Q. How do the two triangles compare in area?
A. They are equal; each is half of the rectangle.
Q. Then, if each is half of the rectangle, what must be the area of one of the triangles?
A. The area of each triangle is 12, for the area of the rectangle is 24, and the area of each triangle is half that of the rectangle.
Q. Then, how may we find the area of a triangle?
A. Multiply the base by the altitude and take one half the product.
Of course the teacher may have to supplement questions like the above by others to assist the child in arriving at the desired answer, but the method is the same in any case. The inductive method is the child's natural way of learning, and should be applied to nearly all school branches. Too many teachers have children learn rules and definitions which mean little or nothing to them. This is not only discouraging to the child and a serious waste of time, but it develops bad habits of study by making the pupil think he is learning something when he is not. Only when the fact or process learned is understood is it true knowledge. The inductive method begins with what the child already knows and, step by step, leads him to understand the new truths. It comes last to the rule or definition after the meaning is clearly seen.
b. Dangers of the question-and-answer method.—No matter how good a method may be, there are always some dangers connected with its use, some points at which a teacher needs to be on guard to see that the method is not misused or over-used. The question-and-answer method is no exception to this rule.
One of the greatest dangers in the use of this method is that pupils will come to depend on the questions as a crutch to help them along mentally when they should be able to proceed by themselves. Not infrequently do pupils say to the teacher when called upon for a topical discussion, "If you will ask me questions upon the topic I can answer them, but I cannot recite upon the topic." It is very much easier to answer a series of questions upon a subject than to discuss it independently. This method is well adapted to younger children; and this very reason makes it a danger when over-used with more advanced pupils. We need to learn to think a subject through and talk about topics without the help of a teacher to stand by and ask questions; we need to become independent in our thinking; we need practice in organizing and expressing our thoughts for ourselves.
The second danger we note in the question-and-answer method is that it does not give as much opportunity for training in self-expression as the topical method. In teaching by the question-and-answer method, the teacher occupies nearly or quite as much time with the questions as the class do with the answers. This does not give opportunity for practice enough in reciting on the part of the pupil, if the question-and-answer method is employed exclusively. The only way for a child to learn to recite well is by reciting; the only way to learn to express one's self is by having opportunity for expression.