HOW FINNS LEARN MATHEMATICS What is the

Influence of 25 Years of Research in Mathematics

Education?

- Erkki Pehkonen
- University of Helsinki, Finland

Introduction

- Today Finland is, because of the PISA reults,

famous in the world as a country of excellent

mathematics teaching. - In each PISA comparison (2000, 2003, 2006),

Finland has been in the group of the top three

(cf. Kupiainen Pehkonen 2008). - This might be a reason why other countries are

interested in our secret weapon, i.e. how the

Finnish educational system functions and what

might be the reasons for our success.

- In order to uncover our teaching system we

produced a couple of years ago the book How Finns

learn mathematics and science (Pehkonen, Ahtee

Lavonen 2007). - Furthermore, in a published paper (Pehkonen 2008)

I gave background information on the development

of the Finnish mathematics instruction and

curricula within last 30 years. - And this presentation continues the same

communication process.

MATHEMATICS TEACHING IN FINNISH SCHOOLS

The school system

- In Finland, we have a nine-year comprehensive

school that begins at the age of seven. - After the comprehensive school, there are two

options the upper secondary school (grammar

school) and vocational school. - In the comprehensive school, mathematics is

taught with 34 lessons per week, and in the

upper secondary school there are two selective

courses advanced mathematics and general

mathematics. - The amount of mathematics taught in vocational

schools varies according to the career, and it

usually is combined with situations of the career

in question.

Development of the mathematics curricula

- A general picture of the development of the

Finnish mathematics curricula from the 1960s to

around 2000 is presented in Figure (below). - Changes adopted in the US curriculum played a

central role in this development, with a delay of

about 10 years. - However, the principles of each trend were not

taken as such, but they were modified in the

process of implementation to better fit the

Finnish education system.

Development of trends in mathematics teaching in

Finland and in the US (according to Kupari 1999).

Changes in learning conceptions

- During the 1980s the established view on learning

began to change, including mathematics teaching. - Cognitive psychology, emphasizing students own

construction of knowledge and learning, began to

replace the older behaviouristic paradigm. - Consequently, the focus of learning shifted to

students activities and to their ways of

perceiving and shaping the world around them (cf.

Lehtinen 1989). - In the 1990s, responding to the new demand, a

group of Finnish mathematics educators wrote a

booklet on mathematics teaching (Halinen al.

1991), presenting a view very similar to the

later concept of mathematical literacy in PISA.

New ideas for teaching

- Besides traditional teachers talk and pupils

independent calculations, other means of teaching

and learning mathematics were to be used problem

solving, exploration, discussions about

mathematics, and dealing with problems rising

from everyday life. - In implementing these ideas, two key points

arose understanding learning as an active

endeavour, and mathematics as a skill to be used

and applied in diverse situations.

New ideas for teaching (cont.)

- The former meant that students should have ample

time for learning and for deliberating on what

they had learnt, while the latter emphasized the

importance of using problems rising from everyday

life. - This meant tasks where the level of mathematics

was not necessarily so high, but where students

could apply the mathematics learnt at school in

situations that were familiar and meaningful to

them.

Mathematics teaching

- A typical Finnish mathematics lesson begins by

checking and going through the last lessons

homework. - Following this, the teacher introduces a new

topic to be learnt, e.g. a new calculation method

or a geometric concept, which will then be

explored collectively with some examples. - Then the teacher assigns students some problems

from the textbook to solve individually, in order

to make sure that everything has been understood

about the underlining idea. - At the end of the lesson he/she gives the

students new homework from the textbook.

- This model was dominant in the 1980s and is still

so today, despite the recurring curriculum

reforms (cf. Maijala 2006 Savola 2008). - According to our experiences, this kind of

textbook dependence is stronger in grades 1 to 6,

i.e. for elementary teachers, than for the last

three years of comprehensive school education

with mathematics teachers.

MATHEMATICS EDUCATION RESEARCH AND ITS INFLUENCE

Developments

- About 30 years ago (in 1974) in connection to the

university study reform, elementary teacher

program was moved from pedagogical high schools

to universities. - At that time eight teacher education units

(Helsinki, Joensuu, Jyväskylä, Oulu, Rovaniemi,

Tampere, Turku, Vaasa) were established

typically there are a compound of department of

education and department of teacher education.

- In this connection new positions in mathematics

education were established, both for professors

and for lecturers. - Professor positions (as a matter of fact

professorships for education of mathematical

subjects) were established four Helsinki,

Jyväskylä, Oulu, Vaasa. - These positions have a research obligation, and

therefore, research on mathematics education got

much new power.

