Dienes’ stages of learning theory
Seeing mathematics as “a gold mine for an indefinite supply of games”, Dienes went on to develop a six-stage theory for learning mathematics, with a focus on games. Many aspects of this theory are easy to identify in the MNP mastery approach through the anchor activities and stories and pictures in the textbooks. Dienes’ theory reflects Bruner’s Concrete Pictorial Abstract (CPA) stages. He advocates the use of manipulative materials, games and stories in maths, believing that children can learn more complicated maths at a younger age than had previously been thought.
Dienes’ first stage uses games to enable initial trial and error and free exploration of materials. Here, learners familiarise themselves with the materials.
Rules of the Game
This is followed by a stage where the regularities of the materials are identified and ‘rules’ are created. Once a number of similar games have been played in class,a discussion begins.
Pupils compare the games, identifying similarities and differences between them. They articulate their discoveries before moving in the direction of abstraction instead of being completely absorbed in the concrete and physical playthings.
In the fourth stage, it’s useful to provide some kind of pictorial representation such as a chart, table, arrow diagram or coordinates system to anchor the patterns and abstractions in a visual way.
Here, these ideas are mapped and pupils start to form a language around games.
Lastly, pupils begin to use what they’ve learned in the previous stages to test, prove and apply their own set of truths and theories around games.