February 11 Day 340: More Appreciative of Less

For those teaching on the quarter system, Winter quarter 2021 is more than half way done. Today I administered an oral midterm assessment in Abstract Algebra. Previously I discussed my struggles with inquiry-based learning in this class because of its low enrollment numbers and I secretly wished for more students. Today I fully appreciated the paucity of enrollments. I administered the midterm interviews entirely during one scheduled class period. Compared to the individual oral assessments last quarter when I gave nearly 60 individual interviews throughout an entire week and finished in a zoom coma, this was a pleasant diversion.

Since my first experiment with oral exams in the Spring of 2020, my assessment methods and rubrics are beginning to converge.

The Method

One week in advance, students were given complete instructions for the assessment including preparation instructions, the grading rubric, and a selection of questions from which the assessment would be drawn.

Each student had 25 minutes (plus a 5 minute fudge factor) to present three questions, the first question being their choice (20 points) , the second my choice (20 points), and the third was a straightforward permutation computation on elements that I provided during the interview (10 points). The rubric was essentially the same as the one used last quarter.

The Questions

For their first presentation, students were allowed to choose any part of question 1 or 2. I would then pick a part from the unselected question for balance. Finally I gave them unique permutations alpha and beta in problem 3 and selected either (a), (b), (c), or (d) for them to compute in real time.

Lessons Learned

My thinking was that students would select one of the Theorems in Problem 2 for their first presentation and ignore the rest. Then they would be ready for any of my selections from Problem 1. I expected problem 1(a) to be tackled with brute force but a pattern would emerge to complete the problem and be extended to 1(b). I hoped they would use their previous knowledge for 1(c) and apply that to extend to 1(d). I was wrong. Instead, they minimized computation (either by selecting 1(a) or 1(c) for their first question) and prepared themselves for all three theorems. In many ways, I think that is the preferred outcome.

For some students, the individual interview was the first time they shared their face with me all quarter. It happened as they gave a tour of their work space. How wonderful to finally connect an image with their voice. I occasionally had enough time for pleasantries, chatting about summer plans, encouraging applications to REUs, and getting to know them just a little bit. I think these assessments are helping to keep me sane in my remote teaching and they are a real joy when there are not too many students.

Published by Jenny Quinn

Mathematician. Mother. Wife. Leader. I am a professor of mathematics at the University of Washington Tacoma. Mother of Anson and Zachary. Wife to Mark. President of the Mathematical Association of America.

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