Slowing Down

“Slow down, you crazy child / And take the phone off the hook and disappear for a while.”
Vienna by Billy Joel

Vienna is probably my favorite song of all time – I love Billy Joel, the lyrics, the piano, the style, just everything.

My plane out of Malpensa airport in Milan

I wanted to do GTL because I love teaching. I never expected myself to — when I started high school, I’d get frustrated trying to explain math to my sister. But 3 summer camps, 1 HSSP, 3 Splarks* and a GTL Italy later, teaching has brought me to where I am today. I’m so much more confident in my presentation abilities, better at explaining ideas to people, and have a deeper understanding of the things that I teach.

A “Splark” is a portmanteau of Splash and Spark, two programs that ESP runs. These programs are a weekend learning extravaganza, where HS (Splash) or MS (Spark) students can take classes on anything that they want. Teachers are usually MIT students (but can be anyone!), and can teach anything they want, whether “Physics without Calculus”, “How to Figure Skate in Socks”, or “Balloon Animal Bonanza.” For more past classes, check out this link!

But even as the focus of GTL is the teaching, the program also gives you lots of time, a scarce commodity in the middle of however many units, psets, midterms, deadlines, clubs, whatever.

I enjoy having time to think. Looking back at this IAP and GTL Italy, I suppose I’ve thought about a lot of things while in Italy. I’ve had incredible new experiences, met awesome people, had interesting conversations, and I always think it’s important to learn from those.

I guess this post is the more serious version of the “fun facts” that I’ve been posting. More serious, in-depth things that I’ve learned during my time in Italy about myself, teaching, or anything else.

1: It’s hard to escape MIT and the world of responsibilities.

When I left campus back in December, I remember thinking to myself that this would be the longest that I’ve been away since MIT since I got to MIT freshman fall. Last summer, I only spent 2 weeks not in Boston. But this IAP would be five entire weeks of being separated from campus, hopefully getting a little bit of a break from the firehose that is MIT.

Every single day over GTL, I did some kind of work for ESP. Whether reserving rooms, helping programs run, thinking about the future of our club, or doing random tasks that needed to be done, I still remained very connected to campus during my stay in Italy.

My responsibilities didn’t end there. I’m in charge of outreach to companies for MCG for our work this spring semester. I worked on my UROP remotely. I began applying to internships and opportunities for the coming summer. And of course, I had to plan out lessons for my actual teaching here.

I’m not trying to say I don’t like having these responsibilities — I live my life trying to do the things that I enjoy. I love ESP and the programs that we run, I’ve grown so much working on cases for MCG, and my UROP has the best professor that I could ever ask for.

But, work is tiring. The last time that I had a day “off” where I did nothing was probably back in August – and even then, I’m not entirely sure I took any “full” days off.

I like taking on responsibilities and doing things, but the things I do tend to follow me around. And if I can’t separate myself from my work over IAP and thousands of miles away, what hope do I have of doing it in the middle of the semester, on campus, potentially drowning in psets?

I’m terrible at taking time for myself. In the past at MIT, it’s just come in little bursts, taking a few hours every couple of days to listen to music or talk to friends or go to a study break or decompress. But this GTL experience has made me acutely aware that I’m bad at stepping back and slowing down.

The kind of life where I’m “always on” is unsustainable and while I enjoy doing it now, to be honest, I have no idea how much longer I’ll like it or how long it’ll take me to burn out. It’s something that I should focus on in the near future.

2: I like people.

After 3 weeks, the extent of Italian is ragazzi, buena giornata, ciao, grazie, tutto bene, allora, and the names of random foods. My level of fluency in Italian is roughly the same as my ability to tolerate spicy foods – none.

Every night, my host family had dinner together, often a delicious pasta with some homemade desserts afterward. Italian dinners tend to run long, spending time talking to each other about anything. My main problem was that I couldn’t follow along with any of it – I’d catch snippets of words that sounded almost like Spanish, would follow along with their gestures, and occasionally, I’d hear the word “inglese” before I was asked something in a language I could understand.

Not to say this wasn’t entertaining – given gestures and certain words, I could catch the gist of conversations with some difficulty, and my host brother helped me follow along with what was happening when I was especially confused 🙂

I define my life by interacting with other people and learning things from them. This is made exceptionally hard when you can’t understand more than a few seconds of conversation during an hour-long dinner, and for the majority of 3 weeks, this was the longest face-to-face interaction I had with people.

