From elementary to high school I've had teachers who've droned on and on trying to explain minute details about the concepts they're teaching. I've almost always found it more difficult to follow the teacher's train of thought than to just learn the concept myself, so I always just read the book during lecture. I mean "read" in the loosest sense of the word though, as I'd just skim through looking for the equations. From middle-school and upwards, the textbooks were written so as to be incomprehensibly dense to any student not three grade levels higher than the grade the book was intended for. The most peculiar aspect of this arrangement was that I always found that solving the problem always depended on only a few things. Far less than the length of the teacher's lectures would suggest. When I got to college and took computer science classes we had to document our code. For each function we needed to present a concise explanation of: 1. What the function does 2. What the function's arguments are and how they relate to what the function does 3. What conditions the function requires in order to work properly. And it hit me. These three things are all you need in order to use any mathematics equation. And so I'm baffled. All the math and science textbooks are designed around the author raising some question about the concept, going through a derivation, and arriving at an equation that answers the original question. Even ignoring the fact that the questions raised by the book have almost always been incomprehensible to me, you still have the fact that this form of teaching results in the important information being strewn all over the place. The explanations on what the variables are could be in any chapter, the explanation of what the function does is written in terms of its derivation and mixed all throughout the section, and the conditions on the function's use are hidden somewhere in the derivation. In the worst case, you have arguments that are only defined in tiny tables in the margins of some page in the last chapter. So this makes me wonder: What is the use in making students go through all this hullabaloo? Why can't a mathematics textbook, for each equation, provide concise summaries of what the function does, what its arguments are and how they relate to the function, and what conditions invalidate the function? I see absolutely no use in making the student skip and hunt around the book every time they want to do a homework problem. I personally find it much easier to understand mathematics by relating the equations to the concepts than trying to piece together some half-hazard imprecise English explanation, or some dense, etymologically sterilized "mathematically correct" explanation.