At ESP, we aim to spread our love of teaching and learning to local students and the MIT community. This IAP, many of our members are taking the “spreading” part a bit farther, quite literally, by going abroad and teaching via MISTI’s Global Teaching Labs program.
Abhijit, Paolo, Sarah, and Sid in Italy,
Wendy in Jordan,
Saranesh and Sophie in Kazakhstan,
Michelle in Korea,
Brandon in Scotland, and
Lexi in Spain.
(Edit) We will also have Phil writing about his experience teaching chemistry to local 10th graders for the MIT Scheller Teacher Educator Program and Evan writing from Palo Alto, CA, about his experience working with Project Invent, a program that supports high schoolers in inventing problem-solving technologies.
We will be sharing our personal stories with teaching and traveling on this blog, and we hope you will join us as we write about our experiences this January.
A note on “Splash on Planes”: ESP used to run a program called Splash on Wheels, where ESP brought Splash (the teachers and courses) to local high schools. In this case, we’re bringing the learning to students by flying to other countries!
Vienna is probably my favorite song of all time – I love Billy Joel, the lyrics, the piano, the style, just everything.
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:
Kazakhstan has had only one president, Nursultan Nazarbayev, since the office was created following the collapse of the Soviet Union. He established the Nazarbayev Intellectual Schools and Nazarbayev University. There’s a naming trend here.
January 26th was Australia Day, the national day of Australia (kind of like Fourth of July in the US), marking the arrival of British ships in 1788. Some people believe it should be called Invasion Day instead. There’s a connection here. Kind of. Only in my experience.
Out of the post-Soviet states in Central Asia, Kazakhstan has arguably developed the most. Although his presidency has not been without controversy or many allegations of corruption, President Nazarbayev has always emphasized the importance of education in the nation’s development.
In 1993, Kazakhstan launched the Bolashak scholarship program, which finances graduate school and living expenses for promising students at overseas universities. In return, the students are required to work in Kazakhstan following their studies. What I learned is that there often do not exist job opportunities that take advantage of the education of those students, which unfortunately consigns them to work in more menial positions. Some people work around this by creating shell companies that are then contracted to overseas companies. I even heard of some students who didn’t want to return and let the government seize their collateral, usually a house property. But hey, if the house was worth less than the education, maybe that’s a good deal.
The Nazarbayev Intellectual Schools (NIS), another initiative of President Nazarbayev’s, are a network of twenty-ish schools for talented grade school students in Kazakhstan. Students take an entrance exam to qualify. Tuition is free, and non-local students are given free boarding as well. My impression is that these schools have much better instruction and resources than the average public school. Many of the scholarship students at Haileybury used to attend NIS. (GTL placed 11 MIT students across NIS schools in five cities.) I met two NIS Astana students, Rakhat and Sayana, and they were wonderful. We visited Hazrat Sultan Mosque, the largest mosque in Central Asia, had delicious beshbarmak at Sayana’s house, and saw a ballet at the Astana Opera.
The Bolashek program is pretty expensive for the state, and maybe it doesn’t make sense to educate everyone abroad, so President Nazarbayev created his own university in Astana. Nazarbayev University (NU) opened in 2010. The university operates entirely in English and hires an international faculty and staff. Tuition and board are free for all students (imagine that!), and students can even receive a stipend to study there. The university has pretty expansive facilities, including new maker spaces, a technocenter, and a hub for entrepreneurship. They are also opening up a new swimming pool.
View of the ground floor of one of the dormitories
In Astana, I was hosted by Chris, Saima, and Saima’s two sons: 13-year-old Emad and 9-year-old Zayd. They had moved to Kazakhstan only three months ago to work for NU. Chris is the current (and first) Chief Information Officer, and Saima works as the Director General for IT projects. Pretty fancy. From what I understand, they are trying to move the university to use more modern systems. Saima and I talked about SAP at some point, which brought back some ehhh nostalgic memories of being ESP treasurer.
