Harry had been sent to the best primary schools - and when that didn't work out, he was provided with tutors from the endless pool of starving students.

In about eight months or so, I will be one of those (hopefully not starving) students. I'll be moving out to London to live with my aunt and uncle in a rather nice middle-class neighbourhood, while I study and work to prepare for university the following year. They know a lot of the parents around there and suggested that I begin teaching small groups of 8-to-12 year old children for maybe an hour or two regularly, and charge their parents/guardians a reasonable sum per child. I would be teaching them math and science in all likelihood. Apparently word will get around quickly if I'm competent so I might have a substantial number of customers within a few months.

My questions:

  • Does anybody on LessWrong have any direct experience at this sort of thing, that could share some advice?
  • What are some good things to teach? I'll probably do the standard bottle rockets and baking soda+vinegar volcanoes, but I'd also want to spice things up and teach them something that they'd be hard-pressed to come across elsewhere (simple rationality techniques come to mind)
  • What is the best way to teach these things to this age group - or rather, what are some good books or other resources that I can use to teach myself how to teach?
  • If I were to teach them some basic rationality skills, which ones and how? Obviously I won't be talking about anything fancy like probability theory unless I strike gold and find a kid on the far-right of the bellcurve, but more like low-hanging fruit. I might do something like that radiator puzzle to warn them against password-guessing for example.

(edit: thanks to whoever fixed the font on this)
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If their homework involves tedious memorization, introduce them to spaced repetition (begin with physical flashcards).

Similarly, I was thinking "teach them how to learn". Most of the things I was taught I have forgotten. I'm only now learning how to learn. Spaced repetition is a big part of that, but there are other tricks too, such as making information "sticky" by making it visual and/or emotional, & learning how to create & use mnemonic devices.

Do you recommend any resources on creating and using mnemonic devices? It's something I've always struggled with.

Most of what I know is pieced together from different resources online. This site has some good info, but is a work in progress: http://mnemotechnics.org/wiki/Main_Page

What I'm doing now is:

  1. Break down a complicated topic into keywords
  2. Assign the keywords more memorable keywords if they are difficult to remember / hard to visualize
  3. String the memorable keywords into a visual story
  4. Plug the story into a spaced repetition system so that it becomes a stable memory

For instance, I wanted to remember how Red blood cells are metabolized, so I made the following story today:

RBCs = Red Buick Coupe

Spleen = Spray & Wash (car wash joint)

Unconjugated bilirubin = Unprecedented + Rubin (guy's name)


Conjugated bilirubin = Congratulate + Rubin

Bile = Bike

Small intestine = Small kids


The story is: "An old man drives his Red Buick Coupe into the Spray & Wash where it is given an unprecedented cleaning by a guy named Rubin, who LOVES to eat Liver. He congratulates Rubin for a job well done, then Rubin rides his Bike home where his 2 small kids are waiting for him. They love eating Liver too."

This helps me remember old RBCs are metabolized in the Spleen to Unconjugated bilirubin, then passed to the Liver where they are processed into Conjugated bilirubin & mixed with Bile, which is released into the Small intestine. Enterohepatic circulation means 95% of the bilirubin goes back to the Liver.

Hope that is all right. At least, it offers an example of the process.

The Memrise community (http://www.memrise.com/) are quite big on that kind of thing. If you're learning a language, you can browse through their community database of mnemonics or "mems" for inspiration, and are encouraged to create your own. Their site is also quite good as a spaced repetition tool for languages.

My uninformed opinion is that games should be a good medium for teaching young children. (I would be very interested in hearing opinions about this from people who actually work in education.) I think a surprising amount can be learned by carefully inspecting even a game as simple as Minesweeper. There are various "lemmas" you can prove in Minesweeper about how various configurations uniquely pin down the location of mines or non-mines and I suspect this could be an accessible introduction to mathematical proof (the advantage being that all of the relevant proofs can be done by analyzing a finite number of cases). I haven't actually tried this though.


