Timeline for Could students learn a lot more from school if they're only taught number theory until way later?
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13 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2019 at 4:15 | comment | added | Timothy | be expressed as an integer divided by a nonzero integer. We could consider a fraction notation to be a way of expressing it that way. Then they could be given an addition and a division problem between rational numbers expressed in fraction notation and since they already mastered number theory, they will easily figure out the answer in fraction notation. | |
| Sep 29, 2019 at 4:09 | comment | added | Timothy | According to nrich.maths.org/2550, students work well with halves. For a reason I'm going to tell you later, I think it should be after students mastered number theory that they are introduced to integers than the rest of the real numbers. We could construct the integers through subtraction of 1 then the dyadic rational numbers through division of 2 than the rest of the real numbers from the Dedekind cuts of the dyadic rational numbers. Then it could be shown that it's possible to divide any number by any nonzero number in that system. A number would then be called rational if it can | |
| Sep 29, 2019 at 3:56 | comment | added | paul garrett | Pedantic number theory is surely far less useful than heuristic half-understood calculus. | |
| Jan 6, 2019 at 20:40 | answer | added | timtfj | timeline score: 2 | |
| Jan 3, 2019 at 19:05 | comment | added | shoover | This question begs for an answer that discusses Piaget's theory of cognitive development, particularly with respect to concrete vs. abstract thinking. | |
| Jan 3, 2019 at 18:27 | comment | added | Dave L Renfro | I'm sorry, but this all seems to me a non-starter solution to some imaginary problems. To take just one example, why is it important that school children know there exist irrational numbers and how (in your experience) has this lack been a problem? Surely general number sense is way more important and age-appropriate. However, I do think some exposure to proof at this age can be good, but by "proof" I don't mean the same thing you mean, but rather things like three $17$'s is three $10$'s and three $7$'s, as can be seen from $(10+7)+(10+7)+(10+7).$ | |
| Jan 3, 2019 at 17:00 | comment | added | guest | "Students" as a generalization don't EVER need number theory. Less than 1% will study it at all (late or early, doing well or poorly). | |
| Jan 3, 2019 at 14:25 | comment | added | Dan Fox | A student with no experience with ordinal numbres certainly will not have "yet thought of their own proof that distinct finite ordinal numbers always correspond to different cardinal numbers." In general notions such a quantifiers and abstract variables are far, far more difficult than is basic arithmetic, and the elementary school student capable of giving formal proofs as in the question - moreover before learning how to add fractions - is a very rare beast - I would say a unicorn if I weren't able to imagine a young Grothendieck. | |
| Jan 3, 2019 at 13:27 | answer | added | orion2112 | timeline score: 4 | |
| Jan 3, 2019 at 7:29 | comment | added | Tommi | Related: matheducators.stackexchange.com/questions/14984 | |
| Jan 3, 2019 at 7:28 | answer | added | Tommi | timeline score: 10 | |
| Jan 3, 2019 at 5:42 | history | edited | Timothy | CC BY-SA 4.0 |
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| Jan 3, 2019 at 5:30 | history | asked | Timothy | CC BY-SA 4.0 |