The family had previously lived in Australia for five years, which is why we were invited to a celebration of Australia Day with a bunch of Australians who currently work at NU. In attendance were Elaine, Janet, and Michelle, who all work at the Graduate School of Education. Loretta, the Vice Provost for Academic Affairs, was there with her husband Tim, who’s been teaching at some other local university. I also met Alex, the head of the Electrical and Computer Engineering department, and Chit, the new Associate Provost for Graduate Studies. Some pretty high profile people were there although I didn’t realize it at the time.
A spread of the lovely food Elaine prepared for Australia Day
My host brothers with a cake they decorated
I got to talk to some of them throughout the evening, which was really interesting for me. I wanted to understand what they did at the university and what drew them there. Michelle teaches inclusive education and is currently researching how clinics in Kazakhstan administer tests for autism and what is happening to the diagnosed children education-wise. Apparently a lot of the time, any child diagnosed with something “abnormal,” whether it be autism or diabetes, does not receive the standard education, if any. Alex recently published a book on hardware chips for machine learning. I think his research deals with cognitive models of machine learning and creating an intelligence that is more general, unlike the models that solve a specific instance of a problem that people throw deep learning at these days.
Loretta used to teach business but now works on the administrative side at NU. I asked her about the admissions process and how the university recruited faculty. She has been in Kazakhstan for around seven years and had many stories to share. The day before the university opened its dorms, there was a mix up with the mattresses, and the Minister of Education (or former one, or something) ended up helping move the mattress onto the beds. Everyone contributed! Several people also shared reimbursement horror stories. One faculty member left with his family during break and never came back. (Just mentioning that this isn’t common.) He didn’t return his boarding passes, which the university needed for proof of travel. Kazakhstan has a culture where the cost of a mistake or incident is not absorbed by the organization but by the individual. The travel person involved in this situation was panicking because he would have had to pay the full cost of the tickets, which was more than a year’s salary. The passes were eventually returned in an unmarked envelope.
Mostly, I heard the story of a university being born. Of the opportunity to establish new systems and programs, to be part of the beginning of something. Throughout January, I asked several people about Kazakhstan’s issue with brain drain, and some responded by pointing to examples such as this – the opportunity to fill a sector that is still underdeveloped – as a possibility for encouraging people to stay. I wonder how things will develop in the upcoming years.
I’m now back at MIT, but I still need to finish writing up part II of my last post, so here goes:
11:25 AM [Lunch]
Students at Nueva have an extremely long lunch period. Part of that time is so students can eat lunch, but part of that time is also for student clubs to meet. I ate a solidly decent lunch of ravioli with Apple. I asked him about his classes, his outside projects, and what teaching is like in general. He asked me a few questions about what I do and what I’m interested in. He mentioned that teaching teaching at private schools often has fewer requirements (no certs required, no test prep required) and more freedoms. Apparently to start as a teacher, you can shadow / be mentored by a more experienced teacher for a bit to prepare for real teaching.
As lunch went on, I was able to take a bit of a mental break from all the activity and interaction. Near the end, I met Donut, a CS teacher and MIT grad. We talked for a bit about MIT, Course 6, and talked some about shared interests. She teaches a machine learning class (that I went to at the end of the day), so we talked about how she runs the class (which I’ll get into later).
Donut is also the new head of Invention Studio (after Connie left), so at the end of lunch, we listened to a team’s dry run presentation for their Design Review event. Along with the two student heads of Invention Studio, we listened to the student’s presentation and gave them some advice to prepare for Design Review (which was in 5 days). Nueva was a school built on design-thinking and a lot of other alternative methods. To Connie Nueva often represents the ideal picture / the extreme bounds that high school education can reach. Despite all of these things aligning, I think I saw the students struggle with lots of the same things students in my high school struggle with and students at MIT still struggle with.
