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Re: How We Teach
Posted:
Dec 27, 2009 9:21 AM


In response to (some of) Jonathan's questions:
1. You are what you test. For many students, if the material isn't tested/assessed in some way, it's not part of the course.
2. Although grades on a final exam are almost always close to a student's final grade, basing the grade on the final misses too many opportunities to help students learn. Jonathan listed a bunch. I'll add one of mine.
In Intro to Real Analysis, I have students take 5 mastery tests on core proofs (repeat up to 3 times, have to get all them essentially perfect to be done). According to students, the first is the key to the course: recreate the basic sequence proofs (sums, constant multiples, convergence implies bounded, products, reciprocals, quotients). It's possible  in theory  to memorize the proofs, but students tell me that doesn't work. It's just too easy to forget something, and any substantial mistake that isn't corrected in an oral followup means that they have to redo the entire set. It's much easier to learn a structure (by the definition) and how to recreate the proofs. So in class I emphasize how I came up with every idea, at every stage of proof creation.
A major benefit of these mastery exams is that I know which proofs work for students, and I can modify proofs in ways that help students understand them. Plus I have 5 minimeetings with every student in the class.
3. Attendance. I don't have much of a problem. I have 50+ students, and 48+ attend a typical day, even at the end. The students are a mix of engineering, science, computer science, and math majors. The nonmath students are there to earn a math minor, which is by their choice, but other than that...
If your attendance is low, I think you need to ask the students what's up. Maybe they're really busy trying to catch up on the work they didn't do during the term. Or other classes have big projects. Maybe they're lost and don't like sitting there feeling stupid for an hour. Maybe they think they've learned enough to meet their grade goal. Maybe they're volunteering in a soup kitchen. Okay, probably not the soup kitchen, but if it's down to 50%, then it's time to have some informal chats with the students. Find instructors who have higher attendance and ask their _students_ what's different. The instructors may have some ideas, but likely as not they're wrong: I will never forget the Calculus student who told me that he was doing the homework this term because he actually understood the material. I'm standing there speechless...
David Olson Michigan Tech



