WEBVTT

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I have to "break the ice".

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

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but start an oral test?

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Are you afraid?

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

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But I really want to break the ice

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

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

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I am almost at home.

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Who was proficient
in Mathematics, back then?

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Eh, a little bit less.

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

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All right, I will keep this in mind.

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Now I know something about you, 
I introduce myself.

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I think that Mathematics is the foundation

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of a fair, just and democratic society.

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For that reason,

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I took this beatiful sentence
of Nobel Prize Malala,

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and I rephrased this way:

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

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

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Who does agree with me
to add Mathematics?

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Oh, they decrease.

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Oh yes, they decrease.

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I often see this thing.

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Why?

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Because each of you
would have thought:

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

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

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I did not sleep at night
to prepare myself".

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Well, I instead chose to study Mathematics

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and to become a math teacher

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because it was fundamental for me
to provide with critical tools

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my students, both boys and girls,

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

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And mathematics is essential to that.

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What I want to do with you, today,

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

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in order to show you the link

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among mathematics, justice and fairness.

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But I need you to come with me,

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trying to go beyond the horizon

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and to understand that we need
a different vision of math

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and then a different model of mathematics.

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

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following a typical math argument.

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What mathematics does, first of all?

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It analyzes the situation,

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and what is the situation analysis?

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Let us go see what mathematics is.

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

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

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I do it using some statements

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written by my former students,

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leaving the high school.

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Then, can we see what?

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Chiara, now attending
the the last year of medicine,

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wrote me that:

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"Thanks for showing me mathematics

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

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making it simpler, 
through reasoning and fantasy".

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The Fifth I class,

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is one my colleagues called
"a desperate class".

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And they were wrong,

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

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

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Watch out:

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"Thanks for giving us the freedom

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and for teaching us
to think and to live".

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The last one is Bianca.

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

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

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When I read these sentences, I said,

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really, with my teaching hours of math,

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

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

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and reconsider this teaching approach.

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But why mathematics?

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Mathematics in my students' words,

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freedom and a liberating force.

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What did they write?

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it's a powerful tool

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which enables us to be what we want to be,

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beyond stereotypes and prejudices.

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Look at, they wrote this:

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

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

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Daniel Kahneman tell us that.

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Daniel Kahneman is a psychologist,

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Nobel prize in 2002 for Economics.

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He studied decision theory.

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If you think about it,
every moment we decide.

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A statistical research affirms

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

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Are we sure that those decisions


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are ours only, or are somewhat biased?

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Today, you decided to come here.

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If you had not come here,

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

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Therefore this is a fundamental point.

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But how are we taking
all these decisions?

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Most part of decisions,
Daniel Kahneman says,

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

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Which is a fast system, it acts quickly;

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but it is a stereotyped one,

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mostly based on emotions and memories,

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what our "belly" tell us.

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But this decision -

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are we sure that the strategies we take

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

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are really ours,
unfettered by stereotypes?

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Let me show you a very simple stereotype:

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if you meet a man -

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with a woman it would be much truer,

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

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and you ask this man, What is jour job?

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And he answers, I am a thinker.

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What do you think he does?

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

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

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If instead he specifies,

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I am a mathematician
working at Geneva CERN.

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And nobody ever guesses
the true answer.

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Because there's the stereotype

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that mathematicians, scientists and so on

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are simply technicians,

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and they do not do an intellectual job.

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Then Daniel Kahneman tells us

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that if we are to take
thoughtful decisions,

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we must activate
what he calls "System Two".

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Which is a system, as he says,

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educated and educable, rational, logical,

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but slow.

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

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we must activate and train
this second system.

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And make it able to check

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

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Well, this System Two, in my opinion,

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is just another name
for mathematical thinking.

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That is, before a problem: analise data;

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tell the key ones from secondary ones;

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set up a startegy; test it;

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

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This is the mathematical thinking,

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

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therefore it has to become fast.

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

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So let's go see what fairness is.

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Let us consider Ulpianus:

NOTE Paragraph

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Ulpianus was one 
of the greatest Roman jurists,

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perhaps the greatest one,

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and he defines justice as:

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"The constant, perennial will

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to give everybody
what they're entitled to".

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Sen, Indian philosopher and economist

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who deals with civil rights,

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what does he says to us?

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"The concept of inequality

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does not consist only
in income inequality,

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but mostly in an inequality


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

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It is crucial, for each individual,

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

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

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the freedom to become
what they mean to be,

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and the same opportunities,

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it means that a mathematical method

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

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So the teaching method of mathematics

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has to be based, first of all,

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on that - I apologize
for mathematical jargon -

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on that is a fundamental axiom:

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

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Because if only one person is left out

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I miss one person

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

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But then you will say me:

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"How can we do? Any second chance?"

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

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beyond the horizon,

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think something
even if it is not yet here.

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We must change the teacher profile,

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and the way we teach Math.

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So what do we do?

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Do a different thing,
which is the second axiom:

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"Mathematics is for everyone and all".

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

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there are no gifted or denied persons;

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only untrained persons exist,

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or ones that are biased by stereotypes.

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Who does tell us so? Carol Dweck:

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Carol Dweck is a Stanford-based
cognitive psychologist,

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a worldwide reference
of cognitive and social psychology.

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She tell us that there are only

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family and school conditions

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which somehow affect talent development.

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So what should you do?

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The teacher, she still tells us -

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and she gives advice
to parents and teachers,

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which is this one:

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give always challenging cases

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to your sons, daughters or students,

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let them delve into that.

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And reward the commitment, 
not the performance,

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because only in challenging cases 
this approach will develop.

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Because if mathematics
is a way of thinking,

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a way of facing life,

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

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then I have to put my muscles at work,

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I have to develop the capability

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

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then measure and quantify
phenomena and real facts.

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This is the important thing.

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So challenging cases, why?

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Because, no matter what,

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mistakes are not a limit,

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but an opportunity.

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An opportunity for reflection and growth.

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So I showed you

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that mathematics goes hand in hand
with justice and fairness.

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But then a last challenge remains

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that I'd like to take with you,

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which is this:

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Italy, and many countries,

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score terribly in math's
functional illiteracy;

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

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has to enter in all the houses.

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

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This is our last challenge,

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let mathematics spread everywhere.

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Maybe somebody is thinking now,

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this is an utopia,
it will never happen,

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and a mathematician as I am

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

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because, in the words
of the great Adriano Olivetti,

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"The word utopia is a shortcut

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

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A dream is always a dream,

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until you do not start from somewhere.

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Then it becomes a purpose,
something extremely greater.

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Today, Lorella's dream

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can only be achieved
with your help, also.

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Let's then dream toghether.

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Thank you.

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(Applause)