The main struggle I saw was an uncomfortability with uncertainty. If students don’t know how to do something, their mind shuts off or it flounders around. These students in particular didn’t know how to get past an engineering blocker in their product. Rather than trying to take some first steps towards progress, they stalled because they couldn’t see most of the steps to get to their goal. Something about the size and unfamiliarity of the problem puts a mental block on students that they need a mentor to pull them up from.
12:55 PM [Third Block]
In third block, I visited a class that was on the philosophy of science. In particular, the discussion was about usefulness of intractable scientific theories. Before class, students read a reading about string theory and multiverse theory, which are essentially grand physics theories we aren’t really sure how to measure. Packed into this problem comes lots of questions — are these valid theories if we can’t support / deny them? how many resources should we put into these problems? are these theories just mathematical models or are they describing how the universe “actually” works?
Lots of these questions were brought up in students’ pre-discussion questions, so during class we slowly tried to step through a few of them. Unfortunately, we weren’t able to get too deep into these questions. Students, while some were happy to contribute, would get distracted from whatever point was being made. They weren’t able to dig deeper into these problems — so it hit me that this was a problem with lots of discussions I had in high school. I’d often feel disengaged because the discussions wouldn’t matter. They would be a bunch of people saying a few surface-level random thoughts about a potentially interesting subject with no actual consequences.
2:15 PM [Fourth Block]
In the last block of the day, I went to Donut’s machine learning class. Class was fairly unstructured work time based on a lab about word vectors and NLP. Through the lab, students were given a brief intro to the subject material and asked to play with the code (potentially in line with some suggested tasks). One super bright side of this structure is that students had the freedom to use these tools for whatever they found interesting. In subjects like ML, this is especially great because these tools can be used for so many things. The downside is that students aren’t necessarily developing a solid understanding. As with all self-studying, students get out however much they put into it and for some students this may not be enough (though it is hard to say what “enough” is).
3:30 PM [End of Day]
After all these classes came to a close, I went back downstairs to pick up my things and Lyft back to work. Before I left, I got to stop by and thank all the wonderful teachers and students I met throughout the day. Nueva truly does seem like an awesome place to work — lots of awesome teachers and students. Reflecting a bit on what it’d be like to work at a private school, I imagine I’d really enjoy it. Each day, I’d get to work with a bunch of bright kids. I’d get to work with and learn with really passionate teachers. I’d also get to face different challenges each day and work on sharing the subjects I love with others.
One drawback that usually comes hand in hand with working at a private school is the feeling of not making a meaningful impact. Why serve the privileged students at the top when there are so many others that need it? If part of the goal of teaching is to make a difference in the world, how much of a difference is working at a private school? Later that night, I ended up talking to Connie about this, and she passed along some insight that I feel like I had started to realize a little bit after teaching in ESP programs and spending the day at Nueva: when you’re teaching at privileged schools like Nueva, you’re directly teaching the next generation of world leaders — the people who need to be able to make the difficult decisions — so hopefully as a teacher, you can rub off on them and prepare them to solve the problems in the world.
Thanks to everyone who read any of my lengthy (and probably confusing) posts! It’s been lots of fun writing these posts over the last month, and I’ve gotten lots out of spending time reflecting on my experiences — hopefully I’ve also helped you learn something new/realize something you didn’t know before!
Yesterday, I visited The Nueva School and shadowed a student and a couple teachers. This trip was a great opportunity to learn more about what teaching looks like in an alternative independent school like Nueva (and was a nice vacation from my work). Here are some random unorganized thoughts from things I observed:
8:25 AM [Before School]
Arrived at school via a Lyft. I walked up to the front desk and said I was visiting teacher Apple (replacing names with food for privacy). The receptionist called Apple, but he wasn’t there. Despite this, she asked if I knew where I was going and let me in anyway.
