Math major from Germany, interested in a bunch of stuff. Find me on limerott.com
Do you visualize the icosahedron as one object or do you split it up and consider each separately, but reminding oneself that it is actually one object?
My answer to your visual thinking riddle is: breath in through your mouth and breath out through mouth + nostrils. But I can't decipher your anagram!
First of all, if you can solve it without visualization, I think that this is preferable, precisely because it is faster. There is no need to force oneself to visualize everything.
To visualize something, you need to create a map from the formal domain you are studying to visual transformations. In other words, you need to understand "what the formula" mean (or at least one way of looking at them). Do you know what it means visually to multiply one complex number to another? If you don't, you will be stuck doing calculations. If you do, then you can visualize it and quickly come up with the solution.
From my experience, some people naturally tend towards visual thinking, while others don't. But if you consistently try to apply it, it will become natural at some point (it may take some time, don't give up prematurely).
One area where a lot of visual thinking is necessary, but that is relatively easy to visualize, is graph theory. Try to prove that a (connected undirected) graph has an Eulerian cycle (i.e. a cycle that contains every edge exactly once) if and only if all of its vertices have even degree.
Say you have two distinct points x and y. Consider all points whose distance to x is the same as to y. What can you say about the location of these points in terms of the line connecting x and y?
Try to solve any geometry puzzle with only your mind and you will be forced to do visual thinking.
I really appreciate you looking this up. Now it is clear that these claims are controversial.
Nevertheless, the question still is what learning ability refers to: Is it the ability to comprehend learning material that explains the topic well, or is it the ability to come up with the simple explanations yourself? It seems that the OP refers to the latter. The first kind probably has lower variation. Also, this means that when measuring learning ability, you should ensure that all involved people have access to the same "source". I would be interested in hearing the OP's thoughts on that.
I couldn't find it quickly, but I think that I read this on codehorror.
In an experiment, a group of people who have never programmed before have been showed how to code. In the end, their skills were evaluated in a coding test. The expectation was that they would be roughly normally distributed. However, the outcome was that the students were clustered in two groups (within each of which you see the expected normal distribution). The students belonging to the first struggled while the second group fared relatively well. The researchers figured out the cause: the students that did better managed to create a mental model of what a variable is (a container or a box that can hold values) while those that struggled didn't manage to do this. Are the students from the second group inherently less intelligent?
Yes, because they did not manage to find the right model on their own. No, because once they were provided a straightforward explanation, they were able to code just as well as the students in the better group.
Thank you for your kind comment. This is why I wrote this!
And the list is not exhaustive by any means. I really think this is a no-brainer.
My opinion is that, in almost all scenarios, if you have a question, you should always ask it. Why?
As long as you stay within reasonable (context-dependent) limits (for example, you should not be the only one asking basic questions while everybody else looks bored) -- you should ALWAYS ask questions. It is definitely worth overcoming the fear of looking foolish. There is nothing more sad than somebody giving a talk and nobody asking follow-up questions. I mean, why not?
This takes on a higher level view of reading than I was intending to cover here. But nevertheless, this is a valuable resource. It reminds me of Adler's How to Read a Book.