Expl_Concepts - Explaining Concepts and Propositions CI...

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Explaining Concepts and Propositions CI 401M&M2 Fall 2009
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Teaching mathematics in a classroom that promotes understanding • Consider these three dimensions of instruction Tasks : What are students asked to do? Tools : How to represent mathematical ideas? – Norms: How are students expected to act in particular situations?
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Mathematical Proficiency Graphic From: “Addning it Up”, 2001, Jeremy Kilpatrick, Jane Swafford, Bradford Findell, Editors ; Mathematics Learning Study Committee, National Research Council
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Mathematical Proficiency Conceptual understanding : comprehension of mathematical concepts, operations, and relations Procedural fluency: skill in carrying out procedures, flexibly, accurately, efficiently, and appropriately Strategic competence: ability to formulate, represent, and solve mathematical problems Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
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Mathematical concepts and propositions • Examples of mathematical concepts – Number – Slope – Function • Examples of mathematical propositions – In a right triangle, the square of the hypotenuse is equal to the sum of the square of the legs.
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Expl_Concepts - Explaining Concepts and Propositions CI...

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