1
00:00:18,000 --> 00:00:19,720
I have to "break the ice".

2
00:00:20,320 --> 00:00:23,960
And what can a teacher do, 
in order to break the ice,

3
00:00:23,960 --> 00:00:26,740
but start an oral test?

4
00:00:26,960 --> 00:00:28,560
Are you afraid?

5
00:00:28,560 --> 00:00:32,320
No, OK, this time I won't go ahead.

6
00:00:32,320 --> 00:00:34,360
But I really want to break the ice

7
00:00:34,360 --> 00:00:38,960
doing a mini-survey in order to know you,
and letting you know me.

8
00:00:39,720 --> 00:00:42,600
Who does love Mathematics,
please raise his/her hand.

9
00:00:43,720 --> 00:00:46,600
I am almost at home.

10
00:00:47,280 --> 00:00:52,180
Who was proficient
in Mathematics, back then?

11
00:00:52,180 --> 00:00:54,060
Eh, a little bit less.

12
00:00:55,560 --> 00:01:00,360
Who does think, proficiency in math
is something one is born with?

13
00:01:03,600 --> 00:01:07,260
All right, I will keep this in mind.

14
00:01:07,640 --> 00:01:10,080
Now I know something about you, 
I introduce myself.

15
00:01:10,080 --> 00:01:14,640
I think that Mathematics is the foundation

16
00:01:14,640 --> 00:01:19,200
of a fair, just and democratic society.

17
00:01:20,080 --> 00:01:22,660
For that reason,

18
00:01:23,710 --> 00:01:29,600
I took this beatiful sentence
of Nobel Prize Malala,

19
00:01:30,160 --> 00:01:31,880
and I rephrased this way:

20
00:01:32,560 --> 00:01:37,880
"A male or female child, 
a teacher, a book,

21
00:01:37,880 --> 00:01:43,840
a pen - and Mathematics! -
can change the world".

22
00:01:44,400 --> 00:01:47,360
Who does agree with me
to add Mathematics?

23
00:01:48,800 --> 00:01:53,720
Oh, they decrease.

24
00:01:53,720 --> 00:01:55,600
Oh yes, they decrease.

25
00:01:55,600 --> 00:01:58,080
I often see this thing.

26
00:01:58,080 --> 00:01:59,246
Why?

27
00:01:59,246 --> 00:02:01,520
Because each of you
would have thought:

28
00:02:01,520 --> 00:02:05,800
"Oh, what's math
got to do with justice?

29
00:02:05,800 --> 00:02:09,840
I had a stomachache,
the night before the math test.

30
00:02:09,840 --> 00:02:12,440
I did not sleep at night
to prepare myself".

31
00:02:12,440 --> 00:02:17,240
Well, I instead chose to study Mathematics

32
00:02:17,240 --> 00:02:19,560
and to become a math teacher

33
00:02:20,080 --> 00:02:26,080
because it was fundamental for me
to provide with critical tools

34
00:02:26,080 --> 00:02:28,480
my students, both boys and girls,

35
00:02:28,480 --> 00:02:33,440
in order to change this world,
to change it for the better.

36
00:02:33,440 --> 00:02:37,200
And mathematics is essential to that.

37
00:02:37,200 --> 00:02:40,440
What I want to do with you, today,

38
00:02:40,440 --> 00:02:45,160
is to let you understand it
and bring you in my journey,

39
00:02:45,160 --> 00:02:48,962
in order to show you the link

40
00:02:48,962 --> 00:02:52,480
among mathematics, justice and fairness.

41
00:02:53,000 --> 00:02:57,488
But I need you to come with me,

42
00:02:57,488 --> 00:03:02,520
trying to go beyond the horizon

43
00:03:02,520 --> 00:03:07,080
and to understand that we need
a different vision of math

44
00:03:07,080 --> 00:03:11,440
and then a different model of mathematics.

45
00:03:11,440 --> 00:03:14,840
I will do it, at least
I will try to do it,

46
00:03:14,840 --> 00:03:17,980
following a typical math argument.

47
00:03:18,440 --> 00:03:20,600
What mathematics does, first of all?

48
00:03:21,400 --> 00:03:23,960
It analyzes the situation,

49
00:03:23,960 --> 00:03:25,960
and what is the situation analysis?

