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)