[ExI] chain rule

[spike]

-----Original Message-----
From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of BillK
Sent: Friday, May 20, 2016 12:02 PM
To: ExI chat list <extropy-chat at lists.extropy.org>
Subject: Re: [ExI] chain rule

On 20 May 2016 at 19:25, spike  wrote:
<big snip>
>>... Conclusion: Sal Khan has offered a free ticket out of the poverty 
> trap, for anyone who will stretch out and grab it...


>...Spike, I appreciate your enthusiasm for educating your son and applaud it.
(So please don't take my comments as criticism)...

Hi BillK, I didn't take this as criticism at all.  On the contrary, it supports where I go with this next.



>...The Sal Khan Academy is one extreme.
Looking at education from the opposite extreme, I have read articles worrying about smartphones causing the dumbing-down of the population.
With a smartphone, nobody needs to remember or know much at all.
Google gives you any info you need. Apps do calculating for you, give directions, organise schedules, buy stuff, etc.
That's why the younger generation are addicted to gossiping on their smartphones.
There's not much else left for them to do.  BillK

_______________________________________________

BillK, I left everything in there again rather than trimming your post, since you know this is a topic near and dear.

What we are seeing here is very important.  The cell phones and the OK Google functions are exactly why we are facing an enormous revolution in education, a fundamental rethinking of all our traditional notions, because technology has handed us the option of externalizing knowledge.  

Plenty of us here are engineers and tech types so you took calculus in college, and somewhere along the line you were asked to do the more esoteric stuff such as integration by parts.  OK cool, you did it, passed the test, congratulations, can you do it now?  If the answer is no, I am not criticizing anyone here.  I can, but I am a hobbyist in that kind of stuff.

OK now, engineers and scientists (but not math teachers) this next question is for you please:  since you took and passed that test, have you ever integrated by parts (or did partial fraction decomposition, or did a LaPlace transform or any of that cool stuff) in your job, or even as a real-life analysis, even once, or used in the line of duty any of that stuff you learned how to do?  No criticism, I haven't either.  That isn't how real-world tasks are done, and this is remarkable, considering I was the office math geek, so when the other engineers needed some oddball math skill they knew who to see.  Oh I loved that.  However, in all those years in a really techy office doing really mathematical stuff being the local go-to geek, I never did any of that cool stuff in the line of duty not even once.

OK then.  Why do we teach it?

Next: you are aware (ja?) that you don't even need to know how the hell to integrate?  You can pull up Google, put in the search window Integrate {yakkity yak and bla bla} and Google will return the integral of yakkity yak and bla bla.  

If you are out somewhere, you can pull up Google on your phone, and you guys with OK Google, pull them out and try it right now.  OK Google, then Integral of {insert your favorite function}.  In some cases it will not only give you the answer, but Miss Google will tell it to you in her beautiful voice (and isn't that a turn-on when girls talk math? (oh my (it works on me even when she mispronounces the function names (and is rather hilarious (such as calling sine sin and cosine koss and secant seck (it is still major boner material (yes I know I am a sicko (but I like me that way.)))))))

BillK, how does this impact what is worthwhile to teach calc students?  Are we finally safe to go ahead and admit that we are asking them to struggle to master something they will neeeeever need in real life, unless they are math professors struggling to perpetuate the illusion that the math professor is at that moment struggling to perpetuate, hoping to continue perpetuating that same illusion perpetually?

Think on it.  I will even give you time, since I am heading out on a weekend camping trip with no phone, no lights, no motorcars, not a single luxury.  Nature, red in tooth and claw, that sorta thing.

Note in particular BillK, you cited the case of video gaming cell phone zombies, attention spans already dwindled beyond hope of mastering the more subtle arts and skills in Sir Isaac Newton's queen of mathematics.  I agree, but I am asking the next question.  Given we are evolving into a species with diminished attention spans, we already understand that some skills do slip away, and new opportunities present themselves.  How do we design the curriculum to be suitable in a world where integration techniques are irrelevant, where every integral in the table is as close as our cell phone, where we can externalize knowledge but still cannot externalize reasoning.

As Adrian asked and I paraphrase: what if we can use current tech, some of the students can master the material in a traditional Bachelor's Degree curriculum by the time they are about 14, and they can sit down in front of a GRE and prove it?  What if the fraction who can do that is 10%?  Is the traditional bachelor's degree still meaningful?  Or do the cap and gown traditionalists get handed a diploma with a snarky "Are you as smart as an 8th grader?"  Is it still worth it for the rest of the students to shoulder a debt bigger than their own parents' mortgage to pay for that degree?  What if the 8th grader still outscores the traditional robed Pomp and Circumstancers?  Wouldn't employers really prefer the 8th grader with that GRE-proven skill level anyway, reasoning she would be cheaper and more adaptable, as well as smarter?

You guys who have known me for a couple decades know I am always screwing around here on ExI chat, but I am not on this topic.  Parenthood has a way of sobering a person, and finding oneself a parent of one with special talents can be especially sobering.  BillW, ja?

You guys with the startups who hire people, your thoughts and opinions are warmly invited, requested please.

Both Bills, Adrian, Anders, Rafal, anyone else following this perplexing and critically important thread, with these considerations in mind, what should we be teaching the next generation, when, how and why?  Do show your work please.

spike