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