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I find kids understand the concept of functions really intuitively if it is stated simply - input -> func -> output, it doesn't have to be difficult maths, and

I find kids understand the concept of functions really intuitively if it is stated simply - input -> func -> output, it doesn't have to be difficult maths, and it can make for some great games. It looks a little intimidating if using the notation in this article but they easily grasp that a function transforms inputs and returns outputs, and it can be a fun introduction to maths and programming, and then later to things like graphs based on functions. Another game I play with my kids to introduce the concept of functions which aren't just for numbers is a haircut function. You start by deciding on what the function does (curls hair, cuts it short, makes it longer), write that in the middle of the page, then you draw some input people on the left of the page, and on the right hand side draw the output for each input. Bonus points for running the function twice to see what happens to that person. This is a popular game with my kids and gets them involved as they can draw their own.

sullyj3 7y ago
The way maths is taught in Australia, for a long time the term function was synonymous with the concept "2D plot that passes the vertical line test" in my mind. I was completely unaware of how much broader and more interesting a concept functions are. There are probably many people whose understanding never progresses beyond this, which I think this is extremely unfortunate.
chrisweekly 7y ago
Agreed! My kids are slightly older but we've long enjoyed a roadtrip game that's a variation on 20 questions: "give me an input, I'll respond with an output, then you guess what the 'machine' [algorithm|function] did". They'd get to provide one input, I'd respond w one output, then they'd get one chance to define the operation -- to which I'd respond only yes or no -- before the next person's turn to test it. Whoever solves it gets a point (if we're keeping score; not important). Then the next person gets to be the function maker. They got pretty good at hypothesizing plausible solutions and refining them to hone in on the precise answer, and it was more interesting than standard 20 questions. It's also fun to go beyond strictly numeric types, eg responding to a number with the name of a country, or turning a letter or word into a number, etc.
- nathancahill 7y ago
  Awesome version of 20 questions. My parents are biologists and we played 20 questions with plants/animals on road trips growing up. The games were intense! Learned a ton.
  - vikramkr 7y ago
    Did anyone ever just try and search through a phylogenetic tree?
    - nathancahill 7y ago
      Basically yes, that is what the games evolved in to.
- bspammer 7y ago
  I taught at a programming camp one summer, and my favourite example of this that I drove several kids crazy with was "above the line, below the line". Given any input word, I would tell them whether it was above the line, or below the line (which corresponded to acceptable and unacceptable behaviour in camp-speak). I think only two kids figured it out on their own, and each time I challenged them to write a program to categorize words automatically. I wonder if hacker news can figure it out :) "Hacker" -> Above the line "News" -> Above the line "chrisweekly" -> Below the line "functional" -> Above the line "programming" -> Below the line
  - jodrellblank 7y ago
    Curious that the way we play these games is “race to the answer” in fewest tests, and as soon as someone else gets it, the game is over and spoiled for anyone who didn’t. Is there a good way to play to train for “most confidence before answering” without making it a drudge of endless tests and humhawing? Making each question a more powerful test would be good, but that’s not what racing to the answer encourages, that encourages guessing the teacher’s password. What about tests are free, first to answer wins, but a wrong answer or two disqualifies you completely?
correct_horse 7y ago
I sure hope the haircut function mutates it's input, and doesn't return a clone whose hair is cut.
- grey-area 7y ago
  ;)
- mcny 7y ago
  Reminds me of a YouTube video which said every time someone gets beamed in Star Trek they are killed and someone else is created with their body and mind somehow. If that were possible, why wouldn’t they just store backups and “restore” from backup when someone died?
  - pbhjpbhj 7y ago
    A type of restoring from backup, well the short-term pattern buffer memory, has been a feature of several "transporter" episodes I think? Like "no, we lost them; maybe they're 'in' the pattern buffers".
  - bmn__ 7y ago
    > a YouTube video CGP Grey: The Trouble with Transporters https://www.youtube.com/watch?v=nQHBAdShgYI https://www.youtube.com/watch?v=nQHBAdShgYI Steve Shives: Is Star Trek's Transporter Actually a Murder Machine? https://www.youtube.com/watch?v=f-8zEkIaB0c https://www.youtube.com/watch?v=f-8zEkIaB0c > why wouldn’t they just https://allthetropes.fandom.com/wiki/Story-Breaker_Power https://allthetropes.fandom.com/wiki/Story-Breaker_Power For purpose of storytelling, these powerful side effects of transporters need to be restricted. Hence, as an in-universe explanation, a pattern buffer ∙ is a physical phenomenon that cannot be (fully) expressed as information ∙ deteriorates over time, so needs to be rematerialised soon. For the exception, see https://memory-alpha.fandom.com/wiki/Relics_(episode) https://memory-alpha.fandom.com/wiki/Relics_(episode)
  - danidiaz 7y ago
    There's a notable book by philosopher Derek Parfit called "Reasons and Persons" that—among other things—uses "transporter" thought experiments to explore the nature of personal identity. The quasi-buddhistic conclusion, with which I agree, is that personal identity is largely an illusion. It's an easy illusion to maintain however, given that in practice our "software" is very difficult to "copy" exactly. https://en.wikipedia.org/wiki/Reasons_and_Persons#Personal_identity https://en.wikipedia.org/wiki/Reasons_and_Persons#Personal_i...
roosterdawn 7y ago
For what it's worth, this intuition is sound and I think it works just as well if you formalize[1] it to be used to illustrate the lambda calculus. [1] http://dkeenan.com/Lambda/ http://dkeenan.com/Lambda/

sullyj3 7y ago

The way maths is taught in Australia, for a long time the term function was synonymous with the concept "2D plot that passes the vertical line test" in my mind. I was completely unaware of how much broader and more interesting a concept functions are. There are probably many people whose understanding never progresses beyond this, which I think this is extremely unfortunate.

