How children learn: A socio-constructivist perspective

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How children learnA socio-constructivist
perspective

• Monty PaulRGSEUniversity of Southampton

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Context of this presentation

• Background - primary school teacher.
• Main interest the effective learning of
  mathematics.
• Current focus lecturer preparing students to be
  effective facilitators of mathematical learning
  in primary schools.

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Constructivism

• A theory about knowledge and learning. Describes
  what knowing is and how one comes to know.
• Describes knowledge as temporary, developmental,
  nonobjective, internally constructed, and
  socially and culturally mediated.
• Learning a self-regulatory process of struggling
  with the conflict between existing personal
  models of the world and discrepant new insights,
  constructing new representations and models of
  reality as a human meaning-making venture with
  culturally developed tools and symbols, and
  further negotiating such meaning through
  cooperative social activity, discourse and
  debate. Fosnot, 1996ix.
• Knowledge is not passively received but actively
  built up by the cognizing subject. Von
  Glasersfeld, 1989.

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Knowledge is meaning making,

• Learning occurs not as students take in
  mathematical knowledge in ready-made pieces but
  as they build up mathematical meaning on the
  basis of their experience in the classroom.
• Yackel, Wood, Merkel, Clements, Battista (1990)

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sense making,

• Knowledge is a matter of human interpretation.
• Knowledge is the meaning assigned to facts,
  rather than the facts themselves.
• Knowledge does not exist independently waiting to
  be found knowledge comes into being only when
  humans examine data and assign meaning to it.
• Knowledge is the sense that that humans make of
  factual information.
• Berry, W. 1998

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constructed individually and

• There is no one true reality rather, individual
  interpretations of the world. These are shaped by
  our experience and our social interactions.
  Learning is a process of adapting to and
  organising ones quantitative world, rather than
  discovering pre-existing ideas imposed by others.
• Clements and Battista, 1990

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Socially.

• Learning is a social process in which we grow
  into the intellectual life of those around us.
  Mathematical ideas and truths are cooperatively
  established by the members of a culture. As such,
  the constructivist classroom is a culture in
  which children discover and invent their
  knowledge socially, by sharing, explaining,
  negotiating and evaluating ideas.
• Clements and Battista, 1990

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Social constructivism

• Social constructivism regards individual
  subjects and the realm of the social as
  indissolubly interconnected
• The underlying metaphor is that of conversation,
  comprising persons in meaningful linguistic and
  extra-linguistic interaction.
• Ernest, P. (1993170)

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The place of language in socially constructed
knowledge

• Adopting conversation as the underlying metaphor
  of social constructivism gives pride of place to
  human beings and their language in its account of
  knowing. ..language is regarded as the shaper of,
  as well as being the product of individual minds.
  It is increasingly recognized that much
  instruction and learning takes place through the
  medium of language.
• Ernest, P. (1993172)

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Contrasting views of learning

• Traditional (Positivist)
• Knowledge is fixed, lying out there for us to
  find, like a pebble on the beach. (Clements
  Battista, 199034).
• Learning is remembering facts. Understanding is
  secondary.
• Facts are facts one true reality, one ultimate
  truth.

• Constructivist
• Knowledge is constructed by individuals, often in
  a social context.
• We can only learn when we make meaning or sense
  of the task in hand.
• No one reality we each see and understand
  things differently.

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For mathematics teaching

• Traditional approach
• Children are expected to learn tables etc by
  rote.
• Children learn efficient algorithms (methods) to
  achieve solutions.
• Understanding good, but not necessary.
• Chalk and talk teacher the expert filling empty
  heads with knowledge.

• Constructivist
• Children must understand tables before learning
  them.
• Children invent their own methods, approaches.
• Understanding is paramount and essential for
  learning.
• Teacher a co-learner, facilitator, guide on side
  not sage on stage.

