I wrote in the blurb for my book, Trigonometry for Self-Learners, that there were minimal explanations. Surely that is a bad thing! Books, after all, are meant to explain, to teach, and to provide knowledge the reader can memorise.
Try memorising a mathematics book!
You can’t, of course, and the accepted way to learn maths, and I suppose to teach it, is to explain everything in detail, and then give lots of problems. It works, I guess, even if it is like the old-fashioned method of learning to spell by spelling the word 100 times. I bet you can spell it now.
Truth is, there are other reasons why textbooks are like they are – especially ones aimed at high school students. There is a range of question difficulty, from easy to hard, which allows the teacher to grade students. Trigonometry is taught in years 9, 10, and 11; therefore, questions for year 11 students may be unsuitable for year 9. Many factors determine what is taught, including the expectation that the student will be tested. Understanding the material is secondary to the ability to apply it and pass a test; these are not the same.
I wrote this book with a determination that all pedagogical approaches, anything that might be in a syllabus, anything that was not central to the aim of understanding trigonometry, would be ignored. More than that, I was utterly oblivious to it. You, the reader, are learning independently, and this book serves as a guide. That is all. No one can teach you anyway – you can only learn.
And learning is not memorising.