Quale informatica?
Tecnica e metodologia
http://tfa.di.uniroma1.it
Anna Labella
L’informatica una scienza
sperimentale?

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I calcolatori sono strumenti fisici
I calcolatori sono la materializzazione del
nostro pensiero
L’informatica potrebbe esistere con calcolatori
completamente diversi
……. Cos’è l’informatica?
Cos’è utile insegnare nella
scuola?
•Computer literacy
•Programming skills
•Applications like games, robots and simulations
Cos’è utile insegnare nel TFA?


Ai futuri docenti non dobbiamo insegnare le
basi né temi avanzati di informatica: le prime
sono conosciute, i secondi non servono
Dobbiamo convincere i futuri insegnanti che
l’informatica, come la matematica, è un
metodo
L’informatica: una disciplina
particolare

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Computational thinking
Problem solving
Interdisciplinarietà
Il metodo informatico

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L’informatica come disciplina, ma soprattutto come
metodo nell’insegnamento.
Pensare come un informatico, anche prescindendo
eventualmente dalla tecnologia.
sperimentazioni fatte nel mondo in questo senso.
Astrazione ed automazione.
Il pensare informatico a confronto con il pensare
matematico ed altri tipi di “pensiero” nell’educazione
dei giovani del 21° secolo.
Il pensare informatico e l’interdisciplinarietà.
Cos’è il Computational Thinking?
Cos’è il Computational Thinking?
Many adjectives describe modes of thinking:
Abstract,
analytic,
conceptual,
concrete,
constructive,
creative,
critical,
deductive,
strategic,
synthetic,
tactical and…
computational and procedural.
J. Wing
My Grand Vision for the Field
Computational thinking
will be a fundamental skill used by everyone in the
world by the middle of the 21st Century.

Just like reading, writing, and arithmetic.
Imagine every child knowing how to think like a computer
scientist!
Incestuous: Computing and computers will enable the
spread of computational thinking.

In research: scientists, engineers, …, historians, artists
In education: K-12 students and teachers, undergrads, …

J.M. Wing, “Computational Thinking,” CACM Viewpoint, March 2006, pp. 33-35.
http://www.cs.cmu.edu/~wing/
Le due A del CT
La prima A del CT
Abstractions are our “mental” tools
The abstraction process includes

Choosing the right abstractions
 Operating simultaneously at multiple
layers of abstraction
 Defining the relationships the between
layers

La seconda A del CT
The power of our “mental” tools is amplified by
our “metal” tools.
 Automation is mechanizing our abstractions,
abstraction layers, and their relationships


Mechanization is possible due to precise and
exacting notations and models
There is some “computer” below (human or
machine, virtual or physical)
Le due A combinate

Computing is the automation of our
abstractions


They give us the audacity and ability to
scale.
Computational thinking
 choosing the right abstractions, etc.
 choosing the right “computer” for the task
Il Problem solving
David Moursung : Introduction to problem solving in the information age
http//uoregon.edu/˜moursund/dave/index.html
Cos’è il problem solving?
Critical thinking
Quale matematica nel
secolo?
La relazione tra matematica e
informatica
Prof. Madhu Sudan - Massachusetts Institute of
Technology (MIT)
°
21
Cos’è la matematica?

Temi

Metafore

Linguaggio

Rigore
Temi







Geometria
Aritmetica
Algebra
Combinatoria
Calcolo Infinitesimale
Probabilità
….
Perché non ?

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Musica
Astronomia
Calcolo
Logica
…….
Una scorsa storica
Schema
Problem
Formalization Machine Algorithm Tavola
Partition
Division
Canon
One or more
congruences
?
Riddle
One or more
linear
equations
?
Abacus
Algorithm Mensa
for the
pitagorica
abacus
?
Tabula
mirifica
?
?
Matematica
Divisione su abaco
divisore
dividendo
resto
quotiente
6
4
5
4
9
5
2
1
4
4
2
6
2
1
1
9
5
2
1
9
4
2
5
9
3
6
2
1
1
1
1
549 : 6
1
2
3
4
5
6
7
8
9
2
4
6
8 10
12 14 16 18
3
6
9
12 15
18 21 24 27
4
8
12 16 20
24 28 32 36
5
10 15 20 25
30 35 40 45
6
12 18 24 30
36 42 48 54
7
14 21 28 35
42 49 56 63
8
16 24 32 40
48 56 64 72
9
18 27 36 45
54 63 72 81
Rythmomachia (XI sec.)
??????
1
2
3
4
5
6
7
8
9
2
4
6
8 10
12 14 16 18
3
6
9
12 15
18 21 24 27
4
8
12 16 20
24 28 32 36
5
10 15 20 25
30 35 40 45
6
12 18 24 30
36 42 48 54
7
14 21 28 35
42 49 56 63
8
16 24 32 40
48 56 64 72
9
18 27 36 45
54 63 72 81
Musica
Labella,A. and Scozzafava, C.: Music and algorithms: a historical perspective.
Studi Musicali Volume: 32 Issue: 1 (2003-01-01) p.3-25. ISSN: 0391-7789
Canone infinito
1*
2
3* 4
2
1*
2
3* 4
1*
2
h(n+k) ≈ h(n)
Two voices at
unisono
3* 2
4
Two voices at a h(n+k) ≈ h(n) + h
given interval
1
2
3
1
5* 4
7
3
4
1
2
5
3
1
3
4
5
5
5* 6* 7
3* 4
1* 2
5*
3* 4
1* 2 3*
3* 2
6* 5* 4
5* 6*
3* 4
1* 2
3* 2
6* 5* 4
8* 7
5
2
8* 9
5* 6* 7 8*
3* 4
3* 2
6* 5* 4
8* 7
9
1*
3* 2
6* 5* 4
h(n+k1) ≈ h(n) + h1
h(n+k2) ≈ h(n) + h2
……..
More voices
3* 2
5* 6* 7
1* 2
3* 2
1*
Canone cancrizzante e inverso
h(n) ≈ h(N - n)
…..
Cancrizzante
1
1
2
7
3
1
Inverse
recursion?
4
5
7
6
1
7
1
6
7
5
4
3
2
1
h(n) ≈ [h(n-1)-h’(n-1)]+ 2[h(n)-h(n-1)]
…..
Canone Mensurale


