Comparing Theories of Mathematical Development free essay sample

Sensorimotor (0-2 years of age) children begin to use imitation, memory and thought. They begin to recognize that objects do not cease to exist when they are hidden from view. They move from reflex actions to goal-directed activity. 2. Preoperational (2-7 years) Children gradually develop language and the ability to think in symbolic form. They are able to think operations through logically in one direction and they have difficulty seeing another person’s point of view. 3. Concrete operational (7-11 years) Children are able to solve concrete (hands-on) problems in logical fashion. They understand the laws of conservation and are able to classify. They also understand reversibility. 4. Formal operational (11-15 years of age) Children are able to solve abstract problems in logical fashion. Their thinking becomes more scientific, they develop concerns about social issues and about identity. † He also developed the idea of schemas as ideas or concepts that children need to master in order to learn about relationships. We will write a custom essay sample on Comparing Theories of Mathematical Development or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Chris Athey is a constructivist. She has applied the theory of ‘schema’ to the practical observation and analysis of children’s learning. Athey built on Piagets early work, and she sees schemas as a means to arrive at categories and classifications. For example, a baby will try out a wide range of schema on one object for example, sucking, shaking and throwing. This demonstrates the need and importance of a wide and varied range of experiences. Schemas can be put together over a period of time to create powerful and higher level schemas. According to Athey’s theory, schemas evolve from early actions and perceptions; they are part of the way in which young children make sense of relationships and of the environment around them. Athey identified four stages that children go through in exploring and using schema: 1. a period of physical action where the movement does not carry any real significance. 2. using schema to symbolise something. 3. beginning to see the functional relationship between two things. 4. using schema to support thought. For example, a child interested in rotation (which is linked to mathematics): Stage 1 The child twirls around and around. Stage 2 The twirling is used to symbolise a carousel. Stage 3 The child becomes interested in a yo-yo in that it can be shortened or lengthened when the string is wound around the yo-yo. Stage 4 The child puts all of these ideas into words and expresses their own thoughts about rotation. Athey identified a number of schemas which are all linked to maths including: * vertical * back and forth and side to side * circular or rotational * going over, under and on top of * going around a boundary * containing and enveloping * going through a boundary. Schemas are happening in practice all of the time. Children’s dominant interests of the moment will provide ways for them to represent their ideas in which they will include their preferred schema. Schema-spotting has become an analytical tool in many early years’ settings. Practitioners often think that very young children are acting in a random manner but once they scrutinise what is happening, a schema pattern may begin to emerge. (http://juliangrenier. blogspot. co. uk/2009/11/schema-theory-in-early-years-edu cation. html) In comparison these two theories both use the thought of schemas in their theories. But whereas Athey believed that schemas dominate children’s play as they explore, experiment and the way they learn, Piaget believed that children progress through three stages of learning when they are absorbing events into existing schemas they already have. Athey developed Piaget’ theory and showed how children forms of thought develop through experiences and developed a framework for teaching which extends schema through curriculum experiences. In my placement the teacher planned a group activity that all the children could take part in to learn about a certain subject which was a write up on the counting cars activity that they did the week before. Children and their partners created their own piece of work that was added to a class group display on a wall. The work included drawing of the cars, tables and charts recording the results, diagrams and short sentences on the activity. The wall represented the group as a classroom project. The nature of this kind of activity demonstrates the sharing of information, which can be a key component of learning and links well with Piaget’s theory as it shows that children think in symbolic form as the diagrams were written up as a symbolic form of a tally chart and every tally mark represented a vehicle. According to Squire G â€Å"children become totally absorbed and will spend a great deal of time carrying out related activities as they develop a particular schema. † For example in placement children love to spend a lot of time building towers independently or along with other children, which develops a vertical schema. Bibliography Squire G (2007) BTEC National Children’s Care Learning and Development, Heinemann, Oxford http://ponce. inter. edu/cai/tesis/lmrivera/cap2. htm 29/05/2013 http://juliangrenier. blogspot. co. uk/2009/11/schema-theory-in-early-years-education. html 29/05/2013