50
00:03:26,400 --> 00:03:29,240
Let us go see what mathematics is.

51
00:03:29,760 --> 00:03:31,840
I do not want to say it with my own words:

52
00:03:31,840 --> 00:03:34,880
it would be too easy,
and you might object, it ain't so.

53
00:03:35,640 --> 00:03:37,720
I do it using some statements

54
00:03:37,720 --> 00:03:41,840
written by my former students,

55
00:03:41,840 --> 00:03:44,640
leaving the high school.

56
00:03:44,640 --> 00:03:47,080
Then, can we see what?

57
00:03:47,720 --> 00:03:51,000
Chiara, now attending
the the last year of medicine,

58
00:03:51,000 --> 00:03:52,390
wrote me that:

59
00:03:52,390 --> 00:03:56,160
"Thanks for showing me mathematics

60
00:03:56,160 --> 00:04:01,760
not only as a set of formulas,
but as a way to to face life

61
00:04:01,760 --> 00:04:05,920
making it simpler, 
through reasoning and fantasy".

62
00:04:08,720 --> 00:04:09,800
The Fifth I class,

63
00:04:09,800 --> 00:04:15,640
is one my colleagues called
"a desperate class".

64
00:04:16,240 --> 00:04:17,920
And they were wrong,

65
00:04:17,920 --> 00:04:23,480
because people who write
this things, as you can see,

66
00:04:23,480 --> 00:04:26,675
do not lack hope, 
indeed they have a lot of it.

67
00:04:26,675 --> 00:04:27,720
Watch out:

68
00:04:27,720 --> 00:04:31,320
"Thanks for giving us the freedom

69
00:04:31,320 --> 00:04:35,430
and for teaching us
to think and to live".

70
00:04:36,440 --> 00:04:38,240
The last one is Bianca.

71
00:04:38,240 --> 00:04:42,800
Bianca is at the the last year of Physics,
and she wrote me this:

72
00:04:42,800 --> 00:04:47,800
"Thanks for giving me eyes
to look for new lands".

73
00:04:48,360 --> 00:04:52,560
When I read these sentences, I said,

74
00:04:52,560 --> 00:04:55,480
really, with my teaching hours of math,

75
00:04:55,480 --> 00:04:58,680
my integrals, my stuff, 
did I inadvertently do that?

76
00:04:58,680 --> 00:05:04,440
Well, then they showed me a way
to go ahead, further

77
00:05:04,440 --> 00:05:10,320
and reconsider this teaching approach.

78
00:05:10,320 --> 00:05:12,770
But why mathematics?

79
00:05:13,400 --> 00:05:18,960
Mathematics in my students' words,

80
00:05:19,320 --> 00:05:23,050
freedom and a liberating force.

81
00:05:23,670 --> 00:05:25,280
What did they write?

82
00:05:25,280 --> 00:05:28,320
it's a powerful tool

83
00:05:28,320 --> 00:05:34,280
which enables us to be what we want to be,

84
00:05:34,960 --> 00:05:37,880
beyond stereotypes and prejudices.

85
00:05:38,480 --> 00:05:40,880
Look at, they wrote this:

86
00:05:40,880 --> 00:05:46,610
math is life, it is a way
to simplify our life.

87
00:05:46,610 --> 00:05:50,200
But, why it is that? 
Who ever told us that?

88
00:05:50,610 --> 00:05:52,800
Daniel Kahneman tell us that.

89
00:05:53,400 --> 00:05:56,520
Daniel Kahneman is a psychologist,

90
00:05:56,520 --> 00:06:00,280
Nobel prize in 2002 for Economics.

91
00:06:00,280 --> 00:06:03,830
He studied decision theory.

92
00:06:04,240 --> 00:06:09,160
If you think about it,
every moment we decide.

93
00:06:09,160 --> 00:06:11,348
A statistical research affirms

94
00:06:11,348 --> 00:06:17,000
that in a typical day,
we decide about 35.000 times.

95
00:06:17,760 --> 00:06:21,360
Are we sure that those decisions


96
00:06:21,360 --> 00:06:26,000
are ours only, or are somewhat biased?

97
00:06:26,520 --> 00:06:29,840
Today, you decided to come here.

