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Different Ways to Conceptualize Math?
rook a asks: "I've always been an avid reader but my math skills were poor, and TV had taught me that math was difficult. I knew only the concepts of the basic operations. From seventh grade through high school, I did only what was needed to get by and so my math skills remained below par. Now, as a freshman pre-cal student, I am struggling. I believe that I have a flaw in the basic way I think about numbers. I can think logically, but it does not carry over to math. I read somewhere that Feynman gave a lecture on arithmetic but I could not find it. I believe that different people have different thought structures for the same ideas. Has there been any research or books on the difference between how a mathematician, or a Richard Feynman, thinks about math and the way that the average person thinks about math? Or, did any of you initially find math difficult in college but go on to higher maths? If so what changed for you?"
"I wanted to be an EE and want very much to be good at math but if my ability does not increase I will not be able to. I am willing to do anything to increase my skill. I hate rote and do not want to be merely 'good' at math, I want to speak it. If math is a mindset then it's one I want to be part of.
This is similar to another question, however I found several interesting books but no comments toward learning a more efficient way to think."
This is similar to another question, however I found several interesting books but no comments toward learning a more efficient way to think."
Look up "Mathematics: From the birth of numbers" by Jan Gullberg. It should do the trick. Incredible book.
Many people don't "get it" with math because they are not cognitively wired to absorb stuff the way it is presented. Yet, if something is presented a bit differently they might then "get it" and be able to move on to the next step.
I was very fortunate to have an excellent math teacher. This teacher was able to teach kids who had previously not done well at math and get them scoring As. I think his secret was this: He used many different wasy to explain things to the kids. Some would get it immediately. Some would only get it when he explained things differently. Quite often he'd explain things in thee or four different ways. Now sometimes he'd be stumped and could not get an idea across.... So here's where he was different from other math teachers..... He'd get one of the kids that "got it" to sit and explain to the kid that didn't "get it", and he'd watch and take notes. Eventually someone would manage to get through. Better still, the teacher would then have a few more ways of explaining things to future classes.
Engineering is the art of compromise.
Keith Devlin addresses your concerns. His recent book "Math Instinct" looks at the conundrum of mathematics being easier in practice than in theory.
I haven't read it but I have read his "Math Gene" book looking at innate abilities for mathematics.
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It doesn't have to be difficult. I think the reason it is or isn't for most people is emotional, or psychological. I for one loved math as a student. It was the only subject where you were either right, or wrong. I could walk into an exam, write it, verify my answers, and be sure of how I did. The teacher couldn't slant, because if there was a mistake in the marking, it could be proven a mistake.
On the other hand, there's a friend of mine who hates math. He's no good at it, and he can't learn it because when he tries, he spends too much time worrying about the fact that he's not good at it. He calls it a mental block. It's probably the same reason why a lot of nerds are no good at sports.
I'd suggest to the submitter to stop looking for "different ways" to conceptualize math, and actually just follow through with one way.