> It might sound bizarre and weird, but I met more than once person, that did their best to learn, and were intelligent with many other things (one of these persons had a degree in law, another in international relations, and was doing a masters in international law), yet could not do 29/3 without a calculator...
There are multiple ways to learn even something like arithmetic.
Some people can naturally juggle a lot of numbers in their head and can basically brute force problems.
Others can break problems down into component pieces, work out each individual piece, and reassemble them into an answer. This requires a different type of mental juggling than the above.
And then there are those who just have to memorize a lot of problems.
When I was in school, we started off with memorization (multiplication tables and such), which requires a large time investment that I am sure many students did not make. (My peer group tended to stay inside during recces and practice our multiplication!) After that I think we were supposed to "naturally" progress to breaking problems down into parts, but that was never really covered all that well. From what I understand, other countries make this part of learning arithmetic very explicit.
A good deal of this involves training ones working memory. Right at the end of college my working memory for numbers was amazing, I could do 3 digit divides in my head, and at one point I could even do a binary search to find logarithms down to a decimal place or two!
But as with many other skills, they degrade from a lack of use.
29/3? I have a minor on mathematics. If you give me that problem, I'd honestly type "win-r calc 29/3 enter".
Now days I have problems just adding up large strings of numbers, I play a bunch of D10 games and I have to actually do math rather than it coming to me instantly!
> People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other,
Well yes of course, but we choose what to specialize in! I really do believe that anyone can learn math if they put the time and effort into it. My math classes took 2-3 hours a day of studying a good 4 days a week in order for me to completely grasp the concepts being taught.
Repetition of hundreds of problems, as much as I hated it, was the only real way to burn technique into my head, and even then most of those techniques have fallen by the way side! A few still bounce around inside my skull, but it has been a good 8 years since my last math class, so the amazing feats of mental gymnastics I could perform are long gone.
On the flip side, ask me to design a test infrastructure for code sometime, and I'm right on it! How about a custom memory allocation scheme? No problem! Specialization indeed.
There are multiple ways to learn even something like arithmetic.
Some people can naturally juggle a lot of numbers in their head and can basically brute force problems.
Others can break problems down into component pieces, work out each individual piece, and reassemble them into an answer. This requires a different type of mental juggling than the above.
And then there are those who just have to memorize a lot of problems.
When I was in school, we started off with memorization (multiplication tables and such), which requires a large time investment that I am sure many students did not make. (My peer group tended to stay inside during recces and practice our multiplication!) After that I think we were supposed to "naturally" progress to breaking problems down into parts, but that was never really covered all that well. From what I understand, other countries make this part of learning arithmetic very explicit.
A good deal of this involves training ones working memory. Right at the end of college my working memory for numbers was amazing, I could do 3 digit divides in my head, and at one point I could even do a binary search to find logarithms down to a decimal place or two!
But as with many other skills, they degrade from a lack of use.
29/3? I have a minor on mathematics. If you give me that problem, I'd honestly type "win-r calc 29/3 enter".
Now days I have problems just adding up large strings of numbers, I play a bunch of D10 games and I have to actually do math rather than it coming to me instantly!
> People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other,
Well yes of course, but we choose what to specialize in! I really do believe that anyone can learn math if they put the time and effort into it. My math classes took 2-3 hours a day of studying a good 4 days a week in order for me to completely grasp the concepts being taught.
Repetition of hundreds of problems, as much as I hated it, was the only real way to burn technique into my head, and even then most of those techniques have fallen by the way side! A few still bounce around inside my skull, but it has been a good 8 years since my last math class, so the amazing feats of mental gymnastics I could perform are long gone.
On the flip side, ask me to design a test infrastructure for code sometime, and I'm right on it! How about a custom memory allocation scheme? No problem! Specialization indeed.