98
00:06:30,280 --> 00:06:31,550
If you had not come here,

99
00:06:31,550 --> 00:06:36,620
you would likely not be
who you will be when you leave.

100
00:06:37,640 --> 00:06:39,960
Therefore this is a fundamental point.

101
00:06:39,960 --> 00:06:43,320
But how are we taking
all these decisions?

102
00:06:43,840 --> 00:06:48,240
Most part of decisions,
Daniel Kahneman says,

103
00:06:48,240 --> 00:06:52,380
are taken on the basis
of what he calls "System one".

104
00:06:52,600 --> 00:06:58,160
Which is a fast system, it acts quickly;

105
00:06:58,160 --> 00:07:00,177
but it is a stereotyped one,

106
00:07:00,177 --> 00:07:05,720
mostly based on emotions and memories,

107
00:07:05,720 --> 00:07:08,680
what our "belly" tell us.

108
00:07:08,680 --> 00:07:11,420
But this decision -

109
00:07:11,420 --> 00:07:15,680
are we sure that the strategies we take

110
00:07:15,680 --> 00:07:19,040
and the relevant decisions
we take with this "system one"

111
00:07:19,040 --> 00:07:22,920
are really ours,
unfettered by stereotypes?

112
00:07:22,920 --> 00:07:26,960
Let me show you a very simple stereotype:

113
00:07:27,480 --> 00:07:30,880
if you meet a man -

114
00:07:30,880 --> 00:07:34,440
with a woman it would be much truer,

115
00:07:34,440 --> 00:07:37,280
with a gender conplication
I do not want to put in -

116
00:07:37,840 --> 00:07:40,760
and you ask this man, What is jour job?

117
00:07:41,760 --> 00:07:46,240
And he answers, I am a thinker.

118
00:07:46,760 --> 00:07:49,180
What do you think he does?

119
00:07:49,520 --> 00:07:54,200
Most of the people say,
A philosopher; A writer -

120
00:07:54,720 --> 00:08:00,510
my student says, Nothing;
but let's put that aside.

121
00:08:00,510 --> 00:08:03,220
If instead he specifies,

122
00:08:03,220 --> 00:08:07,720
I am a mathematician
working at Geneva CERN.

123
00:08:08,400 --> 00:08:12,500
And nobody ever guesses
the true answer.

124
00:08:12,500 --> 00:08:15,040
Because there's the stereotype

125
00:08:15,040 --> 00:08:18,760
that mathematicians, scientists and so on

126
00:08:18,760 --> 00:08:21,850
are simply technicians,

127
00:08:21,850 --> 00:08:25,040
and they do not do an intellectual job.

128
00:08:25,040 --> 00:08:27,760
Then Daniel Kahneman tells us

129
00:08:27,760 --> 00:08:32,559
that if we are to take
thoughtful decisions,

130
00:08:32,559 --> 00:08:36,039
we must activate
what he calls "System Two".

131
00:08:36,600 --> 00:08:39,638
Which is a system, as he says,

132
00:08:39,638 --> 00:08:44,240
educated and educable, rational, logical,

133
00:08:44,240 --> 00:08:45,510
but slow.

134
00:08:46,160 --> 00:08:50,840
Therefore, if we want our decisions
to be nobody's ones but ours,

135
00:08:50,840 --> 00:08:56,280
we must activate and train
this second system.

136
00:08:56,960 --> 00:09:00,320
And make it able to check

137
00:09:00,320 --> 00:09:04,600
whether System One's solutions 
are indeed the right ones.

138
00:09:04,600 --> 00:09:07,400
Well, this System Two, in my opinion,

139
00:09:07,400 --> 00:09:11,120
is just another name
for mathematical thinking.

140
00:09:11,120 --> 00:09:14,560
That is, before a problem: analise data;

141
00:09:14,560 --> 00:09:20,120
tell the key ones from secondary ones;

142
00:09:20,120 --> 00:09:23,800
set up a startegy; test it;

143
00:09:23,800 --> 00:09:28,880
reset it if it proves wrong;
and go straight to the target.

144
00:09:29,110 --> 00:09:33,560
This is the mathematical thinking,

145
00:09:33,560 --> 00:09:38,830
and this give us the freedom 
that my students told about,

146
00:09:38,830 --> 00:09:41,300
therefore it has to become fast.

