Math textbooks are written to fully explained each concept. This unavoidably can include much discussion, definitions, theorems, exceptions, and even intimitating proofs. They are written in very formal mathematical language. Given that math texts all share these elements, many are not particularly well organized or written in clearly understandable terms. Most students find math textbooks very intimidating and actually avoid trying to read them altogether.
Teachers have the obligation to translate the text for the students. In short time frames and with ever waning attention spans, paraphrasing and creating outlines of the text in classroom instruction can be a challenge for both the teacher and the students.
In fact, the functional essentials of most math concepts for each new topic can be summarized on a single page with a few formulas and a few lines of notes.
In Math Clinic tutoring sessions the student receives clear and concise instruction on any specific math concept they may present. The goal is to de-mystify each concept, reduce it to its most fundamental elements, and help the student to realize that each topic is not as difficult as they may have imagined. For most topics, the student receives a concise 1-2 page Math Clinic Study Guide.
Students are instructed to use the study guide to do their classwork problem sets. This enables the student to immediately realize success and gain confidence with class assignments and problems sets. This also demonstrates that the simplified and understandable study guide solves most problems. If they run into an exception, they are encouraged to simply annotate their study guide.
Their study guides become a valuable part of their class notes. And a great aid for review before quizzes, tests, and exams. But more importantly, the study guides demonstrate to the student how concepts that first appear to be complex and intimidating can consistently be reduced down into very concise and understandable terms. A lesson well learned for a lifetime in our ever more complex and technological world.
The real goal is that the student will begin to develop the skill to reduce what first appears to be complex topics to more simplify workable elements. This is what being “educated" is all about.
P.S. Once the student is successful working a full range of problems using the study guide, reading the text will be more understandable and beneficial. When the student sees concepts they already understand presented more formally, they begin to refine their fluency in the “language" of mathematics. The text can then become more of a useful reference.