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Methods/ Mathematics

He outlined 7 learning situations students had to go through. They are:.
             Stimulus response.
             Simple chaining.
             Verbal sequences.
             Multiple discrimination.
             Concept learning and.
             Problem solving.
             (Students should verbalize math concepts promptly and properly.).
             One of the major contributions to curriculum development was analyzing the structure of a task or concept to be learnt. What Gagne emphasized was a curriculum-centered approach to learning. Curriculum view, looked at, and then broken down into small stages. He organized a curriculum-centered approach.
             Cognitive Theory.
             Constructivist theory is an addition to the cognitive theory. They consist of 2 major hypothesis.
             1. Knowledge is actively constructed by the individual and is not passively received from an outside force.
             2. Knowledge is an adoptive process that organized ones world, not the discovery of some independent, pre-existing world outside the mind of the individual.
             Characteristics of constructivist/cognitivist Classroom.
             1. The emphasis would be on students' autonomy, responsibility and group work.
             2. Students spend much time interacting with materials representing math ideas and processes in different ways.
             3. Students interact with the teacher. Teacher encourages, nurtures, and provides help.
             4. A teacher is responsible for creating an environment where students are motivated to learn.
             Jean Piaget.
             Learning is a change in behavior.
             Key concepts:.
             Schema.
             Adaptation.
             Operation.
             Schema: A cognitive structure that one constructs by putting pieces of knowledge together to make sense.
             Adaptation: The process by which the schemas are developed.
             Adaptation can take two forms: assimilation and accommodation.
             Assimilation occurs when one's existing cognitive structure requires little modification to include a new idea.
             Accommodation occurs when no relevant schema exists and learning occurs or new behavior is developed through experimentation, instruction or both.
             Operation: This is the mechanism by which a schema is assimilated or accommodated-internalized action that modifies knowledge.


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