What I would add to the K-12 list

I often gripe about how standard K-12 education is overly focused on specific knowledge (how to solve a quadratic, memorizing dates for history, etc.) rather than general skills (e.g. “how to figure out how to solve a quadratic”). On the other hand, I understand why; teaching general skills is much more difficult than preparing a cookbook.

So now I will instead gripe about specific things that should be taught and aren’t.

Any amount of programming or computing literacy

To me the following are all comparable:

• Refusing to learn how to use Google Docs, and shrugging it off by saying “I’m not planning to be a writer”.
• Refusing to learn how to use a spreadsheet, and shrugging it off by saying “I’m not planning to be an accountant”.
• Refusing to learn how to use a shell or git, and shrugging it off by saying “I’m not planning to be a programmer”.

And yet people say the third thing to me.

(Okay, there is one difference. Learning to use Google Docs is easy; learning how to use GitHub could take up a weekend. I know, the horror.)

The reason I get so riled up about people not knowing how to code is exactly because it matters even for (especially for) people outside software. Like, are you just expecting to never edit a website or scrape data?

I wrote about this on my website too so I won’t belabor the point more in this blog post.

Probability and statistics

I have to tell you a story about this. I was reading old entries on rrusczyk’s blog and found the following one:

Ex-San Diego ARML coach Andy Niedermeyer was telling me about a conversation he had with some fellow math grad students at UCSD. They were debating what one area of math should every student at UCSD take — calculus or linear algebra. I quickly gave Andy my answer. Andy laughed, because that was also the answer they came up with after some discussion.

And then there was a link to a TED talk from Art Benjamin that was supposed to have the same answer Richard and Andy+co had.

I kind of blinked for a moment, because I was like — “Okay, it’s definitely not calculus, but really, linear algebra? That doesn’t seem that much better”.

Then I clicked on the TED link and started laughing too.

I was reminded of this because I found out recently my students were never taught what a p-value means. Which means, whenever studies claim “statistically significant” correlations, no one knows what it means. Which seems… kind of bad.

Even pure probability isn’t well-understood (in ARML author land, we have a saying “probability is automatically hard”). Not just the theory, but even on a practical level: when people say “I’m 90% sure that X”, the accuracy is more like 60% or 70%. If you don’t believe me, you can try it yourself — there’s a quiz where you’re given 10 questions, and for each you want to specify an interval for which you’re 90% sure the correct answer lies in that interval.

Game theory

I was a bit reluctant to include this for two reasons.

One is mean people exist, and if you teach mean people game theory, the results might not be pretty. However, I have more nice students than mean students, so I’m including this with the former in mind, albeit hesitantly.

The second is that people might inadvertently think game theory is enough to understand all social interaction. This isn’t true, because humans make absolutely no sense.

However, while game theory is woefully insufficient for understanding social behavior, I’m going to claim it’s close to necessary. Because to me, game theory is the machinery which studies the outcome of simplified, idealized scenarios. And I think if you can’t even grasp the results of almost trivial-looking models, well, good luck with the real world.

To be concrete: I just think you will never be able to fully understand other people’s behavior if you can’t even wrap your head around prisoner’s dilemmas or chicken.

(There’s this related word called “empathy” whose literal definition is “being able to put yourself in someone else’s shoes”, but this word is so emotionally charged and misused that I avoid it. I propose we just call this “mind-reading” instead. I think mind-reading is a cool skill and 100% endorse developing it.)

Writing

Okay, this is not really a specific skill, but I’m going to include it anyway.

The kids can’t frikkin write sdfgrdeugdhnsqcevt;huva.

I’m not talking about math proofs (although those are terrible too). I’ve been skimming some college application essays recently, and if I see one more essay about the Millennium Problems then NSEUIDFGTEHUIDNTHEUNIS

Here’s a subset (not contiguous) of sentences from Richard Rusczyk’s talk:

You should write something that’s not homework.

We have a lot of college students work for us as assistants in our classes and even the ones at fair Harvard are terrible writers. Almost every single one of them.

The problem is, their classroom writing assignments, they’re rewarded for using big words, complicated sentence structures, and they write stuff that is gibberish. They don’t have to write anything that’s going to be read by someone who wants to read it. The English teachers don’t want to read that kind of stuff, they have to.

Write something that someone else is going to edit and give back to you and force you to re-write.

Here’s a hint: write like you talk. I swear the application essays look like they were generated by GPT-3. I don’t think most of my kids could read one of their essays out loud to me with a straight face. So why do they write that way?

Because in high-school English, you’re taught to write persuasive essays by making up weak arguments (where is the number of paragraphs your teacher requires) and dressing them in eloquent flowery language to hide the fact they’re hot-air filler.

It’s just a recipe for trouble whenever you have situations where (a) the student is writing something up because their teacher forced them to, and (b) the grader is reading it because they have to. This includes not only high school, but college essays, the SAT/ACT, and the USAMO (hence USAMO writing quality is often quite poor).

If your only writing experience in your entire K-12 education is confined to faking, you have a lot of bad habits to unlearn, sorry. Blame the system.