MATHEU

1
MATHEU
??????S??S, ??????? ??? ???S??????
??T??????O? ??????O? S? ???O?????
S?????? Identification, Motivation and Support
of Mathematical Talets in European Schools
G??????? ?a???d?? S??t???st??
2
?? p??ß??µa
?? µe????t???? a?t??e?µe????? st???? t??
????pa???? ??pa?de?t???? S?st?µat??, ?p??
s?µf??????e st? d??s?e?? t?? St?????µ?? st?? 12
Feß???a???? 2001, p??sd???????? ta ?a??µat??? ??
??a ap? ta p??te???ta µa??µata. ? ßas???? st????
e??a? ?a a?apt???e? t? e?d?af???? ??a ta
µa??µat??? ap? µ????? ?????e? ?a? ?a ?a???e????e?
? ?fes? ?a a??????????? ?a????e? se a?t??? t???
t?µe??, ?a? e?d???te?a ? ??e??a.
3
?? p??ß??µa
?? e?d?? t?? µa??t?? p?? ?a ??e? t?? d??at?t?ta
?a s??e?sf??e? e?e???t??? st?? ep?st?µ? ?a? t??
te???????a e??a? p??? p??a??te?? ?a e??a? µa??t??
?? ?p???? ????? ep?de??e? ta???t? se a?t??? t???
t?µe??, ?a? e?d???te?a sta µa??µat???.
4
?? p??ß??µa
???sµ??e? ???e? p?? s?µµet????? st? e? ????
p????aµµa ????? ?d? d?ast????p????e? p??? a?t?
t?? ?ate????s?. ? st???? t?? p?????µµat?? e??a?
?a s???e?t?????? e?d???? ?? ?p???? e??a?
d??spa?t?? st?? d??f??e? ???e? p?? s?µµet?????
st? p????aµµa ?ste ?a ???e? a?ta??a?? ?de??,
ap??t??e?sa? pe??a? ?a? ???s??, ?a? ?a a?apt???e?
??a s?st?µa t? ?p??? ?a ?e?t????e? ??a ????????
t?? ????p?.
5
?? p??ß??µa
?? ta?a?t????? µa??t?? sta µa??µat??? p??pe?
p??ta ?a e?t?p?s????, ?a? µ???sta se p???µ?
st?d?? ?a? s?st?µat???. ? s?????? t??p??
e?t?p?sµ?? t?t???? µa??t?? e??a? µe µa??µat?????
d?a????sµ???. ???a? ?µ?? ????? ap?de?t? ?t? p???
ta?a?t????? sta µa??µat??? µa??t?? ??d?p?te
e?t?p????ta? ??a t?? ap???stat? ???? ?t? de?
s?µµet????? st??? d?a????sµ??? ? d??t? de?
?atat?ss??ta? st??? ????????µ??? ????fa???? ?,
t????, de? ????? t?? d??at?t?ta ?a e?e?????
a?t???a t?? ??a??t?t?? t??? ?p? t?? ???????
pe?????sµ? p?? ??t??? ?? d?a????sµ??.
6
?? p??ß??µa

• ?a ????pa??? ???t? ?fe????? ?a ep????s???
  µe??d??? ?a s????at??? sta ed?f? t???
  ta?a?t?????? ?a? ta ?s???? µ?a??. G?a ?a t?
  ep?t????? a?t?, ?? µa??µat????, ?? a?ad?µa????
  ?a? ?? e?pa?de?t???? ?fe????? ?a s??e??ast??? se
  ????pa??? ep?ped? ?ste ?a ?ata?t?s??? ??a
  p????aµµa t? ?p??? ?a pe?se? ??ße???se??,
  ?a?ep?st?µ?a ?a? ?d??µata ?? p??? t??
  a?a??a??t?ta ?p?st?????? µe??d?? ?? ?p??e? ?a
  ????? ?? ap?t??esµa t?? e?s??? ta?a?t?????
  µa??µat???? st?? ????p? ?a?, pa??????a, t??
  s?????t?s? t?? f???? t?? se ???e? e?t??. ??
  ta?a?t????? µa??t?? ????? a????? p??s????,
  ?a?p????, st??????, d?das?a??a?, a?a?????s?? ?a?
  d?????s??.