chrisweekly 7y ago

Agreed! My kids are slightly older but we've long enjoyed a roadtrip game that's a variation on 20 questions: "give me an input, I'll respond with an output, then you guess what the 'machine' [algorithm|function] did". They'd get to provide one input, I'd respond w one output, then they'd get one chance to define the operation -- to which I'd respond only yes or no -- before the next person's turn to test it. Whoever solves it gets a point (if we're keeping score; not important). Then the next person gets to be the function maker. They got pretty good at hypothesizing plausible solutions and refining them to hone in on the precise answer, and it was more interesting than standard 20 questions. It's also fun to go beyond strictly numeric types, eg responding to a number with the name of a country, or turning a letter or word into a number, etc.

nathancahill 7y ago
Awesome version of 20 questions. My parents are biologists and we played 20 questions with plants/animals on road trips growing up. The games were intense! Learned a ton.
- vikramkr 7y ago
  Did anyone ever just try and search through a phylogenetic tree?
  - nathancahill 7y ago
    Basically yes, that is what the games evolved in to.
bspammer 7y ago
I taught at a programming camp one summer, and my favourite example of this that I drove several kids crazy with was "above the line, below the line". Given any input word, I would tell them whether it was above the line, or below the line (which corresponded to acceptable and unacceptable behaviour in camp-speak). I think only two kids figured it out on their own, and each time I challenged them to write a program to categorize words automatically. I wonder if hacker news can figure it out :) "Hacker" -> Above the line "News" -> Above the line "chrisweekly" -> Below the line "functional" -> Above the line "programming" -> Below the line
- jodrellblank 7y ago
  Curious that the way we play these games is “race to the answer” in fewest tests, and as soon as someone else gets it, the game is over and spoiled for anyone who didn’t. Is there a good way to play to train for “most confidence before answering” without making it a drudge of endless tests and humhawing? Making each question a more powerful test would be good, but that’s not what racing to the answer encourages, that encourages guessing the teacher’s password. What about tests are free, first to answer wins, but a wrong answer or two disqualifies you completely?

correct_horse 7y ago

I sure hope the haircut function mutates it's input, and doesn't return a clone whose hair is cut.

grey-area 7y ago
;)
mcny 7y ago
Reminds me of a YouTube video which said every time someone gets beamed in Star Trek they are killed and someone else is created with their body and mind somehow. If that were possible, why wouldn’t they just store backups and “restore” from backup when someone died?
- pbhjpbhj 7y ago
  A type of restoring from backup, well the short-term pattern buffer memory, has been a feature of several "transporter" episodes I think? Like "no, we lost them; maybe they're 'in' the pattern buffers".
- bmn__ 7y ago
  > a YouTube video CGP Grey: The Trouble with Transporters https://www.youtube.com/watch?v=nQHBAdShgYI https://www.youtube.com/watch?v=nQHBAdShgYI Steve Shives: Is Star Trek's Transporter Actually a Murder Machine? https://www.youtube.com/watch?v=f-8zEkIaB0c https://www.youtube.com/watch?v=f-8zEkIaB0c > why wouldn’t they just https://allthetropes.fandom.com/wiki/Story-Breaker_Power https://allthetropes.fandom.com/wiki/Story-Breaker_Power For purpose of storytelling, these powerful side effects of transporters need to be restricted. Hence, as an in-universe explanation, a pattern buffer ∙ is a physical phenomenon that cannot be (fully) expressed as information ∙ deteriorates over time, so needs to be rematerialised soon. For the exception, see https://memory-alpha.fandom.com/wiki/Relics_(episode) https://memory-alpha.fandom.com/wiki/Relics_(episode)
- danidiaz 7y ago
  There's a notable book by philosopher Derek Parfit called "Reasons and Persons" that—among other things—uses "transporter" thought experiments to explore the nature of personal identity. The quasi-buddhistic conclusion, with which I agree, is that personal identity is largely an illusion. It's an easy illusion to maintain however, given that in practice our "software" is very difficult to "copy" exactly. https://en.wikipedia.org/wiki/Reasons_and_Persons#Personal_identity https://en.wikipedia.org/wiki/Reasons_and_Persons#Personal_i...

roosterdawn 7y ago

For what it's worth, this intuition is sound and I think it works just as well if you formalize[1] it to be used to illustrate the lambda calculus. [1] http://dkeenan.com/Lambda/ http://dkeenan.com/Lambda/