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Topic: How We Teach
Replies: 2   Last Post: Dec 27, 2009 3:44 PM

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 David A. Olson Posts: 109 Registered: 12/6/04
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
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 follow-up 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 mini-meetings 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 non-math 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

Date Subject Author
12/27/09 David A. Olson
12/27/09 Joel Feinstein