I’ve never had the chance to really “iterate” a course. Like I briefly mentioned in my last blog post, for the past 3 summers, I’ve taught at the same* math camp. The first two summers, I was given a curriculum to teach, and each day after we were done, we were expected to make edits to the lecture notes and problems for future years to use.

*The third year, I worked for a different camp got run in a very similar manner by people who worked on the previous camp. Confusing, I know, but it bascially counts as the same camp IMO?

The 3rd year was different – I had to write all of the lesson plans and problems (6 hours worth of content) for 12 days of classes AND teach them the next day. While it gave me complete control over the curriculum in terms of material, ordering, and the way it was presented, I only got to build off of the lessons I remembered from how I presented content last year.

But GTL so far has been a different experience, because not only do I get to re-use the content I prepared for the first week, I get to make direct adjustments to what I taught to make it even better.

Relativity Week 1 was an imperfect experience. I taught a 9-hour course on relativity to two separate classes. There were many, many things which went wrong.

- I spent the entirety of the first day boring students. There was a solid hour where I spent helping them derive the mathematics behind the Michelson-Morely experiment because I thought it was interesting, but I was halfway through it and realized that I had the attention of maybe 1 kid in 20.
- I may have accidentally stated the formula for time dilation backward for an example, only serving to confuse the kids more in a subject that’s already confusing to begin with.
- I didn’t have any fallbacks on activities to do when my timing was off by a few minutes – figuring out how to spend the remaining 5 minutes of class when I’ve already asked “Do you have any last questions?” and they’ve been silent for the last 10 seconds.
- I really like interactive activities, and I knew coming in I didn’t have many of them planned out for relativity. That fact was made very apparent during my classes.
- I spent a lot of time on derivations in general, but I’m not sure if that’s a bad thing. More to discuss later.
- Oftentimes, I’d realize during lectures that my slides were not what I wanted them to be. As a result, I’d just ignore them and lecture with a board (like I usually do).

*Wrong* is a strong word here. Especially in the context of me getting to teach this class again during the second week, it gives me a chance to actually make use of all of the things, big and small, that I noticed could be better.

But also, even with all of these things that could be improved, there was *so much that went right*.

- I love teaching. Sometimes it’s easy for me to forget this (especially maybe a little bit last summer when I spent 16 hours a day teaching or prepping notes for the next day), but wow, I love teaching. Getting to see their excitement when thoroughly unintuitive concepts make sense, when after just 9 hours I can talk about black holes and parts of the math
*actually*make sense, when I’ve given them enough intuition behind the material that they start me asking the questions that*I’m*about to ask*them*to think about. - These students ask incredibly good questions. Clarifying my scribblings on diagrams, wondering about how FTL travel could possibly work, asking about connections to SciFi movies. Absolutely awesome questions.
- Someone gave a fully correct answer to the Ladder and Barn paradox! !!!!!!!!!!!!!!!
- I gave students the velocity addition formula, and one of them was interested enough to ask me how he could derive it!
- A teacher sitting in on my class complimented my ability to lecture, and to tell a story. She really liked the way that I taught relativity–by first bringing up the comparisons to classical mechanics in almost every lesson, to help them gain intuition, and then connecting it to the idea that exists in special relativity. She was surprised I hadn’t taught relativity before.
- Blew people’s minds with dotted lines. Always fun.
- I got an applause at the end of one of the classes ❤

Hm, a 9-hour course on relativity. Potential HSSP class? Maybe not this semester, TBH.

Teaching is fun and I love it. And the nature of my GTL school means that I get to actually *improve* upon all of the things that I noticed–they’re not just passing comments that might get lost to time, but real, actionable things that I know I can do better. And I did!

- More examples, put directly into the slides. I qualitatively bring up the idea of the Barn and Ladder paradox (renamed to Snake and Gates for visuals) the day I introduce time dilation and length contraction, then as days progress, continue coming back to that example (using it for Lorentz boosts and spacetime intervals)!

- A lowered emphasis on derivations. I reduced the number of “let’s work through the algebra” moments to focus on the important conclusions: light
*always*travels at*c*, moving clocks run*slow*, moving rulers get*short*.- However, they’re not gone entirely. A good number of the derivations serve to make their intuition clearer and to truly understand where concepts are coming from. For example, my “derivations” in a spacetime diagram all simply revolve around the spacetime interval and saying x/t is a velocity, which provides direct intuition into what each region in a spacetime diagram means!
- I think for me personally, I’m slightly biased towards lots of derivations because that’s how I like to learn. Need to keep in mind that that’s definitely not the same for everyone 🙂

- More planned “talk to your friends about ____” times! One of them that I like in particular is asking students to discuss what happens to the length that is perpendicular to movement – whether it stays the same, there’s length contraction, or there’s length expansion. This one is great because there are feasible explanations for them all.
- Same: Your velocity perpendicular to movement is 0, so

γ=0 (correct explanation). - Bigger: The volume that gets compressed has to go somewhere, so it should get bigger.
- Smaller: If length contraction happens parallel to movement, why should that axis be special?
- From here, I go through a solution using proof by contraction to justify why the answer is “same.”

- Same: Your velocity perpendicular to movement is 0, so
- Sliiightly less lofty goals in terms of content. Much like with derivations, I’ve decided to cut out some planned material (especially towards the end) in favor of moving slower, emphasizing the content that I think they should be getting out of the course.

Of course, 1 round of iteration is not enough. Even this week, I’m noticing many, many things that could be better. This may be my last time teaching this class, but I’m hoping that what I’m learning this week doesn’t go to waste. I’m making comments on my lesson plans and slides that I have, hoping that when I send these materials to the GTL Italy coordinator, someone in the (maybe not-so-distant) future who’s teaching relativitiy can look at them. And maybe, just maybe, they’ll continue the process of iteration.

This blog post would be complete without some random photos, so here they are 😛

And of course, some fun things I’ve noticed about Italy 😛

- Toast refers to a sandwich which is toasted (meat and cheese), not just the bread.
- Lots of music from 10 years ago. This Is Me by Demi Lovato? You Touch My Tralala?
- Some teachers drive us to the school in a neighboring town for the second week. They’ve complained about Italian drivers no less than 3 times. They’ve been driving us to this school only for 3 days. “Everyone has their own rules. And their rules are exactly what the real rules are not” (paraphrased).
- There’s a town here (Basiglio) with a significant Filipino population.
- Prego is just another word here. It’s not pasta sauce. It has many meanings, including “you’re welcome” and “after you” (which are the two most common ones I hear). Salsa means “sauce” and refers to condiments–mayo is a salsa.
- Grande is just a word they use here. After seeing my FB friend request: “Grande, Paolo!” Anyone who knows me IRL will know how happy I am.
- Some students asked my age, and I asked them to guess. They said 24 or 25. Others said 20, 23, and 25. Someone asked if I dress up like this (business casual) normally at MIT.
- My host mom baked me a birthday cake! There was a” rose” on the top, and before I ate it, I asked what it was. “It’s the same as in church, the Body of Christ.” And lo and behold, it was actually a Eucharist wafer, just without all of the holiness.

This’ll be my last blog post on the relativity class. Time to talk about other adventures 🙂

I challenged myself to write this blog post in 30 minutes to procrastinate, and it only took 50, mostly because I decided to add photos 😛