Grube method popularized in America, 1870. — One of the chief influences in popularizing the Grube method in the United States was an essay describing it, read by Mr. L. Soldan before the St. Louis Teachers' Association in 1870. According to its author, this essay was "republished extensively in state and city school reports and educational magazines . . . from California (see San Francisco Report, 1872) to New Hampshire (see State Report, 1876)." A larger treatment of the subject was contained in "Grube's Method of Teaching Arithmetic," by Levi Seeley, published in New York in 1888. According to Professor David E. Smith,

it thus became . . . almost the only German "method" known in America. Thus it has come about that Grube has been looked upon as a name to conjure by, and neither the faults nor the virtues (much less the originality) of the system seem to have been well considered. (10: 90.)

Grube method unnecessarily thorough. - The Grube method has been severely criticized by the two leading American writers on the theory of teaching arithmetic. Professor Smith says:

To know all there is about a number before advancing to the next one is as unnecessary as it is illogical, as impossible as it is uninteresting.

[Two of] the chief defects of the system are these: I. It carries objective illustration to an extreme, studying numbers by the aid of objects for three years, until 100 is reached. 2. It attempts to master each number before taking up the next, as if it were a matter of importance to know the factors of 51 before the child knows anything of 75, or as if it were possible to keep children studying 4 when the majority know something of 8 before they enter school. (10: 90.)

Professor John Dewey, the other prominent critic of the Grube method, says:

It seems absurd, or even worse than absurd, to insist on thoroughness, on perfect number concepts, at a time when perfection is impossible. . . . If the child knows 3, if he has an intelligent working conception of 3, he can proceed in a few lessons to the number 10, and will have all higher numbers within comparatively easy reach. (10: 118; 7: 172, 176.)

Criticism of proceeding from simple to complex. - PestaIozzi thought he was psychologizing instruction by having the teacher analyze each subject into a graduated series of elements which were to be learned by the pupil in order. He thought that the work of the educator should be analytic and that of the learner synthetic. This implied that the natural process of learning, which he was trying to discover, consisted in building up complex wholes from elements which could not be further analyzed.

Pestalozzian theory held by English associationists.—This theory of the way in which we learn was not unique with Pestalozzi. Many psychologists have believed it. Prominent among these were the whole English school of associationists and Herbart, the German follower of Pestalozzi. The subject is too involved to be discussed here in a clear and satisfactory manner, but a little must be said to suggest the recent criticisms of Pestalozzi's fundamental principle. Reference has been made several times to Spencer's discussion of this theory. What he believed is not perfectly clear, but certainly one of his most important contentions would be rejected by many modern psychologists as being just the opposite of the truth. I refer to his statement of the theory as follows:

Manifestly decomposable states of consciousness cannot exist before the states of consciousness out of which they are composed . . . [thus] no articulate sound [for example, a word] is cognizable until the inarticulate sounds which go to make it up have been learned.

It was on this theory that Pestalozzi said that the mother should address the infant with inarticulate sounds such as ba, ba, ba, da, da, da, etc., before she tried to teach him to recognize whole words (articulate sounds) like "bottle," "mother," etc.

William James (1842–1910) rejected simple to complex theory of learning. The best criticism of this theory occurs in William James's "Principles of Psychology." In direct

opposition to Spencer's point, James (the greatest of American psychologists) said that the child's experience, instead of beginning with nicely separated elements, is

one big, blooming, buzzing confusion. That confusion is the baby's universe; and the universe of all of us is still to a great extent such a confusion, potentially resolvable, and demanding to be resolved, but not yet actually resolved into parts.

Experience from the very first presents us with concreted objects vaguely continuous with the rest of the world which envelops them in space and time, and potentially divisible into inward elements and parts. These objects we break asunder and reunite.

Analysis by the learner prominent in ordinary learning. As a rule, in the ordinary process of learning, the individual things with which we become acquainted are complex wholes; we recognize, identify, and remember them without completely analyzing them, and may never analyze them unless some practical necessity requires it. Thus in the case of the so-called taste of coffee or onions, this necessity usually does not arise, and as a consequence we do not know ordinarily how much of the so-called "taste" is really taste and how much is odor. Or, to take the example that Spencer suggests as a matter of fact, the child recognizes spoken words as wholes long before he has become acquainted separately with the elementary sounds which compose these words. In the same way the child recognizes visual wholes (doors, windows, etc.) long before he has become acquainted with the various kinds of lines, angles, and shades of color which are fused in the total experience.

In mastering any new situation or material, for example, in becoming familiar with a strange city, or in solving a geometry exercise, or in studying pictures to determine their artistic qualities, the following process takes place: The mind begins by apprehending the situation as a vague, unanalyzed whole; proceeds by comparison or selective attention to break this whole up into its parts (as far as necessary for the practical

purpose of the moment); and then reconstructs (synthesizes) these parts into an organized whole in which the relation of the parts is more or less clearly perceived. Hence the natural method of learning involves an initial analysis by the learner (not by the teacher) followed by a synthesis by the learner; that is, it is analytic-synthetic.

Partly as a consequence of this change in psychological theory, the Pestalozzian methods of teaching reading and drawing by proceeding from simplified elements to complex wholes have been rejected in many places, and methods substituted which are more in harmony with the analytic-synthetic theory of the psychology of learning which is maintained by James and his followers.

Widespread and varied influence of Pestalozzi demonstrated. This will conclude our four chapters on the Pestalozzian movement and methods. The first of these chapters demonstrated the intimate connection which existed between the work of Pestalozzi and the social-reform movement led by Rousseau, and showed the widespread influence of Pestalozzi in Europe and America. The second Pestalozzian chapter described the development of the system of industrial training for the reform of juvenile delinquents. The third showed the large and beneficial influence exerted on the teaching of language, science, geography, and primary arithmetic by the application of the Pestalozzian principles of objective and oral instruction. The present chapter, on the other hand, has shown the pernicious influence of certain aspects of Pestalozzianism, which resulted in the memorizing of bare facts in the content subjects (geography, etc.), and in the long and dreary grind on meaningless elements in the form studies (reading, etc.). The next two chapters will trace further developments in elementary-school theory and practice during the nineteenth century. Some of these developments started with Pestalozzi, some were directly opposed to his theories, and all went far beyond what he had been able to achieve.

BIBLIOGRAPHICAL NOTES

1. SPENCER, HERBERT. Education. (1861.) Chap. ii, entitled Intellectual Education, contains the best critical accounts of Pestalozzian formalism.

2. BARNARD, H. Pestalozzi and his Educational System. (C. W. Bardeen, Syracuse, n.d.) Article by Dr. Wilbur, pp. 479-498. A criticism of Oswego formalism by a contemporary. Reflects Spencer.

3. BARNARD, H. National Education in Europe. (C. W. Bardeen, Syracuse, 1854.) