My Approach to Teaching
My approach uses simple principles to prevent that problems described above and to make Math easy and not hard, simple and not complex, fun to practice and not frustrating because of its difficulty. The principles are:
Complete and Concise. I provide a complete set of instructions at the beginning of each topic and each section in a topic, and each subsection. It is clearly outlined. It is explained in simple language and simple sentences. It is presented as a step-by-step procedure that is easy to follow.
The next smallest step. Using my deep understanding of math, I break each topic to its ingredients and create a skill map, which outlines the progression of skills and requirements. Using that I advance only by the smallest step possible when I present something new (example: learning multiplication of fractions before learning to change fractions). Similarly, within a section in a topic (example: multiplication of fractions) I advance one step at the time (example: first multiplication of simple fractions, than when a whole number is present, then with mixed numbers, etc.). If the new step requires a modification of the solution method, I explicitly present the modified method completely, not just the modified part.
This ensures that all required skills have been studied. If a skill that is outside the scope of the book is required, I explicitly point it out.
All possible examples. To prevent the generalization problem, I provide examples for all possible variations. This way, when the student reaches they practice questions, s/he had seen, and can draw on, an example to use as a basis for applying the procedure s/he learned. There is no need to guess how the “generalized” procedure works since it is shown explicitly.
Sparseness. In the books, I do not put too much information on any given page. A page usually has at most one new method and few examples. The student, therefore, is not flooded with information and can discern the information flow, and the relationship between the examples and methods taught.
Subject focused. Each book is focused on a specific subject or topic. This is how I teach as well. One topic at a time.
How and Why. For each topic I first explain the method. Then I explain the mathematical principle that makes this method work.
Motivation. For each subject, I provide motivation; reasons why this subject is important and how that knowledge can be used for practical problems we face in our life (I try to make the problems applicable to kids…)