The way people think and conceptualize ideas varies greatly for different people. Even for things as basic as counting, people do it in different ways. http:/

The way people think and conceptualize ideas varies greatly for different people. Even for things as basic as counting, people do it in different ways. http://mdzlog.alcor.net/2010/07/12/read-listen-or-comprehend-choose-two/ http://mdzlog.alcor.net/2010/07/12/read-listen-or-comprehend... > What’s interesting is that the pattern varies from person to person. Feynman shared his discovery with a group of people, one of whom (John Tukey) had a curiously different experience: while counting steadily, he could easily speak aloud, but could not read. Through experimenting and comparing their experiences, it seemed to them that they were using different cognitive processes to accomplish the task of counting time. Feynman was “hearing” the numbers in his head, while Tukey was “seeing” the numbers go by. So while pushing around abstract symbols might be the way that you really grok things, I don't think this applies to everyone. I have an undergrad math minor, and the only math class that I didn't get an A in and that I really struggled with was Linear Algebra. I think it mostly had to due with excessive symbolic abstraction. Matrix notation still really troubles me. About 5 years after that Linear Algebra class that I struggled with, I was took a computer graphics class for a masters degree. We were talking about the non-invertibility of some operation (I think it was about figuring out how far something was away given a 2d rendering of a 3d scene, where you have a degree of freedom in the scale, everything could be twice as large and twice as far away). And that gave me a really intuitive understanding between matrix invertibility and full rank matrices. I am sure that I would have done much better in a combined Linear Algebra/Computer Graphics class than I did in just the mostly symbolic and proof based Linear Algebra class. So be careful in believing that the thought processes that obviously work well for you will also work well for others.