7
S??p?? ?a? st????

• ? s??p?? t?? p?????µµat?? e??a? ? a??pt???
  µe??d?? ?a? a?t?st????? ?????? ??a t?? e?t?p?sµ?
  µa??t?? se s???e?a t?? ????p?? µe ta???t? sta
  µa??µat???, t?? st????? ?a? t?? ?a??????e?a t??
  de???t?t?? t??. ?? p????aµµa p??t??eta? ?a
  d?µ??????se? ??a p???µa µ???µ?? st?????? t?? µ?s?
  ?a?ep?st?µ???, ??????? ?a??µat???? ?ta??e??? ?a?
  ?d??µ?t?? t?? ????? p?? s?µµet????? a??? ?a?,
  a???te?a, ???? t?? ????? t?? ????p??.

8
S??p?? ?a? st????

• ?? ?a????t?? st?? ????p? ??e?????ta? ?at??????
  e?pa?de?s? ?a? p??µ??e?a ?????? ??a t?? ep?te???
  t?? st???? t?? p?????µµat??, ?ste ?a e??a? se
  ??s? ?a a?a????????? ?a? ?a st??????? t???
  ta?a?t?????? µa??t?? t???.
• ? ?????? st???? t?? p?????µµat?? e??a? ?a
  s?µß???e? ?ste ? ????p? ?a ?fe???e? ?s? ???eta?
  pe??ss?te?? ap? t?? µe????t??? s?µß??? t?? e?
  ???? µa??t??, ?? ?p???? a???? ?a e??a? ?? ta???
  t?? ep?st?µ?????? ?a? te?????????? ???s?? ? ?p??a
  apa?te?ta? ?ste ?a ß??s?eta? ? ????p? st??
  eµp??s??f??a?? t?? te?????????? p???d?? ?a?
  ??????µ???? d??at?t?t??.

9
??e? p??se???se??

• ??? a??pt??? e??a??? ????pa???? p?????µµat??
  ep?µ??f?s?? t? ?p??? ?a pa???e? ta ef?d?a ??a t??
  e?t?p?sµ?, ta ????t?a ?a? st? ?p?st????? µa??t??
  ta?a?t????? sta µa??µat??? e??a? µ?a ??a
  p??s????s? ? ?p??a µp??e? ?a ?e?t?????se?
  ep???????? sta ?p?????ta a?a??t??? p?????µµata
  t?? ????pa???? ???s??, ????? d?a???se??.
  ?p?p????, µe ???s? ???? te????????? ??a t??
  pa???? sta?e??? ?a? µa????????a? st?????? se
  ?µ?da µa??t?? µe ?????? d??at?t?te? se ??a
  s???e???µ??? ped??, e??a? µ?a ??a µe??d?????a.

10
??e? p??se???se??

• ? s?????t?s? ta?a?t????? sta µa??µat??? µa??t??
  st?? ????p? ?a? ? e?s??? e??ef???? (brain gain)
  e??a? ep?s?? ??a f???s?f?a ?a? p??s????s? t??
  ??µat??. ?p?s??, µ???? t?? p?????µµat?? ?a
  e?e???se? t? p??ß??µa t?? ta?a?t????? sta
  µa??µat??? µa??t?? a??? ?? ?p???? pa???s??????
  µa??s?a??? d?s????e?, ??a ??µa t? ?p??? de? ??e?
  µ???? t??a µe?et??e?.

11
????? ? ????? t?? e?pa?de?t????

