# Teaching as a Primary Instructor. Day 1.

Today was designed to be an introduction / icebreaker sort of day. I passed around a prop, and had the students introduce themselves to the class when the prop got to them. Once I got the prop back, I asked them if they knew what it was, knowing that none of them would. It was a slide rule. I told them it was a calculator, watching for a moment as the blank looks on their faces turn into dumbfounded looks before telling them a little bit about how slide rules were the calculators used before electronic calculators came on the scene in the 1970s. Of course I brought half a dozen slide rules with me today as part of what was probably the geekiest icebreaker ever. I showed them how to use the C and D scales to multiply 2 by 3, and split the class into groups with a slide rule in each group and gave them the task of multiplying 4 by 3. That was a trick, of course, because the opposite 1 is used for those two multiplications. Then I had them look at the A and D scales, using the hairline to line up with the 5 on the D scale. And I had them do the same with 3 on the D scale. They were pretty quick to notice that the operation there is squaring, despite the initial appearance that 5 takes you to 2.5. After asking what else they could expect to be able to do with a slide rule, given that you can multiply and square numbers, I asked them to find the square root of 2, using the slide rules I handed out. I hope they had fun with that. I know I did.

Still in their groups, I had them talk to each other for about ten minutes to round out the icebreaking in a more… normal? way. I wandered around for a bit, answering questions and addressing concerns, and after the ten minutes was up, I handed them their Problem of the Day. I wanted to make it very light for a very light day, so the questions were: What is my name? What are the names of the people in your group? and What is the name of the prop we used today? I had my name and the words “slide rules” written on the board, so it was mostly a matter of, “Are you paying any attention?” After I collected the PotDs, I pointed out the reason I decided to use slide rules as a prop for the icebreakers – logarithms are what make slide rules work, and they will be learning about logarithms later on in the Precalc class portion of their Summer Bridge ensemble. The point of the geeky icebreaker: I whetted their appetites for things to come. I also explained that the multiplication on a slide rule would be addition if the scales were linear instead of logarithmic, which means logarithms effectively turn a multiplication problem into an addition problem.

By then, they started asking questions, like why I like mathematics. I answered that “mathematics is fun (interruption: frustrating) – yes, it can be frustrating at times, but it is still fun – and beautiful. No, I’m serious.” I think any subject, if you go deep enough into it, has some kind of beauty. Math has lots of really cool things you can look at. Some examples I gave were that we can show $\sqrt{2}$ is irrational… primes are 0% of all whole numbers, but there are just as many primes as whole numbers… just some snippets of cool stuff that would be accessible at the precalc level.

There was another question about what’s the hardest math I’ve dealt with. I told them the most abstract I’ve dealt with is Category theory, but the one with most nitpicky detaily nuissances that I’ve dealt with is Analysis. I don’t think I explained very well. I mean, how do you start to outline what’s so cool about Categories or any branch of Analysis when they’re taking precalc? For the sake of having somewhere to start, I reduced Categories down to manipulating arrows, and I reduced Analysis down to the details for why you can do what you will do in calculus. That is a gross oversimplification, and I don’t think I did a very good job of explaining that much. They seemed kind of bored with my answer to that question. Oh well. The remainder of the time I spent with them was answering questions about course materials and the like.

I suppose I should also note some notable things that happened last week.

Last week the other class I was supposed to teach today got cancelled because there was insufficient enrollment. That kind of sucks because it means my paycheck will be half as much. In anticipation of something like that, along with finances already being tight, I filed the FAFSA the weekend before so I could be eligible for student loans. I’ve never taken out a student loan before, so that’s kind of new territory for me. Don’t ask me how I managed to get to the beginning of my fourth year in a Ph.D. program without taking out any student loans; I would just say it’s a miracle. Turns out, even if I get offered student loans, the earliest they could possibly be disbursed would be somewhere in the middle of September. I was able to get an emergency loan through Grad Division, though. That should at least help tide me over. Basically, finances are stressful.