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Learning algebra in my 60s

theguardian.com

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Re: Learning algebra in my 60s

#61

Post by jrmg »

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…

This is addressed in the article - just after the ‘(7/2) / 2 = 7’ misunderstanding:

[I called] Deane Yang, my friend who is a mathematics professor at NYU.

“The way you remember procedures is you remember why,” he said.

“Because?”

“Because people learn math as a collection of procedures,” he said. “When things get difficult, they’re lost, and math becomes religion class. The teacher says what’s right and wrong, and for all you know math came out of the sky, and some prophet told you how to do it, and it’s just blind belief then.

Interesting that he wants to know _why_ knowing why helps too!

I do wonder if this is covered more in-depth in his book.

Re: Learning algebra in my 60s

#62

Post by rawgabbit »

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 agree. He tried to memorize his way through Algebra. It is hard to understand his mindset because of the stream of consciousness writing. But he appears to be confused with definitions versus equality. E.g., By definition (a+b)^2 is (a+b)(a+b). It is not just "equal".

Re: Learning algebra in my 60s

#63

Post by wawjgreen »

My litmus test of someone being intelligent or not--among other such tests--is what they say about Shakespeare. This might anger the Brits, but Shakespeare is garbage--and the guy says: "I read .... most of Shakespeare."

One famous guy lambasting Shakespeare (Tolstoy) was only marginally smarter, because according to his "Confessions", he read it many times over (incl. in English) and STILL could not find any artistic value in it. I could not have put up with that--for me, it was the first few pages that I knew this was a waste of time. You don't need to drink the whole festering junk of a decayed meal to know it is not edible.

He also claims he wants to test the limits of his intelligence by tackling Mathematics once again--implying wrongly, as it were, that math education is fine and it is our brains that are incapable of learning. Not so fast: how am I less intelligent if the bozo teaching me does not know how to teach maths?

Citing Carl Jung does not help either, though he namesdrops to mitigate the shame of not being able to do maths...Jung was not as bright as is commonly believed as well. He once claimed that UFO's were all imaginary-- a sweeping generalization by someone claiming to be scientist-- whereas I for sure know that UFO's are real for I have seen one and to prove that I wasn't seeing things, I had a camcorder ready which recorded the space-ship going vertically up very slowly. I have lost the video though but it certainly happened 20 years ago and I still remember it.

EDIT: I see I have touched quite a few nerves.

Re: Learning algebra in my 60s

#64

Post by stinkytaco »

zxcvbn4038 wrote: post #30

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.

I really liked the Common Core early math curriculum. My daughter was taught to do calculations the way I had to come to them myself later on: break the problem apart into easier pieces. A simple example: If you are adding 73 and 29 break it to 70+20 and 3+9. Quick calculations takes the burden off on harder problems later on. Also, she learned to round and estimate and they did lots of practical math applications -- especially in probability -- so she's learned to think of math in a "common sense" way, for lack of a better word. It's easier for her to look at an answer and say "wait, that doesn't make any sense considering the givens".

Re: Learning algebra in my 60s

#65

Post by SketchySeaBeast »

JKCalhoun wrote: post #37

"Sometimes I dreamed that there were numbers falling from the sky into chasms I couldn’t see the bottom of." Reminds me of the night terrors I had when I was younger. I remember often having dreams that involve the unknowable, unseeable or in some other way were impossible for my finite mind to comprehend. In the worst of those nightmares I was left shaken with fear — feeling as though I had peered from just over the…

As a child I experienced sleep paralysis where I would hallucinate shapes of impossible dimensions, both simultaneously incredibly large and incredibly small, hanging over my bed and leaving me to question the nature of everything. Looking back on it I can't even begin to understand why I dreamed those dreams.

Re: Learning algebra in my 60s

#66

Post by auggierose »

Benobba wrote: post #48
bryanrasmussen wrote: post #20

Earlier quoted context omitted.

sure https://www.youtube.com/watch?v=UIKGV2cTgqA I used to listen to that several times a day when I was a kid.

