The author also wrote this excellent article:
https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
Learning algebra in my 60s
41–50 of 158 posts
Re: Learning algebra in my 60s
#42It'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…
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 :-)
Re: Learning algebra in my 60s
#43Earlier quoted context omitted.
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!
That's certainly the hard way!
There are shortcut formulas, and before calculators a lot of calculations were done using drafting equipment.
Re: Learning algebra in my 60s
#44It'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…
Right. >Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. This is so true. I was exactly like the author. I could not understand any math beyond algebra. Trigonometry was way beyond my ability. But one day, I found an old trig book lying around when I went…
I've had a couple moments like that in my education. I've described it as stumbling about in a dark room, and suddenly the lights came on. One was when I struggling to learn how a computer worked. It was just a collection of arbitrary facts to me, more and more, until suddenly -- shazaam! And the rest was obvious and trivial.
Thanks for your version. I enjoyed reading it!
Re: Learning algebra in my 60s
#45The 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 tri…
The title is there to get you to click, there's not much need to analyze it. The article has little to do with it.
This reminds me of On Cinema At the Cinema when Gregg Turkington, as a parody of the film critic persona, often bases his critical opinion of the films based on what he thinks of the title and runtime.
Re: Learning algebra in my 60s
#46It'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.
Ditto. I've got more understanding of Math under mathisfun.com over months than in 4 years of edu in Spain akin to up to 10th grade in the US.
Contextless Algebra is not intuitive.
Re: Learning algebra in my 60s
#47It'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 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) decades and yet nobody alive today is reporting that it happened that way for them.
It's possible that every future teacher getting certified to teach politely pretends to believe these things, but secretly wishes to spend their career torturing children, so they abandon the teaching of concepts as soon as they step into a classroom. Or maybe they go through the motions of teaching kids to understand the meaning behind fractions, but they intentionally do it wrong and laugh with each other about it in the teacher's lounge. That's one explanation.
Another explanation is that this opposition of "understanding" to "execution" and "concepts" to "skills" is an incomplete way of looking at things that has limited application to how people learn but isn't a panacea, and people still struggle with skills no matter how much you try to prepare them with concepts.
I think it does a vast disservice to anyone when we assume that their job performance would be radically improved by the first cliché we ever learned about their field.
If the idea is so magical, and we know that it has permeated the field of education for generations, where are the generations of students who remember math as being "trivial, intuitive, beautiful, clever?" Different educational philosophies have come and gone, emphasis has shifted, so where's the generation of parents saying math was much easier for them than for their kids? Where's the PTA meeting where all the parents say, "We think there's something wrong with the way math is taught here, because we all remember fractions being trivial and intuitive, but our kids are finding them hard?"
Maybe teachers aren't such idiots that they consistently overlook the value of the most cherished and shopworn truism their field has produced in its history?
Re: Learning algebra in my 60s
#48Earlier quoted context omitted.
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!
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?
Re: Learning algebra in my 60s
#49It'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 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 that seem to have a natural aptitude end up really learning anything. The rest discard the information as soon as it's no longer necessary.
I don't think it's a disservice to teachers to say it's a better way of teaching, because they say it themselves. It's just a model that only really works one on one. It can't be done in a room full of 30 bored children, and especially in a room of 400 university sophomores who are ready to get out of class to go to a party.
Re: Learning algebra in my 60s
#50It'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…
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?