A picture of me with one of my Week 1 relativiy classes!

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)!
The “snake and the gate” paradox slide used for the spacetime interval lecture
  • 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.”
  • 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.
cake c:

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 😛


Lesson planning and teaching philosophies

I’m sitting in my host family’s kitchen preparing to eat breakfast, finishing up my plans for the lessons I’m teaching. What better way to procrastinate than writing a blog post about lesson planning and how I approach teaching? 😛

(This post is probably going to be long because it’s both a first post and I’m really into procrastinating. Other ESPloggers please take note because this should not set precedent for you I’m just really procrastinating a lot)

I’m teaching in Italy this IAP, in a town called Rozzano in the metro area of Milan (30 mins south of the city center by car, 1 hour by public transport). This is my first time teaching at a GTL. I got here just over 24 hours ago, and am super excited for this ~wild~ time! I’m teaching 6 classes in total covering 2 topics:

  • 9 hours of relativity to 3 separate classes (of 18-year-olds who have seen mechanics, e/m, and some introductory calculus)
  • 9 hours on stats to 2 separate classes (of 16-year-olds who have seen algebra and geometry)
  • 5 hours on stats to 1 class (basically the same as above, but I only cover the first half of the material)

In all honesty, the actual amount of work that I’m doing for lesson planning isn’t too bad. First off, I only really need to plan around 18 hours of content, which should not be difficult at all. (Over the summer, I had to plan around 6 hours of content every day, 6 days/week, for 2 weeks, so this is going to feel loads less stressful.)

My planning was made a lot easier because my contact at the school gave me a suggested syllabus with a list of all of the topics he wanted me to cover. Because that’s out of the way, I instead get to focus on two things:

  • Thinking at a very high level about how I want this class to run and my philosophy of teaching
  • Figuring out the curriculum, the details of the lessons and how exactly I want to cover it

Both of which I think are far more interesting than deciding a list of topics to cover.

Because of the scheduling, this week I’m teaching 2 of the relativity courses, which means most (read: all) of my preparation so far has been for that.

High-level thinking

I don’t think that the biggest lesson that I can teach my students is about the science of relativity.

The summer after my 10th grade, I went to a math camp. Yeah, one of those math camps, where nerds get together and take classes for 3 weeks — one on Geometry and one on Number Theory. I came out of camp feeling like I knew so much more, but now, almost 4 years later, I remember:

  • My geometry teacher was really, really, bad. he would answer I couldn’t do 99% of the material right now. Choice quotes (as best as I can remember):

These are not problems. They are exercises. The only real problems are the Millenium Problems.

Referring to IMO Problems Exercises

This is trivial.

To any question asked
  • My number theory teacher was amazing. Fun explanations, and showed the intuition behind the material. Awesome person. However, time still makes you forget, and I am sure that I couldn’t do 98% of the material right now. However, what I do remember is feeling like I actually understood so many interesting concepts, feeling like math had so many interesting fields and problems, and that number theory was my new favorite math subject.
  • Funnily enough, this number theory teacher also made an offhand comment after I explained my thoughts on a problem at the board. “That was a good explanation, you showed the ideas behind your steps” followed by something about how I should teach more. 4 years later, having taught at 3 math camps and at loads of ESP programs, I still credit him with giving me that push that got me interested in teaching and education.

The experiences that I’ve had, both when I teach and when I learn, have shaped the way that I view education, especially in contexts where I have very limited time with students (in the end, that’s the only kind of teaching experience I have).

I don’t think that I should expect students to achieve mastery by the end. Nine hours is far too short of a time for people to truly understand everything about relativity.

In my opinion, there’s a good chance that most of the details of this material will inevitably be forgotten, especially because I’m teaching “outside” of their normal curriculum. And there’s not too much I can do to change that.

In light of that, there are a couple of things that I hope my students can learn that aren’t just the concepts and the formulas and the physics, things that I hope they remember long after this IAP.

  • Physics is a science. The ideas they learn didn’t pop out of nowhere, divined by geniuses who had some deeper knowledge about the world. People had ideas, they tested them, and they gradually made a model that described more and more of the world.
  • They can build intuition behind these complex ideas, even in a science where almost everything that happens is unintuitive.
  • I want them to enjoy. To enjoy the challenge, enjoy learning about some of the coolest physics that we know today. And maybe when they look back in a few days, weeks, or years, that they’ll remember physics being exciting.

Of course, I have to do this all in a context where English isn’t their first language — and maybe these goals will go to the wayside to just focus on explaining concepts. But as I plan all out these lessons, I’m trying to keep these goals in mind, and hopefully they happen to a non-zero degree.

The nitty-gritty of teaching

Of course, all of these goals are fine and dandy, but I also need to prepare lessons themselves.

Like I mentioned above, I plan on explaining concepts as intuitively as possible. To me (in the context of relativity), this means introducing ideas without mathematics when I can and focusing on qualitative examples. From there, I’ll build up the algebra and mathematics necessary to understand material.

While I’m still working on planning out my lessons right now (in other words, procrastinating on it with this blog post, here’s a couple of small-level ideas, choices, and other thoughts on the specifics of how I’m teaching.

  • I’ll be presenting content using powerpoints that have an outline, but lots of white space on each slide. I plan on presenting them and writing equations/notes on them as I go using a smartboard. I’ve never actually used a powerpoint structure in any of my classes (mostly have just written on chalkboards/whiteboards/smartboards), so I’m excited to see how this goes. This also forces me to do prep beforehand, which, as you can see, is kind of working despite my procrastination. Slide examples below!
  • Teaching when English isn’t people’s first language will be hard. Those that know me IRL know that I am very excited, and that when I talk, I tend to talk fast. I’m going to have to actively slow myself down a lot as I teach, and I wonder how I’m going to be able to keep the same level of excitement as I normally do when I teach.
  • Because I’m teaching for so short of a time to each group, it will be difficult to get to know students. I’m hoping that I can get to know them a little as class goes on, but the fact that I’m teaching 6 separate groups for very short amounts of time will make this difficult.
  • I’m really rusty at relativity. It’s been about a year since I’ve studied it, and I’ve forgotten lots of my own intuition behind material. I’ve spent the last week or so attempting to re-teach myself, and need to do more of that as the week progresses.
  • I’ve also never “learned” it in a class with algebra. I took 8.033 (Relativity) at MIT, and talked about concepts in high school with my physics teacher (using algebra), and so this will be an interesting time.
  • Very generally, relativity is hard. The intuition is oftentimes nonexistent and there will definitely be times where I’m going to have trouble finding the best way to explain material. Hopfeully I’ll document this as it goes, but I think that this will be one of the hardest things I’ve ever tried to teach.

Before I end this first post, some fun things that have happened while here in Italy.

  • My host family has two dogs. one is named Cannella, because someone vetoed “Nutella”. For the other, my host brother suggested “Goku” but that got vetoed. They went with the next idea (which was a joke when suggested) and their other dog is named “Shopping.”
  • My host brother’s friend asked me if I knew Shrek. Shrek memes exist here. They started singing All-Star.
  • At the supermarket we went to, you could pick up these cool devices that you use to scan everything you put into your cart, to make paying at the end simpler. Truly wild.
  • “American Coffee” is different, but my host brother enjoys Starbucks. He also translated “frappucino” for me as “smoothie”.

Alright, this post (and my procrastinating) has gone on long enough. Wish me luck as I start finishing the actual work that I need to do!