## The ultimate, authoritative, Finnish refutation of the claim that Finnish K-12 students are among the world’s very best in mathematics.

**This in part in response to the Wall Street Journal article “What makes Finnish children so smart?”** – http://online.wsj.com/public/article/SB120425355065601997-7Bp8YFw7Yy1n9bdKtVyP7KBAcJA_20080330.html

For skandinaviske lesere: Finland – presis samme problemer som i Skandinavia og i USA.

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**Thanks to faculty member Richard Askey, Professor of Mathematics at the University of Wisconsin and member of the National Academy of Sciences, for bringing these important open letters to everyone’s attention.**

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**Our comment**: It is important to put Finnish “#1 in the world” students’ performance in stark perspective so that education decision makers other countries stop thinking that emulating Finland will get them all the way to where they need to be. Highly selective teachers college admission is very helpful for system performance generally – but for a mathematics education system **content culture** is **decisively** important. PISA would, given its actual math content, be a reasonable math competence test for Grade 6. It is not a productive such test for 15-year olds. ====================================================================================

http://solmu.math.helsinki.fi/2005/erik/PisaEng.html

## 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 Jyväskylä

**Olli Martio**, Professor of Mathematics, University of Helsinki

Dr. **Marjatta Näätänen**, Senior Lecturer, University of Helsinki

Dr. **Kyästi Tarvainen**, Senior Lecturer, Helsinki Polytechnic Stadia** **

**and 201 mathematics teachers in universities and polytechnics**

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**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.**** If one does not know how to handle fractions, one is not able to know algebra, which uses the same mathematical rules. Algebra is a very 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** senior lecturer, Helsinki University of Technology

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