Principles of the Policy One of the key learning principles behind this policy is the concrete pictorial abstract approach (CPA). The concrete-pictorial-abstract approach, is based on research by psychologist Jerome Bruner, and suggests that there are three steps (or representations) necessary for children to develop understanding of a concept. For children to have a deep understanding of the mathematical concepts developed, they need to all three phases of the CPA approach. If a child has moved on from the concrete to the ‘master’ pictorial, it does not mean that the concrete cannot be used alongside the pictorial as an additional scaffold. If a child is working at the abstract stage, something or out’ then concrete or ‘proving’ ‘working pictorial representations could be used to develop a greater depth as pupils articulate their thinking /reasoning. Reinforcement is achieved by going back and forth between these representations. Linking abstract notation to pictorial/concrete representations and then the concrete/pictorial models to an abstract notation. Concrete Representation The enactive stage. Children are first introduced to an idea/skill/concept by acting it out with real objects, this could include large scale with the pupils themselves and also utilise resourced available in the outdoor environment. This is a 'hands on' stage using real objects linked to real-life and the wider curriculum and/or mathematical equipment, (i.e. counters, cubes, bead string, five and ten frames, Dienes, place value counters etc.) and it is the foundation for CONCEPTUAL UNDERSTANDING. Pictorial Representation The iconic stage. A child has sufficiently understood the hands-on, CONCRETE experiences performed and can now relate them to PICTORIAL representations, such as a DIAGRAM or PICTURES of the problem. PICTORIAL representations, such as the bar model, can also be used to scaffold understanding. Abstract Representation
Principles of the Policy One of the key learning principles behind this policy is the concrete pictorial abstract approach (CPA). The concrete-pictorial-abstract approach, is based on research by psychologist Jerome Bruner, and suggests that there are three steps (or representations) necessary for children to develop understanding of a concept. For children to have a deep understanding of the mathematical concepts developed, they need to ‘master’ all three phases of the CPA approach. If a child has moved on from the concrete to the pictorial, it does not mean that the concrete cannot be used alongside the pictorial as an additional scaffold. If a child is working at the abstract stage, ‘proving’ something or ‘working out’ then concrete or pictorial representations could be used to develop a greater depth as pupils articulate their thinking /reasoning. Reinforcement is achieved by going back and forth between these representations. Linking abstract notation to pictorial/concrete representations and then the concrete/pictorial models to an abstract notation. Concrete Representation The enactive stage. Children are first introduced to an idea/skill/concept by acting it out with real objects, this could include large scale with the pupils themselves and also utilise resourced available in the outdoor environment. This is a 'hands on' stage using real objects linked to real-life and the wider curriculum and/or mathematical equipment, (i.e. counters, cubes, bead string, five and ten frames, Dienes, place value counters etc.) and it is the foundation for CONCEPTUAL UNDERSTANDING. Pictorial Representation The iconic stage. A child has sufficiently understood the hands-on, CONCRETE experiences performed and can now relate them to PICTORIAL representations, such as a DIAGRAM or PICTURES of the problem. PICTORIAL representations, such as the bar model, can also be used to scaffold understanding. Abstract Representation
MH-Calculation-Policy-Overview.docx