Chapter Review Two
The educational theories mentioned in this chapter are constructivist theory and sociocultural theory.
Jean Piaget's constructivist theory suggested that children or learners "are not blank slated but rather creators of their own learning". Piaget mentioned that when we learn and construct ideas, we are actually creating schema; and such schema can be changed through assimilation and accommodation. Assimilation is the acquiring of new ideas or concepts while accommodation is 'fitting' new ideas to prior ideas to replace existing schema. And, when reflect, we look for ideas that are newly acquired which can be connected to the existing ones.
The other theory that is stated in the chapter is the sociocultural theory, which is the work of Lev Vygotsky. Vygotsky's believe that when learners interact with the people in his environment, especially those who are more knowledgeable; can help the learner to reach his full potential learning capacity, which is his Zone of Proximal Development (ZPD).
This two theories implies that I, as an educator, have to help children to build on their prior mathematical concepts by first getting to know what they have already know; and build on their knowledge by introducing new ideas that build on their existing concepts. Using real life mathematical questions, giving children a chance to express their mathematical views and allowing the multiple approaches to solving mathematical problems can help children to build on their concepts and introduce new ideas. It is about helping children to find the connection and relationship between their old and new ideas, thereby creating new concepts to replace existing ones. Furthermore, I am working within the range of their ZPD when I scaffold them through teaching strategies such as questioning, reasoning, explanation; by using manipulative and models to aid them in understanding mathematical concepts.
When I help children to see the connections between the mathematical ideas and concepts, I can help them to understand mathematics relationally. It is an effective way to help children to learn new concepts and procedures as compared to getting children to learn mathematical concepts by rote counting, which is not effective for the long term. Relational understanding also help children to remember less, increased in retention and recall concepts as they see the relationship between such ideas. It also enhanced children in their problem-solving skills as they transfer ideas they had use in one concept and apply it in another. I also strongly believe that when children or learners managed to solve a mathematical problem, they would feel confident and have an improved attitude towards learning of mathematical concepts and a sense of belief and faith in themselves.
Jean Piaget's constructivist theory suggested that children or learners "are not blank slated but rather creators of their own learning". Piaget mentioned that when we learn and construct ideas, we are actually creating schema; and such schema can be changed through assimilation and accommodation. Assimilation is the acquiring of new ideas or concepts while accommodation is 'fitting' new ideas to prior ideas to replace existing schema. And, when reflect, we look for ideas that are newly acquired which can be connected to the existing ones.
The other theory that is stated in the chapter is the sociocultural theory, which is the work of Lev Vygotsky. Vygotsky's believe that when learners interact with the people in his environment, especially those who are more knowledgeable; can help the learner to reach his full potential learning capacity, which is his Zone of Proximal Development (ZPD).
This two theories implies that I, as an educator, have to help children to build on their prior mathematical concepts by first getting to know what they have already know; and build on their knowledge by introducing new ideas that build on their existing concepts. Using real life mathematical questions, giving children a chance to express their mathematical views and allowing the multiple approaches to solving mathematical problems can help children to build on their concepts and introduce new ideas. It is about helping children to find the connection and relationship between their old and new ideas, thereby creating new concepts to replace existing ones. Furthermore, I am working within the range of their ZPD when I scaffold them through teaching strategies such as questioning, reasoning, explanation; by using manipulative and models to aid them in understanding mathematical concepts.
When I help children to see the connections between the mathematical ideas and concepts, I can help them to understand mathematics relationally. It is an effective way to help children to learn new concepts and procedures as compared to getting children to learn mathematical concepts by rote counting, which is not effective for the long term. Relational understanding also help children to remember less, increased in retention and recall concepts as they see the relationship between such ideas. It also enhanced children in their problem-solving skills as they transfer ideas they had use in one concept and apply it in another. I also strongly believe that when children or learners managed to solve a mathematical problem, they would feel confident and have an improved attitude towards learning of mathematical concepts and a sense of belief and faith in themselves.
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