I ended up filling my need for interaction with lots of talking with people through online chats. Friends back at MIT, doing GTL around the world, externing at different places were all awesome people to talk to throughout IAP.

And when I did get the chance to talk to people in person – whether the other MIT student at my school, at MIT meetups, on trips to Venice, or wandering around Milan, I think I appreciated those times even more than I usually do 🙂

3: Independence and Initiative – how much do I do things by myself?

I’ve always thought of myself as being bad at making decisions. I’m not a terribly decisive person. My opinions always feel half-formed, not as fleshed out as everyone else’s. When I’m pushed to say something, I’ll often just say the first thing that comes to mind, and then back-justify those thoughts.

This plays out in different ways in my life.

When traveling around Venice with the group, I was the follower. I let other people plan our adventures, the cool sights to see.
Most of the traveling that I did at all in Italy was based on other people’s initiatives. My host brother taking me around Milan, a teacher bringing me to the Last Supper, going to Venice.
Wandering around Milan by myself on my last day tended to not actually happen — I went to the nearby park, grabbed some food to eat, and just sat around and thought a lot. (This one’s probably a weaker example, mostly because I also wanted some time to sit and think, and was exceptionally tired from the previous days of wandering around Milan with Sarah – I walked 25K and 36K steps, the latter an all-time high.)
I tend to be a red pen, revising and building off of what’s been done before, rather than a black one, and making my own new ideas.

I’ve looked at this part of me before, and it leads naturally to wondering about how original I am: how often I make new ideas or do things on my own.

I think I’m a pretty reflective person; I just wonder how much this thinking translates into action.

At the beginning of the year, I did YearCompass as a way of reflecting on everything that happened this last year. One thing that I wanted to prioritize for myself this year was to live during this next year. Not just let life guide me to adventures, but to actively live life. I don’t think this was something I particularly succeeded at during GTL.

Now, I’m trying to do more things that are of my own initiative – things that I care about happening in ESP, trying to do things to bring friends together, and more. Even still, I know this is something that I need to work on a lot.

4: There’s so much to do.

Walking around an art museum with a teacher from my school, telling me about the stories behind paintings, their creators, the historical context.
Wandering around Milan and seeing so much history, architecture, and art all around me.
Talking to a teacher who went back to school after graduating with a degree in biology, studying mathematics and becoming a teacher.
Listening to other people at MIT talk about their experiences about GTL, going through MIT and how different those experiences are from mine.
Being a teacher in a real school for the first time.
Teaching large classes, where students were English Language Learners, for the first time.
Meeting people from Minnesota and talking to them about their own experiences teaching abroad.
Talking to someone my age about her experiences studying abroad in Canada (from Italy).

Throughout GTL, I’ve talked to people about all of the different experiences and adventures that they’ve had, and had some new ones of my own.

I know that I always have room to improve – the Growth mindset is something that I internalize. Another thing I figured out during my end-of-year reflections is that the way I best identify growth areas is not via introspection, but rather going through life and seeing where I fall short, where I could be better.

The things I learn about other people’s experiences play a crucial role here. There’s only so much that I can ever experience in life, and by learning from other people’s experiences, I can help to define my life even better.

GTL has helped me realize more directly that there’s so many different life experiences that I haven’t had and that I may never have. So, I need to keep talking to people about their own experiences and keep trying to have as many new ones of my own.

I’m finishing up this blog post almost 3 weeks after getting back. The semester’s already started, classes are in full swing, and it’s finally time for me to say goodbye to this GTL blog. If you’ve been reading, thanks for following along with all of the posts – it’s been fun writing c:

A spicy plate
Combat of Centaurs VI, by Picasso. Found in a random art museum we came across.
An exceedingly fancy Starbucks, found in Milan.

Interactivity

Classes are so much more fun when it’s not just a lecture. From the teacher point of view, I think it’s pretty boring to just drone on at students for an hour without a break. And for students, it’s even more boring — trying to concentrate on someone talking at you for hours on end is incredibly difficult. But when there’s interactivity — something to get you out of your seat, a cool demonstration, problems that make you participate — suddenly, the class is far more engaging.

