These are all good projects but you are underestimating the difficulty of them by a lot. Even something conceptually simple like card counting has a lot of details that are difficult to get right. Just programming the rules of blackjack is a fiddly problem in itself (no standard ruleset and hard to explain the edge cases).

In my opinion these would be great things to introduce at the start of a course for motivation, but they either need a lot of handholding/scaffolding or a lot more time per project. There is a tradeoff between how much handholding you do and how much people learn. It's very easy for people to fool themselves into thinking they understand something just because they can follow along while someone else does all the thinking for them.

I'd say this view overestimates both the depth and abstraction at which people actually understand the things they do in the course of normal living. These exercises won't turn anyone into a trivia master or gatekeeper, but it will give them working knowledge.

The point is that each of these things requires actually doing them and they are fun enough to practice, so nobody merely follows along. Sure, a class of 30-40 kids won't be able to do it, but that's the worst possible way to teach anyone anything while only guaranteeing they are all evenly disadvantaged.

A blackjack tournament or poker tournament over a few days is enough to get card counting principles down, and even if you are crap at it, you understand that probability is a thing, it has distributions, it's not always right, and you can bet against other peoples ability to interpret them.

> - bet on a stock market return (brownian motion, randomness, shannon portfolio / information theory)

You can observe that many many day traders with real money on the line don't see these as important. Students who aren't even in it for real money need a lot of guidance to avoid chasing the greatest (fake) return by pursuing high variance strategies. Or maybe you discuss that's what they're doing. Could be interesting.

All of these are much more interesting if you do them after you understand the mathematics behind them.

To me the greatest feeling of understanding always came if I saw a complex system and could see how and why all the parts worked. I had a grear course about computer tomography and the one thing which really struck with me was that fractional detivatives have saved lives.

Teachers need to ask every student in the class one basic question right from the offset:

- Are you more interested in things or are you more interested in people?

Once you’ve separated the students into these two camps you can tailor the content to match the interest much better. You’re probably going to have to tunnel down some more into their interests and get creative to really engage them but in my opinion this is the most bang for your buck question that teachers should be using to tailor their mathematics education to the individual student.

Forcing a group of kids to not only rote learn formulas but also to rote learn formulas to solve problems that have no relevance to any of their interests in real life is the reason mathematics is so hated by so many people. Creating problems about “how many sweets can Gary buy if…” is such a poor attempt at making it interesting to kids it’s actually insulting. Educators need to start putting some proper effort in and stop treating kids like they’re robots.

This is a great idea!

You should write a book about this, and include some sample calculations in the appendix

Love this list, thank you. My simple contribution is building a parabolic solar cooker.