1. 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

2. SIMPLE ARITHMETIC INDUCTION INTUITIVE PROCESSES COMPLEX ALGEBRA DEDUCTION PROOF PRODUCTS 1. TRANSITION

3. WG 2 2.UNIFYING CONCEPTS MATH COGNIT CONTENTS PROCESSES DIDACT.

4. WG 2 2. UNIFYING CONCEPTS MATH COGNIT CONTENTS PROCESSES DIDACT. A) PROCESSESB) CONTENTS C) COGNIT.

5. WG 2 A) PROCESSES vs/PRODUCTS CONTENTS asACTIVITIES &CREATIVITY

6. WG 2 B) CONTENTS: Which? How much? Functions (linearity) Algebraic thought

7. WG 2 C) FLEXIBLE PATTERNS THROUGH OPEN PROBLEMS SISTEMATICITY ?

8. WG 2 3. LANGUAGE INNER PROCESSES LOGICAL SKILLS COMMUNIC. READING & WRITING

9. 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

10. 4. TECHNOLOGY + DIFFICULT PROBLEMS LOGICAL SKILLS - NUMERACY ? FINAL EXAMS (paper&pencil) DGS: 3D INTUITION/PROOF GIRLS ISSUES CALCULATORS

11. WG 2 HOW TO DEVELOP IT ? DEFINITIONS: ideological features cultural issues 5. CREATIVITY

12. WG 2 6. TESTING OPEN ENDED VS/ STRUCTURED PRODUCTS VS/ PROCESSES

13. WG 2 7. SOME CONTRADICTORY ISSUES CHALLENGING THE INNOVATION CHALLENGING THE TRADITION ? BUT !

14. 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)

15. WG 2 CHALLENGING THE TRADITION 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 seem to contradict their general performances

16. WG 2 BUT IN CHILE, JAPAN,… SOME OF THE CHALLENGED INNOVATIVE ISSUES ARE AT THE BASIS OF THE NEW REFORMS OF THE SCHOOL

17. WG 2 8. WHAT DO THEY MEAN THESE WAR WINDS THAT ARE NOW BLOWING?           

18. 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.

19. 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

20. WG 2 10. SOME DATA: # STUDENTS: 20 - 60 FOR EACH CLASS # HOURS PER WEEK: 2.5 - 5

21. WG 2 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