One of the most important uses of this method is found in inductive teaching. The famous "Socratic method" was simply the question-and-answer method applied by Socrates to teaching new truths. This noted teacher would, by a series of skillful questions calculated to call forth what the pupil already knew, lead him on to new knowledge without actually telling the youth anything himself. And this is the very height of good teaching—the goal toward which we all should strive.
It is a safe maxim never to tell a child what one can lead him by questioning to see for himself. To illustrate: Suppose an elementary arithmetic class already know thoroughly how to find the area of a rectangle by multiplying its base by its altitude, and that we are now ready to teach them how to find the area of a triangle. Let us see whether we can lead them to "develop" the rule instead of learning it out of the text; that is, we will proceed inductively. First draw a rectangle 4 by 6 on the board.
Q. What do we call this figure?
A. A rectangle.
Q. How shall we find its area?
A. Multiply its base 4 by its altitude 6; the area is 24.
Q. Now I draw a line diagonally across the rectangle; how many figures are there?
A. Two. (Teacher here gives new word "triangle" and explains it.)
Q. How do the base and altitude of the triangles compare with the base and altitude of the rectangle?
A. They are the same.