A reader emailed these links regarding the recent article on Finland’s education system:

• 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.

• 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).