there are many who could handle being introduced to some basic concepts from calculus and quantum mechanics at 12 years old.
Here we get into a debate over "basic concepts." I completely agree that some of the ideas from calculus can be taught much earlier: I self-taught intro calc when I was 13 or 14. On the other hand, part of my disagreement with this thread is what I see as a problem in our education system.
See, you can't learn what I would call "the basic concepts of quantum mechanics" until you've already learned A LOT of calculus. Specifically, basic quantum mechanics boils down to solving differential equations, and applying appropriate boundary conditions. One of the problems with the way I was taught quantum is that we were taught how to solve specific problems, but not how to approach these problems in general.
Why were we taught that way? Because the pressure to get us (as college sophomores) through a basic class on quantum denied us the opportunity to first learn differential equations.
If you're a wizard at solving DiffEqs, you'll find the math behind an intro to quantum class easy, and only the physical solutions would matter. Toss in a solid grasp of linear algebra, and you could easily cover the 2 semesters of quantum courses I took in one semester, with time to spare. What's more, you'd probably actually UNDERSTAND it, instead of just cramming enough before the exams.
Currently, we don't expect our undergrads to understand it. Understanding is supposed to come during grad school, when you do all this stuff again (or so I've heard from dozens of professors and grad students to whom I've complained about the fact that I don't feel like I understood a lot of the details from my undergraduate education). But in general, you can only expect to make important contributions when you grok those proverbial shoulders you're standing on, I would say.
but there's probably a lot more we could do to help smart kids learn at something like their full capability
I'll agree completely on that. But there's also a difference between offering enrichment for the rare gifted student and providing an education for the average student. For me, offering self-paced study of math was a great way to make sure math remained a challenge to me. The program only failed when, after buzzing through 3 textbooks, the school didn't offer anything else for me to do for a little over a year. On the other hand, that's an educational design which obviously will NOT work for everyone.
First, I'm sorry that your program was so slow. Mine was not: multiplication began in second grade, and the brilliant idea of "self-paced math" got me starting so-called "pre-Algebra" at the end of 4th grade. Then the system failed, but in any case, I was certainly not doing multiplication tables in grade 9.
The issue is that there is a reason that curricula (math in particular) are structured as they are. You know when something that just didn't make sense for the longest time suddenly clicks? That comes from a combination of age/development and exposure to ideas. The current math educational system is designed according to an "expected" profile of brain development, providing the new ideas when the student is expected to be ready for them. The accuracy of the current expectations are fair game for debate, but I think that your compression vastly overestimates the potential of the average 8 year old.
Finally, for those who do want more, you never "have to wait" until your classroom offers the material. In the USA, at least, public libraries are excellent for self-teaching. (In France... well, sneak into university libraries. No one cares.) Structuring mainstream education to challenge the highest achievers guarantees the failure of the majority.
If we had any brains in our heads, we'd be exposing 8-12 year olds to ground breaking work, when their brains are still maleable.
Right. And find me a 12 year old who can understand recent groundbreaking work. Let's take density functional theory, for example (part of the 1998 Nobel Prize in Chemistry, IIRC). I've been working in theoretical chemistry since 2001. I'm about to start my PhD, and I still don't fully understand DFT. Do you know many 12 year olds who do?
I'm much more productive (at this point in my life, at least) with a keyboard under my hands than with a pencil in my fingers.
I can understand this, but how sure are you that your productivity would transfer to the tiny keyboard the post describes? I would think that it has more to do with "what you're used to." I'm most productive (for most things) at my laptop keyboard (which I'm using now.) I'd rather switch to pen and paper than either a tiny keyboard like the author wants, or, for that matter, to a typewriter. For me, it's not the keys, it's the overall feel.
Of course, it's also activity-specific: I can't use Maple on an American keyboard, nor can I program C on a French keyboard. Just a question of where I learned to do what.
A lot of the current applications for Google Maps (like this one) [chicagocrime.org] don't work in Safari.
Erm, that one works for me in Safari 1.3. Of course, your link tells me that I've been a "naughty slashdotter," but that has nothing to do with Safari!
Sounds like the first computer virus from what I remember. The one where some repair shop in India had the virus lock the user out of the system. It kindly displayed an ad for the repair shop that said they could fix it though.
