Unit 17, P1
Describe two different theories of how understanding of mathematical concepts develops in children.
Piaget – Piaget believed that physical knowledge develops the use of senses that helps a child create mental pictures of various objects and it helps the child understand a various characteristics of that object. Piaget believed that logico-mathematical knowledge helps the child to begin to see similarities and differences in objects or things and the child would see it in detail. Piaget believed that logico-mathematical thought was in comparison to physical knowledge and this would help the child gain information on individual objects such as a shape but the child would unable to form comparison. Piaget believed that logico-mathematical knowledge required a level of abstraction from the child for example the similarities and differences in an object that are based on the relationship between that the child has created between the objects. Piaget thought that logico-mathematical thought had an effect on a child in a way that organises and adapts his/her information. Piaget believed that the child takes in the information and tries to fit in with their existing information or knowledge. Piaget’s understanding of number is he believed that numbers fall into the category of logico-mathematical, he thought the knowledge cannot bring any understanding of quantity to the child and that numbers can only have a value to the child when they create a relationship between them. An example of this is if the child picks a number such as 5 then the number can only have a meaning if the child actually understands that it is more than four but less than higher numbers. The child will find it hard to abstract concepts and will therefore require concrete materials to help them form a relationship between them and the numbers. Once the child is older the concrete materials will decrease. Piaget believed that a child’s understanding of numbers develops in two stages; these two stages are ordering and hierarchical inclusion. The child’s understanding of numbers can come from ordering because the sequence of quantities. For example 2 comes before 3 but 4 comes after 3. Then the child can understand the inclusion this is when the child starts to grasp numbers for example that 1 is actually part of 2, and that 1 and 2 are part of 3. When the child is older math’s materials will decrease and the number of activities requires the child to work entirely in the abstract. For example addition, subtraction, multiplication and division – the child has to abstract those concepts fully to be able to reach a solution with no materials or help. The concept of logico-mathematical thought is believed to make sense to Piaget. Materials helped support children in development with their knowledge. It represents the logical way that would could success to learning.
Brunner- Brunner’s theory is stated as ‘learning is an active process that allows humans to discover new things beyond the information given to them’
Brunner’s theory has three different stages, these are 1. The process of acquiring new information - Brunner believed that the learning of new information can occur through reading, listening and from the teacher’s explanations that is taught. 2. The process of transforming the information received – Brunner believed that the process of knowledge transformation is a process of how the knowledge has been transformed and accepted which can abstract concepts. 3. To test the relevance and accuracy knowledge – Brunner believed testing the knowledge of mathematical structures could help with the child’s learning.
Brunner believed that the learning in mathematics should be introduced to the problems in accordance to each situation. Children are gradually guided to the concepts of maths. Brunner believes the increased effect of learning should be supported by the communication of technology, computers, props or other