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Methods/ Mathematics


             Developmental stages mentioned by Piaget, (occurs while learning is taking place).
             Sensorimotor.
             Pro operational.
             Concrete operational.
             Formal operational .
             Four factors that affect/influence how rapidly one moves through the developmental stages.
             The four factors are:.
             Maturation - organic growth.
             Experience - physical and psychological experiences an individual has.
             Social transmission - teaching or the imparting of knowledge.
             Equilibration - process of bringing conflicting ideas into balance.
             Implications for teachers.
             Since most primary students are at concrete operational stage, teacher must provide the kind of concrete operational experiences that will enhance learning.
             Piaget's conservation task provides us with some ingenious methods for assessing readiness for certain concepts.
             Piaget's work can also provide direction for sequencing the curriculum. Children conceive numbers earlier in the concrete operational stage while mass and volume are not conserved until the end of that stage.
             Zoltan Dienes.
             He developed a theory of math learning with the following four steps:.
             Dynamic.
             Perceptual variability.
             Mathematical variability .
             Constructivity principle.
             Dynamic is a 3-phase process and the first phase is what Dienes refereed to as preliminary or unstructured play. The activities that the children are involved in are relatively unstructured ( first phase).
             Structured play or games (second phase).
             Explicit representation (third phase).
             Perceptual variability: the principal says that learning is facilitated when the children see the concept in a variety of forms.
             Mathematical variability: Like the perceptual variability principle mathematical variability principle suggests children be exposed to a variety of variables so that essential ones become evident by there presence in all examples, non examples as well should be used.
             Constructivist: This principle suggests that children be allowed to build up or construct their own experiences.


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2. Individual Philosophy on Mathematics

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3. What is Mathematics?

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7. The Philosophies of Arts and Mathematics

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