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Finse 15-jarigen
scoren volgens Finse onderzoekers en docenten wiskunde zwak voor wiskunde en
PISA is misleidend. En onze Vlaamse
14-jarigen? (Raf Feys)
1.Uit Evaluatiestudies van
de universiteit van Helsinki (2004, 2010, 2012) bleek telkens opnieuw dat de Finse leerlingen secundair onderwijs
opvallend zwak scoorden voor wiskunde e.d. en dat de PISA-scores misleidend
waren. Zelf stellen we ons ook ernstige vragen over de resultaten wiskunde in
de eerste graad s.o.
In Onderwijskrant berichtten we destijds ook over een
manifest van 200 Finse docenten uit 2005
met als titel :The first place in the PISA study is a Pyrrhic victory. Volgens
die 200 docenten was de wiskunde-kennis van de Finse leerlingen s.o. zorgwekkend
en werd Finland misleid door PISA. De docenten waren vooral niet te spreken over het lage niveau in de
gemeenschappelijke (comprehensieve) lagere cyclus.
2.Dit betekent uiteraard ook dat we de
goede PISA-score voor Vlaanderen moeten relativeren - ook al zijn we tevreden
met het feit dat we voor PISA-2012 samen
met Zwitserland de hoogste Europese score behaalden (als we even abstractie maken van het kleine
en rijke Lichtenstein.)
Er zijn volgens ons voldoende redenen om ons toch zorgen te
maken over de leerresultaten wiskunde in de eerste graad s.o. - los nog van de daling in PISA-2012 in vergelijking
met 2003.
De TIMSS-evaluatiestudie sluit beter aan bij de
'school-wiskunde', maar na 2003 mochten we vanwege de minister van onderwijs
niet meer participeren. In TIMSS 2003 behaalden we nog de topscore - een flink
stuk hoger dan Finland - en dit
niettegenstaande Vlaanderen veel meer anderstalige allochtone leerlingen en
veel meer armoede telt dan Finland.
Het was wel zo dat het aantal toppers met een heel hoge
score (minstens 625 punten) in 2003 met de helft was gedaald in vergelijking
met 1999 (in 4 jaar tijd). Ook op de één na hoogste standaard werd een
belangrijke daling opgetekend. We vermoed(d)en dat de invoering in 1998 van de
nivellerende en constructivistisch getinte eindtermen en de erbij aansluitende
leerplannen hier een rol speelde.
3.Mede op basis
van de achteruitgang voor TIMMS, van de
vele klachten van Vlaamse docenten wiskunde en van de tegenvallende evaluatie
van de eindtermen wiskunde eerste graad,
schreven we destijds in Onderwijskrant nummer 146 een kritische bijdrage
over het wiskunde-onderwijs in de lagere cyclus. We gingen ook niet akkoord met
de professoren Lieven Verschaffel, Dirk De Bock en Dirk Janssens die destijds
in het tijdschrift 'Karakter' de hervorming van 1998 en de invloed erop van de constructivistische
wiskunde van het Nederlandse Freudenthal-Instituut de hemel in prezen. De
auteurs verwezen ook even naar de goede score voor PISA 2003, maar intussen
wisten we al dat PISA weinig zegt over
de toestand van de 'echte' (school-)
wiskunde. Ze verzwegen wel de daling
voor TIMSS 2003 in vergelijking met 1999.
4. De
leerkrachten eerste graad zijn er ook van overtuigd dat de invoering van een
gemeenschappelijk eenheidsleerplan in 2009 tot een verdere niveaudaling heeft
geleid. Met die aanpassing wou de VVKSO- onderwijskoepel vooruitlopen op de
invoering van een gemeenschappelijke eerste graad (middenschool). We
moeten o.i. dringend het leerplan en de
eindtermen voor de eerste graad bijwerken en opnieuw meer vak-wiskunde -
aansluitende bij de wiskunde als cultuurdiscipline - invoeren. Destijds steunde
de Gentse prof. Leo Apostel mij in de strijd tegen de constructivistische
wiskunde van het Freudenthal-Instituut.
In Nederland weerklonk er de voorbije 15 jaar veel kritiek op de visie
en invloed van het Freudenthal-Instituut,
die er een kleine schooloorlog uitlokt(e).
