181–190 of 225 posts
Peripheral, but not totally irrelevant: Psmith was an Edwardian dandy of PGWodehouse’s imagination https://en.wikipedia.org/wiki/Psmith
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As far as I understand the article, the author (and myself) absolutely wants people to practice longhand addition etc., and is pushing back on the idea that you can teach how to calculate XOR how to understand place value. If some of the kids go on to study CS, they can then think about the similarities and difference between decimal, hex and binary addition, how half and full and ripple-carry adders work, and how yo…
New math or common core or any approach that tries to center ‘understanding’ over rote procedure is definitely pushing in the right direction. I think that people who have the closed understanding of addition, that there is one true algorithm for doing it and who will start your 25137+1486 problem off by adding six and seven to get three and carry the one… are missing out on a deeper intuition about numbers, because…
This is precisely the dichotomy that is bogus according to the article.
25137 = 20000 + 5000 + 100 + 30 + 7 and 1486 = 1000 + 400 + 80 + 6, then you add (7 + 6) + (30 + 80) + (100 + 400) + (5000 + 1000) + (20000 + 0) to get the result. The fact that we can do that and combine it all tightly into columns is IMO a very deep insight into what a "number" really is, while also providing a general pen-and-paper algorithm for adding any two numbers. The insight provides an algorithm, and the algorithm leads us to an insight.
Discovering that 1486 = 1500 - 14 isn't a particularly deep insight into numbers either. It's a useful technique and I think it's fine that we teach it, but I don't think it has any particular conceptual merit that the standard algorithm lacks. I certainly don't see how it puts a child any closer to understanding what addition really means.
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> This theory is related to the curious fact that, on average, the more feminist your society, the fewer women there are in math and science — which makes total sense if you assume that on average women are good at math but uninterested in it. This isn't a complete explanation: we can see this by looking at other STEM fields. The early years of computer programming were dominated by women, yet nowadays, women are pro…
> The early years of computer programming were dominated by women, yet nowadays, women are proportionally uninterested. We eliminated the job women were dominating (programmer) by combining it with the one men were dominating (analyst). At the same time law and medicine were seeing huge increases in the proportion of women practitioners, so the status thing doesn’t make a ton of sense as an explanation. Besides, it w…
Low-status tasks (e.g. vital, but "unpromotable" ones) are delegated to women, and tasks that are associated with femininity are considered low-status. This is a well-documented (https://noidea.dog/glue) and easily-measurable phenomenon. I expect there are many harder-to-measure instances of institutional sexism that might make classes of workplace unpalatable, even if there's no gender bias in desire to do the actual work.
If this (or a similar) effect has been going on for a while, I'd expect that to have significant knock-on effects.
As a teenager who dislikes the current schooling system, what I am most curious about is actually why something like the "mathematical circles" do not exist in the west. To some extent, a similar social group is formed by robotics teams in my experience. A dedicated teacher/coach and a bunch of people who like electronics can really get amazing things done. Why is this the case?
Maybe you already know or could try to find other peers who like math, and see if you can get something started? I think there's a good chance that if you approached a supportive teacher with "my four friends and I want to start a math club, can you help us?", it would get the ball rolling. Perhaps you could put something up on the bulletin board or equivalent you kids have these days, data kiosks or hovergrams or wh…
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Hah. In the USSR an average engineer earned less money than an average worker. I'm not joking. But STEM was seen as far more prestigious than manual labor. This was very much a cultural thing, pushed by the government (engineers are useful!). Another thing, there was a huge societal pressure to excel at school. It was common for parents to check their children's marks every day. There's a very famous picture about it…
in case anyone else were interested: https://www.youtube.com/watch?v=2NlnJsCEzSM "The country of undone homework" https://www.youtube.com/watch?v=YpygndkMSWA "Vovka in a Faraway Kingdom" (I was already shocked that one of the leading roles in the romcom Три плюс два was a physicist, but then again Young Sheldon might provide evidence that pop culture in the Old Country is more STEM-accepting now than it had been in m…
Yes. It literally translates as "self" in "yourself/himself/myself", and in compound words it can be translated as "auto" (which also means "self" in Greek).
It ends like this, largely cancelling out the rest of the article: >In the second iteration of the circle, all of his notes are completely useless, and all of his initial attempts to teach anything fail, because these are different kids with different aptitudes and different interests. Zvonkin, raised in a communist society and a believer in the absolute malleability of human nature, is fairly bowled over by this, es…
This was a surprisingly interesting and well-written article. I hope people read it and not just the comments here :-) I'm unsure if it implies that "lame school exercises" are unnecessary or just not sufficient (I've recently read articles about how teaching "insight" without exercises is detrimental, though perhaps doing problems implies getting that repetition-work). Does anyone have good experiences with keeping…
> Does anyone have good experiences with keeping kids math-interested as they get into their teens? The first step would be to get them into a math circle. There are 100s of them https://mathcircles.org/map/ . I run a math circle as well, and work with a bunch of teens/preteens. I've had a lot of success with them. AMA.
For example UCLA math circle is very exclusive and there’s effectively no admission in elementary school if you miss enrollment or don’t do well on their kindergarten test.
Is there any alternative?
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As far as I understand the article, the author (and myself) absolutely wants people to practice longhand addition etc., and is pushing back on the idea that you can teach how to calculate XOR how to understand place value. If some of the kids go on to study CS, they can then think about the similarities and difference between decimal, hex and binary addition, how half and full and ripple-carry adders work, and how yo…
New math or common core or any approach that tries to center ‘understanding’ over rote procedure is definitely pushing in the right direction. I think that people who have the closed understanding of addition, that there is one true algorithm for doing it and who will start your 25137+1486 problem off by adding six and seven to get three and carry the one… are missing out on a deeper intuition about numbers, because…
This very book argues against teaching these tricks without allowing the student to discover it themselves.
Why is 4 + 7 = 7 + 4? Is it a general phenomenon?
Earlier quoted context omitted.
New math or common core or any approach that tries to center ‘understanding’ over rote procedure is definitely pushing in the right direction. I think that people who have the closed understanding of addition, that there is one true algorithm for doing it and who will start your 25137+1486 problem off by adding six and seven to get three and carry the one… are missing out on a deeper intuition about numbers, because…
1500 take away 14 is presupposing commutativity. This very book argues against teaching these tricks without allowing the student to discover it themselves. Why is 4 + 7 = 7 + 4? Is it a general phenomenon?
Earlier quoted context omitted.
New math or common core or any approach that tries to center ‘understanding’ over rote procedure is definitely pushing in the right direction. I think that people who have the closed understanding of addition, that there is one true algorithm for doing it and who will start your 25137+1486 problem off by adding six and seven to get three and carry the one… are missing out on a deeper intuition about numbers, because…
> 25137+1486 problem off by adding six and seven to get three and carry the one… are missing out on a deeper intuition about numbers, because they only think of those numbers as sequences of digits. This is precisely the dichotomy that is bogus according to the article. 25137 = 20000 + 5000 + 100 + 30 + 7 and 1486 = 1000 + 400 + 80 + 6, then you add (7 + 6) + (30 + 80) + (100 + 400) + (5000 + 1000) + (20000 + 0) to g…
Seven plus six is thirteen carry the one leaves three, four plus eight is twelve carry the one leaves two, two plus four is six, five plus one is six, two six six two three…
Seeing that as a decomposition of multiples of powers of ten and how that makes ‘carrying’ happen is exactly a result of having a deeper understanding of the way the numbers work.