I agree and would emphasize that deriving concepts from an existing game is preferable to constructing an educational game from scratch. It makes it more engaging and teaches the skill of modelling.

What games do children that age play nowadays?

What's your level of math and science knowledge? Can we recommend that you teach the kids group theory?

Also, what's the goal for the kids? You'll want to teach different things depending on whether they want to keep up with schoolwork, skip ahead in schoolwork (and hopefully proceed to skip grades), or just learn more about math and science. Fir the first two you'll need to cover a known curriculum, for the latter you need to avoid that curriculum like the plague of boredom.

For math resource, you might check out Vi Hart's videos and A Mathematician's Lament.

For science resources, check out museums :P Also, I highly recommend pH paper as a powerful experimental tool an 8 year old can use. Lots of cool chemistry experiments out there. For biology, growing plants and growing germs on agar and taking nature walks with a book about trees and making Punnett squares are good activities. Kid physics is mostly like engineering - making telescopes from lenses and water bottle rockets and freezing rubber bands on dry ice and having a competition over who can make something out of paper and tape that will catch dropped eggs from the highest height.

By the time I'll be teaching I'll have finished my Maths and Further Maths A-Levels and I would also have studied a fair amount of higher material.

Those are all good suggestions. One thing troubling me is that I want to help kids develop their problem-solving skills. Ideally I'd introduce some new puzzle and give them a few hints and they would work it out, but from my limited experience with my 9 year old cousin (who is fairly bright), it either ends up with me giving too little help (so he gets stuck and gives up in frustration) or too much help (so he's just following along with what I'm saying rather than discovering something for himself). How can I best strike the balance?

One of the cool teacher tricks you eventually figure out is how much time to give after asking a question. Beginner teachers always jump in too early - it seems easy to the people who already know the answer :P Sometimes you even have to add on some extra time for people to realize that this is one of those questions where they actually have to think. It can get uncomfortable for you, the questioner, but that's okay, you just have to not crack first.

Not sure how well this generalizes to puzzles. One useful tip is that there's an intermediate level of help, where you basically just ask questions to make the other person walk through their thought process out loud. "What have you done so far?" are the most common first words out of my mouth when someone asks for help.


Followed by "What do you think you could do next?"

Have lots of problems prepared over a wide range of difficulty. Start with problems you're pretty sure the student can solve, and turn up the difficulty slowly.

I drew on How to Solve It for teaching bare bones rationality skills to grade and middle schoolers.

TBH the curriculum is easy, the real trick is getting the kids to perceive you as high status so they actually pay attention.

If you are being paid to improve their grades, warning them against password-guessing is a breach of contract.

If you are being paid to educate them, it's not really low-hanging fruit, although it is a very tasty one. Most people are more likely to learn the wrong lesson (beware of trick questions) than the right lesson.


There's nothing wrong with password-guessing -- as long as you know when you're doing it and don't mistake it for actual understanding. I'd have thought a tutor could teach students those skills without ruining their ability to grab extra marks in examinations by password-guessing.

I'd argue against this. I always saw through password-guessing as fake and not really understanding anything when I was young, but lacked the people skills to notice that the teachers and examiners wanted me to guess the password rather than demonstrate that I really understood (because I didn't understand why), and lost a few exam marks along the way to figuring that out!

Password-guessing skills are the lowest hanging fruit in terms of improving grades; your experience seems to support that as well.

So-called "test skills", which improve performance on tests without improving mastery of the nominal subject of the test, are strong evidence of inefficiency in the school system. Are you proposing remaking the entire game of quittich instead of getting the bludgers better brooms?

Sorry, I don't seem to have made myself clear. I was arguing against warning students against password guessing. I.e. don't remake the game, just play it as intended.

There's a certain amount of remaking the game desired, but the way to remake the game isn't to tell students to follow the rules that should be in place instead of the rules that are in place.

