This morning I “Stumbled upon” Rick Garlikov’s essay

describing his impressively successful experience teaching, by means of questions alone, binary arithmetic to a third grade class. Throughout the entire session Rick made no categorical declarations and, apparently, the children came to understand binary arithmetic by means of their own answers to Rick’s questions.

As I have some experience teaching children, the piece invoked in me plenty of comment material. I am not arguing against anything Rick says in his piece; his piece is far more descriptive than prescriptive.

My central point in this post is a simple one: a good teacher must constantly tailor his teaching method to fit the subject matter and the level, aptitude, and attitude of his students. No one method can ever suffice.

The methods of teaching employed by a teacher for the benefit of student can be divided, generally, into

two classes, each with it’s own advantages. I shall call them *Bottom Up* and *Top Down*, respectively. A good teacher, I insist, will employ a mixture of both, even, most often, in the same teaching session.

*Bottom Up*: Basically, what Rick did in the session described in his post is a perfect example of this method in its most extreme manifestation. The teacher brings his students (bottom) up to the level of the information. The advantage is obvious; the students

really get it; in fact, they got to it ‘themselves’; the students now hold at the level of the concept.

*Top Down*: Basically the teacher brings the concept *down* to his students. The advantage is simple: the ceiling of *Bottom Up* is mainly determined by the current level of the students, while

the ceiling of *Top Down* is mainly determined by the level of the teacher; the better the teacher the further he can bring concepts down. Thus, a teacher can give to his students what they are not at the level yet to arrive at themselves.

(Relatedly, it’s a safe bet that almost all of the answers offered by the students to Rick’s questions were, rightly, transmitted to them, originally, through a top down method.)