I was disappointed by this. It’s just a caricature of only one side - It’s the easiest form of come. Almost things that are innovative will not be best on the first iteration. Why not offer (funny) ideas on how to improve it?

You could read the article I linked, if you want to know why new math is problematic. It's not that easy to improve things. And who said that comedy needs to be balanced?

Re: Learning algebra in my 60s

#67

Post by WalterBright »

mmmpop wrote: post #50
WalterBright wrote: post #42

Earlier quoted context omitted.

When I remarked yesterday that engineering curriculums that emphasized memorization of engineering formulas rather than understanding how to derive them were inferior, I was dismissed as arrogant and egotistical :-)

By whom? An instructor/professor or a student/engineering graduate?

It's yesterday in my comment history, you shouldn't have any trouble finding it. I prefer people interpret it for themselves as I said my piece in it.

Re: Learning algebra in my 60s

#68

Post by WalterBright »

gamerDude wrote: post #57
WalterBright wrote: post #42

Earlier quoted context omitted.

When I remarked yesterday that engineering curriculums that emphasized memorization of engineering formulas rather than understanding how to derive them were inferior, I was dismissed as arrogant and egotistical :-)

I work with K12 schools in the U.S. and one of our really sad stories is how a calculus students failed to solve a "A t-shirt that costs $15 is 20% off today. How much does it cost after the 20% discount (don't include tax)?" They responded, "I don't remember the formula for a sale". Only knowing formula's is terrible, it makes knowledge super fragile. So, I for one support your idea of emphasizing understanding over…

I feel that way about the % key on calculators that also have a / key. If you need a % key, you have no business using one :-/

Re: Learning algebra in my 60s

#69

Post by jonathanlydall »

jjice wrote: post #54
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…

> ...still ended up going down an execution rather than concept focused route. This is something that made me really disappointed when I realized it in school. It was always a step by step process taught to me, and I loved math. I took my AP Calculus class in my senior year of high school and my teacher (fantastic man) showed us how the formula for a derivative is derived. I was blown away. We had just learned and it…

When learning trigonometry in high school (in South Africa, ‘98), we were taught how to use the correct operation for a particular situation and then use a calculator to get the correct answer.

I asked the teacher where the numbers which were spat out by the calculator came from and was only told “in my day we didn’t have calculators and had to lookup the answers from a table on a book!”.

Which was such a thoroughly disappointing response and I hated trigonometry since it was mostly about memorisation rather than applying logic from understanding.

About 10 years later I did a math course through the UK’s Open University and the text book taught trigonometry through explaining the unit circle.

It made me so happy to finally understand and see the actual logic as opposed to punching numbers into a calculator, but I was also sad and a bit upset the unit circle was not taught in high school.

Re: Learning algebra in my 60s

#70

Post by dkarl »

thesuitonym wrote: post #49
dkarl wrote: post #47

Earlier quoted context omitted.

> this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions Leaving aside that you concluded this from a one-sentence story about solving a single problem, it's funny that the idea that a "clear understanding of fractions" can make the skills easy to learn is something that virtually every trained teacher has believed for the last (I'm not sure how many) d…

I'll start my reply with this: I'm not a teacher, nor am I an understander of maths, but whenever I talk to teachers at any level, and especially mathematics teachers, they lament that they want to teach differently, but due to time constraints, or predetermined lesson plans, or any number of reasons, they simply can't. They have to teach in a way that gets students enough knowledge to pass the test, but only those t…

You are saying some things that are guaranteed to generate skepticism. First, that the great power of this teaching method only manifests under circumstances that very few people get to experience. Second, that concepts make skills "trivial" and "intuitive" but testing skills prevents teachers from teaching concepts.

Both of those statements call into question the effectiveness of what you're promoting.

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