Comparing Theories of Mathematical Development

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For this assignment I will describe two theories of mathematical development. I will discuss Jean Piaget’s and Tina Bruce’s theories about how children’s understandings of mathematical develop.

Jean Piaget’s research led him to believe that we develop by taking in information, which is then processed by the brain and as a result of this our behaviour changes. He stated that there are stages of development that children move through. The ages are approximate but the sequence is the same for everyone.  According to http://ponce.inter.edu/cai/tesis/lmrivera/cap2.htm “The stages of cognitive development that Piaget distinguished are: 1. 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.

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 Piaget's 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...
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