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Math from Three to Seven

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Re: Math from Three to Seven

#171

Post by 082349872349872 »

spydum wrote: post #123
lain98 wrote: post #88

I have been trying to join/create a circle as an adult. I asked some of my online friends but no interest so far.

It's interesting to me, as if you read Benjamin Franklins biography, he mentions creating a literary circle being super important. I suspect many of our important thoughts leaders through history created small social circles where they hyperfocused on their domain with friends in a more social way

Mailing lists (the N:N variety, not the modern 1:N abomination) were such, and for a few, still are.

Re: Math from Three to Seven

#172

Post by graemep »

kreyenborgi wrote: post #80

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…

I took my kids out of school before they were teens. The younger one who did not like maths at school does like it now and is doing maths A level (UK exam, similar level to APs in the US AFAIK) at school (well, "sixth form college" school for 16+) and got a 9 (top grade) in her maths IGCSE (UK exams taken at 16 in schools, but mine took some of them younger).

I think the problem is that schools here (and I think most countries have similar problems) is that they focus on grades rather than keeping kids interested. Too much pressure takes away the fun. The article has some other clues to things that can go wrong with bad teachers: for example

> "Worst of all, the teacher docks points when the kids use techniques that they “aren’t supposed to know yet.”"

That is really terrible (and not typical, I hope - would not have happened in my school, I think) but it does happen.

I think there maybe a problem with insight without repetition, but it is definitely possible to keep kids interested while doing repetition as long as they feel they are getting better. My kids did do a lot of practice with minimal supervision.

I also think you absolutely have to provide enough interesting stuff to make kids feel the subject is interesting, even if there is some grind. Having a parent who is interested and will do things like answer questions is a huge help.

Re: Math from Three to Seven

#173

Post by Izkata »

kreyenborgi wrote: post #80

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…

Here's one possibility it looks like no one has suggested yet: it's boring because it's too slow.

I was bored with math up until 8th grade (age 13-14) but didn't realize why until that year. Up until that point I got straight As pretty effortlessly, but due to an administrative error I skipped a year of math. I was supposed to have a year of pre-algebra, but got placed into algebra instead. Luckily that teacher decided to do a month of review before starting new topics, which effectively meant I was taking a year long class in just a month. I actually had to put in effort for once and averaged a C.

It was during that year when the pace slowed back down that I realized I did like math in general, it was how slow classes had to go to accommodate all the students that I didn't care for.

Re: Math from Three to Seven

#174

Post by fifilura »

I simply think the basic assumptions that anything was better in Soviet is wrong.

They just focused much higher percentage of GDP on military and space stuff. Meanwhile, life in Russia was miserable. They got tanks, nuclear weapons and rockets. No companies that made people's life better.

This is what kept the cold war going.

Until it didn't.

If you are wrong the basic assumptions, you can look for clues anywhere, it does not matter.

Re: Math from Three to Seven

#175

Post by jameshart »

red_admiral wrote: post #153
nerdponx wrote: post #133

Earlier quoted context omitted.

I haven't read this whole article yet (PDF here https://math.berkeley.edu/~wu/wu1999.pdf ), but this idea is my #1 problem with Tom Lehrer's "New Math" song. His big complaint at the beginning is that the emphasis is too much on understanding and not on efficiently/correctly calculating an answer. As funny as the song is, I don't think that complaint has aged well at all. Also the old algorithm was just as complicate…

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 they only think of those numbers as sequences of digits.

But someone who sees that as ‘add fifteen hundred and take away fourteen’ is much closer to understanding what that expression actually represents, as well as being able to produce 26623 almost immediately without writing anything down.

It’s not about ‘neat tricks’, it’s about numbers having shape and feel and flavor.

Re: Math from Three to Seven

#176

Post by Izkata »

vundercind wrote: post #151
wizzwizz4 wrote: post #113

Earlier quoted context omitted.

> 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…

> We eliminated the job women were dominating (programmer) by combining it with the one men were dominating (analyst).

Gender disparity is usually shown as a percentage, but years ago I ran across one for programmers that used absolute numbers and the pattern showed a different story than usual - which this reclassification could probably explain.

I don't remember what year exactly the flip was, but before the flip the number of men and women were increasing at around the same rate. After it, the number of men skyrocketed while the number of women kept increasing at the same rate as before. As a percentage this looks like women lost interest or got pushed out, but the absolute numbers look more like men flocked to it without pushing anyone out. Or, perhaps, got grouped into it.

Re: Math from Three to Seven

#177

Post by Suppafly »

Izkata wrote: post #173
kreyenborgi wrote: post #80

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…

Here's one possibility it looks like no one has suggested yet: it's boring because it's too slow. I was bored with math up until 8th grade (age 13-14) but didn't realize why until that year. Up until that point I got straight As pretty effortlessly, but due to an administrative error I skipped a year of math. I was supposed to have a year of pre-algebra, but got placed into algebra instead. Luckily that teacher decid…

>it was how slow classes had to go to accommodate all the students that I didn't care for.

This is a huge problem across all classes, not just math. It's not as bad if the lowest portion of the bell curve is shuffled off to remedial learning classes, but really you need 3 tracks or more to keep the highest performing students challenged enough.

Re: Math from Three to Seven

#178

Post by Suppafly »

dan-robertson wrote: post #118
kreyenborgi wrote: post #80

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…

I think the amount of approachable math content online is incredible. Some comments mention 3Blue1Brown on YouTube, which is good but can go on a bit and maybe be a bit advanced. I think Numberphile is great for having a lot of videos, each of which is pretty short, and which still show some small proof of some problem. There are also books of interesting mathematical tidbits or puzzles, eg the Martin Gardener or Ian…

Khan Academy is great for learning math, the old school videos or the newer gamified stuff both.

Re: Math from Three to Seven

#179

Post by Suppafly »

fifilura wrote: post #174

I simply think the basic assumptions that anything was better in Soviet is wrong. They just focused much higher percentage of GDP on military and space stuff. Meanwhile, life in Russia was miserable. They got tanks, nuclear weapons and rockets. No companies that made people's life better. This is what kept the cold war going. Until it didn't. If you are wrong the basic assumptions, you can look for clues anywhere, it…

>I simply think the basic assumptions that anything was better in Soviet is wrong.

Agreed, it's bizarre to assume the Soviet version of anything is better than the what the US or other western nations are doing.

Re: Math from Three to Seven

#180

Post by photochemsyn »

hyperbrainer wrote: post #135

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?

Probably cultural - if a society celebrates physical prowess (sports etc. especially for males) and physical appearance (fashion etc. especially for females) but doesn't celebrate intellectual prowess for either gender - often the opposite - then children, teenagers, and young adults won't view working hard to improve their mental abilities as something worthwhile that they will be rewarded for. It's a symptom of a fairly unhealthy society.

There are a great many historical reasons why this situation arose - aristocrats feared the rise of well-educated groups within the serf class that might challenge their power, and plantation owners famously forbid teaching their slaves how to read and write, and some of that thinking persists to this day.

Regardless, people who spend roughly equal time on developing both their mental and physical capabilities via deliberate (and time and energy consuming) practice are the ones that tend to turn out healthiest and happiest.

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