Some of the best fun in my own teaching experiences has come from the interactive activities that I’ve created for students. For the last 2 weeks of my GTL experience, I taught statistics to 4 different classes. These students were in years 3 and 4 of high school, which means that any activities needed to strike a balance between usefulness, non-cheesiness, and actually being engaging. Throughout the different classes, I tried a couple of different interactive segments, and wanted to share how I thought they went!

(This point of view has been slightly shaped by my experiences running teacher orientations for ESP, sharing many tips, including some on interactive techniques. We’ve modified our own handout from the one here.)

Guts Round

Those of you who did math competitions in high school might remember something called a “guts round” – a team-based competition to answer questions quickly. I first tried writing a guts round as a review session for a summer camp 2 years ago and found that it worked amazingly. It’s become my review session activity-of-choice, especially for groups that I have very limited time with.

My guts round consists of 15 questions divided into 5 sets of 3 questions. Each team (of 3-4 people) only gets 3 questions at a time, and in order to see the next 3 questions, they have to submit their final answers to the previous 3 questions. Each question has a certain number of points, and the point value (and difficulty) increases as time goes on. As students submit their answers, I grade them in real-time and project the team’s point progress onto the board.

A team that strategizes well will try and speed through the first sets of questions to spend time on the far more difficult later sets that are worth more points. However, going too fast can lead to careless errors, losing out on “easy points”.

The final scores for one class’s guts round, an *incredibly* close game. Note the systematic errors in problems 3, 9, 13, and 15 — immediately after finishing, reviewed those problems to show them how they work.

From what I’ve seen, guts rounds are incredibly fun. Students like working together and competing against each other to be the best team. But they’re also invaluable learning tools.

Students get to work with each other, and so have a chance to learn from each other. For most questions, at least one person on the team knows how to do the problem. Team sizes are also small enough that everyone works together on every problem, meaning that the knowledge gets shared with everyone.
The difficulty gradient allows students to directly review of problems that they’ve seen before and also see questions that they haven’t seen, pushing their knowledge even further.
The live grading lets me see if there are any questions that most groups are having trouble on, letting me review specific problems and concepts with them.

Of course, they’re not perfect, as teams might be uneven and so the “losers” learn less. As a whole, though, guts rounds are probably my favorite activity to run.

Height and Standard Deviation

Wholesome notes written to me by the class I did this activity with!

I was at the end of my lecture on measures of variation – range, variance, and standard deviation – and managed to run out of content with 20 minutes left. To fill the rest of the time, I decided that I wanted to show them why we care about standard deviation as a measure using a live demonstration of the standard deviation and the normal distribution!

I had each student tell me their height in centimeters. I wrote them all out on the board and used my computer to calculate the mean and standard deviation. Then, calculating the mean plus or minus one standard deviation, we found that 11/16, or 68.75% of students, were within that range. Supposing that human height is normally distributed, statistics predicts that 68.3% of people should be within this range – very, very close to what we found!

The point of this demonstration is to show that the standard deviation has interesting properties that relate to how far away numbers are from the mean. The definition of standard deviation seems pretty arbitrary, especially when you see the content for the first time. Why are you squaring things? Why the square root? Why not just the variance?
But when students see the most useful property of standard deviation, its relevance to the normal curve, even if the definition isn’t completely clear yet, they see why it is used.

The activity also led to lots of fantastic questions from students. Why 68.3%? What does “normal” mean? How far away from 68.3% can it be? The fact that these questions get asked means two things: first, students actually understood the activity; second, that it was an interesting enough activity to pique their curiosity.

In hindsight, one thing I should have done was predict 68.3% before getting their results. I had never done this activity, so wasn’t sure how well it would work. But for the future, I now know to put faith in height being normal.

Mental Math

I really like mental math – squaring and multiplying numbers in my head, calculating days of the week across any year, and more. The actual math content of mental math is not difficult, as it’s simply learning the tricks to keep numbers organized in your head. With lots of practice, the math becomes second nature, and it can seem like “mathemagic”.

Art Benjamin, a professor at Harvey Mudd, does “mathemagic.” I learned these tricks from his book of the same name.

Students in years 3 and 4 are already immensely familiar with algebra and variables – but the jump from arithmetic to algebra often leaves people wondering about the connection back to reality. Mental math lets me do that in a very “practical” way.

