In many inductive lessons the step of application really involves a process of deduction. For example, after teaching the definition of a noun by a process of induction as outlined above, we may, in the same lesson, seek to have the pupil use his new knowledge in pointing out particular nouns in a set of given sentences. Here, however, the pupil is evidently called upon to discover the value of particular words by the use of the newly learned general principle. When, therefore, he discovers the grammatical value of the particular word "Provender" in the sentence "Provender is dear," the pupil's process of learning can be represented in the deductive form as follows:
All naming words are nouns. _Provender_ is a naming word. _Provender_ is a noun.
Although in these exercises the real aim is not to have the pupil learn the value of the individual word, but to test his mastery of the general principle, such application undoubtedly corresponds with the deductive learning process previously outlined. Any inductive lesson, therefore, which includes the above type of application may rightly be described as an inductive-deductive lesson. A great many lessons in grammar and arithmetic are of this type.
=What Constitutes a Lesson Problem.=--The foregoing analysis and description of the learning process has shown that the ordinary school lesson is designed to lead the pupil to build up, or organize, a new experience, or, as it is sometimes expressed, to gain control of a unit of valuable knowledge, presented as a single problem. From what has been learned concerning the relating activity of mind, however, it is evident that the teacher may face a difficulty when he is called upon to decide what extent of knowledge, or experience, is to be accepted as a knowledge unit. It was noted, for example, that many topics regularly treated in a single lesson fall into quite distinct sub-divisions, each of which represents to a certain extent a separate group of related ideas and, therefore, a single problem. On the other hand, many different lesson experiences, or topics, although taught as separate units, are seen to stand so closely related, that in the end they naturally organize themselves into a larger single unit of knowledge, representing a division, of the subject of study. From this it is evident that situations may arise, as in teaching the classes of sentences in grammar, in which the teacher must ask himself whether it will be possible to take up the whole topic with its important sub-divisions in a single lesson, or whether each sub-division should be treated in a single lesson.