Block Plan Round 1: Linear Algebra in 3.5 Weeks Flat

Cheesy prom-style photo of my Linear Algebra class after the final poster session

Four weeks since the start of fall semester, and I just submitted final grades. How is this possible? For those of you who didn’t catch my update earlier this month, I just started a new position at Colorado College, which operates on a distinctive yearly schedule of eight 3.5 week blocks. Students take one course and faculty teach one course per block. So my students from last week are now totally immersed in a new class. Luckily, I am not—this is a non-teaching block for me, so I have a month to regroup, do research, and get ready for the next round (Calculus 2 in block 3).

During the first block I taught Linear Algebra, one of my favorite courses so a bit of a treat to start out with. Some general info about the course: I had 23 students, with majors including math, math-econ, computer science, physics, biochemistry, and geology. All students had taken Calculus 2, but some had taken more advanced courses including Differential Equations and Number Theory. We met every morning from 9:15 to noon for lecture and classroom activities. I had office hours scheduled from 2-3:30 or so every afternoon, but, to be honest, my real office hours were more like 1-4:30 or 5. Then it was home to grade and prepare for the next day, just to go to bed and go back to work in the morning. Rinse and repeat.

This was probably more intense than it will always be, because I was redesigning my Linear Algebra course and essentially re-preparing all of my notes, and because I was starting a new job, which has a lot of start-up cost in itself. But it is clear that even as I get into the groove here at Colorado College, my teaching blocks will always be solidly busy with teaching. And the first few days after teaching will be solidly busy with sleeping, laundry, and catching up on email.

I feel tired, and a little disoriented, but somehow… satisfied? Yes, it was really satisfying to work so closely with my students, and to be able to ask for their full attention. Not every student gave it their all, but actually most students did, and they produced some really excellent work. They seemed satisfied, too, because they had totally immersed themselves in the topic and were able to remember knowing very little about it only weeks before. The huge progress of a math course, always hard to keep in perspective over a whole semester, was observable and exciting.

Highlights of the block:

• First day activity: We started with an icebreaker: as they entered the classroom, I gave each student a SET card. They were assigned to spend the first 5-10 minutes finding and introducing themselves to other students with whom they formed a SET. This developed into how we could use linear algebraic data structures to model the game SET, and then a discussion of what linear algebra really is and how it generalizes to finite fields. Though this course was only linear algebra over the real numbers, some students had taken number theory and knew about finite fields, while others had worked over the complex numbers, so over the course of the block we were able to touch on what the theorems we proved would look like over these fields. SET gave us the simple example of the integers modulo 3 to reference, and let me talk about how my own research in curves over finite fields uses linear algebra constantly. I will work on this activity and use it to start my linear algebra courses in the future.

• Sticky note questions: In the last three years, I have begun assigning daily or weekly pre-reading and reading questions for classes beyond calculus. I hadn’t tried this at CC yet, and I didn’t want to swamp the students with reading every night when they also have homework problems to do every night, so I decided to modify my approach. I assigned the first part of each section as reading, and asked students to write a question from the material on a sticky note before class. When they got to class, they were supposed to go to the sticky note board, read the questions there, and arrange them to group similar questions. We started class with a discussion of the important parts of the reading, and when we took our first break I would go to the board and read the questions. Some of them would already have been covered, but I could make sure to cover some of the others in the next discussion. I really liked having immediate response on their reading assignments, and I liked that they could see that all their classmates had questions, too. They put their names on the back of the sticky notes, and I counted them for a small portion of the final grade. It was fun to give each student their sticky notes back at the end of the block—for the most part, all the questions were answered, and it was a nice look back at the progress we’d made.

• Field trip: In the second week of the course we took a field trip to a park for a picnic lunch. We set math aside and just talked for a while, then sat together in a circle and had a group discussion. The starting point was a set of questions that the students had for me—in an email before the block started, I asked them what they would want to know about a professor when starting a new class. There were a wide range of questions, from “How do you grade?” to “What was your mathematical path?” and “What is your research about? Does it use linear algebra?” So I started out by answering some of these questions, mostly the more personal ones. My math history seemed very surprising to my students. I think they expected that I had always known what I wanted to do, and that perhaps I had always been on a straight path to becoming their math professor. In fact, I drifted around a lot and tried many things, and probably had much less direction at their age than they do. The questions front the emails also included the less serious “what is your sign?” and “what is your favorite color?” so we all went around the circle and answered these. It sounds ridiculous but was kind of fun.

After talking for a while, the students helped me set up a white board that we had brought along, and I gave a 5-10 minute lecture on computer graphics and linear algebra. Finally, I revealed the surprise final destination: the Manitou Springs penny arcade. This is large indoor/outdoor arcade filled with coin operated games dating from the 1920s to the present. It has lots of old cool pinball games and the original arcade video games: Galaga, Space Invaders, etc. I had a bag of quarters (now that I don’t need to go the the laundromat, they are really stacking up) and asked the students to each play at least one of the old-fashioned 2-D graphic video games and consider what matrices would create the graphics of the game. I walked around, answered questions, and played a few rounds of Space Invaders myself. So fun, and the math questions were surprisingly insightful!

• Final project poster session: The students took their final exam on the second to last day of class. The last day, I returned the exams (after a marathon grading session the night before), answered questions, and we then embarked on an hour-long poster session where they presented their final projects. The students worked in groups of 3-4 on topics that were not covered in the course, and created some really ambitious projects. One group actually built a complicated circuit and tested the current to see if it matched what they got by solving the linear system (not a great match, in fact… I guess the old resistors were not very predictable, and apparently one burst into flames in the process). Another group used images from a student’s work in a biochemistry to show principal component analysis in action. The poster session was an interesting, upbeat way to end the semester, unlike the stress and uncertainty of a last-day final exam.

Thoughts about the block plan? Linear Algebra ideas? Thoughts on how I should adapt Calc 2 to the 3.5 weeks? Let me know in the comments!

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