Defining Constructivism in Mathematics
“Constructivists believe that learners actively construct their own understanding rather than passively absorb or copy the understandings of others”. Under this way of learning the teacher does not simply present information and expect the children to 'learn it off by heart', the children construct their own concepts. This is more the process of problem solving/discovering meaning rather than finding out about the teachers mathematical ideas. The children modify their existing ideas to accommodate new ideas and the teacher's role is crucial in resolving these 'conflict'. This mental process requires connections are made between concepts.
The role of the teacher has changed where 'knowledge is in the head of the teacher' and the teacher has to find ways how to transfer/present it to the students. In the constructivist way of learning the teacher is the facilitator. The teacher's role is to also ask probing questions, paraphrase ideas, refocus to discussion if need and explore misconceptions and conflicting ideas. Rather than children doing lots of individual text book work, children work in small groups to work out problems and have opportunities to discuss, explain and justify their solutions. It is the teachers responsibility to create a 'problem solving atmosphere' and design appropriate tasks to stimulate mental activity. In the this atmosphere the children view problems are personal challenges, believe mathematics makes sense and feel free to discuss their ideas in small groups and whole class discussions. The children are encourages to assume some responsibility for their learning/conduct and take pride in their own achievements. As well as the teacher taking responsibility for their learning the teacher needs to take responsibility for their own teacher. Teachers need to explore other methods of assessment and emphasise that children assess their own learning.
Reference: Mayers, C and Britt, M. Constructivism in the Mathematics Classroom. Article 6. Neyland J (Ed). (1995). Mathematics Education. A Handbook for Teachers. Vol 6, 60-69. Wellington. Wellington College of Education.