This was, to me, the first of many oddities at Nueva. At my middle school or high school, I would’ve been promptly and rudely escorted off school premises with the harsh warning that if I came back, there would be consequences. If you weren’t there with a purpose, you meant trouble. Even if you were an alumnus there to visit a teacher one year after graduation, they assumed you meant trouble. I think there were even times when I was a student when they saw us as troublemakers. I think this attitude from staff / security directly led to less behaved kids. At Nueva, it seemed like none of this existed.
At some point, I met my student host, Barley, who gave me a tour of the school. The school itself has an awesome innovation-lab — makerspace, chemlab space, and art studio space equipped with the materials, tools, and staff to make almost anything! Everything about the school is very open. Students are free to walk anywhere. Teachers have desks at pods out in the open. Almost all classrooms are glass walled. There are lounge spaces everywhere for students to hang out and work.
8:45 AM [First Block]
During my first block, I observed an advanced computer programming class. This class felt a lot like the independent study computer science classes I had in high school. Students were roughly left on their own to work on whatever they wanted. This ranged from learning a new language to working on fairly deep systems or ML problems. For me, this kind of class was super important for furthering my cs knowledge and developing self-study skill, but unfortunately I saw kids struggle with the same problems I did. In particular, this kind of self studying is heavily dependent on the teacher’s knowledge of resources or the availability of “good” textbooks (with the right pace for a HSer). A second problem is self motivation. If kids aren’t internally curious, they won’t learn anything. Luckily for Nueva, most of the kids seem rather curious except for a couple 2nd semester seniors I talked to.
This first takeaway I had from this is that it is important to learn skills. In particular, I’d want to learn enough breadth of topics to be able to help my students at least get started in any area. On the flip side, though, it’s unclear how much knowledge is enough. At what point should I focus less on learning and focus more on teaching? The second takeaway (or rather question) I left with is how can we teach kids to be internally curious? Connie pointed out to me one morning that waking up and directly going into watching econometrics lectures on youtube is something that even kids in higher education don’t have. I’m not exactly sure why people like me randomly enjoy learning things or if it was a learned skill at all, but maybe some answer to this question could help motivate other students.
10:05 AM [Second Block]
In my second block, I followed Barley to linear algebra class. Connie told me the teacher, Cauliflower, changed the way in which she saw math so she was really excited that I’d get to meet her. The linear algebra class was structured with students presenting solutions to problems (which generally asked for some proof). As the student presented their solution, other students, along with Cauliflower, would ask questions and note how ideas could have been explained more clearly. Naturally, the students’ presentations were full of mistakes and confusing explanations, so personally I couldn’t follow the line of questions Cauliflower and other students were asking. They never really led to a better understanding for me, so at some point, I started zoning out the questions until I found a solution. To me, this seems like the main downside — if a student doesn’t think about the problem in the same way (e.g. I saw many of the problem very visually), then the questions asked just add to the confusion.
On the positive side, though, there were so many awesome things the students seemed to get out of the class. Even though it seems like many of their linear algebra knowledge is very jumbled, I think they are developing what people describe as “mathematical maturity” fairly visibly. Students were comfortable with admitting they didn’t understand things. Nearly all of them were comfortable with asking questions or adding comments even though there were ~17 students in the class. Students were also comfortable with going slow and making sure they understood and believed each step before moving on. While they’re not quite all the way there yet (they still miss points and little details), it’s clear that they understand what math is really about (in contrast with classes like calculus). I really admire Cauliflower’s ability to foster question-asking and slow thinking about all the problems.
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.)
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”.
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
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.
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”.
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: .
Calculating in your head seems like a daunting task, until cleverly seeing is as part of a difference of squares.
Adding 25 to both sides, we can then find that is simply !
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 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 😛
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.
I first started drafting this in an Edinburgh hostel, halfway through our first weekend trip – first to Edinburgh and then to Glasgow. Now as I’m waiting for my Aberdeen to London flight (after which I’ll be doing some travel around Europe), I’ll try to finish this post up – since my flights been delayed almost 3 hours :(.
