1. TRANSITION 2. UNIFYING CONTENTS 3. LANGUAGE 4. NEW TECHNOLOGIES 5. CREATIVITY 6. TESTING

1. TRANSITION

2. UNIFYING CONTENTS

3. LANGUAGE

4. NEW TECHNOLOGIES

5. CREATIVITY

6. TESTING

7. SOME CONTRADICTIONS

8. WINDS OF WAR

9. THE ISSUE OF GEOMETRY

10. SOME DATA

WG 2

WG 2

SIMPLE

ARITHMETIC

INDUCTION

INTUITIVE

PROCESSES

COMPLEX

ALGEBRA

DEDUCTION

PROOF

PRODUCTS

1. TRANSITION

WG 2

2.UNIFYING

CONCEPTS

MATH

COGNIT

CONTENTS

PROCESSES

DIDACT.

WG 2

2. UNIFYING

CONCEPTS

MATH

COGNIT

CONTENTS

PROCESSES

DIDACT.

A) PROCESSES

B) CONTENTS

C) COGNIT.

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 ?

WG 2

3. LANGUAGEINNER

PROCESSES

LOGICAL SKILLS

COMMUNIC.

READING & WRITING

COMMUNICATION

It is related with: processesculture

Pupils express themselves

Helps students to set down their working into a framework

Differences between pupils/teacher/book

WG 2

WG 2

4. TECHNOLOGY

+ DIFFICULT PROBLEMS LOGICAL SKILLS- NUMERACY? FINAL EXAMS (paper&pencil)

DGS:

3D

INTUITION/PROOF

GIRLS ISSUES

CALCULATORS

WG 2

HOW TO DEVELOP IT ?

DEFINITIONS:

ideological features

cultural issues

5. CREATIVITY

WG 2

6. TESTING

OPEN ENDED

VS/

STRUCTURED

PRODUCTS

VS/

PROCESSES

WG 2

7. SOME

CONTRADICTORY

ISSUES

CHALLENGING THE INNOVATION

CHALLENGING THE TRADITION

?BUT !

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 traditional way)

WG 2

CHALLENGING THE TRADITION

Challenging the stability of mathematical thinking development in students

Examples: hierarchies vs/ networks (van Hiele hierarchy for geom. Concepts)

LEVEL

SCORE

E D C B A

results got by pupils in some specific objective tests seem to contradict their general performances

WG 2

BUT IN CHILE, JAPAN,… SOME OF THE CHALLENGED INNOVATIVE ISSUES ARE AT THE BASIS OF THE NEW REFORMS OF THE SCHOOL

WG 28. WHAT DO THEY MEAN THESE WAR WINDS THAT ARE NOW BLOWING?

WG 2

There are elements which are difficult to construct in a constructivist approach to theoretical knowledge and difficult to mediate through a traditional approach.

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

WG 21. TRANSITION

2. UNIFYING CONTENTS

3. LANGUAGE

4. NEW TECHNOLOGIES

5. CREATIVITY

6. TESTING

7. SOME CONTRADICTIONS

8. WINDS OF WAR

9. THE ISSUE OF GEOMETRY

10. SOME DATA