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Math from Three to Seven

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Re: Math from Three to Seven

#151

Post by vundercind »

wizzwizz4 wrote: post #113
eru wrote: post #93

Earlier quoted context omitted.

As mentioned in the article, that might be completely explained by their comparative poverty.

> 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 was not high status in the 80s when this was going on (or the 90s… arguably it’s still not, just high pay)

Re: Math from Three to Seven

#152

Post by hugetim »

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…

For me it was this curriculum, which should be better-known: https://www.elementsofmathematics.com/

One place it is offered in-person is the St. Louis area where I grew up: https://megsss.org/about-us/

Re: Math from Three to Seven

#153

Post by red_admiral »

nerdponx wrote: post #133
red_admiral wrote: post #130

Earlier quoted context omitted.

For the "exercises are important and also build conceptual understanding", see "BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING, A Bogus Dichotomy in Mathematics education" by H. Wu. The big challenge in teaching is not to make the exercises seem lame.

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 you add bigints. At that point you need both a conceptual and a procedural understanding of digit-wise addition.

If you want to do say 67 + 24, perhaps even in your head, there are more efficient ways to add than the standard algorithm, and I think that's what new math was trying to get at. But at some point you might want to add 25137 + 1486 and then your neat tricks no longer work and you need something that scales.

Re: Math from Three to Seven

#154

Post by eru »

richardw wrote: post #109
eru wrote: post #97

Earlier quoted context omitted.

You say it like trying to get paid well is a bad thing?

No human on earth doesn’t want to get paid well. Some are purely mercenary. Those I would prefer not to work with or hire. (There are a lot of caveats. Someone might have always worked for jerks and has checked out, etc.)

I like to be passionate about what I am doing, but there's plenty of great projects / companies to work for. So might as well look after the money, too.

(Generally, the companies that can afford to pay you well, are also those that can afford to treat you well.)

Re: Math from Three to Seven

#155

Post by hugetim »

jarvist wrote: post #92
timthorn wrote: post #83

Axiom Maths is trying to import the concept of maths circles to the UK, providing support and materials for schools to host their own circles. It is run by a team with deep expertise in mathematics education, including the founding head of King's Maths School, a state school that is one of the top performing sixth forms in the country. https://axiommaths.com/how-we-work/

Practically speaking (running a little maths circle in the UK for my children, and some of their friends from nursery and primary school), I have found the Nrich website to be the single best source of resources: https://nrich.maths.org/about-nrich There is also https://parallel.org.uk/ by Simon Singh, but this is aimed at ages ~10+. The book by Rozhkovskaya has some really nice activities in it. https://www.amazon.c…

A nice source of middle- and high-school aged problems: https://www.usamts.org/

One of the joys of high school was discussing these with a friend (after submission---but one could forego the contest and just do the circle thing with them for fun).

Re: Math from Three to Seven

#156

Post by pokerface_86 »

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 didn’t even know i enjoyed math until i was fortunate enough to take multivariable calculus my senior year of HS, you don’t really get to do any cool shit in typical public schools so it’s hard to keep the interest

Re: Math from Three to Seven

#157

Post by pokerface_86 »

kreyenborgi wrote: post #103
082349872349872 wrote: post #96

Earlier quoted context omitted.

have you tried TFA's tack of, instead of throwing him on the mercy of the school exercises, presenting a problem or two? > " Problems worthy of attack prove their worth by fighting back " —PH

In a small way, yes, and throughout "three to seven", actually up until she was nine, we had a lot of fun with what I think I can call problems (especially while home-schooling during the pandemic, where we had time to keep going back to these from different angles). But I'm not able drum up much interest these days, so I was wondering if people here had any insights on what if anything has worked with tweens, as opp…

when i was 12,13 i really enjoyed the algebraic manipulation parts of calculus without having to think too hard about setting up problems. just practicing integration, differentiation and limits was a good start

Re: Math from Three to Seven

#158

Post by dxbydt »

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…

> 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.

Re: Math from Three to Seven

#159

Post by pokerface_86 »

harimau777 wrote: post #136

My biggest issue with math education is that after we learned the theory we never went back and developed an actual plan for solving the problems. For example, we learned a dozen different ways to approach integration, but after all this we never really put together a workable strategy for approaching a problem and deciding what tools to use. It's like trying to teach someone to swim by just throwing them in the wate…

you face the exact same problems with coding, arguably more so as the trial and error and debugging process is worse than any proof i’ve ever had to do. if you can’t figure out how to apply basic integration techniques without a teacher formally sitting you down and saying exactly what situations to use each formula in, you haven’t learned shit

Re: Math from Three to Seven

#160

Post by eitally »

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?

I am under the impression that such things do/can exist, but ad hoc. For example, if you were to take extracurricular lessons at a RSM or similar private tutoring business, you could/would probably find a number of similarly inclined teens who might be interested in creating a circle.

Similarly, my experience attending a science & math magnet school in the 90s was that -- basically mirroring my later experience in college -- a subset of the kids taking advanced math classes in high school naturally tended toward hanging out & studying/practicing/researching together.

More formally, there are tons[1] of local, state, regional and national math competitions that target elementary, middle and high school students, and -- just like robotics -- it's up to volunteers (teachers, students, parents) at the school level to decide whether to invest time & resources to create a local team/club.

When I was in school, we had MathCounts teams at younger ages, and Math Olympiad (and Science Bowl & Science Olympiad -- my team made it to the national event in Science Bowl, actually) in high school. I'm under the impression that this is pretty common, at least in urban/suburban areas.

[1] https://artofproblemsolving.com/wiki/index.php/List_of_Unite...

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