147
00:09:41,300 --> 00:09:46,000
All right, but you still may say me:
"What's fairness got to do with it?"

148
00:09:46,000 --> 00:09:49,720
So let's go see what fairness is.

149
00:09:53,000 --> 00:09:54,920
Let us consider Ulpianus:

150
00:09:54,920 --> 00:09:58,800
Ulpianus was one 
of the greatest Roman jurists,

151
00:09:58,800 --> 00:10:01,440
perhaps the greatest one,

152
00:10:01,440 --> 00:10:04,470
and he defines justice as:

153
00:10:04,640 --> 00:10:07,360
"The constant, perennial will

154
00:10:07,360 --> 00:10:12,240
to give everybody
what they're entitled to".

155
00:10:14,720 --> 00:10:20,044
Sen, Indian philosopher and economist

156
00:10:20,044 --> 00:10:23,600
who deals with civil rights,

157
00:10:23,600 --> 00:10:25,200
what does he says to us?

158
00:10:25,200 --> 00:10:27,760
"The concept of inequality

159
00:10:27,760 --> 00:10:32,200
does not consist only
in income inequality,

160
00:10:32,200 --> 00:10:35,220
but mostly in an inequality


161
00:10:35,220 --> 00:10:41,280
of opportunities, of possibility,
of choice, of individual freedom.

162
00:10:42,320 --> 00:10:45,640
It is crucial, for each individual,

163
00:10:45,640 --> 00:10:51,990
to have the freedom to decide
how to shape himself".

164
00:10:52,760 --> 00:10:58,760
So, if a State must give
to each and every one of us

165
00:10:58,760 --> 00:11:02,760
the freedom to become
what they mean to be,

166
00:11:02,760 --> 00:11:05,280
and the same opportunities,

167
00:11:05,280 --> 00:11:09,560
it means that a mathematical method

168
00:11:10,160 --> 00:11:16,400
has to bring the mathematical competence
to each and every one of us.

169
00:11:16,400 --> 00:11:20,880
So the teaching method of mathematics

170
00:11:20,880 --> 00:11:22,960
has to be based, first of all,

171
00:11:22,960 --> 00:11:26,640
on that - I apologize
for mathematical jargon -

172
00:11:26,640 --> 00:11:29,680
on that is a fundamental axiom:

173
00:11:29,680 --> 00:11:33,960
"No one girl, no one boy left behind, 
in mathematics and life".

174
00:11:33,960 --> 00:11:37,840
Because if only one person is left out

175
00:11:37,840 --> 00:11:39,920
I miss one person

176
00:11:39,920 --> 00:11:44,600
and therefore the State turns out to be
an unfair and iniquitous State.

177
00:11:45,360 --> 00:11:46,910
But then you will say me:

178
00:11:46,910 --> 00:11:50,445
"How can we do? Any second chance?"

179
00:11:50,445 --> 00:11:55,050
We must go - remember what
we told at the beginning -

180
00:11:55,050 --> 00:11:57,110
beyond the horizon,

181
00:11:57,110 --> 00:12:00,470
think something
even if it is not yet here.

182
00:12:00,470 --> 00:12:04,660
We must change the teacher profile,

183
00:12:04,660 --> 00:12:07,480
and the way we teach Math.

184
00:12:07,480 --> 00:12:09,610
So what do we do?

185
00:12:09,610 --> 00:12:14,120
Do a different thing,
which is the second axiom:

186
00:12:14,120 --> 00:12:18,690
"Mathematics is for everyone and all".

187
00:12:18,690 --> 00:12:23,500
Therefore there are not -
that's why I asked to raise your hands -

188
00:12:23,500 --> 00:12:27,040
there are no gifted or denied persons;

189
00:12:27,740 --> 00:12:31,820
only untrained persons exist,

190
00:12:31,820 --> 00:12:36,120
or ones that are biased by stereotypes.

191
00:12:36,120 --> 00:12:39,750
Who does tell us so? Carol Dweck:

192
00:12:39,750 --> 00:12:44,620
Carol Dweck is a Stanford-based
cognitive psychologist,

193
00:12:44,620 --> 00:12:51,320
a worldwide reference
of cognitive and social psychology.

194
00:12:51,320 --> 00:12:54,550
She tell us that there are only

195
00:12:54,550 --> 00:12:59,974
family and school conditions

196
00:12:59,974 --> 00:13:05,900
which somehow affect talent development.

