Timeline for What are some "deep" questions to explore in elementary school math?
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8 events
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| Nov 9 at 16:29 | comment | added | wizzwizz4 | @PasserBy Euclid didn't think it was more complicated than what you call the "standard one". In fact, his direct proof as described in Elements (book 9, proposition 20) describes a concrete instance of a general algorithm, which is how I remember most mathematics being taught to me at that age. It might take a couple of days to understand the proof (trying lots of examples, with blocks), but I see no reason to believe it's beyond a child capable of understanding multiplication and division with remainder. | |
| Nov 9 at 9:22 | comment | added | Passer By | @wizzwizz4 If you write your proof rigorously, you will find it more contrived than the standard one by contradiction. And that is besides the point, I don't believe first graders understand any of this. | |
| Nov 8 at 18:52 | comment | added | wizzwizz4 | @PasserBy The proof that there are infinitely-many prime numbers isn't by contradiction. "Suppose we have some prime numbers. Multiply them all together, and add 1, to get our new number. What's the remainder, compared to all the primes in our set? 1: so none of them divide it! None of its prime factors are in our original set. Therefore, no matter how many prime numbers we have, we can always find more prime numbers." | |
| Oct 30, 2023 at 14:30 | comment | added | BigMistake | @PasserBy @ BenI. It certainly depends on the individual child, but it is possible to explain without notation / terminology. But yes, it may be a bit challenging depending on the person's background. OP said the 1st grader is "very advanced in math." | |
| Oct 30, 2023 at 14:25 | comment | added | Ben I. | @PasserBy Agreed. Without understanding divisibility, it's hard to imagine understanding primes. There may be some dozens of first graders who can understand the proof, but that statement does not support OP's assertion. I suspect that OP just used "first grade" as a stand-in for "surprisingly young". | |
| Oct 30, 2023 at 7:26 | comment | added | Passer By | "The proof is actually simple enough for a first grader to understand" uhhhh... what? Proofs? For a first grader? That uses contradiction? I have a hard time believing first graders can understand it. | |
| S Oct 29, 2023 at 17:01 | review | First answers | |||
| Oct 29, 2023 at 18:28 | |||||
| S Oct 29, 2023 at 17:01 | history | answered | BigMistake | CC BY-SA 4.0 |