these,
but I just want you to get the big picture.

OK? Let me move on to second grade.

And we're just going to jump up
to sixth grade for you.

You'll notice a similarity
between this and our title screen.

It's pretty overwhelming as you can see,
why some students

get to sixth grade math and go,
"I'm done, can't do this anymore."

So, what we wondered was,
is it possible to organise these?

Well, not only is it possible,
we've actually done it.

So, instead of having a confusing
mess of words,

you can cognitively organise them
based on definition.

Right, so when a student is
on the first grade

instead of having a bunch
of words strewing around,

they start connecting them
to everything else.

Now we're going to jump up to sixth grade again
for the second time,

now we realize you can't see
everything on there.

However, things are now organised.
So they can perceive and understand

all this information in a proper manner.

The observation that Sean
and I had from this was:

well, what if they don't know
any of these words?

what if they don't have one
of these connections?

What if one of these connections is connected
in a not-so-efficient way?

So, what we thought was,
not only will it affect their success,

but if they're overwhelmed
by all this information,

it's going to affect their confidence
in mathematics

and it's going to affect their motivation
to even try mathematics.

So Sean, do you want to give a little context to that ?

SB: Yes, I will try to give you guys some context.

So stop, think for a moment:

what is an activity, a job or an interest
that you are personally doing right now

that you feel very confident in?
I would imagine that if I asked you to list

a whole series of words
that were related to that,

you could give me a long list,

you could even describe to me
how they were connected.

Imagine when you first started that.
What if Dan and myself gave you a map?

What if we showed you
how those words were connected?

How would that have affected your perceptions?

How would that have affected your motivation?

How much quicker could you've gotten
to the level you're at now?

With that, we're going to show you
how this works in our class:

all critical terms plus organization
leads to effective perceptions

which help to drive
motivation and success.

DN: So, as Sean just said,
we are going to talk about

how we created an experience
in our classrooms

where students can now cognitively
organise information,

effectively perceive information

and have an overall clear
understanding of mathematics.

Now, just like this basic outline here,

what we do is we get our students to move
from something that's scary and messy

– this is like kindergarten information –

into something that's organised
and understandable like this.

So, as you said before,
we start off with vocabulary.

Ok, we'll show just a few terms up here,
in just a moment,

that you've probably seen before.

We're not going to test you, don't worry!

You're after TEDxHonolulu stuff,
it's not going to be dependent on passing a test,

but from gaining to go through and build
their vocabulary in literacy with these,

we then have them start mapping them out,
based on definition.

In kindergarten,
the starting point is normally numbers.

And then from there,
we have our students go through

word by word and look at the definition,

and you can actually see connections
in those definitions:

Whole Numbers, Counting, Place Values,
all have numbers in the definitions.

SB: So, you can start to do as you saw
with operations as expressions,

– I'll just go back real quick –
kinda show you what that looks like.

We can even start to hit them
with more terms

and they start to know where to place them.

What we've categorized
in this slide is a tipping point:

you can see that as you get more and more,
it starts to become more and more clear,

without even showing them math,
how these ideas relate.

The best part is that they can do this
on their very own.

Dan now is going to show you what it looks like
when we show them math content.

DN: So, notice, we haven't done
any math problems yet.

Our students now
have a big picture understanding

of how everything is related.
They are not quite as overwelmed

when we start presenting them with activities,
labs, examples that they go through on their own.

So, we do a thing in our class where essentially

when I go through this content,
they make a tweet.

Now if you're not familiar with Twitter,
and hopefully all of you are now,

essentially it's just a quick
little visual and a phrase

that attaches to that word.

So for example with numbers,
they might say something like,

"How many? Give a few examples."
OK?

And then they run the whole numbers
and an observation they might make is,

"Zero, count up by one."
I give a quick little example.

This continues on and on,
but we realize sometimes

two things can come up at once.

Now that they have a structure in place,

they can now handle working with multiple ideas
at the same time,

and know how this content fits together
to create an overall big picture understanding.

So, we move from something
that's kinda scary like this

into something that's organised
and makes sense like this.

Now some of the effects
this has had on our students is,

they now have this perception
in their mind of –

"Ok, well, if I see this word, I know
what content's connected to it from my tweet.

If I see this word I know
what other words it's connected to

and the content that's connected to those,

instead of this disorganised mess
that's in their heads sometimes

when they are doing things high-pressured
like taking a test,

ACT, PSAT, things like that.

So, Sean is going to show us
some more results.

SB: So, what does this afford us
in our classroom?

As far as performance goes,
we've completely and entirely

started getting our students
to teach themselves, OK?

Stop and think about that:
actually teaching themselves,

that can go on to any other class.
So we've created a lasting student achievement,

regardless of whether they connect
with the next year's or following years' teacher

or then they go off to college
where it's lecture blaze, hands-on –

they can actually have the confidence
to teach themselves.

The most amazing part is: we've managed
to do this without lecturing.

That's right!
Not one day of standing up like this

towards you guys right now, lecturing.

In fact, if we had it our ways,
we would have just given you

the list of words of how to do this
and we would've had you start building the map, all right?

But for you non-teachers,
our students come in every day.

