SUMMARY TO CONGRESS

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WG 2 MATHEMATICS EDUCATION IN JUNIOR SECONDARY
SCHOOL Ferdinando Arzarello (Italy), CO Alwyn
Olivier (South Africa), CO Rick Billstein
USA, AO Keiichi Shigematsu Japan,
AO Suwattana Utairat Thailand, AO Nanae
Matsuo , LAO IPC Liason Member Julianna Szendrey
Hungary
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. AIMS AND GOALS 11. SOME DATA
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WG 2
THE ITEMS SUGGESTED BY IPC
A brief statistics 1. Interesting issues 2.
Interesting research questions 3. Which
developments since last ICME 4. Where might the
WGA go on the next ICME 5. Which obstacles to the
implementation of new ideas
MORE THAN 100 PARTECIPANTS 3 HALF AN HOUR
LECTURES 5 TWENTY MINUTES PRESENTATIONS 1
WORKSHOP 160 MINUTES DISCUSSIONS (3 SUBGROUPS AND
A PLENARY ONE)
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WG 2
MORE THAN 100 PARTECIPANTS 3 HALF-AN-HOUR
LECTURES 5 TWENTY-MINUTES PRESENTATIONS 1
WORKSHOP (50 MINUTES) 160 MINUTES DISCUSSIONS (3
SUBGROUPS AND A PLENARY ONE)
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WG 2
THE MAIN PROBLEM TRANSITION
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ICME 9
School education from grade VI to grade X is
characterised by TRANSITIONS ? from compulsory
education to jobs and/or vocational school
education ? from school-for-all to different
schools (or curricula). ? from child to adult
behaviours of learners within the 11-16 age
range.
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ICME 9
Mathematics education plays a special function in
these transitions ? it must ensure the
acquisition of crucial tools for life and many
professions ? it must prepare students for
further studies in scientific and technological
areas ? it is supposed to pass over relevant
components of modern scientific culture.
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ICME 9

• The problem of transition has been investigated
  and discussed from different points of view,
  e.g.
• MATHEMATICAL
• COGNITIVE
• CULTURAL
• POLITICAL

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ICME 9
From a MATHEMATICAL point of view, it has been
underlined the necessity of introducing important
and challenging issues, which appear as UNIFYING
and crucial in the present historical moment
(which is itself also featured by deep transition
-social and political- aspects).
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ICME 9
From a CULTURAL point of view the learning of
mathematics evolves differently in different
countries, because of cultural reasons.
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ICME 9
From a POLITICAL point of view, the transition
has been considered underlyning The evolution
of the school organization. The specific
tendencies and the general features of the
teaching of mathematics in JSS in different
countries have been considered. The
suggestions mathedu research can give to
politicians in order to improve mathematics
teaching in the school.
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WG 2
WITHIN THIS FRAMEWORK THE FOLLOWING ISSUES HAVE
BEEN DISCUSSED
1. TRANSITION 7. SOME CONTRADICTIONS 2.
UNIFYING CONTENTS 8. WINDS OF WAR 3.
LANGUAGE 9. THE ISSUE OF GEOMETRY 4. NEW
TECHNOLOGIES 10. AIMS AND GOALS 5.
CREATIVITY 11. SOME DATA 6. TESTING
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WG 2
ISSUES
NEW
NEXT
OBST.
RESEARCH
TRANSITION
?
?
?
UNIF. CONC.
?
?
LANGUAGE
?
TECHNOL.
?
?
?
?
CREATIVITY
?
TESTING
?
CONTRADICT
MATH WAR
?
GEOMETRY
?
AIMS ,GOALS
?
?
NUM. DATA
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WG 2
1. TRANSITION
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WG 2
MATH
PROCESSES
2.UNIFYING CONCEPTS
COGNIT
CONTENTS
DIDACT.
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WG 2
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WG 2
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WG 2
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WG 2
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WG 2
LOGICAL SKILLS
INNER PROCESSES
COMMUNIC.
READING WRITING
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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
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WG 2
4. TECHNOLOGY
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WG 2
HOW TO DEVELOP IT ? DEFINITIONS ideological
features cultural issues
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WG 2
OPEN ENDED VS/ STRUCTURED PRODUCTS VS/ PROCESSES
6. TESTING
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WG 2
CHALLENGING THE INNOVATION
CHALLENGING THE TRADITION
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WG 2
CHALLENGING THE INNOVATION ? OPEN ENDED
MATHS problem solving with open, non routine
problems (possibly, no systematic
learning) ? INTEGRATED LEARNING (basic
skills in a more or less traditional way)
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WG 2
CHALLENGING THE TRADITION Challenging the
stability of mathematical thinking development in
students Example hierarchies vs/ networks
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WG 2
BUT IN CHILE, JAPAN, SOME OF THE CHALLENGED
INNOVATIVE ISSUES ARE AT THE BASIS OF THE NEW
REFORMS OF THE SCHOOL
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WG 2
8. WHAT DO THEY MEAN THESE WAR WINDS THAT ARE NOW
BLOWING?
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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.
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WG 2
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WG 2
10. AIMS AND GOALS COGNITIVE (understanding,
math literacy) METACOGNITIVE (thinking in
a developmental way ways of looking
positively at maths)
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WG 2
THE LAST THREE QUESTIONS of IPC

• WHAT NEW FROM LAST ICME?
• WHICH NEW RESEARCHES FOR NEXT ICME?
• WHICH OBSTACLES TO THE IMPLEMENTATION OF NEW
  IDEAS?

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WG 2
WHAT NEW FROM LAST ICME?
THE MATHEMATICAL WAR
AND THE NECESSITY OF A 3RD ROUTE IN BETWEEN
CONSTRUCTIVISM AND TRADITIONAL METHODS
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WG 2
NEW RESEARCH ISSUES FOR ICME 10
1. WHICH EXPERIMENTAL EVIDENCE THAT COMPUTERS,
WEB,... DO INCREASE MATH LEARNING ? WHAT AND HOW
TO ASSESS? 2. TWO DIFFERENT APPROACHES TO
TRANSITION a) CONTENTS-ORIENTED b)
SYSTEMIC-ORIENTED
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WG 2
3. AIMS AND GOALS ARE CULTURALLY DEPENDENT
USEFUL A COMPARISON BETWEEN STATES WITHIN A
STATE (DIFF. SUBJECTS) 4. FOCUSING TRANSITION
FROM ELEMENTARY AND TO HIGHER SEC. SCHOOL. 5.
CONSEQUENCES OF TESTING IN DIFFERENT COUNTRIES.
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WG 2
OBSTACLES
THE LACK OF TECHNOLOGY FEABLESS OF TEACHERS
TRAINING IN NT
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WG 2
11. SOME DATA STUDENTS 20 - 60 FOR EACH
CLASS HOURS PER WEEK 2.5 - 5 DIFFERENT AGES
OF STUDENTS DIFFERENT AIMS