old. Similarly, a graduate student in the university, aged thirty-eight, began the study of French and after twenty-four weeks with a class of beginners (during which time he carried on some extra outside French reading) easily passed the reading test in French required of candidates for the degree of Doctor of Philosophy. Finally, a man of forty-five began the study of German in the university and made grades of A and B in his classes.

Mature beginners succeed in proportion to native linguistic talent. Shall we say that these men succeeded so well with the languages because they began them when so mature? Of course not. The fact is that all of them have a natural talent for language, as shown by the fact that they all express themselves easily and fluently in English. On the other hand, many of the mature beginners who fail in studying a foreign language have little native linguistic ability, as is shown by the fact that they have little facility in expressing themselves in English.

These examples, however, are beyond the age limits with which we are concerned in our discussion in this chapter, namely, from six to eighteen. They are cited here simply because they are of the same type as the examples ordinarily used to show that mature beginners of a language are at a distinct disadvantage. In order that they may not confuse the issue, we repeat that during the period from six to eighteen years of age the experimental investigations of memorizing indicate that the later years of the period are as favorable to the systematic learning of a foreign vocabulary as are the earlier years.

Social economy also justifies postponing study of foreign language. — The above psychological discussion lends additional force to the conclusion reached upon social grounds, that the beginning of the study of a foreign language in American schools, for children of American parents, should be delayed until there is large and reasonable assurance that the particular students who begin the study will have occasion

to use it as a practical tool. If this were done, a very few students would begin the study in high school, but most students who began at all would do so in college.

Delay beginning until some assurance that language will be used. Ordinarily, nearly all high-school students are required or advised to study a foreign language, in order, if the occasion should ever arise, that they may be able to use it as a tool for study or research. In what per cent of the cases is the occasion to use the language as a practical tool likely to arise? If we ever really determined exactly what per cent of high-school students do actually use a foreign language as a tool in later life, the number would in all probability be so small that we should be justified in exactly reversing the argument stated in the first sentence of this paragraph; that is, we should say that, inasmuch as over 90 per cent of high-school students will not have occasion to use a foreign language as a practical tool in later life, we shall avoid an enormous social waste (of community money, teachers' time and energy, and students' time and energy) by making little or no provision for the study of a foreign language by most students in American high schools. Those who will use it as a practical tool in reading may begin to learn it when it becomes reasonably certain which students they are. If they are to be candidates for the degree of Doctor of Philosophy, as many of those are who use the language as a tool for studying, they can learn to read French in one year and German in two years during their college course. Moreover, learning the language at this period will obviate the waste of time ordinarily entailed in relearning the language when it has been studied early in life. That this necessity of relearning is a serious fact is shown by the large number of failures in efficiency and reading examinations in French or German by students in college who have studied the languages from two to ten years before taking the examination.

Use of foreign language as a tool for study is very infrequent. To make the contentions of the preceding paragraph specific, let us consider 1000 students who enter high school. Of these probably 500 will not continue to graduation. Practically none of the nongraduates will have occasion to use French or German as a practical tool for further study. Of the 500 who graduate, 250 may go to college. Of these, 100 may graduate and be eligible to become candidates for the doctor's degree. But as a matter of fact, probably only 10 out of the original 1000 will ever do serious graduate study to the extent of receiving the master's degree (that is, one year after graduation from college). Probably not 5 out of the original 1000 who entered high school will become serious candidates for the doctor's degree. Of the 5, some will try to choose topics for dissertations in connection with which they will not have to use French or German. Of those who secure the degree very few will continue to do productive research work which will require a reading knowledge of a foreign language. Many of them will get positions as professors in small colleges, normal schools, or high schools, and do routine teaching the rest of their lives.

Combined psychological and social arguments justify postponing study of foreign language. Putting together the psychological evidence concerning the facility with which a reading knowledge or the vocabulary of a language is acquired at different ages, and the facts concerning the enormous social waste that is entailed by requiring or advising students to begin the study of foreign languages early, we feel justified in maintaining that in most cases the study of a foreign language should be begun in later adolescence (from eighteen to twenty-two years of age), when the few students who will use the language begin to arrange their elections of studies with definite reference to a practical goal in connection with which they will use them.

Changes with age in reasoning processes. Maintained here that elementary children use same processes as adolescents.— When we take up a consideration of the reasoning processes of students at different ages, we again confront a condition in which the dogmas of ordinary observers are controverted by scientific evidence. The ordinary opinion, often found expressed in pedagogical books, is that young children do not reason as older persons do, and that some magic change takes place at the beginning of adolescence which results in the appearance or development of the reasoning powers. As opposed to this opinion, scientific psychology, which is based upon carefully conducted, precise, experimental investigations, shows that children solve problems and acquire and use abstract and general ideas by the same general mental processes as adults use. In other words, children carry on reflective, analytical, abstract, generalized, reasoned thinking in the same way as adults, although not as extensively as adults who are engaged in certain specialized professional and scientific pursuits.

Reasoning abilities of children demonstrated by Bonser.— The abilities of children in the intermediate grades to solve problems and do reflective thinking of various types were thoroughly investigated by F. G. Bonser and the results reported in his monograph entitled "The Reasoning Abilities of Children in the Fourth, Fifth, and Sixth School Grades." His experiments included, among other tests, the working of mathematical problems of the following types:

I. A. 1. If 3 of a gallon of oil costs 9 cents, what will 7 gallons cost?

2. John sold 4 sheep for $5 each. He kept of the money and with the other he bought lambs at $2 each. How many did he buy?

3. A pint of water weighs a pound. What does a gallon weigh? I. B. 1. A man whose salary is $20 a week spends $14 a week. In how many weeks can he save $300?

2. How many pencils can you buy for 50 cents at the rate of 2 for

3.

5

cents?

A man bought land for $100. He sold it for $120, gaining $5 an acre. How many acres were there?

II. A. 1.

132 plus what number equals 36?

2. If John had 15 cents more than he spent to-day, he would have 40 cents. How much did he spend to-day?

3. What number minus 7 equals 23?

II. B. 1. What number subtracted 12 times from 30 will leave a remainder of 6?

2. If a train travels half a mile in a minute, what is its rate per hour?

3. What number minus 16 equals 20?

Concerning the kind of mental processes involved in these problems Bonser says:

Tests I and II, the problems in arithmetic, test the mathematical judgment, in general that form of deductive reasoning most closely resembling the syllogistic movement of formal logic. The steps here involved are three: First, the analysis of the situation, by which the essential features of the problem are conceived and abstracted; second, the recall of an appropriate principle to be applied to the abstracted problem-a search among various principles which may suggest themselves for the right one; and third (involved in the second), the inference, the recognition of identity between the known principle and the new situation. While this process goes on as implicit, explicitly there are made the concrete applications in the resolution of the problems. Clearly these are examples of deductive reasoning of the usual scientific type, involving data, principles, and inferences. The only element omitted is that of verification, which, by the nature of the tests, cannot here be brought out. (2: 14)

As would be expected by anyone familiar with the children of the grades tested, the problems used in the tests were solved successfully by children in all of the grades, although there was improvement through the grades. Some