Overarching (Constructivist) Philosophy:
"Multiple Representations"
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So preservice teachers deepen their understanding
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Children need multiple levels of "seeing" arithmetic
-- Concrete objects (manipulatives)
-- Pictures, Diagrams, etc
-- Symbolic representations
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Within each level, multiple representations help students having
different learning styles and backgrounds build understanding.
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Each instrument (manipulative, worksheet, computer program, etc)
has both advantages and limitations
-- Help preservice teachers build a rich repertoire
-- Encourage "life-long learner" attitudes, and habits of
sharing and discussing with colleagues by having them use, then
critique, and eventually create instruments
-- Emphasize deep understanding of content as inseparable from
and inherent in sound pedagogical choices (does your instrument model
the mathematical structures accurately?)
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