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

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

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

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  1. 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

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

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

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

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

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

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

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

  9. 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

  10. WG 2 + DIFFICULT PROBLEMS LOGICAL SKILLS - NUMERACY ? FINAL EXAMS (paper&pencil) DGS: 3D INTUITION/PROOF GIRLS ISSUES CALCULATORS 4. TECHNOLOGY

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

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

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

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

  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

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