HOW FINNS LEARN MATHEMATICS:
What is the Influence of 25 Years of
Research in Mathematics Education?
Erkki Pehkonen
University of Helsinki, Finland
1
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.
2
 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.
3
MATHEMATICS TEACHING
IN FINNISH SCHOOLS
4
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 3–4 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.
5
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.
6
Development of trends in mathematics
teaching in Finland and in the US
(according to Kupari 1999).
USA
ΣNew MathΣ
1960
Finland
ΣBack to
BasicsΣ
ΣProblem
SolvingΣ
1970
1980
ΣNew MathΣ
ΣBack to
BasicsΣ
New national
curriculum 1972
1960
1970
ΣStandardsΣ
1990
ΣProblem
SolvingΣ
ΣNational
standardsΣ
New national
curriculum 1994
New national
curriculum 1985
1980
2000
1990
2000
7
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.
8
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.
9
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.
10
Mathematics teaching
 A typical Finnish mathematics lesson begins by
checking and going through the last lesson’s
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.
11
 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.
12
MATHEMATICS EDUCATION
RESEARCH AND ITS
INFLUENCE
13
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.
14
 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.
15
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).
16
Finnish Dissertations
Learning requirements
Kall onen-Ršnkkš(1984)
Aitola (1989)
Yrjšnsuur i (1989)
Malmi vuori (2001)
Linnanmš
k i (2002)
Hannula (2004)
Teaching in e lementary
school
Vornanen (1984)
Lindgren (1990)
Sinnemš
k i (1998)
Hš
gg blom (2000)
Niemi (2004)
Ršty-Zaborsky (2006)
Leppš
a ho (2007)
Tikkanen (2008)
Teaching in midd le school
Silf verberg (1999)
Joki (2002)
Hihnala (2005)
Tšrnroos (2005)
Atto rps (2006)
Hassinen (2006)
Nšveri (2009)
17
Finnish Dissertations (cont.)
Teaching in hi gh school
Repo (1996)
Merenluoto (2001)
Joutsenlahti (2005)
Hšhkišniemi (2006)
Unive rsity students
Huhtala S. (2000)
Kaasil a (2000)
Pietil š(2002)
Viholainen (2008)
Mathematics teachers
Kupari (1999)
Huhtala M. (2002)
Lilj a (2002)
Perkkil š(2002)
Soro (2002)
18
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.
19
The 1st project
 The first project “Open tasks in mathematics”
was implemented in the upper grades (grades
7–9) of the comprehensive school in 1989–92 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).
20
The 2nd project
 The second project “Development of
pupils’ mathematical beliefs” was
implemented in 1996–98 in schools of
Helsinki area.
 In the first research project teachers’ and
pupils’ beliefs were recognized as
obstacles for change (cf. Hannula & al.
1996).
21
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).
22
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 2003–
06 by the Academy of Finland.
23
Other Academy research projects
 Other research projects that were financed by
the Finnish Academy were Erno Lehtinen’s
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).
24
Other big research projects
 One of other bigger and long-lasting
research project was Lenni Haapasalo’s
MODEM project.
 He began the project in the 1980’s 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).
25
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
26
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 50–70 % 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.
27
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.
28
My evaluation
 The direction to emphasize problem-solving and selfinitiativeness 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 selfinitiative thinking to learning objectives.
 Problem posing is in a near connection to such a
teaching style.
29
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 solving30
as a teaching method.