• Te????µe t??? ?a????t?? t?? µa??µat???? ??
  e?pa?de?t????? ?? ?p???? e??a? ??a??? ?a
  e?pa?de?s??? µa??t?? t?s? se tµ?µata µe µ??t??
  ??a??t?te? µa??t?? ?s? ?a? se ep??e?µ??a ???? t??
  e?d???? ??a??t?t?? t???. ??e???t?ta ap? t?
  pe??ß?????, ?? ?a????t?? t?? µa??µat???? ?fe?????
  ?a ????? ta ef?d?a ?a a????????? t?? ???se?? t??
  a???at????? t??, ?a? ?a e??a? se ??s? ?a
  e??a???????, ?a pa?????? ????t?a ?a? ?a st???????
  e?e????? ?? ?p???? fa??eta? ?a ????? ???s? se
  µa??µata ?p?? ta µa??µat???.

12
????? ? ????? t?? e?pa?de?t????

• ??d???, t? p????aµµa ?a ??e? ?? st??? t??
  a??pt??? a?a??t???? p????aµµ?t?? ta ?p??a
  a?ade??????? t?? ???? t?? e?pa?de?t????
• St?? e?t?p?sµ? ta?a?t????? µa??t?? sta µa??µat???
  µe ???s? e??? f?sµat?? µe??d?? p??a ap? ta
  ?a??e??µ??a test. ?? µ???d?? ?a pe???aµß?????
  pa?at???se??, s??e?te??e?? µa??t??, e??t?se??
  a????t?? t?p??, ?a?t?f?????? e??as???, a???????s?
  ap? das??????, ???e?? ?a? e?d????? ?a?, t????,
  ap? a?t?a???????s?.
• St?? apas????s? t?? µa??t?? µe e?d?af????ta
  ??µata ta ?p??a t??? ??????? ?ste ?a a?apt?????
  t?? µa??µat???? t??? de???t?te?.

13
????? ? ????? t?? e?pa?de?t????

• St? ße?t??s? t?? e??a????? ??a ap??t?s?
  µa??µat???? ???se?? ?a? st? a??pt??? p??
  apa?t?t???? a?a??t???? p?????µµat??, ?????
  ??p?ast???? epa?a???e??, ?a? p?? ????????µ????,
  ?ste ?a ß??????ta? ?? µa??t?? ?a a?apt?????
  µa??µat???? de???t?te?. ?? µa??t?? p??pe? ?a
  ?p???????ta? ?a ep?????? d??? t??? e??t?µata, ?a
  e?e????? ?a? ?a pa?????? µa??µat??? ta ?p??a t???
  e??a? ??a. ?? ?d??? ????? a????? d?e??d?? ?ste
  ?a µ???????ta? t?? a?a?a???e?? t??? µe ??????.
• St? ???s? e??? e???te??? p???µat?? µe??d??
  s?µpe???aµßa??µ???? t?? s????????? e??as??? ?a?
  d?ast????t?t?? p??a ap? a?t?? t?? a?a??t????
  p?????µµat??, ?p?? e?as????s? e?t?? ??a????,
  ?e???? s???e?a, d?a????sµ?? ?.t.?.

14
????? ? ????? t?? e?pa?de?t????

• St? ße?t??s? t?? µe??d?? µe t?? ?p??e? ap??t???
  ???se?? ?? µa??t??. ?? ?a????t?? ?fe????? ?a
  d?e????????? t?? e?pa?de?t??? d?ad??as?a t??
  µa??t??, ?a t??? e??a??????? ?a ?ata????? ??e?
  ?a? p?? p???p???e? µa??µat???? ?????e?. ??
  µa??t?? p??pe? ?a ?aµß????? ????t?a ?ste ?a
  a?eß????? s??e??? t? ep?ped? t?? µa??µat???? t???
  ???se??.