Software writers, not repair shop. Pakistan, not India. Not the first virus. It was intended to prevent piracy, and wasn't at all intended to be a "ransom."
That's the short version of the story. "Welcome to the Dungeon. Beware of the VIRUS.";-)
Slashdot Mirror
Here we get into a debate over "basic concepts." I completely agree that some of the ideas from calculus can be taught much earlier: I self-taught intro calc when I was 13 or 14. On the other hand, part of my disagreement with this thread is what I see as a problem in our education system.
See, you can't learn what I would call "the basic concepts of quantum mechanics" until you've already learned A LOT of calculus. Specifically, basic quantum mechanics boils down to solving differential equations, and applying appropriate boundary conditions. One of the problems with the way I was taught quantum is that we were taught how to solve specific problems, but not how to approach these problems in general.
Why were we taught that way? Because the pressure to get us (as college sophomores) through a basic class on quantum denied us the opportunity to first learn differential equations.
If you're a wizard at solving DiffEqs, you'll find the math behind an intro to quantum class easy, and only the physical solutions would matter. Toss in a solid grasp of linear algebra, and you could easily cover the 2 semesters of quantum courses I took in one semester, with time to spare. What's more, you'd probably actually UNDERSTAND it, instead of just cramming enough before the exams.
Currently, we don't expect our undergrads to understand it. Understanding is supposed to come during grad school, when you do all this stuff again (or so I've heard from dozens of professors and grad students to whom I've complained about the fact that I don't feel like I understood a lot of the details from my undergraduate education). But in general, you can only expect to make important contributions when you grok those proverbial shoulders you're standing on, I would say.
but there's probably a lot more we could do to help smart kids learn at something like their full capability
I'll agree completely on that. But there's also a difference between offering enrichment for the rare gifted student and providing an education for the average student. For me, offering self-paced study of math was a great way to make sure math remained a challenge to me. The program only failed when, after buzzing through 3 textbooks, the school didn't offer anything else for me to do for a little over a year. On the other hand, that's an educational design which obviously will NOT work for everyone.
The issue is that there is a reason that curricula (math in particular) are structured as they are. You know when something that just didn't make sense for the longest time suddenly clicks? That comes from a combination of age/development and exposure to ideas. The current math educational system is designed according to an "expected" profile of brain development, providing the new ideas when the student is expected to be ready for them. The accuracy of the current expectations are fair game for debate, but I think that your compression vastly overestimates the potential of the average 8 year old.
Finally, for those who do want more, you never "have to wait" until your classroom offers the material. In the USA, at least, public libraries are excellent for self-teaching. (In France... well, sneak into university libraries. No one cares.) Structuring mainstream education to challenge the highest achievers guarantees the failure of the majority.
Right. And find me a 12 year old who can understand recent groundbreaking work. Let's take density functional theory, for example (part of the 1998 Nobel Prize in Chemistry, IIRC). I've been working in theoretical chemistry since 2001. I'm about to start my PhD, and I still don't fully understand DFT. Do you know many 12 year olds who do?
I can understand this, but how sure are you that your productivity would transfer to the tiny keyboard the post describes? I would think that it has more to do with "what you're used to." I'm most productive (for most things) at my laptop keyboard (which I'm using now.) I'd rather switch to pen and paper than either a tiny keyboard like the author wants, or, for that matter, to a typewriter. For me, it's not the keys, it's the overall feel.
Of course, it's also activity-specific: I can't use Maple on an American keyboard, nor can I program C on a French keyboard. Just a question of where I learned to do what.
Eep! nope. I was just checking to see where, within a short walk of the UChicago campus, homocides tended to occur. Oops, my bad!
Erm, that one works for me in Safari 1.3. Of course, your link tells me that I've been a "naughty slashdotter," but that has nothing to do with Safari!
Point may be right; example isn't.
I think you mean the Pakistani Brain Virus.
Software writers, not repair shop. Pakistan, not India. Not the first virus. It was intended to prevent piracy, and wasn't at all intended to be a "ransom."
That's the short version of the story. "Welcome to the Dungeon. Beware of the VIRUS." ;-)