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!



4 thoughts on “Lesson planning and teaching philosophies

  1. I’m somewhere between an honorary admin and honorary cruft, but I teach professionally, so I’m delighted to read about your thinking.

    Two things I encourage you to think about:

    1. Give your students time to process stuff and show them that confusion is normal. An n-hour class is not n hours of lecture. (I know it might be when you’re in a college class, but college teaching isn’t always a good model for teaching-teaching.) You might lecture a little bit, then break from lecture with an activity, a question, a reflection, or just a time to sit, digest, and go over confusions. Your *own* learning process and struggle with the material will make you better able to teach it, because you’ll recognize where students mis-step and why.

    2. Be ready to adjust and re-adjust your learning targets based on what you are seeing from the students. This is hard to do on the fly, but if you realize that most students aren’t going to get to XYZ in your slides, don’t stress. A big part of lesson planning for me is really failure mode planning — what am I going to do if students aren’t ready for this step? How will I shift gears?


    1. Hi old admin/cruft! thanks for commenting – it’s always exciting to talk to people that do professional teaching, since my experiences have been limited to
      a) teaching splash classes
      b) teaching math at 3 week summer camps
      neither of which feel like “formal” experiences teaching, and neither of which i got “training” for – most of these thoughts on teaching i’ve just ended up developing through my own experiences (and occasionally reading things online).

      to respond to your comments,

      1. definitely agreed on this one. i don’t think i talked about it in particular above, but i try to plan activities throughout, whether just having them think about thought experiments, work on problems, show online demonstrations, etc. especially for a subject as unintutive as relativity, making time to clear up confusion in the subject is vital to understanding

      2. oh yes, absolutely! i think this is one of the main reasons i don’t really like using powerpoints for lectures (only reason i am is because this was the requested format o.o), and instead just write things on the board – to keep classes fluid, spend more time on concepts when necessary, etc. i’ve also tried to do this by purposefully making these lectures less than the alloted class time – right now i’m approximating that just going straight through slides/activities would take maybe 40 minutes? which hopefully leave ample time for interesting asides, answering questions, and running through more examples.

      thanks for bringing these up! i don’t think i’ve ever thought about these ideas from the perspective of them as a “failsafe” to address confusion. definitely will try and think about these things more explicitly in the future!


  2. Thanks, Paolo, for starting off the blog! It’s great that your school gave you a suggested syllabus ahead of time. Last year, in Spain, I figured out what I was teaching the first day I stepped into the school.

    I’m always surprised when I hear that people are asked to reach relativity. I don’t think I knew what it was in high school beyond a basic definition. Is this part of their normal curriculum, or did the school want you to present a special topic? Stats seems more standard.

    Last year, I didn’t have a chance to develop any electronic material, but I am incorporating slides (among other things) into my classes this year. I also talk too fast, so this is something I will be working on as well. Post incoming! (My flight is in an hour!)


    1. Figuring out what exactly I was going to teach more than the day before definitely helped a bit. It’s always nice to know what exactly it is that you’re doing before you get there.

      Relativity is actually a unit in their curriculum — something that I wasn’t actually expecting to be true. Now that I’m looking back at this post, one of the underlying assumptions of the “people won’t remember most of this” was that what I was doing was outside of their normal curriculum. The first day, I was talking with the physics teacher who mentioned that they weren’t sure if this would be on their (government) final exam, which made me realize that this is actually a part of what they’d actually learn in school even if I wasn’t there. Because of that, needed to adjust my plan and goals a good amount. But things have been turning out well so far, and I think I ended up achieving these goals (for some of the students, at least).

      Hope you flew safe! Yay planes! Maybe less yay for talking fast (rip working on that is always hard)!


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