Menu:

News:

Joint Meetings:
I will be attending the 2009 Joint Meetings in Washington, DC. Please contact me if you would like to arrange an interview.

Teaching

Instructor

Duties included choosing textbooks, designing syllabi, writing and grading homework and exams, lecturing and leading class discussions, and holding office hours.

1. Matrix Algebra

Math 309, Washington University in St Louis, Summer 2007.
Enrollment: 3
Class time: Every weekday for 1 hr and 45 minutes for 5 weeks.

Selected Course Materials:
1. Syllabus (pdf)
2. Take-home Exam 1 (pdf)

As indicated in the syllabus, one of my primary goals was to enhance students' communication skills. I incorporated three teaching techniques to develop and assess their ability to articulate conceptual and computational understanding of the material.

Lectures and Discussion:
Class time was a hybrid of lecture and group discussion. Open class discussion allowed the students to discover new ideas and problem solving strategies together. The students felt comfortable proposing ideas and collaborating with each other. The positive classroom environment carried over to a positive environment during office hours as well.

One-on-One Meetings:
The second technique was to schedule a 20-30 min meeting with each student each week. In these meetings, I asked them to talk me through the solutions to two exercises from their recent homework sets. I allowed the student to choose the first exercise and then I chose the second. Gradually we would deconstruct the exercise and its solution into fundamental pieces, noting the concepts and computations involved at each step. As we chatted, I would complement their strengths, address their weaknesses, reinforce the conceptual storyline, and point out problem solving techniques. One student in Matrix Algebra commented,
"I was a big fan of the weekly meeting portion of the class as it sort of told you where you were at in the class and allowed for more in-depth discussion of the material."
As the semester progressed students generally showed improved ability to communicate mathematics and the depth at which they understood the material grew. In addition, I was able to evaluate the overall strengths and weaknesses of the class and adapt my teaching accordingly. In a class size of 35 students or less, I believe a variation on this technique where students meet with the professor twice per term would be an effective way to assess conceptual understanding of the material and develop verbal communication skills.

Essays:
Each of the two take-home exams included a 300-400 word essay question. The essays asked the students to synthesize substantial amounts of course material and develop a cohesive picture of an important topic. Since the exam was a take-home exam, I hoped the students would spend considerable time reflecting on the material and form their own "Big Picture" for the course. On the first exam, student performance on the essay was lower than expected. They found it difficult to write complete sentences and structured paragraphs about mathematics. Their performance on the second essay was dramatically improved though. I attribute that to their success in the weekly meetings and classroom discussions where I continually emphasized the need to keep the conceptual storyline in mind as we learned new material.

2. Finite Mathematics

Math 220, Washington University in St Louis, Summer 2006.
Co-taught with grad student Scott Cook.
Enrollment: 6
Class time: Every weekday for 1 hr and 45 minutes for 5 weeks.

Selected Course Materials:
1. Syllabus (pdf)
2. Quiz 8 (pdf)
3. Group Work (pdf) (7/24/2006)
4. Group Work (pdf) (8/11/2006)

Quizzes:
We decided to use 9 quizzes as our primary method of individual assessment. We reasoned that because the material was evenly split between counting arguments, graph theory and number theory and since these topics were mostly self-contained, we didn't need to use comprehensive exams throughout the term. The intense 5 week schedule of the class also made it difficult to find time for in-class exams. Quizzes twice a week helped the students keep up with the material and assisted us with finding weaknesses in their understanding. From this were were able to make adjustments to the course as the semester progressed. For example, one quiz showed that students were struggling with induction proofs long after we had covered the topic. Scott and I decided it was worth taking class time to readdress induction.

Weekly Group Work:
Developing communication and problem solving skills and fostering collaboration were primary goals for the course. In order to achieve those goals we incorporated group work into the second half of the Friday lectures. We split the class into groups of three and gave each group the same three challenge problems. The questions required the groups to find clever applications of the course material and were substantially harder than homework and quiz questions. Though the groups generally began by working at their desks, most soon found their way to a corner of the blackboard where they would scribble ideas and have animated deliberations about problem solving strategies. The students were given 45 minutes to work and at the end of class each student was assigned one of the three problems. They then had to write a one page essay using complete sentences and well-structured paragraphs detailing their strategies for tackling the problem and the key concepts involved in the solution. If they were unable to find an answer, they were to detail the strategies they tried and how and why they failed. We provided them with an example essay at the beginning of the semester so that they would understand our expectations for this assignment. Since the students did not know which problem they would be assigned, it was in their best interest to collaborate and try to solve all three problems before the end of class. We were very happy with how well these activities worked. The elegant and ingenious solutions they discovered were points of great pride for the students. They were especially happy when they discovered elegant solutions that Scott and I had not found.