That's a helluva good question! Every one of those methods is used because different people find the different ones useful. A lot of people just can't deal with word problems to save their souls. So to speak. I know that when I had to "regurgitate" a theorem or proof in a math or physics class, having some little comment on a line explaining what I was doing went quite well with the professors. To simply memorize and regurgitate on demand isn't going to help one understand the material, but just to maybe get a good grade. I crammed for a test maybe 3 times in the course of getting my B Sc. I knew that anything I did later depended on that foundation.
Bottom line, it's just what people like. For my first two semesters of Calculus, I had Leithold's text. He's really wordy. First semester, we just did the work. Second semester, the prof complained that Leithold "Talks too much!"
Applications always seemed to give people trouble, but I had kids in class who asked, "What will we ever use this for!?" (in a disparaging way). I was more than happy to provide an example, because that's the kind of thing that cemented it into their little concrete heads...not that I think that you are in that category- I'm certain of the opposite.
Bottom line, it's just what people like. For my first two semesters of Calculus, I had Leithold's text. He's really wordy. First semester, we just did the work. Second semester, the prof complained that Leithold "Talks too much!"
Applications always seemed to give people trouble, but I had kids in class who asked, "What will we ever use this for!?" (in a disparaging way). I was more than happy to provide an example, because that's the kind of thing that cemented it into their little concrete heads...not that I think that you are in that category- I'm certain of the opposite.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.
