- Piaget argues that learning consists primarily in being faced with experiences that do not fit into our current understanding, meaning that such understanding needs to be adjusted (constructivism).
- By implication, the teacher’s role is to discover pupils’ current levels of understanding, and offer learning experiences that challenge that understanding.
- This will encourage pupils to develop new theories, and the teacher’s role is then to prompt pupils to test and refine those theories to reduce errors.
- Social constructivism (e.g. Vygotsky) takes this theory further, arguing that effective learning can only take place in a social context.
- By implication, mathematical discussion is much more important than transmission of knowledge from the teacher to the pupils.
- The teacher’s role is to provide the scaffolding on which pupils construct their learning, by providing an appropriate level of challenge to each pupil.
- Drawing this together, the teacher should: make the purpose of the lesson clear; build non-threatening relationships and environments; select challenging activities; intervene to help pupils develop their understanding of key ideas.
- Possible lesson format based on constructivist approach:
Presentation – Exploration – Reflection – Consolidation
- Another implication of the social constructivist approach is the value of group work, and particularly posing problems that generate disagreement and thus discussion amongst pupils.
- Most misconceptions arise from over-generalisation of earlier mathematical learning.
- Simply explaining that a method is wrong and showing the correct method often isn’t enough to address the misconception.
- Instead the teacher needs to create uncertainty in the pupils through cognitive conflict, and be brave in doing so!
- This can be achieved through designing activities that will encourage misconceptions to come to light by pupils getting two contradictory answers.
- Swan discusses this model in five steps:
Assess pupils’ initial understanding
Pupils complete a task that exposes misconceptions and causes cognitive conflict.
Pupils share their methods and solutions through discussion.
The teacher organises whole-class discussion to resolve conflict.
Pupils consolidate learning through applying it to new problems.
- Activities that suit this type of teaching include sorting activities, and always, sometimes, never, classifying into two-way tables, pupils making up questions, pupils marking answers to questions.