81–90 of 175 posts
Spelling too is also memorization before higher concepts like grammar or essay construction. Perhaps its perceived as easier than math because it has a natural cognitive map.
"we need to provide our children with better cognitive maps of the subjects we want them to learn" This style of learning works for everyone -- including children. There is a growing community of people sharing educational, animated gifs on Reddit that recognizes the value of visual learning. Popular subreddits include: - /r/educationalgifs - /r/mechanical_gifs/ - /r/GifRecipes/
I'm not sure that is what he means with a "cognitive map". I believe, he means that children need a better understanding of what is possible to do with, and what the point is with math.
Click on "Topic map" in the header — it is a real domain-expert-created topic map of many areas of math and science.
It's a free, interactive, crowd-sourced learning platform that does exactly this, especially for math — the founder is lead Coach of the USA International Mathematical Olympiad team, and a math professor at CMU.
f/d: I interned there last summer.
It's difficult to make initial progress and you see no path, with little rewards along the way, to get good at it. What's the reward at the end?
Math doesn't have a path and there's no "cool" prize at the end, for most people.
Computer programming has a path with lots of little rewards and "cool" prizes at the end. So, you get lots of self-taught programmers.
Create an interesting path for math with lots of "rewards" along the way and many more people would be interested.
Earlier quoted context omitted.
I don't know, I always remembered things like 6+7 = 13 and if numbers I was adding were close to 6 and 7 I knew instantly how to proceed. Of course there's other tricks like, subtracting the 1 out of 6 to get 5 and then adding it to 7 making 8 then removing the 5 to get 10 with the other 5 and you are left with 10 and 3 which is easy, I guess. At least for me it was just silly shortcuts that stuck with me like 6+7=13…
I think that's what you get with unsupervised learning. Tricks only get you so far, you can't do 6+7 on fingers or 7·7 as (4+3)(4+3) (I had a huge problem with this one, too many numbers to track) . So you fail. And when you fail, you memorize the problematic cases and go on with tricks based on those. And yes, it's completely incomprehensible for people who learned the pencil-and-paper algorithms and think that thos…
(2)(16) = (2)(15 + 1)
[0] http://slatestarcodex.com/2014/03/03/do-life-hacks-ever-reac...
While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
Instead of memorizing multiplication tables, you instead have to memorize derivative formulas, or the formulas for the Fourier and Laplace transforms, or the difference between a bijection and an injection, or all the conditions on an elliptic curve that make it suitable for cryptography. I could go on and on and on.
The stupid notations that mathematicians use doesn't help either. All math should be done using S expressions (and I'm pretty sure Minsky would have agreed!)
R.I.P. Marvin.
Earlier quoted context omitted.
The correct method might be the method that scales better. Counting on your fingers for example is a pretty decent method to add until you reach bigger numbers. If you don't use the more complicated methods, you'll never improved past some point.
Then ask harder questions that show the value of the harder (more complicated, less intuitive) methods. But at the same time, show the value of those answers, because on the face of it, knowing how much is 342x520+92 is not really valuable. Even knowing how much is any number plus any number is not that interesting for basically 90% of the population.
I had dinner with Prof Minksy, about 15 years ago. He asked what I was working on (evolutionary algorithms) we got talking about domains of knowledge. He said all knowledge has a half-life, the time it takes for half of what you know to be redundant or wrong. Math, he said, is the longest, measured in centuries or millennia. One should feel sorry for neuroscientists: they can go to the bathroom and half their knowled…
While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
The next step is algebra at 8th or 9th grade. Letters and numbers confuses people too.
In my case I succumbed at Analysis. I like applied math, but dislike constructing proofs.