15
????? ?fe?e?ta? ap? t? ?????aµµa

• ?? ?a????t?? µa??µat???? se ??a ta ep?peda
  (???t?ß??µ?a ? ?e?te??ß??µ?a ??pa?de?s?) ??
  ?p???? s??e??????ta? µe t? p????aµµa ?a ?????
  ?µes? ?fe???. ?? e?pa?de?t???? ????? ???d??
  µp????? ep?s?? ?a ?fe?????? d??t? t? ????? t?
  ?p??? d?e??????e? st?? e?t?p?sµ? ta?a?t????? sta
  µa??µat???, µp??e? ?a ???s?µ?p????e? ?a? ??a
  e?t?p?sµ? ta?a?t????? se ?????? ???d???. ?e t??
  d??d?s? t?? ?????? ?a? t?? µe??d?? ??
  e?pa?de?t???? ap? ??e? t?? ???e?, µ?sa ?a? ???
  ap? t?? ????pa??? ?????t?ta, ?a??? ?a? ??
  a?t?st????? f??e?? ?a e??a? se ??s? ?a ?fe??????
  ap? t? p????aµµa µe t?? s?µµet??? t??? st??
  ep?µ??f?s? p?? ?a p??sfe??e? ?p? t?? a???da t??
  Comenius ???s? 2.2. ?? s?µe???e? ?t? ? µe?a??te??
  ?µ?da p?? ?a ?fe???e? e??a? ?? e? d???µe?
  ta?a?t????? sta µa??µat??? µa??t??.

16
??S? ?? st???? t?? p?????µµat?? ?a ep?te??????
µe

• ?????s? t?? ?pa????t?? a?a??t???? p????aµµ?t??
  t?? ??at?? p?? s?µµet????? st? p????aµµa
• ?????s? t?? µe??d?? p?? ???s?µ?p?????ta? ??a t??
  e?t?p?sµ? ?a? t?? st????? µa??t?? t?? ????p??, µe
  ta???t? sta µa??µat???

17
??S? ?? st???? t?? p?????µµat?? ?a ep?te??????
µe

• 3. ???pt??? µe??d?? ?a? e??a?e???, ??a ???s? t??
  d?das???t??, ??a t?? e?t?p?sµ? ta?a?t????? sta
  µa??µat??? µa??t??
• 4. ???pt??? pa?da??????? µe??d?? ?a?
  e?pa?de?t???? ?????? ??a st????? d?das???t?? ?a?
  µa??t??

18
??S? ?? st???? t?? p?????µµat?? ?a ep?te??????
µe

• 5. ??e???? µe??d?? ?a? e??a?e??? ??a t??
  e?t?p?sµ? ta?a?t????? sta µa??µat??? µa??t??.
  ????????s? t?? e??????.
• 6. ??e???? t?? ?????? se ?µ?da ta?a?t?????
  µa??t?? ?? ?p???? ?a ep??e???? ap? ta ???t? p??
  s?µµet?????. ????????s? t?? e??????. ?e?t??s?.

19
??S? ?? st???? t?? p?????µµat?? ?a ep?te??????
µe

• 7. ??aµ??f?s? ?de??, p????f???a??? ?????? ?a?
  e??? p?????µµat?? ??a a??a?? t?? ap??e?? ep? t??
  ??µat?? µ?sa st?? ??ße???se??, ta ?a?e-p?st?µ?a
  ?a? ta ?d??µata.
• 8. ??????s? S?µp?s??? ??a t?? p????f???s? ?a?
  t?? d??d?s? t?? p?????µµat??, µe st??? t??
  ??ße???se??, ta ?a?ep?st?µ?a ?a? ta ?d??µata se
  ???????? t?? ????p?.

20
??S? ?? st???? t?? p?????µµat?? ?a ep?te??????
µe

• 9. ?e???? µ??f? t?? µe??d??, e??a?e??? ?a?
  ??????.
• 10. S?ed?asµ?? µa??µ?t?? ??a t?? e?pa?de?s?
  e?pa?de?t????.
• 11. ?e???? a???????s? ?a? ???es? t??
  p?????µµat??.

21
S??e??a??µe??? F??e??
22
?p????????a

• www.matheu.org
• www.matheu.eu
• makrides.g_at_intercollege.ac.cy