5.Voor het lager
onderwijs deden we in de periode 1988-1998 ons uiterste best om zoveel mogelijk
de constructivistische en realistische wiskunde-aanpak à la
Freudenthal-Instituut en Amerikaanse Standards ('doing mathematics') buiten de eindtermen en de leerplannen te
houden. Dat is ook grotendeels gelukt.
We waren dan ook wel tevreden dat onze 10-jarigen voor TIMSS-2011 als de beste
presteerden - iets beter ook dan de Finse .(TIMMS-2011 was geen initiatief van
minister Smet, maar van de KU-Leuven.)
Verheugend was ook dat de Vlaamse 10-jarigen zelfs stukken beter presteerden dan in de meeste landen met een universitaire
lerarenopleiding. Ook uit andere studies
bleek dat de duizenden oud-studenten van
onze geïntegreerde en praktijkgerichte
normaalschool blijkbaar niet zo
slecht presteren. (Dit alles belet niet
dat we ons moeten inspannen om het niveau (van de voorbije jaren) weer
wat op te krikken.)
Bijlagen over Finland
1.Manifest van 200 docenten:
The
PISA survey tells only a partial truth of Finnish children's mathematical
skills
The results of the PISA survey (http://www.jyu.fi/ktl/pisa/)
have brought about satisfaction and pride in Finland. Newspapers and media have
advertised that Finnish compulsory school leavers are top experts in
mathematics.
However, mathematics teachers in universities and
polytechnics are worried, as in fact the mathematical knowledge of new students
has declined dramatically. As an example of this one could take the extensive
TIMSS 1999 survey, in which Finnish students were below the average in geometry
and algebra. As another example, in order not to fail an unreasonably large
amount of students in the matriculation exams, recently the board has been
forced to lower the cut-off point alarmingly. Some years, 6 points out of 60
have been enough for passing.
This conflict can be explained by pointing out that the PISA
survey measured only everyday mathematical knowledge, something which could be
- and in the English version of the survey report explicitly is - called
"mathematical literacy"; the kind of mathematics which is needed in
high-school or vocational studies was not part of the survey. No doubt,
everyday mathematical skills are valuable, but by no means enough.
Out of the 85 assignments in the survey about 20 have been
published. The assignments are simple numerical calculations, minor problems or
deductions, interpretation of statistical graphics and evaluation of situations
where text comprehension is an essential part. However, hardly any algebra or
geometry is included. Nevertheless, the assignments are well in agreement with
the goals of the survey; in fact, the goal was to study everyday mathematical
knowledge.
The PISA-survey leaves us, thus, with unanswered questions
regarding many skills, like computing with fractions, solving elementary
equations, making geometrical deductions, computing volumes of solid objects,
and handling algebraic expressions. Still algebra is perhaps the most important
subtopic in mathematical studies after the compulsory comprehensive school.
In comprehensive school, the goal should be to learn the
basic concepts of mathematics so that they can be used as a basis for more.
Even the use of calculators does not change this situation: although
calculators nowadays might be able to handle fractions, manual computation is
essential to master since it is part of the foundations in handling algebraic
expressions. Further study becomes impossible if the basics are not learned
properly.
One reason for the increase of poor standards in the
matriculation exam and in the beginning of university studies is, undoubtedly,
the weakness of the foundation received in the comprehensive school. New, more
difficult concepts are hard to learn because still in upper secondary school
much energy is spent in reviewing concepts that should have been learned in the
comprehensive school. This vicious circle continues in tertiary education: the
high-school concepts are not properly learned, and further learning becomes
more difficult. The PISA survey provides us with useful information regarding
the mathematical literacy needed in everyday life and the ability to solve
simple problems. These skills are simply not enough in a world which uses and
utilizes mathematics more and more.
A proper mathematical basis is needed especially in
technical and scientific areas, biology included. The PISA survey tells very
little about this basis, which should already be created in comprehensive
school. Therefore, it would be absolutely necessary that, in the future,
Finland would participate also in international surveys which evaluate
mathematical skills essential for further studies.
Kari Astala, Professor of Mathematics, University of
Helsinki, President of Finnish Mathematical Society
Simo K. Kivelä, Senior Lecturer, Helsinki University of
Technology, Pekka Koskela, Professor of Mathematics, University of
JyväskyläOlli Martio, Professor of Mathematics, University of Helsinki; Dr.
