Mathematics: a foundation for a fair and modern society | Lorella Carimali | TEDxLivorno

Mathematics has not to be understood as a set of rules, but as freedom, lightness, lifestyle that drive us beyond stereotypes and prejudices, improving our life. A way of thought that enhances Mathematics cultural value in modern society and which the Teacher effectively summarizes in three axioms: 1. Mathematics is for everybody (men and women); 2.Not one, but not one less in mathematics and in life; 3. Mistake as a limit but as an opportunity.
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I have to "break the ice".

And what can a teacher do,
in order to break the ice,

but start an oral test?

Are you afraid?

No, OK, this time I won't go ahead.

But I really want to break the ice

doing a mini-survey in order to know you,
and letting you know me.

Who does love Mathematics,
please raise his/her hand.

I am almost at home.

Who was proficient
in Mathematics, back then?

Eh, a little bit less.

Who does think, proficiency in math
is something one is born with?

All right, I will keep this in mind.

Now I know something about you,
I introduce myself.

I think that Mathematics is the foundation

of a fair, just and democratic society.

For that reason,

I took this beatiful sentence
of Nobel Prize Malala,

and I rephrased this way:

"A male or female child,
a teacher, a book,

a pen - and Mathematics! -
can change the world".

Who does agree with me
to add Mathematics?

Oh, they decrease.

Oh yes, they decrease.

I often see this thing.

Why?

Because each of you
would have thought:

"Oh, what's math
got to do with justice?

I had a stomachache,
the night before the math test.

I did not sleep at night
to prepare myself".

Well, I instead chose to study Mathematics

and to become a math teacher

because it was fundamental for me
to provide with critical tools

my students, both boys and girls,

in order to change this world,
to change it for the better.

And mathematics is essential to that.

What I want to do with you, today,

is to let you understand it
and bring you in my journey,

in order to show you the link

among mathematics, justice and fairness.

But I need you to come with me,

trying to go beyond the horizon

and to understand that we need
a different vision of math

and then a different model of mathematics.

I will do it, at least
I will try to do it,

following a typical math argument.

What mathematics does, first of all?

It analyzes the situation,

and what is the situation analysis?

Let us go see what mathematics is.

I do not want to say it with my own words:

it would be too easy,
and you might object, it ain't so.

I do it using some statements

written by my former students,

leaving the high school.

Then, can we see what?

Chiara, now attending
the the last year of medicine,

wrote me that:

"Thanks for showing me mathematics

not only as a set of formulas,
but as a way to to face life

making it simpler,
through reasoning and fantasy".

The Fifth I class,

is one my colleagues called
"a desperate class".

And they were wrong,

because people who write
this things, as you can see,

do not lack hope,
indeed they have a lot of it.

Watch out:

"Thanks for giving us the freedom

and for teaching us
to think and to live".

The last one is Bianca.

Bianca is at the the last year of Physics,
and she wrote me this:

"Thanks for giving me eyes
to look for new lands".

When I read these sentences, I said,

really, with my teaching hours of math,

my integrals, my stuff,
did I inadvertently do that?

Well, then they showed me a way
to go ahead, further

and reconsider this teaching approach.

But why mathematics?

Mathematics in my students' words,

freedom and a liberating force.

What did they write?

it's a powerful tool

which enables us to be what we want to be,

beyond stereotypes and prejudices.

Look at, they wrote this:

math is life, it is a way
to simplify our life.

But, why it is that?
Who ever told us that?

Daniel Kahneman tell us that.

Daniel Kahneman is a psychologist,

Nobel prize in 2002 for Economics.

He studied decision theory.

If you think about it,
every moment we decide.

A statistical research affirms

that in a typical day,
we decide about 35.000 times.

Are we sure that those decisions

are ours only, or are somewhat biased?

Today, you decided to come here.

If you had not come here,

you would likely not be
who you will be when you leave.

Therefore this is a fundamental point.

But how are we taking
all these decisions?

Most part of decisions,
Daniel Kahneman says,

are taken on the basis
of what he calls "System one".

Which is a fast system, it acts quickly;

but it is a stereotyped one,

mostly based on emotions and memories,

what our "belly" tell us.

But this decision -

are we sure that the strategies we take

and the relevant decisions
we take with this "system one"

are really ours,
unfettered by stereotypes?

Let me show you a very simple stereotype:

if you meet a man -

with a woman it would be much truer,

with a gender conplication
I do not want to put in -

and you ask this man, What is jour job?

