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

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


... two options: the upper secondary school (grammar school) and vocational school. ... school, mathematics is taught with 3 4 lessons per week, and in the upper ... – PowerPoint PPT presentation

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

Influence of 25 Years of Research in Mathematics
  • Erkki Pehkonen
  • University of Helsinki, Finland

  • 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.

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
  • 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
  • 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

Mathematics teaching
  • A typical Finnish mathematics lesson begins by
    checking and going through the last lessons
  • 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.

  • 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.

  • 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
  • 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
  • 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

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

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,
  • 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

  • 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
  • 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
  • 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.
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