h(n) ≈ h(q n -i)
5
2
0≤ i ≤ q-1
3
3
3
2
7
5
5
1
5
8
3
8
6
6
4
7
5
6
5
1
6
6 1
8
8
10
7
10
9
6
5
6
8
4
Indovinelli
Alcuino di York
Problema 26: Ilcane e la volpe

Un cane insegue una volpe che è 150 piedi più avanti
di lui. La lepre fasalti di di 7 piedi, il cane di 9. Dopo
quanti salti il cane raggiunge la lepre?

In 75 salti, cioè 150:2
The computational attitude:
algorithms

An algorithm is a step-by-step set of
directions guaranteed to achieve a task,
which may be to solve a particular problem,
in a finite number of steps.

http://iae-pedia.org/Computational_Thinking#Computational_and_Procedural_Thinking

A heuristic is like an algorithm except that
accomplishment of a specific task or
solution of a specific problem is not
guaranteed.
Algorithms and computers
A computer is a machine that can automatically,
rapidly, and accurately carries out the steps in
certain types of procedures.
Computer programmers think in terms of solving
problems and accomplishing tasks through the use
of procedures.
Attenzione al linguaggio
Language and philosophy
Sophists and philosophers
Language and mathematics
Mathematical rigor
The discovery of “languages”
Wittgenstein: linguistical games
The “analogy”
Transfer cocepts and methods from one language
to another one:
useful, but very dangerous!!!
Scientifical languages
(and others)
•"Measuring" the diagonal of the square
• Establish the following "equations":
Fe +H2SO4 = FeSO4 +H2
Cu +H2SO4 = CuSO4 +H2
Denotational antinomy
• 343
is
73
• 343
is
three-digit
• 73
is
three-digit
A logic for every language
(also in computer science)
Axioms and rules
la comunicazione diretta
DIRETTA
LINGUAGGIO
CORPOREO
ODORARE
SEGNI
SUONARE
PARLARE
la comunicazione mediata
In modo tradizionale
TESTO
DISEGNO
RIPRODUZIONE
ANALOGICA
IMMAGINI
SCRITTURA
SUONI
la comunicazione mediata
via computer
TESTO
SUONI
IMMAGINI
ANALISI
SINTESI
INTERPRETAZIONE.
PR & IP
SCENE
ANALYSIS
Visual
Programming
Spreadsheet
DOCUMENT
IMAGE
OCR
Visual Query
Systems
Visual
Languages
Scientific
Visualization
Algo Animation
SW Visualization
Code Animation
Process
Visualization
Environment Dev.
Data Animation
la comunicazione mediata
via computer
TESTO
SUONI
IMMAGINI
ANALISI
SINTESI
INTERPRETAZIONE.
PR & IP
SCENE
ANALYSIS
Visual
Programming
Spreadsheet
DOCUMENT
IMAGE
OCR
Visual Query
Systems
Visual
Languages
Scientific
Visualization
Algo Animation
SW Visualization
Code Animation
Process
Visualization
Environment Dev.
Data Animation
Old and new metaphores


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
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
Space
Time
Game
Images
Light
Grammars
Biological structures
…….
Interfaces construction
Interface is a program allowing a user to use programs contained in a
computer
Hence it is aimed to “non technical people” (Myers 93)

Difficulty in understanding users attitudes

Complexity

Balance among graphic, writing, languages, detail levels, social- legal
constraints, implementation time t...
Theories and guidelines are not sufficient

Visual metaphors
Use of visual metaphors in a
didactical context

An example: e-learning for deaf people
The problem
Difficulty in learning to read and to
write
 Diacronical and syncronical
arrangement of language
 Sign language and representation
difficulty

New tecnologies and iconical
information

Introduction of a video in LIS?

This is possible, but it does not solve
the problem
58
Metafora e embodiement

La matematica è un campo di “criticità
sensoriale” anche per persone senza
deficit, perché “astratta” e “non
raccontabile”

Necessità di metafore spaziali e non:
geometria, teoria degli insiemi,
operatività…
Informatica e interdisciplinarietà
Applicazioni
Ambienti virtuali
 Videogiochi
 E-learning

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