Marjatta Näätänen, Senior Lecturer, University of HelsinkiDr. Kyösti Tarvainen,
Senior Lecturer, Helsinki Polytechnic Stadia;
and 201 mathematics teachers in universities and polytechnics
2. Severe
shortcomings in Finnish mathematics skills
Basic school teacher Antero Lahti expressed (HS 28.2.) the
opinion that the concern of over 200 university teachers for the mathematics
teaching (HS 17.2.) were merely academic criticism.
In fact, about one half of those signing are teachers at
polytechnics (universities of applied sciences) and technical universities.
They do not teach "academic" mathematics but mathematics needed in
technical practice and engineering sciences. Over 12 000 students start
engineering studies yearly.
The mathematics skills of new engineering students have been
systematically tested during years 1999-2004 at Turku polytechnic using 20
mathematical problems. One example of poor knowledge of mathematics is the fact
that only 35 percent of the 2400 tested students have been able to do an
elementary problem where a fraction is subtracted from another fraction and the
difference is divided by an integer.
Every important field of mathematics in engineering studies.
It was not properly tested in the PISA study. Finnish basic school pupils have
not done well in many comparative tests in algebra (IEA 1981, Kassel 1994-96,
TIMSS 1999).
The polytechnic teachers of professional subjects are
astonished at how poorly students can handle algebraic expressions and solve
equations. The decreased mathematical skills of the students have forced to
reduce the teaching material in those engineering courses that most heavily
rely on mathematics. This is a serious matter taking into account the
importance of engineering knowledge to the Finnish economy and welfare.
In technical universities the situation is not as bad, but
it has been noticed also there that especially algebraic skills have weakened
and that students have difficulties to handle comprehensive mathematical structures.
The same deficiencies are noticed in the matriculation examinations for the
graduates of the upper secondary schools.
There are positive aspects in mathematical knowledge and
teaching in Finland. The success of basic school pupils in the practice-oriented
numerical problems of the PISA study is fine. A contributory factor to this
success is basic school mathematics books, which include excellent examples of
everyday life. In addition to the compulsory courses, upper secondary school
students have the possibility to deepen their knowledge in good optional
mathematics courses. In Finland, the teachers are known to be motivated and
they have obtained a good education.
However, it is undeniable that new students in universities
and in polytechnics have poor mathematical skills on the average. To improve
the situation, Ministry of Education should appoint a working group to find out
what are the reasons for the deficiencies in the skills and to suggest measures
for improvement. In this group, there should be a considerable representation
of university and polytechnic teachers, since they know what kind of
mathematics is really needed in follow-up studies and various applications.
At the same time, one has to consider the possibility that
the first place in the PISA study is a Pyrrhic victory: are the Finnish basic
schools stressing too much numerical problems of the type emphasized in the
PISA study, and are other countries, instead, stressing algebra, thus
guaranteeing a better foundation for mathematical studies in upper secondary
schools and in universities and polytechnics.
The effect of the present upper secondary school practices
to the poor average knowledge has to be examined, too. It is clear that a
serious mistake is the practice of most upper secondary schools that one can
get a final pass, even if he or she has failed some of the courses, and that
one can be absent from many classes without a reason.
These things hamper the follow-up studies. Especially in
polytechnics, it is apparent that the students do not any more have a common
mathematical knowledge base, upon which to build. Students have different gaps
even in important basic knowledge according to which upper school courses they
failed or followed only partly. This causes inefficiency in teaching: a great
part of the first-year mathematical teaching in polytechnics is a review of
upper school mathematical subjects.
The mathematics of the upper secondary school and also that
of engineering mathematics requires no special mathematical talents. We see
this clearly from the fact that also those students (a third of all students)
that come from vocational schools to polytechnics learn these mathematical
skills.
The following fact has also to be considered. The national
LUMA development project set a target of 17 000 advanced syllabus examinations
in upper secondary school mathematics. This target is far off; for example,
last year 12 000 graduates passed this examination. The difficulties culminate
in polytechnics, where about 40 percent of the students coming from upper
secondary schools have passed only the basic syllabus examination.
Kyösti Tarvainen principal lecturer in mathematics Helsinki
Polytechnic Stadia
Simo K. Kivelä, Helsinki University of Technology
See also The PISA survey tells only a partial truth of
Finnish children's mathematical skills by Kari Astala, Simo K. Kivelä, Pekka
Koskela, Olli Martio, Marjatta Näätänen, Kyösti Tarvainen, and 201 mathematics
teachers in universities and polytechnics.
Solmu © 2005
Matematiikkalehti Solmu 23.9.2005
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