One example is with squaring numbers, and the difference of squares. Students have had this factoring ingrained into them: $x^2 - y^2 =(x-y)(x+y)$ .

Calculating $65\cdot65$ in your head seems like a daunting task, until cleverly seeing is as part of a difference of squares.

$65^2 - 5^2 = (65-5)(65+5)=60\cdot70=4200$

Adding 25 to both sides, we can then find that $65^2$ is simply $4200+25=4225$ !

The trick works any square ending in 5 – for 2 digit numbers, it’s as simple as taking the tens digit, multiplying it by one more than itself, and then sticking “25” at the end of that number. With some more explaining on the board and a few extra examples, I can get students to do $95^2$ in their heads without me saying anything!

Throughout GTL, I did a few examples of mental math during my introductions to showcase things I do for fun. (Wow, what a nerd, Paolo.) My main goal in demonstrating mental math to them was so I could promise them to teach the tricks to them later in the week, I think I also earned a little respect by doing math faster than they could type it into their calculators 😛

Exercise Pairing

This isn’t so much an “activity” that I did, but instead a small technique I used in lessons to make it less boring. I get tired of lecturing, and students get tired of listening. Oftentimes, when I had an example that I wanted to work through, I used a technique that I love telling people about during ESP Teacher Orientations – Think-Pair-Share (#100 on the link above!).

I’d write the problem on the board, then let students copy it down, try to understand it, and think about how they’d solve it by themselves for a little bit. After a minute or so, I’d have them talk to their neighbors about their different approaches, then work together to find a solution. When it seemed that most people had worked through it, I brought everyone back together to talk about the different ways that they got to the answer.

Think-Pair-Share is fantastic for breaking up the monotony of lectures without having to plan out an entire activity. I just need to prepare different exercises, and students get the chance to work through problems individually and collaborating.

I know for a fact that I’m still not a perfect teacher. I made mistakes in explaining content, bored students occasionally, and used inefficient or ineffective ways of explaining material. There are always things to improve, and so here’s to improving during future ESP programs and maybe future GTLs 🙂

Much like Sarah, this post was truly a “Splash on Planes” for me – sitting in JFK waiting for my flight to BOS. I’ve got a few final thoughts on everything that I learned during GTL, teaching and otherwise (mostly the latter), that I’m very excited to share in my last Splash on Planes blog post.

Ve(ry)nice

channeling my inner ahaan since 2019

It’s time for a blog post that isn’t about teaching – this weekend, I went exploring!

At my school in Rozzano, there’s another MIT student, Luke (also from Nevada!). On his plane ride over here, Luke met another MIT student who’s also in the Milan area. Last week, that person invited both of us to join him and 2 other MIT students to travel from Milan to Venice. I’m not exactly sure how the rest got connected, but somehow we did, and 5 near-strangers went off on a trip!

Getting around

I love the trains in Europe. I first rode them as a boxboi in Switzerland, and now I’ve gotten to experience Italian trains, too!

I’ve mentioned that it’s around 50 minutes into the city via public transit. There’s a tram (commuter rail) that extends beyond the city and an underground that runs throughout the city. They connect directly to each other (woo!) and a single ticket is €1.90 for an hour of traveling to the city center. They’re always on time, very regular, and the (new) subway trains are incredibly modern. I want this in Boston 😦

Our train left from Milano Centrale, the big train station near the center. It’s a 2.5-hour train between the two cities, and the roundtrip ticket was €49. They’re so smooth! And big! And comfortable! Free wifi, giant seats, power outlets, ugh. They’re the best.

choo choo — Milan Centrale! Our train ended up being the one visible on the right.

In contrast to all of this transit, Venice is a city of canals – no roads, anywhere. Anything that you might imagine to require a car (taxi, police car, garbage truck) has an analog in boat form. Taxis (and gondolas) are incredibly expensive, and so the best way to get around is simply to walk. I walked 44K steps and 20 miles over the 2 days o.o

There’s other islands near Venice, and traveling to them involves a highly commercialized (and tourist-oriented) system of ferries that effectively functions like a subway system or a commuter rail. During the middle of the day, there was standing-room only for the 45-minute boat ride, oof.

