vice the expressions render to the conscious side of our study. First of all, we note that the expressions help to make the acts and ideas in study habitual. We find ourselves, with each expression, better able to perform such acts as the pronunciation of foreign words. Second, they furnish new impressions through the kinæsthetic sense, thus being a source of sense-impression. Third, they give rise to a greater number of ideas and link them up with the idea dominant at the moment. There is a further psychological effect of expression in the clarification of ideas. It is a wellattested fact that when we attempt to explain a thing to someone else, it becomes clearer in our own minds. You can demonstrate this for yourself by attempting to explain to someone an intricate conception such as the nebular hypothesis. The effort involved in making the explanation makes the fact more vivid to you. The habit of thus utilizing your knowledge in conversation is an excellent one to acquire. Indeed,

expression is the only objective test of knowledge and we cannot say that we really know until we can express our knowledge. Expression is thus the great clarification agency and the test of knowledge.

Before leaving this discussion, it might be well to remark upon one. phase of expression that is sometimes a source of difficulty. This is the embarrassment incident to some forms of expression, notably oral. Many people are deterred from utilizing this form of expression because of shyness and embarrassment in the presence of others. If you have this difficulty in such excess that it hinders you from free expression, resolve at once to overcome it. Begin at the very outset of your academic career to form habits of disregarding your impulses to act in frightened manner. Take a course in public speaking. The practice thus secured will be a great aid in developing habits of fearless and free oral expression.

This discussion has shown that expres

sion is a powerful aid in learning, and is a most important feature of mental life. Cultivate your powers of expression, for your college education should consist not only in the development of habits of impression, but also in the development of habits of expression. Grasp eagerly every opportunity for the development of skill in clear and forceful expression. Devote assiduous attention to themes and all written work, and make serious efforts to speak well. Remember you are forming habits that will persist throughout your life. Emphasize, therefore, at every step, methods of expression, for it is this phase of learning in which you will find greatest growth.

CHAPTER IX

THE PLATEAU OF DESPOND

In our investigation of the psychology of study we have so far directed our attention chiefly toward the subjective side of the question, seeking to discover the contents of mind during study. We shall now take an objective view of study, examining not the contents of mind nor methods of study, but the objective results of study. In doing this, we choose certain units of measurement, the number of minutes required for learning a given amount or the amount learned in a stated period of time. We may do this for the learning of any material, whether it be Greek verbs or typewriting. All that is necessary is to decide upon some method by which progress can be noted and expressed in numerical units. This, you will observe, constitutes a statistical approach

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to the processes of study, such as is employed in science, and just as the statistical method has been useful in science, so it can be of value in education, and by means of statistical investigations of learning we may hope to discover some of the factors operative in good learning.

Progress in learning is best observable when we represent our measurements graphically, when they take the form of a curve, variously called "the curve of efficiency," "practice curve," "learning curve." We shall take a sample curve for the basis of our discussion, showing the progress of a beginner in the Russian language for sixtyfive days (indicated in the figure by horizontal divisions). The student studied industriously for thirty minutes each day and then translated as rapidly as possible for fifteen minutes, the number of words translated being represented by the vertical spaces on the chart. Thus, on the tenth day, twenty-five words were translated, on the twentieth day, forty-five words.