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

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 | ISSN 1458-8048 Tekijänoikeudet |