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What are good problems for learning Curtis Bennett Loyola Marymount University

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Expert Novice Differences Factual Knowledge – how it’s classified and remembered. Methodology – Experts know more methods. Response to not knowing (difficulty) – Experts treat not knowing as an opportunity for investigation. Novices tend to treat not knowing as a problem. (Salvatori)

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Characteristics of Questions Complexity – level of difficulty. Often –Factual questions are easy. –Methodological questions are medium level. –Dealing with unknown is hard. Time frame to response (mathematics) –Short – 5-10 minutes in class, next day for HW –Medium – Weeklong problem sets. –Long – Term long projects

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Investigation Complexity – Time grid. Analyze student responses to different types of problems with different time frames. My mathematics grid has two surprising features: –Giving students longer time frames allows greater student comfort with not knowing –Short frames for hard problems gives students comfort with difficulty too.

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Proviso Instructor support is crucial – Long term assignments constant check ins are necessary to keep students from compressing the time frame. Then you can avoid the office hour “dance.” –Short time frame with not knowing – It is crucial that the instructor support not knowing and partial answers as valuable.

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Classroom presentation and community Math students rarely see mathematical knowledge as socially constructed. Short frame complex problems can foster a belief, but require community so students see difficulty in the problem, not their own knowledge.

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Student Quotes – after short term hard problem class. “Just because the answer isn’t right, doesn’t mean it isn’t useful information.” “Trying to solve something together.” “I have so much to learn from the people around me versus having to be the best.”

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