I’ll give an overview of impressions of Scotland and Aberdeen and my host school. This was eventually one long post but I’m going to split it.
Scotland and Aberdeen
Aberdeen is located in Northeast Scotland – and it is is *really* north. It lies just above 57 N, placing it just at a higher latitude than Kodiak Island, and just around the northern border of Newfoundland and Labrador – (thanks Wikipedia). It’s industry is quite reliant on the North Sea oil and gas industry – you see this as soon as you land in the ads for random oil/gas industrial services as you go to baggage claim.
Aberdeen is the 3rd largest Scottish city by population, behind Glasgow and Edinburgh (“pronounced edinbruh as I figured out”). People from Aberdeen are called Aberdonians, similar to the Dundonians of Dundee to the south, and different from the Glaswegians of Glasgow. I asked one of the CS teachers what Edinbrugh-ians? were called and she didn’t know :P. Update – wikipedia says “Edinburgher”.
The first thing I noticed about Aberdeen was that it was really gray (sorry, grey). Scottish weather seems to oscillate between clear + sunny, and damp + drizzly. And it always feels just slightly damp here, so it seems like winters here are very wet. Aberdeen in general is surprisingly several degrees C warmer than Boston, despite being 15 degrees north. The architecture in Aberdeen has grown on me! It’s quite pretty – even though the gray Aberdeen granite is a bit lacking in color (see pics below)
Random fact: HTML <center> tags throw off British people because here, it’s spelt <centre>. My host teacher has actually converted to defaulting to the American spelling because he uses these so often. Same goes for stuff like color vs colour. Hmm I wonder how universally US/English-centric programming languages syntax is. I wonder if there are any examples of non-English/non American-English syntax programming languages. If you’re bored check out the wikipedia page on esoteric programming languages: https://en.wikipedia.org/wiki/Esoteric_programming_language#Examples. And I just realized I should have done a lesson in one of these. But Lolcode tho:
HAI CAN HAS STDIO? VISIBLE "HAI WORLD!" KTHXBYE
And regarding food – according to my host teacher – Scottish food is very “stodgy” (read: unhealthy but filling). Stuff like butteries – which are like really lard-y/salty croissants, haggis, meat pies, sausage rolls, etc. I’ll write more about food later! I’ll leave you with some food pictures from my first week.
This post was brought to you by a 12-hour flight from Milan to Miami. Splash actually on a plane!
I want to share some of my experiences teaching. My
experience may be different from other GTLers because it was so unstructured
and varied. All of my classes were one-off lectures or activities, and I
usually didn’t have a set curriculum or hint about what the teachers were expecting
before the day-of. I ended up teaching with 8 teachers and met 19 class
sections (out of the 20 in the school). However, my classes generally fit a few
categories, so I’ll break this into parts.
This is what I came to Italy to teach. I originally had
ideas about doing a series of classes where I taught how to structure an
argument and how to refute it, ran some fun public speaking activities, and
then had the students debate to practice the skills. However, because I often
only met with the classes to debate once or twice and the teachers just wanted
to run the debates immediately, that’s what we did. I would describe how
debates worked, the students would choose a topic they were interested in, and
they would split into teams.
I enjoyed hearing the suggested topics to debate. I think
because I introduced myself as interested in climate, they always suggested
debating climate change. We dissuaded them from that topic because the
vocabulary would be difficult and it would require a lot of prior research. For
the younger students, they mostly chose school-related debates, such as whether
students should have full-day schools (they currently don’t), if there should
be school on Saturday, if schools should use online or paper textbooks (none of
the students preferred ebooks), and if homework is good for learning. We got to
more complicated topics with the older students, including universal health
care, weed legalization, and immigration.
Debate classes were some of my favorites because the
students really got into it. They enjoyed being able to argue with each other,
and because we required everyone to speak at least once, everyone felt
involved. It’s hard to get shy students involved in regular discussions, but
they all seemed involved in working with their teammates and giving their part
of the speeches. Having a bit of healthy competition can often spark interest and
participation. I was very impressed by their English skills and ability to pick
apart each other’s arguments. (These classes also required very little prior
preparation by me.)