197
00:13:05,900 --> 00:13:08,640
So what should you do?

198
00:13:08,640 --> 00:13:11,280
The teacher, she still tells us -

199
00:13:11,280 --> 00:13:16,020
and she gives advice
to parents and teachers,

200
00:13:16,020 --> 00:13:17,000
which is this one:

201
00:13:17,000 --> 00:13:21,800
give always challenging cases

202
00:13:21,800 --> 00:13:25,190
to your sons, daughters or students,

203
00:13:25,190 --> 00:13:27,630
let them delve into that.

204
00:13:27,630 --> 00:13:34,720
And reward the commitment, 
not the performance,

205
00:13:34,720 --> 00:13:40,210
because only in challenging cases 
this approach will develop.

206
00:13:40,210 --> 00:13:43,420
Because if mathematics
is a way of thinking,

207
00:13:43,420 --> 00:13:45,500
a way of facing life,

208
00:13:45,500 --> 00:13:50,030
I must train math thinking
as if I [were] in a gym;

209
00:13:50,030 --> 00:13:53,070
then I have to put my muscles at work,

210
00:13:53,070 --> 00:13:54,770
I have to develop the capability

211
00:13:54,770 --> 00:13:58,190
to guess, imagine, design, 
to infer and check,

212
00:13:58,190 --> 00:14:02,730
then measure and quantify
phenomena and real facts.

213
00:14:02,730 --> 00:14:04,600
This is the important thing.

214
00:14:04,600 --> 00:14:06,870
So challenging cases, why?

215
00:14:09,540 --> 00:14:10,970
Because, no matter what,

216
00:14:10,970 --> 00:14:16,747
mistakes are not a limit,

217
00:14:16,747 --> 00:14:18,607
but an opportunity.

218
00:14:18,607 --> 00:14:24,140
An opportunity for reflection and growth.

219
00:14:24,140 --> 00:14:26,760
So I showed you

220
00:14:26,760 --> 00:14:32,090
that mathematics goes hand in hand
with justice and fairness.

221
00:14:32,090 --> 00:14:35,130
But then a last challenge remains

222
00:14:35,130 --> 00:14:39,702
that I'd like to take with you,

223
00:14:39,702 --> 00:14:41,200
which is this:

224
00:14:41,200 --> 00:14:43,750
Italy, and many countries,

225
00:14:43,750 --> 00:14:49,250
score terribly in math's
functional illiteracy;

226
00:14:49,250 --> 00:14:54,300
so math, if our State
is a fair and just one,

227
00:14:54,300 --> 00:14:56,360
has to enter in all the houses.

228
00:14:56,360 --> 00:15:01,900
Not only in boys and girls,
but in all of us, in all adults.

229
00:15:01,900 --> 00:15:06,060
This is our last challenge,

230
00:15:06,060 --> 00:15:09,520
let mathematics spread everywhere.

231
00:15:09,520 --> 00:15:12,500
Maybe somebody is thinking now,

232
00:15:12,500 --> 00:15:15,860
this is an utopia,
it will never happen,

233
00:15:15,860 --> 00:15:18,310
and a mathematician as I am

234
00:15:18,310 --> 00:15:22,420
I say that it is just about
finding the right strategy,

235
00:15:22,420 --> 00:15:26,970
because, in the words
of the great Adriano Olivetti,

236
00:15:26,970 --> 00:15:31,820
"The word utopia is a shortcut

237
00:15:31,820 --> 00:15:38,450
to dismiss what you're not willing,
able or brave enough to do.

238
00:15:38,450 --> 00:15:40,620
A dream is always a dream,

239
00:15:40,620 --> 00:15:43,880
until you do not start from somewhere.

240
00:15:43,880 --> 00:15:49,420
Then it becomes a purpose,
something extremely greater.

241
00:15:49,420 --> 00:15:52,030
Today, Lorella's dream

242
00:15:52,030 --> 00:15:57,950
can only be achieved
with your help, also.

243
00:15:57,950 --> 00:16:00,330
Let's then dream toghether.

244
00:16:00,330 --> 00:16:01,360
Thank you.

245
00:16:01,360 --> 00:16:04,750
(Applause)