Dissertations

- Here we will concentrate on dissertations done in

Finnish school mathematics within the last 25

years (since 1984, altogether 34 studies). - Most of them are written in Finnish, there are

only five dissertations in English, and two in

Swedish. - The dissertations can be roughly divided into six

sections learning requirements (6), teaching in

elementary school (8), teaching in middle school

(7), teaching in high school (4), university

students (4), mathematics teachers (5).

Finnish Dissertations

Finnish Dissertations (cont.)

Research projects

- Here I will focus on some research projects in

mathematics education that have an established

status e.g. by getting finance from the Academy

of Finland, and that might have influenced

mathematics teaching. - The red line in the research program of Erkki

Pehkonen has been the use of open problem tasks

in school the program is a compound of three

Academy projects.

The 1st project

- The first project Open tasks in mathematics was

implemented in the upper grades (grades 79) of

the comprehensive school in 198992 in Helsinki

area. - It was focused on how problem fields (a certain

type of sequences of open tasks) could be used as

enrichment of ordinary mathematics teaching and

what kind of influences the use of the problem

fields has (cf. Pehkonen Zimmermann 1990).

The 2nd project

- The second project Development of pupils

mathematical beliefs was implemented in 199698

in schools of Helsinki area. - In the first research project teachers and

pupils beliefs were recognized as obstacles for

change (cf. Hannula al. 1996).

The 3rd project

- The third project Teachers conceptions on open

tasks that was implemented in 1998, concentrated

on the second observed obstacle teachers

pedagogical knowledge (cf. Vaulamo Pehkonen

1999).

The other Academy projects by Erkki Pehkonen

- Research project Understanding and

Self-Confidence in School Mathematics, financed

2001-03 by the Academy of Finland. - Research project Elementary Teacher Students

Mathematics, financed 200306 by the Academy of

Finland.

Other Academy research projects

- Other research projects that were financed by the

Finnish Academy were Erno Lehtinens Pythagoras

project (University of Turku), and the bigM

project by Simo Kivelä (Technical University,

Espoo). - The first one focused on real number concept in

upper secondary school (cf. Merenluoto 2001), and

the second one developed virtual materials for

the first-year mathematics students mainly in

technical universities (cf. Kivelä Spåra 2001).

Other big research projects

- One of other bigger and long-lasting research

project was Lenni Haapasalos MODEM project. - He began the project in the 1980s at the

University of Jyväskylä. - It focused i.a. to teach the concept of straight

line for an eight-grader using computers (cf.

Haapasalo 1994).

Influence of research on mathematics teaching

- Changes happening within 20 years, and the

meaning of research for these changes - The authors have presented results of their

dissertation studies both in Finnish teacher

journals, and during the in-service training days

of the Mathematics Teachers Union (MAOL). - The meaning of the Association for Research in

Mathematics and Science Teaching

Conclusion

- Although Finland ranked well in all three PISA

comparisons (2000, 2003, 2006), a closer look at

the results shows that the Finnish achievement

level in many basic tasks of the PISA tests was

only 5070 or less (cf. Kupiainen Pehkonen

2008, 130). - The fact that the other countries achievements

were still worse, does not make the Finnish

achievement good. - It only shows that the level of mathematics

teaching in all countries should be raised, also

in Finland.

Perspectives in Finland

- Now we can ponder, to which direction and how far

we are moving on a short time interval. - In Finnish mathematics teaching the direction

seems to be to more individualizing in the

comprehensive school, and mass teaching in the

secondary schools. - Teachers try to balance between large teaching

groups and those children who demand special

attention. - Even more such children are coming to school who

are accustomed to have the unshared attention of

their parents and who have difficulties in their

social relationships.

My evaluation

- The direction to emphasize problem-solving and

self-initiativeness seems to be a correct one. - But problem-solving should be used as a teaching

method, and not only to solve separate problems. - All new information should not be given in a

ready form, but the teacher should lead pupils

via self-initiative thinking to learning

objectives. - Problem posing is in a near connection to such a

teaching style.

The concluding note

- Now we can say e.g. in the case of problem

solving in Finnish schools using the language

proposed by the published paper Schroeder

Lester (1989) - Most teachers are in the teaching problem solving

in the first phase (teaching about problem

solving), i.e. they deal with separate problems,

mathematical puzzles, in order to develop their

pupils thinking skills. - Only a few teachers are in the phase 3 (teaching

via problem solving), i.e. using problem solving

as a teaching method.