A. In Ordinary Life.—Suppose a young child has received a vague impression of a cow from meeting a first and only example; we find that by accepting this as a problem and by applying to it such experience as he then possesses, he is able to read some meaning into it, for instance, that it is a brown, four-footed, hairy object. This idea, once formed, does not remain a mere particular idea, but becomes a general means for interpreting other experiences. At first, indeed, the idea may serve to read meaning, not only into another cow, but also into a horse or a buffalo. In course of time, however, as this first imperfect concept of the animal is used in interpreting cows and perhaps other animals, the first crude concept may in time, by comparison, develop into a relatively true, or logical, concept, applicable to only the actual members of the class. Now here, the child did not wait to generalize until such time as the several really essential characteristics were decided upon, but in each succeeding case applied his present knowledge to the particular thing presented. It was, in other words, by a series of regular selecting and relating processes, that his general notion was finally clarified.
B. In the School.—Practically the same conditions are noted in the child's study of particular examples in an inductive or conceptual lesson in the school, although the process is much more rapid on account of its being controlled by the teacher. In the lesson outlined above, the pupil finds a problem in the very first word John, and adjusts himself thereto in a more or less perfect way by an apperceptive process involving both a selecting and a relating of ideas. With this first more or less perfect notion as a working hypothesis, the pupil goes on to examine the next word. If he gains the true notion from the first example, he merely verifies this through the other particular examples. If his first notion is not correct, however, he is able to correct it by a further process of analysis and synthesis in connection with other examples. Throughout the formal stages, therefore, the pupil is merely applying his growing general knowledge in a selective, or analytic, way to the interpreting of several particular examples, until such time as a perfect general, or class, notion is obtained and verified. It is, indeed, on account of this immediate tendency of the mind to generalize, that care must be taken to present the children with typical examples. To make them examine a sufficient number of examples is to ensure the correcting of crude notions that may be formed by any of the pupils through their generalizing perhaps from a single particular.
INDUCTION AS A LEARNING PROCESS
In like manner, in an inductive lesson, although the results of the process of the development of a general principle may for convenience be arranged logically under the above four heads, it is evident that the child could not wholly suspend his conclusions until a number of particular cases had been examined and compared. In the lesson on the rule for conversion of fractions to equivalent fractions with different denominators, the pupils could not possibly apperceive, or analyse, the examples as suggested under the head of selection, or analysis, without at the same time implicitly abstracting and generalizing. Also in the lesson below on the predicate adjective, the pupils could not note, in all the examples, all the features given under analysis and fail at the same time to abstract and generalize. The fact is that in such lessons, if the selection, or analysis, is completed in only one example, abstraction and generalization implicitly unfold themselves at the same time and constitute a relating, or synthetic, act of the mind. The fourfold arrangement of the matter, however, may let the teacher see more fully the children's mental attitude, and thus enable him to direct them intelligently through the apperceptive process. It will undoubtedly also impress on the teacher's mind the need of having the pupils compare particular cases until a correct notion is fully organized in experience.
TWO PROCESSES SIMILAR
Notwithstanding the distinction drawn by psychologists between conception as a process of gaining a general notion, and induction as a process of arriving at a general truth, it is evident from the above that the two processes have much in common. In the development of many lesson topics, in fact, the lesson may be viewed as involving both a conceptual and an inductive process. In the subject of grammar, for instance, a first lesson on the pronoun may be viewed as a conceptual lesson, since the child gains an idea of a class of words, as indicated by the new general term pronoun, this term representing the result of a conceptual process. It may equally be viewed as an inductive lesson, since the child gains from the lesson a general truth, or judgment, as expressed in his new definition—"A pronoun is a word that represents an object without naming it," the definition representing the result of an inductive process. This fact will be considered more fully, however, in [Chapter XXVIII].
FURTHER EXAMPLES OF INDUCTIVE LESSONS
As further illustrations of an inductive process, the following outlines of lessons might be noted. The processes are outlined according to the formal steps. The student-teacher should consider how the children are to approach each problem and to what extent they are likely to generalize as the various examples are being interpreted during the analytic stage.
1. THE SUBJECTIVE PREDICATE ADJECTIVE
Analysis, or selection: