22 Feb 2008
Class Observation comments for Dr. Amanda Beecher
I visited Dr. Amanda Beecher’s class on Fri 22 Feb. We had coordinated for me to visit
one of her classes, but she asked me to visit without telling her the date in advance so she
could be observed on a “typical” day, and that is what I did.
This particular class was on related rates in Calculus I, the second consecutive day
scheduled for this topic. Class began with the submission of graded homework. I asked
the student next to me how long he had worked on it, and he replied “for a while”, and
that he had sought and received help on a few of the problems from his classmates. It
was clear that the routine of having graded homework assigned, working through it over
some period of time, and seeking and documenting help when needed was a familiar one
to this student and the others in the class. Dr. Beecher announced her policy on late
submissions; the 10% penalty for every day late reinforced her expectation that students
develop good managerial skills by planning ahead.
One student asked a question, and then the class took a 15-minute class quiz. The quiz
was well-constructed, with each of its three questions covering a different aspect of
related rates. Some students finished within 8 minutes; another approach here would
have been to give the quiz at the end of class so that more questions might be raised and
answered and so that students finishing early could leave early. All students had brought
their laptops with Mathematica to class and were authorized to use them (network access
was prohibited) during quiz; a few did, but most only consulted notes and the text.
After the quiz, all students were randomly paired (with a slick Mathematica random-listgenerating tool) to work problems together at the chalkboards. Each student team
worked one of two related rates problems. Students found the problems to be a step up in
difficulty from the problems they had worked the previous lesson. As students worked,
Dr. Beecher moved from group to group, giving assistance and ideas and making
corrections. After most groups had come to a solution, Dr. Beecher had one student who
had some difficulty with his solution brief the solution from another student’s completed,
correct board. The briefer was familiar with the initial steps, then worked his way
through explaining the portions of the problem which he had not quite completed on his
own. When he was finished, both the student and the class were satisfied with the
explanation.
In the final phase of the class, student teams remained at boards and were challenged with
the “ferris wheel” problem, where they calculated vertical velocity from angular velocity
by using the ideas of related rates. Students had not had college physics yet and so were
dependent on the mathematics to help solve. Dr. Beecher gave suggestions to several
groups until time expired, and then challenged them to complete this interesting problem
on their own.
The class was very interactive, with students doing most of the solving and Dr. Beecher
doing most of the posing, suggesting, and correcting. It was very clear that the students
were used to learning by doing, were comfortable using both their computers and their
text as resources when they needed assistance, and found it very natural to work
collaboratively, both in giving and receiving assistance. Dr. Beecher has wonderful
rapport with these students, addressing each by name and moving around the room to
engage each one. I left with the understanding that this group of students was working
hard to not just learn the days material, but toward becoming competent, confident
problem solvers.
Joseph D. Myers
COL, OD
Academy Professor