What men call knowledge is of all degrees, from the first dim glimpse of a fact or truth to the full and familiar understanding of that fact or truth in all its parts and aspects-its philosophy, its beauty, and its power. He knows his subject. It is only when truths are known in their fullest light can a teacher teach and illustrate the interrelationships of truths. Reason and logic dictates that what a teacher does not sufficiently know and understand, he cannot satisfactorily teach. There is no substitute for knowing the subject you teach.
Teaching is more than requiring students to memorize facts.
The times tables have little, if any, value until they are applied to practical, mathematical situations. The power of multiplication quickly solves a problem that would be time consuming if long addition was used. When teaching emphasizes rote facts, it produces good memorizers but poor mathematicians. This concept applies to all academic disciplines. Unless a teacher knows and understands his subject, he will never make the subject content alive and exciting to his students.