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 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)

… 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 extra- linguistic 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   = 1728 Chris: 144 x 12  144 x x 2    = 1728 David: 144 x 12  144 x 3 x 4  140 x x 3  x 4  = 1728

Vicki’s solution for – 98 Vicki was in a combined 1 st and 2 nd grade classroom in Madison, Wisconsin Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier & Human, (1997:90)

Different folks… James and Karen’s solutions to 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.