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13 Cards in this Set
- Front
- Back
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The NCTM Standards are arranged in terms of
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Standards.
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The Content Standards refer to
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the main topics under which all of the concepts we teach/learn in math fall.
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The Process Standards refer to
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abilities we help students develop in order to make it possible for them to store, retrieve, and use necessary mathematical information.
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It is a Behaviorist notion that if we teach students
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skills, facts, processes (algorithms), and formulas and if we provide them with enough practice in the form of workbooks and textbook exercises that they will develop the skills necessary for problem solving in the real world.
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What is missing from this kind of teaching is the development of
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thinking skills.
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A problem is
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a situation for which we have no readily available way to find an answer.
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If we must search for a strategy and through that strategy find an answer that makes sense, then we have
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engaged in problem solving. This requires high-level (higher-order) thinking.
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3x16 is not a problem. 25467x985286 is not a problem. They are both
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algorithms.
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A non- routine problem will always have
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data embedded in a story and will have no readily available way of finding an answer.
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Translation problems are those for which
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the solver must simply select an operation and do the arithmetic.
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Metacognitive abilities develop when we
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engage in activities that require us to “think about our thinking”.
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Some Metacognitive abilities that are used in mathematics learning (problem solving) are:
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Translation
Finding and using properties Determining conditions Finding equivalent conditions Recognizing independent conditions Detecting and using patterns Critical evaluation for the purpose of finding contradictions Discerning needed information Generating cases Approximation Elaboration |
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Problems solve for 3 reasons:
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1.Learn new concepts (NR)
2.To practice previously taught skills (Translation) 3.Problem solve to develop metacognitive abilities (NR) |
