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Posing Problems: Two Classroom Examples
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DOI：10.5951/mtms.5.2.0112.png)
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Abstract
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IN ONE NCTM YEARBOOK TITLED PROBLEM Solving in School Mathematics, Butts (1980) reminded teachers of the importance of posing problems properly. What happens if we fail to do so and pose a problem that cannot be solved? This embarrassing moment can be made profitable if we ask students to help fix the problem. Here we share two lessons in which students help teachers pose problems. In the first lesson, fifth graders found a mistake in a proportion problem, and the teacher asked students to help her pose it properly. In the second, a geometry problem with insufficient information taken from an eighth-grade mathematics test was posed intentionally to future teachers in a teacher-training college as a problem-posing challenge. We first describe the two lessons and then close with suggestions on having learners help teachers pose problems properly.
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