On the other hand, some students act as though the exam problems have been decided in advance, and expect the lectures and assignments to be leading up to performance on those problems, or ones just like them. The latter would constitute the avoidance of our goal. The best way to study mathematics is to just memorize everything very carefully. . . . Here, problem-solving refers to the ability to take a problem and attempt to carry out whatever methods might be relevant to solve it. This is a skill that grows with experience.
Students learn best when everything they have to know is presented slowly in the classroom. . . .
If everything the student has to know is presented slowly in the classroom, the total amount of material in the course will be rather little. Thus, students actually learn least that way. It is the teacher's job to cover the material. . . . As covering the material is the role of the textbook , and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. Since you are supposed to be learning from the book, there's no need to go to the lectures. . . .