A large portion of my time teaching was spent in
unstructured discussions. How well these went usually depended on the teacher’s
ability to continue the conversation or pick on students to ask questions or participate.
Teachers had varying levels of discussion-driving skills. A few times, the
teacher didn’t show up to class, so I led the discussion, with varying levels
At first, most of these discussions were about me, MIT, and
America because the teachers thought the students would have lots of questions
when first meeting me. Sometimes this worked. More often, the teacher had more
questions for me than the students, so it was mostly a conversation between the
two of us. Later on, I had discussions about books/movies, social media
culture, climate change, the American school system, the American government
system (which was a really fun class), and the MIT website (lol).
One teacher wanted me to talk about the American school
system to all her classes because she thought it was interesting and a good way
to share culture. As a result, we ended up having the same discussion several
times. This was hard because despite how much I love talking about education
systems, talking about the price of American universities and the high school
social scene can get old.
One teacher once asked me to join her class five minutes after the bell rang, and she had nothing planned. We ended up looking at the spotlight articles on the MIT website, and the students asked me questions about what the words meant/what the article was about. This was probably a waste of class time for the students, but we had some fun times talking about feminism and black holes and what is chemical engineering (hint: I don’t know either).
The discussions that I ran alone were generally unplanned. I had luck with a few classes because the students were young, energetic, and there were a lot of them. In these classes, I picked a few questions to ask to the whole class and made everyone answer. This got everyone involved and able to talk about themselves, which was good. It also made them very excited, so it was hard to keep the room at a reasonable volume. I also led a discussion with an older class. My vague instruction a few minutes before the class was to talk about climate change, so I tried to get them involved in talking about the issues and possible solutions. I did not do a good job at getting them interested. I ended up ranting about the world’s depressing future for 25 minutes and then trying to get them to discuss their other interests for the last 25. It was uncomfortable for everyone involved.
I also got the chance to administer a test. Many of their
exams are oral exams, called ‘interrogations.’ I got to interrogate the
students on an English novel that they read over winter break. I asked them
about the plot, characters, and what they thought about the book. The other
students listened in and also had to ask questions. It was interesting for me,
but the students always have to sit and listen while their classmates get
interrogated, so they looked pretty bored.
I taught three types of science lectures: past and future
climate (twice), ecology (x3), and weather (x10). I actually had enough prior
notice to prepare these lectures, so I made slides and discussion questions
beforehand. This took much more preparation time than the debates and
discussions, but it paid off with reasonably interesting classes. I also gave
the classes multiple times, so I could figure out the best way to explain
certain things over time.
My weather lecture was fun, which is good because I gave it
to 10 different classes. I got to the point where I could predict the students’
reactions to explanations and my stupid jokes. On my 9th class, the
teacher was pulling students outside to interrogate them while I taught the
rest of the class. The students were really distracted by this, and as a result
I got distracted by them. But luckily, I had rehearsed this class 8 times
before and my mouth just kept going without my brain’s input. Practicing
My major takeaways from these classes were that:
Pictures and diagrams are great ways to bridge a language barrier.
Videos or pretty websites can be entertaining and a good break from lecturing.
Having planned questions to ask the students helps because it’s hard to think on the spot.
Students were most interested in things that relate to their lives or what they’ve learned in the past. I would bring up the local winds, how weather affects planes, how wind patterns affected Christopher Columbus, etc. and this often generated questions.
One part of my weather class involved me drawing Italy on the board, which never failed to generate laughs (at me).
Even the 10th time, the class will be a little different because of the students’ responses. Sometimes they have really interesting questions that can take the class on a totally different side quest. I never got bored of teaching the weather class.
