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In Math Cram Sessions, Solving for Why

nytimes.com

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Re: In Math Cram Sessions, Solving for Why

#61

Post by TangoTrotFox »

tesin wrote: post #4
rb808 wrote: post #3

A good example of why well educated parents is more important than getting into the "the best schools".

Isn't that just a matter of chicken and the egg timing tautology? The parents are well educated presumably because they went to good schools.

And so it's turtles, all the way down?

I think a good education is more about the student than the university. The reason for the strong correlation to the contrary is because good universities get to hand pick from those overachievers whom would achieve with or without said university. And that character development happens long before one's applying to universities.

That said a top university, its resources, and atmosphere of being surrounded by other top students, certainly helps foster even more success - but I expect if you take the average merit admitted MIT student and transplanted them into Party State U after 4 years you'd still find an extremely 'well educated' individual. By contrast, transplant your average Party State U student into MIT and you'd find a dropout.

Re: In Math Cram Sessions, Solving for Why

#62

Post by abecedarius »

Koshkin wrote: post #47
ummonk wrote: post #17

Earlier quoted context omitted.

You can just do a lot of multiplications, and let your brain cache the results over time.

Spending time memorizing the multiplication table, then, is more efficient on both accounts: you will not need to do "a lot of multiplications" to begin with, and it takes less time for your brain to "cache the results".

Maybe that works best for some people, but as a kid I didn't do it. I used a printed multiplication table while tackling some more-interesting problems[0], and let the table soak in as a byproduct. It went quickly and did not turn me off on math for life. Paul Lockhart in Arithmetic also recommended this.

[0]: Multiplying two-digit numbers by one-digit, and that sort of thing. Lockhart had more artistic pursuits in mind.

(An obvious reason this might not apply: I was more talented than my grade-school peers. But most kids would learn arithmetic better if not forced to before they're ready, and then the talent difference would matter less.)

Re: In Math Cram Sessions, Solving for Why

#63

Post by chrisweekly »

tsumnia wrote: post #60
chrisweekly wrote: post #13

Earlier quoted context omitted.

Great post. FWIW in discussing this topic I've heard and now adopted the term "(in)numerate" vs "STEM-(il)literate" -- though the latter might be intended to be broader in scope?

As Zeebrommer mentioned, I'd steer clear of this thinking. Carol Dweck's entire research has been on "fixed" and "growth" mindsets, and their impact on people's performance. Instructors that believe someone is or is not an "X person" have a negative impact on students. That is, if I believe in the idea that there are STEM-illiterate and STEM-literature people, why should I both helping someone who is STEM-illiterate?…

I think you've misunderstood me or conflated my comment with someone else's; mine said nothing about fixed vs growth mindset. The term "innumerate" -- just like "illiterate" -- indicates the current state of a person's abilities, not some fixed or inherent trait. The remedy is education.

Re: In Math Cram Sessions, Solving for Why

#64

Post by zodPod »

thomasfedb wrote: post #20
ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

Private maths tutor here — what I find most gratifying about tutoring is revealing to my students how much they already know. Often they'll know that they know the answer, but they don't realise that they also know why it's the answer!

How much are your services? I'm an out-of-school adult that never really grasped math but hate that I don't know more about it to this day. Just wondering what kind of range I'd be looking in to just get some explanations or something. I don't currently have any specific questions though.

Re: In Math Cram Sessions, Solving for Why

#65

Post by richdougherty »

ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

When I was 16/17 I did private maths tutoring for some of my classmates. As a tutor I enjoyed the conversations we had about 'why'. These people were missing a lot of context about why they were even doing anything, so the steps were all mechanical and it was hard for them to do anything beyond what they'd memorised. Conversations about the material, outside what's strictly required to solve a problem, really work wonders.

As for teaching outside the comfort zone, I actually think that's a great opportunity. It puts you in the same place as your student so you can model the meta-cognitive skills of learning, curiosity, etc. You can even demonstrate how to 'fail' at something with grace - and give the student the opportunity to be better than their teacher at something!