What's the best way to teach password-guessing skills? Given a small number of mutually exclusive choices (as in a multiple choice or true/false exam), how do you determine the one that the creator of the question intended without knowing enough about the specific subject?

Given a small number of mutually exclusive choices (as in a multiple choice or true/false exam), how do you determine the one that the creator of the question intended without knowing enough about the specific subject?

  • In general, the second highest numerical answer is right about half the time.
  • When there are all-of-the-above or none-of-the-above questions, the person writing the test will choose the all/none-of-the-above choice either very rarely or above 50% of the time. Thus, if you know that the answer to one all-of-the-above question is "all of the above" and have no clue on the current question, "all of the above" is probably your best guess.
  • Surprisingly frequently, wrong answers don't fit grammatically into fill-in-the-blanks type multiple choice. If it's not grammatically correct, it's probably not the right answer.
  • Read the entire test before you start answering questions. Frequently, answers to early questions are in later questions. Here it's a good idea to learn to read at least twice as quickly as the average student so as to be able to do this with any fair time limit.
  • If two options are the same, they're both wrong. If one is the negation of the other, one of those two is correct.
  • Always guess. "Guessing penalties" don't actually penalize you for guessing, they're designed to offset random guessing on average. Your guess is probably better than random.
  • Unless you can point out the specific way in which the answer you gave first was wrong, don't change it. It's very hard to think "this answer is probably wrong" without thinking "this alternative answer is probably right", and so while your current answer is likely wrong, your next choice is likely to be worse.
  • If an answer contains qualifiers (may, might, sometimes), it's more likely to be correct.
  • One strategy I have heard of but not personally used is to treat multiple-choice questions as a series of true-false questions and pick the "most true" answer.

You're not going to go from random chance to an A with these techniques, but you might go from random chance to a 70% or from a 70% to an 85% (my ballpark estimate is that half of the errors the average person makes on a test are avoidable with the use of heuristics like these).

Materials-wise, I can't recommend the Murderous Maths books by Kjartan Poskitt enough. They're what got me into maths, and introduce topics at a basic level while leaving the top end open for further development. They've got lots of fun puzzles and activities. I think they're aimed at 10-14 year olds, so would be towards the top of your tutee's age range.

Less paper-based and more free is NRICH (http://nrich.maths.org/), which is run by a group at Cambridge (I've done some holiday work writing questions for them). It contains materials for all ages (pre-school up to sixth form! (4-or-5-ish to 8)) and is intended as simultaneous for teachers and keen students. It's got a good selection of mathematical games as well as themed monthly questions, and keen students can type up their solutions and submit it to them for a chance of being featured on the website. The games in particular will be a good way of introducing lots of mathematical concepts, since that's how they're designed.

In fact, teaching your kids basic game theory is probably a good idea. It teaches you them to think rationally and is easy to motivate (beat all your school friends!). Many rationality concepts and techniques are founded upon the basics of game theory!

pre-school up to sixth form!

Given the international nature of the internet, it would be helpful to provide clarifying definitions for country-specific terms.

Good point, fixed.

Thanks for the tips - and yes I know and love the Murderous Maths books too. I even met Poskitt a few times at book fairs, he's a really funny guy from what I remember.

One interesting kid science experiment is to dissolve an egg's calcium shell in vinegar. Naked egg experiments can make a good demonstration of osmosis. (Osmosis comes up a lot in cryobiology, so it is of considerable interest for cryonics.)

Thank you for trying to impart useful, compounding knowledge, even when selling opium is almost certainly more lucrative in a middle-class neighborhood.


Use fun experiments to teach the scientific method instead of trying to impart on them a superficial understanding of chemistry and geology (in the case of the volcano).

For math, try to address any form of mathematical anxiety. I think that is more important than whatever knowledge you could teach them, but if you can make it engaging I recommend introducing some logic and naive set theory. Combinatorial problems are also easily illustrated with physical objects and can serve as an introduction to probability theory.