What are good problems for learning Curtis Bennett Loyola Marymount University

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)

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

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.

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.

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.

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.”