They sit down, they start working
in collaborative groups,

they're on their own and they start
working with the words.

They make their own connections
and they start to start problem solving

creatively, entirely on their own!

So Dan's going to share a little with you
how this has affected his algebra class.

DN: So, this kind of the mess
I can hear of teaching:

I'm an emergency hire, which means
I've no formal teacher training whatsoever.

Last year in my freshman algebra class,
my passing rate was only 52%.

Now, after implementing this,

I have moved from a 52% passing rate
all the way up to an 86% passing rate.

(Cheers)
(Applause)

(Laughter)

SB: I've been teaching geometry now
for five years.

I originally came over with Teach for America,

for those of you that are familiar with that,

I came over in 2006,
the first quarter I actually came to Hawaii.

I was placed to Waipahu,
I did my two years, I stayed longer

'cause I enjoy the students here
in Hawaii so much.

They're great kids out here!

For those of you who haven't had an opportunity
to be in a classroom,

they're amazing!

I've never been able to break 60% pass rate
in my geometry class,

which has driven me nuts!
Last year I actually almost quit!

I had applied, took my LSAT,
I was looking at law-school and then

Dan and I started thinking
about these ideas

and I've been able to move
them from 58 to 89%.

(Cheers)
(Applause)

DN: So, the next class we're going to talk
to you about is statistics and probability.

It's a new course at the school
that we started,

so there is no previous statistics on it.

However, the book that we're using
is a college textbook,

the students are currently
teaching themselves college material,

and I have all of my students passing
my class right now.

Dramatic!
(Applause)

The next group, I'm most proud of,
as for the reason I joined Teach For America,

for those of you who're not familiar with them,

you leave your undergraduate

and you go to schools
where students face many challenges.

Many of my students face things
from teen pregnancy to domestic violence,

homelessness, health care issues,

the list is long and very long.

Because of this, we've had to come up
with new ways of teaching.

There's a lot of teachers doing great things

but one thing we're proud of is,
because we don't lecture,

we can actually work
with each student one-on-one.

So instead of asking,
"Hey, how is that math problem going?"

we move beyond that
and we can now ask students,

"Hey, how is everything in your life going?
Everything all right at home?".

And now that students instead of walking
in our class going, "Oh, God, math!",

they're like, "Oh, hey, I know
Mr. Briel and Mr. Nash care." All right.

Just that simple question has allowed me
to move from 12%

to 65% and these
are students that had failed math 2, 3 –

I have actually quite a handful
of 4th time in algebra!

And now they at least come to class
and they feel that they can learn.

(Applause)

DN: So, what does this actually afford us?

Well, by organizing ideas,
we've been able to change and shift

our perceptions of what learning actually is.

So, from this, we've actually been able
to create a classroom experience

that allows our students to organise ideas

and change their perceptions of learning,

and now we have a class where our students
are learning how to do things like

critically think, creatively problem-solve,
all on their own, instead of listening to me talk.

And thank you for all listening.
I know I'm kind of boring.

On top of that, we as teachers
have also been able to re-establish

our value in the classroom.

Instead of just our content-area expertise,
we can now create an experience

for our students
where it's completely them doing everything

and we're just there to help them through it.

So, and on top of that, what's kind of even more
impressive to us is

now we have students who are seeing
the value of learning and education.

Next two quotes
we're going to show to you are quotes

directly from our students
about their experience in their classroom.

First one says,
"Now, since I had this class,

I think smart is just organised.

If everyone had a mental map
and organised every idea,

then everyone will be as smart as the other."

This is from a student who is currently
taking algebra 1 for the third time.

So, the next quote:

"The day we are born, we pick things up,
learn, and we adapt.

We understand things based on the ideas
we have learned.

Our understanding of new ideas changes
based on the way

we organised past experiences and ideas.

If one of our experiences
or ideas is a bad one,

then it will affect how we perceive
new ideas or experiences.

We can use maps to change
the way we organise things in our mind

to see all the possibilities in our lives."

This is from a second-time student in algebra 1

based on the experiences
they've had in our classroom.

So, what has this afforded us?

Well, we believe we've been able
to actually start developing critical thinkers

by teaching our students to organise ideas,
recognise how they organise these ideas

affects their perceptions.
And this goes way beyond the classroom.

Imagine: thinkers that understand
and recognise the very ideas and the power

and how they organise them

will affect the possibilities
they see in their very lives.

Think of the impact
this would have on individuals:

individuals would recognise
that all they needed to reach

the possibilities in their lives
would be the critical terms,

the time to organise them
and just the time to see it all materialise.

Imagine the impact
that would have on communities:

communities can come together
when individuals meet!

They will recognise that,
"Hey we don't disagree,

these are just perceptual differences!

We can take the time to collect the words
from everyone's maps

and come up with powerful solutions.

They're not just to address just one perception
but many perceptions."

What impact would this have on society?

Think about that: a whole society
where everyone's coming together.

It's because of this
that we think developing critical thinkers

is not only necessary for our children,

but ourselves as well!

The most important part is –
we believe developing critical thinkers

is the lifeline for individuals,
communities, to society

to become what they want,
can, dream and should be.

Thank you very much.

(Applause)
(Cheers)