The books are written in a very specific way, based on the following principles:
1. THE WHY. Students should understand concepts, not just how to do things. Without understanding of the underlying concepts learning is based on memorization of methods. It is not learning in the deep sense. Students cannot remember all the rules, and even if they do, when new subjects are learned, they have difficulty when those subjects are based on previous knowledge which they never really understood. That is why there is a drop in grades when Algebra starts and a further drop when Calculus is studied.
2. THE HOW. The how to solve, or the solution method, should be fully explained. It is a separate part from “The Why”, even though understanding one is linked to understanding the other. That is why, in the books, the explanation of “The Why” and the explanation of “The How” are always one after the other.
3. SIMPLICITY. Explanations should be simple and clear, and be written in a simple language.
4. ONE SMALL STEP AT A TIME. Every lesson should be devoted to the smallest step possible, and one only. Firstly, it is easier to explain and therefore to understand. Secondly, when more than one idea is presented, at the same time, most students miss which idea is responsible for which part of the exercise/solution. As a result, when a similar but somewhat different exercise is presented to them, they get stuck. They are not sure which ideas to use.
5. COMPLETENESS. Every type of example should be covered and explained. The most difficult part of learning is generalization – doing mathematical generalizations correctly is very difficult. Most students generalize incorrectly or on the wrong elements. By providing a complete set of examples, one which covers ALL possible types of exercises, the books ensure that when a student is done with a topic, s/he knows how to solve all possible exercises. It sounds simple when you say it so, but for some reason, none of the books I have seen does so.
6. SUBJECT FOCUSED. Linked to the principles above is the decision to make each book focused on one subject. Doing so, and studying the books in the correct order, ensures full and complete understanding of all topics. If Mathematics is a building, as it is often compared to, one should finish building the first floor before going on to studying the second floor. Yet, in school, and school books, it is not so. Decimal fractions are studied before the subject of fractions is completed, and Algebra is studied before integers are fully learned. it is one of the reasons why students become utterly confused at times. They just never learned the concepts they need to learn this new topic, yet they are asked to do so. It is quite ridiculous if you think of it.
7. MOTIVATION. Why does this topic matter? Without an explanation to such, students have no motivation to learn a topic, and as a result, there’s no reason they would do it well.
8. SPACE AND COLOR. Modern books are filled with lots of text, several topics per page, and lots of meaningless pictures and colors. Extremely wrong – our brains cannot handle all that stimulation and therefore, we stare at the page and even though we read it multiple times, we keep getting out of focus and cannot understand why.
In my books each page has one topic, and lots of empty space. Color is used in one way only – emphasis. Either using color to draw attention to something, or using the same color to create a subliminal link between similar elements in the mind of the student. For example, in the Integers book negative numbers are always in red, and positive numbers are always in blue. See how it works wonderfully in your mind?