### Summary to WG#2 by Ferdinando Arzarello

```1. TRANSITION
2. UNIFYING CONTENTS
3. LANGUAGE
4. NEW TECHNOLOGIES
5. CREATIVITY
6. TESTING
8. WINDS OF WAR
9. THE ISSUE OF GEOMETRY
10. SOME DATA
WG 2
WG 2
1. TRANSITION
SIMPLE
COMPLEX
ARITHMETIC
ALGEBRA
INDUCTION
DEDUCTION
INTUITIVE
PROOF
PROCESSES
PRODUCTS
WG 2
MATH
PROCESSES
2.UNIFYING
COGNIT
DIDACT.
CONCEPTS
CONTENTS
WG 2
A) PROCESSES
MATH
C) COGNIT.
COGNIT
DIDACT.
PROCESSES
2. UNIFYING
CONCEPTS
CONTENTS
B) CONTENTS
WG 2
A) PROCESSES
vs/
PRODUCTS
CONTENTS
as
ACTIVITIES
&
CREATIVITY
WG 2
B) CONTENTS:
Which? How much?
Functions (linearity)
Algebraic thought
WG 2
C) FLEXIBLE PATTERNS
THROUGH OPEN PROBLEMS
SISTEMATICITY ?
LOGICAL
SKILLS
COMMUNIC.
3. LANGUAGE
WRITING
WG 2
INNER
PROCESSES
WG 2
COMMUNICATION
It is related with: processes
culture
Pupils express themselves
Helps students to set down their working
into a framework
Differences between pupils/teacher/book
WG 2
+ DIFFICULT PROBLEMS
LOGICAL SKILLS
- NUMERACY
? FINAL EXAMS (paper&pencil)
4. TECHNOLOGY
DGS:
3D
INTUITION/PROOF
GIRLS ISSUES
CALCULATORS
WG 2
5. CREATIVITY
HOW TO DEVELOP IT ?
DEFINITIONS:
ideological features
cultural issues
WG 2
OPEN ENDED
6. TESTING
VS/
STRUCTURED
PRODUCTS
VS/
PROCESSES
WG 2
CHALLENGING
THE INNOVATION
BUT
!
7. SOME
ISSUES
CHALLENGING
?
WG 2
CHALLENGING THE INNOVATION
 OPEN ENDED MATHS
- problem solving with open,
non routine problems
(no systematic learning;
teaching obsolescence)
 INTEGRATED LEARNING
(basic skills in a more or less
WG 2
Challenging the stability of mathematical
thinking development in students
Examples:
 hierarchies vs/ networks
(van Hiele hierarchy for geom. Concepts)
 results got by pupils in
some specific objective tests
general performances
SCORE
LEVEL
E D
C B
A
WG 2
BUT IN CHILE, JAPAN,… SOME OF
THE CHALLENGED INNOVATIVE
ISSUES ARE AT THE BASIS OF THE
NEW REFORMS OF THE SCHOOL
8. WHAT DO THEY MEAN THESE WAR
WINDS THAT ARE NOW BLOWING?

WG 2
WG 2
There are elements which are difficult
to construct in a constructivist
approach to theoretical knowledge
and difficult to mediate through a
WG 2
9. THE ISSUE OF GEOMETRY
• USEFULNESS FOR 3D
• A BASIC PATH IN SOME
COUNTRIES (but numerical skill
are overemphasized in others)
• A CULTURAL ISSUE: GIRLS
WG 2
10. SOME DATA:
# STUDENTS: 20 - 60 FOR EACH CLASS
# HOURS PER WEEK: 2.5 - 5
1. TRANSITION
2. UNIFYING CONTENTS
3. LANGUAGE
4. NEW TECHNOLOGIES
5. CREATIVITY
6. TESTING