And he answers, I am a thinker.

What do you think he does?

Most of the people say,
A philosopher; A writer -

my student says, Nothing;
but let's put that aside.

If instead he specifies,

I am a mathematician
working at Geneva CERN.

And nobody ever guesses
the true answer.

Because there's the stereotype

that mathematicians, scientists and so on

are simply technicians,

and they do not do an intellectual job.

Then Daniel Kahneman tells us

that if we are to take
thoughtful decisions,

we must activate
what he calls "System Two".

Which is a system, as he says,

educated and educable, rational, logical,

but slow.

Therefore, if we want our decisions
to be nobody's ones but ours,

we must activate and train
this second system.

And make it able to check

whether System One's solutions
are indeed the right ones.

Well, this System Two, in my opinion,

is just another name
for mathematical thinking.

That is, before a problem: analise data;

tell the key ones from secondary ones;

set up a startegy; test it;

reset it if it proves wrong;
and go straight to the target.

This is the mathematical thinking,

and this give us the freedom
that my students told about,

therefore it has to become fast.

All right, but you still may say me:
"What's fairness got to do with it?"

So let's go see what fairness is.

Let us consider Ulpianus:

Ulpianus was one
of the greatest Roman jurists,

perhaps the greatest one,

and he defines justice as:

"The constant, perennial will

to give everybody
what they're entitled to".

Sen, Indian philosopher and economist

who deals with civil rights,

what does he says to us?

"The concept of inequality

does not consist only
in income inequality,

but mostly in an inequality

of opportunities, of possibility,
of choice, of individual freedom.

It is crucial, for each individual,

to have the freedom to decide
how to shape himself".

So, if a State must give
to each and every one of us

the freedom to become
what they mean to be,

and the same opportunities,

it means that a mathematical method

has to bring the mathematical competence
to each and every one of us.

So the teaching method of mathematics

has to be based, first of all,

on that - I apologize
for mathematical jargon -

on that is a fundamental axiom:

"No one girl, no one boy left behind,
in mathematics and life".

Because if only one person is left out

I miss one person

and therefore the State turns out to be
an unfair and iniquitous State.

But then you will say me:

"How can we do? Any second chance?"

We must go - remember what
we told at the beginning -

beyond the horizon,

think something
even if it is not yet here.

We must change the teacher profile,

and the way we teach Math.

So what do we do?

Do a different thing,
which is the second axiom:

"Mathematics is for everyone and all".

Therefore there are not -
that's why I asked to raise your hands -

there are no gifted or denied persons;

only untrained persons exist,

or ones that are biased by stereotypes.

Who does tell us so? Carol Dweck:

Carol Dweck is a Stanford-based
cognitive psychologist,

a worldwide reference
of cognitive and social psychology.

She tell us that there are only

family and school conditions

which somehow affect talent development.

So what should you do?

The teacher, she still tells us -

and she gives advice
to parents and teachers,

which is this one:

give always challenging cases

to your sons, daughters or students,

let them delve into that.

And reward the commitment,
not the performance,

because only in challenging cases
this approach will develop.

Because if mathematics
is a way of thinking,

a way of facing life,

I must train math thinking
as if I [were] in a gym;

then I have to put my muscles at work,

I have to develop the capability

to guess, imagine, design,
to infer and check,

then measure and quantify
phenomena and real facts.

This is the important thing.

So challenging cases, why?

Because, no matter what,

mistakes are not a limit,

but an opportunity.

An opportunity for reflection and growth.

So I showed you

that mathematics goes hand in hand
with justice and fairness.

But then a last challenge remains

that I'd like to take with you,

which is this:

Italy, and many countries,

score terribly in math's
functional illiteracy;

so math, if our State
is a fair and just one,

has to enter in all the houses.

Not only in boys and girls,
but in all of us, in all adults.

This is our last challenge,

let mathematics spread everywhere.

Maybe somebody is thinking now,

this is an utopia,
it will never happen,

and a mathematician as I am

I say that it is just about
finding the right strategy,

because, in the words
of the great Adriano Olivetti,

"The word utopia is a shortcut

to dismiss what you're not willing,
able or brave enough to do.

A dream is always a dream,

until you do not start from somewhere.

Then it becomes a purpose,
something extremely greater.

Today, Lorella's dream

can only be achieved
with your help, also.

Let's then dream toghether.

Thank you.

(Applause)