I’ll stop there. Here are some
pictures from the past three weeks:
After a wonderful week and a half of teaching at Haileybury Almaty, we set off for the sister school in Astana. Originally, we had two options: the 1.5-hour flight or the 14-hour overnight train (the Spanish Talgo train). I like trains, so I indicated my preference for the latter. We were told that we would see very little on the overnight train, so we ended up deciding to take the 24-hour old Soviet train instead! (I like trains.)
The day of departure, it became clear that David, the coordinator, could not come with us due to a contagious illness. He knows enough Russian to get by. As neither Alex nor I knew Russian, the headmistress wanted us to take the plane instead. After a few hours of agonizing and getting a better sense of what the risks realistically were, we decided to keep our train reservation.
The school reserved an entire compartment of four bunks for us so that we didn’t have to share with strangers. One teacher warned us that the ride would be interesting for the first fifteen minutes, but we’d soon get tired of the endless snowy steppes. After school on Tuesday, we took a cab to the Almaty-1 railway station.
Before the journey. This scene was lightened by my camera; it was quite dark outside already.
We found our compartment and settled in. The sun had already set, and it was very dark. It was also extremely warm, a feature that gives this train its “rolling sauna” nickname. I think I was slightly sweating throughout the entire trip. Vendors roamed up and down the train, selling fruits, bread, drinks, snacks, and clothing. I read my book and ate a light dinner of salami, bread, and mandarins before retiring to sleep at 9 pm.
I woke up early the next day and watched the snow and the sunrise.
Pretty cozy in the early hours of the morning
The sun has come!
The next nine hours was a mix of more reading, napping, snacking, contemplating, and stretching. The train would stop for short times at tiny stations along the way. There was no cell service for most of the trip. I tried exploring the train (someone mentioned there may be a dining car) but only found the other cars to be just like ours.
I also amused myself by taking pictures of my travelling companion Totoro.
Totoro on a trip
Look at all this snow!
Snow and more snow
Another view of the compartment
All in all, the ride was pretty uneventful. Nothing more exciting than having to pantomime a it when the train operators came around and tried to exchange bedsheets for our tickets (they didn’t collect the tickets from other people, I think they collected ours because we weren’t local or something?). No run-ins with drunk people, nobody trying to give us food. Before I knew it, the sun was setting and we were arriving in Astana.
Astana train station
Would I do it again? Probably, with the right people. I still want to take the Amtrak across the US at some point. But now I can say I survived a 24-hour train ride in Kazakhstan, and that ups my train cred. 🚆
(lol so I started this like 3 weeks ago but got hosed, so here is it is).
I’ve been shamed into finishing this – so I’m just going to try to push this out while I’m eating dinner. For reference this is my dinner: a steak pie from Morrison’s – the cheapish local supermarket, tomatoes and sugar, leftover stir-fried pork belly, and a pita (8 for 50 pence!). One thing that struck me is how almost all of the meat and produce is locally sourced from the UK – surprising because it’s still quite cheap.
=== back to the original post ===
It’s 20:39 GMT in Scotland right now, and I’m typing this from my hotel room in Aberdeen.
Today was our first day at our school placement, but not the first day for the students. Their semester starts tomorrow, and so today was a professional development day for the teachers and staff. So we got to meet a lot of people! For this post, I’m just aiming for a semi-organized photo dump and travel log of how we got there – since I gotta go and work on a presentation we have scheduled tomorrow.
On to travel!
Transit modes in order: car, subway, train, moving walkway, jet plane, single decker bus, double decker bus, single decker bus, turboprop plane, taxi.
That’s 8 unique modes of transit!
At MIT, I met up with my GTL placement partner and we took the Red Line to South Station.
We arrived at TF Greene, rode some moving walkways, and got on our flight to Dublin. I slept maybe like 4 hours.
Okay, this was rushed – but at least I’ve got one post out. Hoping my next one will be more reflective and have more narrative in it.
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!
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.
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.
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 🙂
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.
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 😀
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 😛
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.
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 🙂