Re: In Math Cram Sessions, Solving for Why

#66

Post by jgamman »

tsumnia wrote: post #60
chrisweekly wrote: post #13

Earlier quoted context omitted.

Great post. FWIW in discussing this topic I've heard and now adopted the term "(in)numerate" vs "STEM-(il)literate" -- though the latter might be intended to be broader in scope?

As Zeebrommer mentioned, I'd steer clear of this thinking. Carol Dweck's entire research has been on "fixed" and "growth" mindsets, and their impact on people's performance. Instructors that believe someone is or is not an "X person" have a negative impact on students. That is, if I believe in the idea that there are STEM-illiterate and STEM-literature people, why should I both helping someone who is STEM-illiterate?…

aside: Sisk et al (To What Extent and Under Which Circumstances Are Growth Mind-Sets Important to Academic Achievement? Two Meta-Analyses DOI 10.1177/0956797617739704) looked at >450,000 students and found little or no effect size for this approach.

standard primary literature caveats etc and where it is/is not applicable but this does put 'growth mindset' on the back foot.

Re: In Math Cram Sessions, Solving for Why

#67

Post by thomasfedb »

zodPod wrote: post #64
thomasfedb wrote: post #20

Earlier quoted context omitted.

Private maths tutor here — what I find most gratifying about tutoring is revealing to my students how much they already know. Often they'll know that they know the answer, but they don't realise that they also know why it's the answer!

How much are your services? I'm an out-of-school adult that never really grasped math but hate that I don't know more about it to this day. Just wondering what kind of range I'd be looking in to just get some explanations or something. I don't currently have any specific questions though.

~150 AUD/hr for in-home

That's a fair bit above the regular rate though, you can get a decent tutor for less.

Re: In Math Cram Sessions, Solving for Why

#68

Post by jgamman »

tesin wrote: post #53
saagarjha wrote: post #31

Earlier quoted context omitted.

No, I think you’re getting the relation backwards. Many parents who were well educated have the opportunities to send their children to good schools, regardless of whether they went to a good school themselves, because they realize that it makes it easier to be well educated there.

How would someone be well educated at a bad school? I feel like that loses any reasonable definition of good.

the best teacher(s) in a 'bad' school overlap with the worst teachers in a 'good' school. Keep in mind that there is a relationship between student and teacher and that clicking with one teacher isn't guaranteed or that after a year of growing up, you might click with a teacher you didn't get on well with the year previous.

Re: In Math Cram Sessions, Solving for Why

#69

Post by abdullahkhalids »

jordigh wrote: post #40

> A ball is thrown off a building at a speed of 15m/s and at 30 degrees to the horizontal. If the building is 100m tall, how far from the base of the building will the ball land? g=9.8m/s² 280.17 metres, right?

Nope. That's too far. I am too lazy to write out the equations, so we can use an app such as this http://www.walter-fendt.de/html5/phen/projectile_en.htm to find out that it falls 69.5 m from the base of the building.

Re: In Math Cram Sessions, Solving for Why

#70

Post by sdenton4 »

somethingroma wrote: post #27
PascLeRasc wrote: post #24

Earlier quoted context omitted.

The best is the 9's table, how all the digits add up to 9. My mom's an elementary teacher and there's always a few third graders who figure that out on their own and love it.

Additionally 9 * n = [n-1, 10-n] for n = 2-11; where n-1 is the digit in the 10's place and 10-n in the single place. This just an aesthetic curiosity. I know the pattern continues for larger n I've just never bothered to generalize it. Also never compared it to other bases.

It's not an aesthetic curiosity at all! 10 is equal to 1 mod 9... So suppose X is written in base 10 (a0 * 10^0 + a1 * 10^1 + a2 * 10^3 +...) and you want to find X mod 9. Then all of the 10^k's are just 1 (mod 9), so you just get the sum of the digits.

So if X is divisible by 9, then the sum of the digits (mod 9) is zero.

Same works for 3 (x is div by 3 iff the sum of the digits id divisible by 3). And 11 gets an /alternating/ sum of the digits, since 10 is -1 mod 11...

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