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Learning algebra in my 60s

theguardian.com

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Re: Learning algebra in my 60s

#21

Post by jonathanstrange »

inetsee wrote: post #4

In my opinion, nothing can make you smarter. Learning rationalist techniques may make you better at thinking through problems, learning memory techniques like Memory Palace may improve your memory, using learning techniques like Spaced Repetition may help you learn and retain large amounts of information with the minimum necessary effort, but nothing can make you smarter.

I'm pretty sure this is wrong. The brain adapts to whatever activity you do and, as far as I know, is way more plastic than researchers thought decades ago. If you're doing dumb things all the time you're making yourself dumber over time and when you're performing difficult tasks repeatedly and daily your brain adapts to them to be able to solve them easier. I realized that a long time ago in a completely different area, in martial arts. When you start it's extremely hard to follow complex movements shown by other people. Beginners struggle with this a lot. Over the years it's getting easier and easier and you can often grasp complicated movements after seeing them once. I suppose it's the same in dancing and ballet.

The brain adapts to sports, painting, writing poems, or solving complex math puzzles. It just happens that some of these activities are considered smart and also (partly) measured with traditional IQ tests. You can even train to become better at IQ tests if you desire to acquire a completely useless skill set.

Re: Learning algebra in my 60s

#22

Post by sirsinsalot »

mattwilsonn888 wrote: post #8

It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…

I left school at 15, never to return to education, in part because of how maths was taught.

There was never an explanation of the _why_ of things. It was very frustrating, and the teaching was very poor.

I ended up a programmer, in part, because I figured if teachers weren't teaching, i'd teach myself. This has been a good strategy for me, however there's serious holes in my pure maths knowledge.

Re: Learning algebra in my 60s

#23

Post by gavinray »

sirsinsalot wrote: post #22
mattwilsonn888 wrote: post #8

It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…

I left school at 15, never to return to education, in part because of how maths was taught. There was never an explanation of the _why_ of things. It was very frustrating, and the teaching was very poor. I ended up a programmer, in part, because I figured if teachers weren't teaching, i'd teach myself. This has been a good strategy for me, however there's serious holes in my pure maths knowledge.

Lol, I've been kicked out of class for asking the teacher to explain why something works in math here in the US

I think it was long division and lattice multiplication in elementary school

Doing math by drawing numbers in predefined shapes so that it magically worked out was the most ludicrous thing I'd ever seen

"Because that's how it works." Wasn't really a satisfactory answer lol.

Re: Learning algebra in my 60s

#24

Post by 2OEH8eoCRo0 »

gavinray wrote: post #23
sirsinsalot wrote: post #22

Earlier quoted context omitted.

I left school at 15, never to return to education, in part because of how maths was taught. There was never an explanation of the _why_ of things. It was very frustrating, and the teaching was very poor. I ended up a programmer, in part, because I figured if teachers weren't teaching, i'd teach myself. This has been a good strategy for me, however there's serious holes in my pure maths knowledge.

Lol, I've been kicked out of class for asking the teacher to explain why something works in math here in the US I think it was long division and lattice multiplication in elementary school Doing math by drawing numbers in predefined shapes so that it magically worked out was the most ludicrous thing I'd ever seen "Because that's how it works." Wasn't really a satisfactory answer lol.

One of my friends in HS was against calculators, and also very stubborn, and got in trouble for asking how to do sin, cos, tan functions without a calculator.

Re: Learning algebra in my 60s

#25

Post by [deleted] »

auggierose wrote: post #16
mattwilsonn888 wrote: post #8

It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…

Ever heard of new math? https://www.americanheritage.com/whatever-happened-new-math-... I agree with you, especially if you are in your 60s and have a math professor as your teacher, one would think a new math approach works best!

[deleted]

Re: Learning algebra in my 60s

#26

Post by bamboozled »

librarianscott wrote: post #11

Brain games do little for the older mind. You are much better off lowering blood pressure and walking. But, if you insist, read [1]. [1]: https://www.nia.nih.gov/health/cognitive-health-and-older-ad...

Not sure why but this just seems so useless and defeatist. Why is learning new things “brain games”?

Re: Learning algebra in my 60s

#27

Post by k_sze »

The title sounds like a non-question.

I posit that learning anything (even fengshui or astrology), at any age, will make you smarter, as long as you bring a pair of critical eyes with you. Besides learning about the actual “thing” (which you can still fail at the end of the day), you can always introspect to figure out why/how you failed and what your limits are, and then you’ll maybe find closure in saying “I’ve tried. It didn’t work out. There was no 'wasted potential' - the potential was never there to begin with. And I’m a wiser person now.”

Re: Learning algebra in my 60s

#28

Post by tankenmate »

zozbot234 wrote: post #14
mattwilsonn888 wrote: post #8

It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…

There's nothing wrong with practicing formal manipulations: these are just "the rules of the game" and are 100% rigorous. Now, if you want to know "why these rules and not others?", they just happen to follow from basic properties like associativity, commutativity, distributivity etc. There's not much else to it. The author's "misintuition" of variables is not critically important; variables can literally just be arb…

The one thing that gave me deep insights into algebra was discovering Peano's axioms.[0] I had been taught the associative, transitive, and distributive laws in 6th grade at school, but discovering the axioms really opened my eyes in high school; especially under what circumstances they could and couldn't be applied. The last penny to drop was to realise that where you have numbers (e.g. x) you could also substitute formulas, provided you adhered to the rules of when the axioms could be applied. Obviously for similar reasons this also applies to matrices (e.g. when can matrices be inverted (additive and multiplicative), and hence why matrix addition is commutative, but multiplication is not).

Don't get me started on subtractive anti-commutativity vs divisive anti-commutativity.

Another thing that bothers me is when helping the my own kids with maths I came to realise that their teachers don't know the Peano axioms, so how the heck can my kids even stand a chance at properly learning algebra.

[0] https://en.wikipedia.org/wiki/Peano_axioms

Re: Learning algebra in my 60s

#29

Post by nobodywasishere »

2OEH8eoCRo0 wrote: post #24
gavinray wrote: post #23

Earlier quoted context omitted.

Lol, I've been kicked out of class for asking the teacher to explain why something works in math here in the US I think it was long division and lattice multiplication in elementary school Doing math by drawing numbers in predefined shapes so that it magically worked out was the most ludicrous thing I'd ever seen "Because that's how it works." Wasn't really a satisfactory answer lol.

One of my friends in HS was against calculators, and also very stubborn, and got in trouble for asking how to do sin, cos, tan functions without a calculator.

Good old taylor series, of course!

Re: Learning algebra in my 60s

#30

Post by zxcvbn4038 »

I have to sit on my hands and not help my son with his math homework. The way they have taught him to do math is great - he can solve just about anything in his head - but I can’t help him without introducing him to the old slow way I learned of doing everything.
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