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    Onderwijskrant Vlaanderen
    Vernieuwen: ja, maar in continuïteit!
    23-12-2013
    Klik hier om een link te hebben waarmee u dit artikel later terug kunt lezen.Onderwijs: Finse 15-jarigen zwak voor wiskunde. En Vlaamse?

    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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