Theoretical considerations: Constructionism Dave Pratt

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Theoretical considerations Constructionism
Dave Pratt Richard Noss
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What's constructivism?

• what the student knows already matters
• students construct their own meanings
• construction is an active process
• teaching isn't the same as learning
• learning isn't the same as understanding

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What are the educational implications of
constructivism?

• student control
• students' knowledge matters
• purposeful activity
• a sense of satisfaction and competence

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constructivism isn't really a theory of
instruction
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• Constructivism

Constructionism
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What is constructionism?
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Learning by making

• Constructionism ... shares constructivism's
  connotation of learning as "building knowledge
  structures" irrespective of the circumstances of
  the learning. It then adds the idea that this
  happens especially felicitously in a context
  where the learner is consciously engaged in
  constructing a public entity (Papert)

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Instructionism v constructionism

• looks like a split about strategies for
  education two ways of thinking about the
  transmission of knowledge. But behind this there
  is a split that goes beyond the acquisition of
  knowledge to touch on the nature of knowledge
  and the nature of knowing. (Papert)

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modify our notions of complexity and hierarchy?

• complexity often inheres in the infrastructure
  as much as in the idea itself
• a shared experience and discourse
• cultural artefacts (pizza)

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transform the social embedding of the knowledge?

• some mathematical ideas are amenable for the
  first time to those who may not otherwise have
  encountered them
• much larger numbers of people need to develop
  techno-mathematical literacies to make sense of
  mathematisation of working and social life

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levels of theory

• broad theories of learning
• constructivism or behaviourism
• broad theories of teaching
• constructionism or instructionism or...
• domain specific
• how to learn about motion...

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The History of Constructionism

• Papert and Feurzig MIT team in 1960s researched
  problem solving
• Can elementary school students learn to program?
• What is the relationship between programming and
  maths?
• What is the relationship between programming and
  cognitive style?
• How can we evaluate the work?

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The History of Constructionism

• Radical idea that playing with a computer might
  precede learning formal mathematicsWhen
  mathematizing familiar processes is a fluent,
  natural and enjoyable activity, then is the time
  to talk about mathematizing mathematical
  structures, as in a good pure course on modern
  algebra. (p. 18)Papert, S. (1972). Teaching
  Children to be Mathematicians Versus Teaching
  About Mathematics. International Journal of
  Mathematics Education and Science and Technology,
  3, 249-262.)

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The History of Constructionism

• Mindstorms put forward fundamental challenges to
  the education world.Papert, S. (1982).
  Mindstorms Children, Computers and Powerful
  Ideas. London Harvester Press.

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• papert's gears

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Principles in Constructionism

• The Power Principle (Using before knowing)
• Project before problem
• Media before content
• Object before operation (Thingness)
• Dynamics before Statics

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The Instructors approach

• How to construct a perpendicular bisector of a
  line segment.
• Place your point of your pair of compasses on one
  end of the line segment and draw a circle whose
  radius of more than half the length of the
  segment
• Repeat, placing the point at the other end of the
  line segment.
• Join up the two points where the circles
  intersect.

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The Motivators approach

• There is a 3m line drawn on the floor.
• I want all the girls to stand 2m away from that
  end of the line
• and all the boys 3m from the other end.
• Now, lets stretch this ribbon between the two
  points where the boys and girls are both standing.

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The Facilitators approach

• Here is a new program called Cabri Geometry.
• I want you to explore the menus and then
  construct the perpendicular bisector of a line
  segment. You choose the line segment.

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The Constructionist approach?

• The Primary Laptop Project story

Pratt, D.C. Ainley, J., (1997), The
Construction of Meanings for Geometric
Construction Two Contrasting Cases,
International Journal of Computers for
Mathematical Learning, 1.3, 293-322, Dordrecht,
Netherlands Kluwer Academic Publishers.
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Two microworlds (?)

• Visual Fractions
• Developed by Ivan Kalas and his team at the
  Comenius University, Bratislava and published by
  Logotron Ltd
• Magic Forest
• Developed within the Playground Project and
  published by Logotron Ltd and Ctnotinfor

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Task 1

• Play with Visual Fractions or Magic Forest.
  Could you use this microworld with children in a
  way that the activity satisfies the principles
  of
• Using before knowing (Power)
• Project before problem
• Media before content
• Object before operation (Thingness)
• Dynamics before Statics

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Task 2

• Discuss how might the notion of constructionism
  impact on classroom activity with or without the
  use of computers?