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As a constructivist I believe that

• In reality, no one can teach mathematics.
  Effective teachers are those who can stimulate
  students to learn mathematics. Educational
  research offers compelling evidence that students
  learn mathematics well only when they construct
  their own mathematical understanding.
• MSEB and National Research Council, in Clements,
  D. Battista, M. 199034

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Therefore, I must

• Understand that children come to school with
  prior knowledge (some of it quite sophisticated),
  which forms the foundation for their personal and
  social constructions.
• Accept childrens understanding of the world, and
  allow them to build on it.
• Accept that children will see things
  differently from me and anothers in the class.
• Accept and encourages different methods of doing
  things.

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• Prepare an environment which provides
  interesting, relevant and challenging tasks.
• Provide for active learning.
• I hear and I forget, I see and I remember, I do
  and I understand
• Take multiple intelligences into account when
  planning and assessing.
• Ask questions, guide thinking, facilitate the
  process of building understanding.
• Make children/students responsible for their own
  learning.

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• Provide a classroom climate which encourages
  experimentation and risk taking.
• Never says wrong rather let the child
  discover and correct his/her own error.
• Encourage sharing of ideas.
• Treat each child as a unique individual.

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Different strokes

• Amy 144 x 12 ? 288 x 6 ? 576 x 3 ? 1500 210
  18 ? 1710 18 1728
• Chris 144 x 12 ? 144 x 10 144 x 2 ? 1440 288
  ? 1640 88 ? 1700 28 1728
• David 144 x 12 ? 144 x 3 x 4 ? 140 x 3 4 x 3
  ? 432432 x 4 ? 1600 120 8 1728

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Vickis solution for 123 456 98

• Vicki was in a combined 1st and 2nd grade
  classroom in Madison, Wisconsin
• Hiebert, Carpenter, Fennema, Fuson, Wearne,
  Murray, Olivier Human, (199790)

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Different folks

• James and Karens solutions to 18 23 37
• Hiebert, Carpenter, Fennema, Fuson, Wearne,
  Murray, Olivier Human, (199788, 83)

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To change the world, emphasise learning by doing
The net for the ball
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by collaborating
Measuring circumference
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sharing ideas, experiences, expertise.
Measuring, recording, analysing, understanding
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Effective Learning environments
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References

• Berry, W. (1998). Rethinking what we know.
  Positivist and constructivist epistemology. In
  Hinchley, P. (ed.). Finding Freedom in the
  Classroom. A practical introduction to critical
  theory. Peter Lang. New York.
• Ernest, P. (1993). Constructivism and the problem
  of the social. In Julie, C., Angelis D. Davis,
  Z. (eds.) (1993). Political Dimensions of
  Mathematics Education. Cape Town. Maskew Miller
  Longman.
• Fosnot, C. (1996). Constructivism theory,
  perspectives, and practice. New York London.
  Teachers College Press.

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References

• Hiebert, J.,Carpenter, T., Fennema, E., Fuson,
  K., Wearne, D., Murray, H., Olivier, O. Human,
  P. (1997). Making Sense. Teaching and learning
  mathematics with understanding, Heinemann.
  Portsmith, NH.
• Mathematical Sciences Education Board (MSEB) and
  National Research Council, in Clements, D.
  Battista, M. (1990). Constructivist learning and
  teaching. Arithmetic Teacher, September. 34,5.

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References

• Von Glasersfeld, E. (1989). In Ernest, P. (1993).
  Constructivism and the problem of the social.
  Political Dimensions of Mathematics Education
  (Julie, C., Angelis D. Davis, Z. (eds.) (1993).
  . Cape Town. Maskew Miller Longman.
• Yackel, E., Cobb, P., Wood, T. Merkel, G. (1990).
  Experience, problem solving and discourse as
  central aspects of constructivism. Arithmetic
  Teacher, December, 34,35.
• Audio reference
• Change the World by Eric Clapton. Written for
  the film Phenomenon starring John Travolta.