Adapting mathematics education to a changing world

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Adapting mathematics education to a changing
world

• Koeno Gravemeijer
• Freudenthal Institute
• for science and mathematics education
• Langeveld Institute,
• Utrecht University
• koeno_at_fi.uu.nl

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The old days

• In the old days youngsters used to learn to work
  with a slide ruler
• In the old days youngsters used to learn to work
  with goniometric tables
• Why do not we teach this anymore?

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The old days

• In the old days youngsters used to learn to work
  with a slide ruler
• In the old days youngsters used to learn to work
  with goniometric tables
• Why do not we teach this anymore?
• Because we have better tools!

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The old days

• We stopped teaching the algorithm for the
  calculation of the square root.
• We have calculators.

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The old days

• We stopped teaching the algorithm for calculation
  the square root.
• Why are we still teaching the algorithm for long
  division?

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Reconsidering the goals of mathematics education

• Practical need in everyday life or at the
  workplace
• Prerequisite for further education
• Cultural value
• Product of our culture
• The beauty of mathematics
• Appreciation for the role of mathematics in
  society
• Mathematical thinking

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Mathematics for the workplace

• Mathematics in the workplace makes sophisticated
  use of elementary mathematics rather than, as in
  the classroom, elementary use of sophisticated
  mathematics.
• (Steen, 2001, p. 55)
• ? Mathematical thinking understanding, complex
  applications

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Mathematics for the workplace

• Competencies (TmLs)
• gt investigating defining a problem, seeing the
  need to quantify, identifying and measuring key
  variables, representing and interpreting data.
• gt reflecting conjecturing about possible causes
  and communicating about the data to come to a
  decision
• (Bakker, Hoyles, Kent, Noss, 2006)

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Information technology employability

• Routine tasks are going to disappear
• Non-routine tasks will stay flexibility,
  creativity, general problem solving abilities,
  and communication skills.
• (Autor, Levy en Murnane, 2003)

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Assessment

• If flexibility, creativity, general problem
  solving abilities, and communication skills in
  mathematics are important goals, we should assess
  flexibility, creativity, general problem solving
  abilities, and communication skills in
  mathematics.

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Assessment

• This means that new forms of evaluation will have
  to be developed.
• But,
• We could start by inserting PISA-type items in
  the assessment instruments that are being used.

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PISA problems

• A pizzeria serves two round pizzas of the same
  thickness in different sizes. The smaller one has
  a diameter of 30 cm and costs 30 zeds. The larger
  one has a diameter of 40 cm and costs 40 zeds.
• Which pizza is better value for money? Show your
  reasoning.

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PISA problems

• If 40 of the population of a country are at
  least 60 years old, is it then possible for the
  average age to be 30?

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PISA problems

• One way to enhance the national results on PISA
  could be to put PISA-type items on the tests.
• Research shows that tests have an extremely
  strong influence on what is learned

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Consequences for Mathematics Education

• Shift in goals for mathematics education
• Less emphasis on routine tasks
• Foster flexibility, creativity, general problem
  solving abilities, and communication skills in
  mathematics education.
• realistic mathematics education (RME)
• ? constructivism

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ConstructivismKnowledge as an individual
construction Sign Express lane
10 items or less
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Constructivism

• Students construct their own knowledge
• Which creates the need for
• Communication co-construction
• Active participation of the students
• Problem solving as a means of steering the
  students learning process
• ? We can build on constructivist research on
  teaching and learning

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InnovatingMathematics Education

• The Dutch RME innovation as an example
• This innovation takes time!!!!!!
• A strong paradigm
• Design Research at the IOWO as the motor of the
  innovation
• Teacher training institutes as the backbone of
  the innovation

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A strong paradigm

• Mathematics as a human activity
• Guided reinvention as a means to reach
  mathematical content goals (mathematics as a
  product)
• ? Elaborations in prototypical instructional
  sequences

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The motor of the innovation

• IOWO, national center of expertise
• Expertise, based on design research (classroom
  based)
• ? primary-school mathematics education
• ? teacher education courses
• Under the banner of Educational Development in
  conversation with practitioners
• via journals, conferences, working groups,

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Teacher training institutes as the backbone of
the innovation

• Teacher educators carried the innovation
• Teacher education (mathematics education)
  tailored to RME
• RME as the mission of the mathematics education
  department as a whole
• Teacher education congruent with reform
• active involvement of students
• emphasis on student thinking and reasoning
• learning of mathematical content by student
  teachers according to RME principles

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To summarize

• Goals for mathematics education are shifting
• The society of the 21th-century asks for
  flexibility, creativity, general problem-solving
  abilities communication skills in mathematics
• ?Assessment has to be tailored to those new goals
• ?Instruction has to be tailored to those new
  goals
• We can build on - RME
• - Constructivism
• Dutch lessons long time, strong paradigm, DR as
  a motor LTPKs as the backbone