Textbooks are the best way to acquire knowledge and prepare for a test. At the same time, it is the least used resource especially those who are academically struggling. Yes, textbooks are more useful than your class notes and packet handouts.
If one textbook is useful, having three different ones would be even more so. Indeed, it is best to have three different books on the same subject. Since, you can get textbooks on any subject for the actual cost of a trip to the library, it would be silly not to. (See “Have a personal textbook library on the cheap“) In my physics and calculus courses, I specify three textbooks for my students.
Having textbooks is not sufficient, of course. You need to use them. How?
There are two levels of using it. One is for truly smart students and the other is for the rest of us where I belong.
The smart way to use it is to look at the theorems and understand everything, not only the meanings but also the pitfalls and exceptions, etc. I found this impossible. To me, this way of understanding no different from looking at an orchestral score and hearing the performance in my mind. It can be done, because all the information is there. But it takes a lot of knowledge and skill, not to mention talent and intelligence.
The “rest of us way” that I employed was to play the music first, then look at the score. That way, I knew what each note meant and I was able to figure out what kind of harmonies they formed. After a few repetitions, I was indeed able to hear the whole music by looking at the score. But, of course, it is just a trick. I was actually hearing the music from my memory, and look for the notes that matched my memory. But, from the outside, it looked like I was able to sight read an orchestral score.
Music? Orchestra? Aren’t we talking about math and physics? Yes, I was speaking metaphorically. What I do with textbooks is to solve examples problems first. Examples problems come with very friendly and complete solutions. Using it, even though I am still in the dark after reading the theorems and proofs, I am able to basically bump into the walls to have some understanding of the shape of the room. The problem with these textbooks is that they have too few examples. But you can easily triple them by having three textbooks. Ha!
Then I solve odd-numbered problems. They are not as friendly because they don’t provide full solutions. But the answers tell me that I did something wrong. Again, I learn the lay of the room by bumping into walls. Bump enough times in enough places, I know the whole room every well. Then I look at the theorem/proof. Suddenly it makes sense. It is like looking at a map of the city you know very well.
Once you reach that point, you’ve got it made.
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