If yesterday’s entry mentioned Piaget’s Constructivism and Vygotsky’s Social-Cultural theory, let’s now talk about Jerome Bruner, who suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept.
The three steps are:-
- Concrete representation
This means using real objects such as cookies, unifix cubes, counters, beads, and blocks, to solve problems.
- Pictorial representation
Putting the concrete into pictures- using shapes for example, to represent the objects.
- Abstract representation (sometimes called Symbolic representation)
No concrete material or picture representation is used- instead, use numbers and math symbols.
The goal of mathematics is the ability to handle abstraction. To achieve this, students must be able to do math in concrete, then pictorial representations before being able to do the abstract. In fact, the CPA approach does not just apply to mathematics but to other areas of learning as well.
Jussssssssssst in case you think the CPA approach ends in preschool, NOPE! It is also used in Primary schools around Singapore.