HOW FINNS LEARN MATHEMATICS: What is the Influence of 25 Years of Research in Mathematics Education?

1
HOW FINNS LEARN MATHEMATICS What is the
Influence of 25 Years of Research in Mathematics
Education?

• Erkki Pehkonen
• University of Helsinki, Finland

2
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.

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• 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.

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MATHEMATICS TEACHING IN FINNISH SCHOOLS
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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.

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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.

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Development of trends in mathematics teaching in
Finland and in the US (according to Kupari 1999).
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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.

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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.

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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.

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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.

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• 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.

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MATHEMATICS EDUCATION RESEARCH AND ITS INFLUENCE
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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.

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• 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.

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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).

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Finnish Dissertations
18
Finnish Dissertations (cont.)
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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.

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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).

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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).

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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).

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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.

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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).

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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).

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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

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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.

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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.

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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.

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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.