Quote:
Originally Posted by tnff
Sorry, didn't see this earlier or I would have answered. Of course I understand the importance of knowing what it's a function of. What I'm talking about is textbooks that use that notation, and worse, when it doesn't communicate anything of value to the student at that grade/knowledge level. And in fact simply adds confusion. We're not talking esoteric problems here, but simple equations of the form y=mx+b made overly complex by using the f(x) notation. May not seem like much to write f(x)=mx+b, but then string a whole page of those together and add subscripts and superscripts and maybe a g(f(x)) somewhere in there and you've lost 90% of the students in the room. Lost not in the math, but the notation.
One of my pet peeves for text books is things are often arranged in what appears to be a logical order (you need A to understand B) but historically that's not how the knowledge developed. Humans learned a little bit of B empirically, but didn't understand it. But that drove learning some of A which then provided the ability to learn more of B and so forth in a feedback loop. I think for a lot of students learning would happen more effectively the same way. Little bit of B to ground A. Then a bit of A to understand B and then bootstrapping upward from there. We try to take things in whole chunks and it's too much to get the mind around at one time for most people.

Two problems with a lot of highlevel textbooks are that they are obsessed with being as formal and general as possible from the very beginning  which is actually not a particularly good idea, because it makes it harder to get a feel for the content  and also that they go on about a topic for a
veeery long time before they give you a chance to do any practice problems.
This is in fact not good teaching  some textbooks are simply worse than others.
One book that proves that even somewhat advanced engineering courses can be taught in a pedagogical, approachable and intuitive way is "Elements Of Electromagnetics" by Matthew Sadiku.
That book explains all the concepts in small chunks, and each chunk is followed by several example problems, and lots of the problems also have detailed solution steps.
This also prevents it from being tedious, because you always read small chunks at a time and then get a chance to test your knowledge.
The whole book is written that way from beginning to end, and I don't see any reason whatsoever for why other books shouldn't be that way.
Some mathematicians almost seem to have
tried to make math courses feel overly formal and abstract, and I know this because there have been times when I have felt very confused by a math book and then I have checked the exactly same topic on YouTube or something  from someone who actually
enjoys teaching stuff to people  and this almost always makes everything crystal clear, and makes me able to answer several of the problems from my old exams.
Then of course there are also teachers who are genuinely great and passionate, like Professor Leonard and Michel Van Biezen for example.