The decline in mathematical competence is a global phenomenon, but when it comes to Finland, performance has truly collapsed. This is how **Arto Ahonen**, the PISA National Project Manager, put it when presenting the dire statistics at a recent briefing of the Ministry of Education.

This was no news to mathematics teachers at different levels of education, and it came as no surprise either to the researchers at the Finnish Education Evaluation Centre (FINEEC), says Counsellor of Evaluation **Jari Metsämuuronen**.

“This trend has been clear in the measurements of FINEEC for a long time.”

The mood among experts and teachers in the mathematical sciences is decidedly more sombre. Some of them have approached policy-makers multiple times over the years, for example by sending open letters (in Finnish) in which they point out that competence in mathematics was falling already back when Finland still scored very high in PISA at the turn of the millennium.

In their statements, they note that the decline began when mathematics courses based on the students’ skill level were removed from comprehensive schools in the mid-1980s.

Another reform with a negative impact on mathematics skills, one that is often mentioned by general upper secondary school teachers, in particular, is the digital leap in Finnish schools, which was enthusiastically promoted by politicians, educational authorities, IT companies and even some educators throughout the 2010s.

Staring at screens, playing games and using calculation software has turned students’ attention towards irrelevancies in mathematics and continues to harm the overall ability of growing students to concentrate.

Finland’s western neighbour decided over a year ago to pull the brakes on digitalisation in schools. A while ago, the Swedish Government announced it would set aside an additional grant worth hundreds of millions of crowns for the purchase of books for schools in 2024 (in Swedish).

This decision was based on research indicating that traditional teaching methods lead to better learning outcomes and also promote peace in the classroom. In line with these policies, Sweden’s Minister for Schools **Lotta Edholm **said in a recent interview (in Swedish) with Vi Lärare, the magazine of the Swedish Teacher’s Union, that what schools need now is "pen and paper, order and discipline".

What about us in Finland? Returning to traditional teaching methods and differentiated teaching may support students’ overall school readiness, but is there some other way, one that specifically promotes mathematical learning, that has not yet been discussed in public?

## Is mathematics constricted by pedagogy?

You do not need to be an expert in the field to notice the difference in mathematics curricula and learning materials from different decades. Some of the topics, such as geometry, have been stripped down to the bare minimum, and essential skills in mathematics, such as proving, are not introduced until the upper secondary level, and even there they are simplified.

Mathematics is based on clearly defined concepts, precise definitions that are presented as symbols and operation signs, or the language of mathematics, to avoid ambiguity. That is why it makes no sense that comprehensive school today tries as if to shelter students from the exact nature of mathematics.

It is difficult to find proper definitions in textbooks. They have been replaced or tried to be replaced by verbal characterizations, unconnected example calculations and drawings. The aim has probably been to make mathematics more accessible, but this approach has done a disservice to both the weaker and the more talented students, because the central core of mathematics has been hidden, as it were.

**Luukas Hallamaa** graduated as a teacher of mathematics in 2022 and had already graduated as a mathematician before then. With this background, Hallamaa is able to examine mathematics curricula and learning materials from two different perspectives.

“I wish that the opinions of mathematicians would also be heard when writing mathematics textbooks and developing curricula,” says Hallamaa and continues by giving a concrete example.

“The lack of definitions is one of the fundamental problems of textbooks. Students are unsure about what each concept means and when they are unsure about the meaning of concepts, it becomes almost impossible to justify arguments. Textbook authors are probably just trying to make mathematics easier to understand, but the lack of definitions actually makes it harder to learn maths.”

Hallamaa provides an example of this.

“Since there are no definitions, the rules for calculating fractions, for example, have to be given only in the form of statements that need to be memorized, instead of giving an interpretation for the arithmetic operations on a number line, for example, and explaining the rules through this. A lack of competence with fractions is unfortunately common.”

Professor and Head of Subject for Mathematics and Science Education at the Luleå University of Technology **Timo Tossavainen **did a PhD first in mathematics and then in mathematics education.

“In upper secondary school and university, students are introduced, as they should be, to the practical applications of various AI and computation software both in their studies and at work. At this point, it is especially important that they have a strong foundation for mathematical thinking. This foundation is built in comprehensive school, and it should be built thoroughly. What this means at this stage is doing things primarily by hand, with a pencil and paper.”

Tossavainen says that, in Swedish universities, the education of mathematics teachers focuses increasingly on pedagogical elements and less on mathematical substance.

“This is a trend that I hope we will not see in Finland,” says Tossavainen.

## Need to set demands for weaker students

Counsellor of Evaluation Jari Metsämuuronen from the Finnish Education Evaluation Centre (FINEEC) urges school teachers to compile and share practices that they use to support their quickest and most talented students. Separate study groups for talented students interested in mathematics could be one option.

“This may have implications for how motivated top performers are to pursue more challenging mathematics studies in upper secondary school. This, in turn, is relevant to ensuring that as many of them as possible pursue professions in later studies that require mathematical expertise, such as technical fields,” says Metsämuuronen.

And contrary to what teachers and parents may generally believe, the experts at FINEEC argue that mathematics learning goals should be set as high as possible also for weak students.

This may sound surprising and new in schools where weak students are offered simplified materials and easier tests.

Metsämuuronen emphasises that learning to practice and make an effort in the early grades is a prerequisite for the development of mathematical competence.

## Grade inflation conceals decline in competence

Some of the parents of pupils and students may be confused as to why the young person is not performing well in mathematics in upper secondary school or in their studies in technology, despite receiving an excellent grade in mathematics on their basic education certificate.

The research conducted at FINEEC reveals an explanation for this that is unfortunate, but intuitively very unsurprising: grade inflation.

This can be seen in mathematics in that while the level of competence has fallen continuously since the beginning of the millennium, the number of tens, the highest grade in the Finnish grading system, awarded to 9th graders in comprehensive school has tripled, and the number of fives, the lowest passing grade, has fallen to a third of what it was before.

No wonder students fail to complete the advanced syllabus in mathematics in general upper secondary school and first-year tech students feel tired already in the beginning of autumn. It is not the young person's fault if schools do not have the guts to introduce them to maths as it is – a subject that requires effort and thinking, but is also highly rewarding.