Transcript How children learn: The constructivist perspective

How children learn:
A socio-constructivist perspective
Monty Paul
RGSE
University of Southampton
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.
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, 1996:ix.
Knowledge is not passively received but actively built up by
the cognizing subject. Von Glasersfeld, 1989.
Knowledge is meaning making,
Learning occurs not as students take
in mathematical knowledge in readymade pieces but as they build up
mathematical meaning on the basis of
their experience in the classroom.
Yackel, Wood, Merkel, Clements,
Battista (1990)
… 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
… 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 one’s
quantitative world, rather than discovering
pre-existing ideas imposed by others.
Clements and Battista, 1990
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
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 extralinguistic interaction.”
Ernest, P. (1993:170)
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. (1993:172)
Contrasting views of learning
Traditional (Positivist)
Knowledge is fixed,
lying ‘out there’ for us
to find, “like a pebble”
on the beach. (Clements
& Battista, 1990:34).
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.
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.
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. 1990:34
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 children’s 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.
…
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.
…
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.
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  432
432 x 4  1600 + 120 + 8
= 1728
Vicki’s 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,
(1997:90)
Different folks…
James and Karen’s
solutions to 18 + 23
+ 37
Hiebert, Carpenter,
Fennema, Fuson,
Wearne, Murray,
Olivier & Human,
(1997:88, 83)
To change the world, emphasise
learning by doing
The ‘net’ for the ball
… by collaborating
Measuring circumference
…sharing ideas, experiences,
expertise.
Measuring, recording, analysing, understanding
Effective Learning environments
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.
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.
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.