Connections

I didn’t actually know 3 of these people before going on the trip. I met two of them at an MIT Milan meetup the Thursday before the trip and then didn’t meet the last person until actually in Venice. This trip and the MIT meetup and have helped me understand the power of the “MIT connection” a little more. It’s so weird to interact with people that you have so much in common with, and yet your experiences are so different. We’re all connected by MIT, GIRs, IHTFP, GTL, and Italy, and yet we’re all leading very different lives at MIT that led to each of us 5 only barely interacting with the others before. For the most part, it just reminds me about how varied the MIT experience is and no matter how much I try, I can only experience so much of it. (And so, interacting with other people is always good c:)

This holds beyond just MIT. On the train to Venice, we met with 4 girls from Minnesota who were also here student teaching, but to help get their teaching license and here for 3 months. We ended up exchanging contact info and meeting up with them in Venice, and it’s so interesting to see the ways that other people go about the world.

We also randomly bumped into other MIT GTLers on the streets of Venice on Saturday night? Are MIT people everywhere? Probably yes.

Connections are fun — I love talking to people. During the 45-minute boat ride, I ended up talking with one of my travel companions about all sorts of things. What they think their non-MIT life would have been, what their best experiences at MIT are, and more. It’s awesome to have these kinds of conversations to learn about other people and the ways that they go through life 🙂

Adventures

This is, after all, a travel post, and so how could I not talk about what happened in Venice?

The biggest canal in Venice is the Canal Grande. Riolta, one of the coolest bridges in Venice, goes right over it. It’s in a very tourist-centered area with shops on the bridge (and a Hard Rock Cafe next to it?). Even with the commercialization, the bridge is still amazing to look at. We woke up at 7AM on Sunday to see the sunrise on the bridge, and the view and the lighting that we got was definitely worth it.

boatboi — Canal Grande. Riolta in the back.

St. Mark’s Cathedral! I don’t have too much to say about it — didn’t have a chance to go inside. Near a suuuper touristy area (with very high-end stores). Hm, this seems like a recurring theme.

Burano, an island near Venice, is known for its colored houses! They’re super cool to look at, take pictures with. The main industry is fishing, so lunch had some awesome seafood 😀

i should have taken a photo in front of an orange house — So many fun colors 😛

Murano is known for its glass blowing! Made me want to get into the lab at MIT, but who knows if I’ll get in or if I’ll ever have time. We saw lots of incredibly complex glass creations, some of which cost tens of thousands of dollars. We weren’t allowed to take pictures of the big boiz, unfortunately, but here’s some others 😛

To become a master, they have to pass a test. Part of it involves making a glass horse in 1 minute.
Spicy
Turtle!

I ended up getting one of the horses that I’ll keep on my desk back at campus 🙂

And now, it’s Italy fun fact time brought to you by yours truly:

Laser tag is “Laser game”.
Gondoliering is usually a family business. There are people that are 8th generation gondoliers. There are around 436 gondoliers in Venice.
A new gondola costs €50K. They last for 20 years.
There is a dessert that is “Arancia e caffè” – sugar cubes in orange liquor mixed with coffee beans. You take the cube and some of the liquor and burn off the alcohol. It also comes with other combinations, like with mint, lemon, and cinnamon.
There is a Twix version of Nutella. I don’t think this is an Italy thing, but still.
I found Pringles that were ketchup-flavored. Also, ham and cheese flavored.
The flag of Venice has areas that are cut and flap around.
An update on “toast” and “salsa”: sometimes they put salsa in toast. I have very mixed feelings.
Kids always enjoy making dotted lines with chalk. Teaching them is so fun. I think I’ve taught most of my classes at this point.
There is a famous painting that just has an egg hanging from the ceiling.

egg — *Brera Madonna* by Piero della Francesca.

Tomorrow marks my last day of teaching for GTL — 3 weeks pass so quickly. I’m hoping to do at least one more post about teaching before I leave (and maybe one about more travels?). But for now, I’ll get some sleep and get excited for GTL Italy teaching one last time 🙂

mlep — I enjoy photos of me in this pose

Iterations

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 😛

“Needle, Thread, and Knot”
Pretty sunrises. The only good part of having to wake up at 6:45AM.
Duomo, the largest church in Italy!
Arco della Pace (Arch of Peace) made to celebrate Napolean’s conquests.

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 😛

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!

Paolo

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