Timeline for Simple, elegant ways to teach the idea of what functions are for the first time
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2018 at 16:04 | vote | accept | orion2112 | ||
| Jun 30, 2018 at 19:45 | comment | added | Mike Pierce | An example of an invertible function I suppose would be the function that takes a book in a library and returns it's call number. A head-scratcher you could give students would be this: Consider the function from the set of all people on earth to the set all people on earth that for each person, the function will output the person nearest to their location. Is this function invertible? | |
| Jun 30, 2018 at 19:45 | comment | added | Mike Pierce | I have yet to establish wacky examples of functions that I come back to each time I teach functions this way; I usually just invent new ones each time. You examples is good because it shows that functions can be used to classify things (is it a vowel or consonant). Related but similar, my example picks out a trait of an input (it color), which if you know about object-oriented programming can be thought of as a function that returns one of an objects member variables. (I've thought about much of this while teaching Discrete Math to computer science majors) | |
| Jun 30, 2018 at 19:28 | comment | added | orion2112 | I like this very much. What I was aiming for specifically was to hear about these wacky examples (is there one that stands out more than the others?). I think it's pertinent to at least explain that a function doesn't need to be $\mathbb{R}\rightarrow\mathbb{R}$ before saying "okay, now we just deal with real functions". Your approach is basically the one I think would help. Don't use the jargon right away, show the idea. And like you said, we don't spend hours on this; it's just a preamble. | |
| Jun 30, 2018 at 19:21 | history | edited | Mike Pierce | CC BY-SA 4.0 |
added 63 characters in body
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| Jun 30, 2018 at 19:16 | history | answered | Mike Pierce | CC BY-SA 4.0 |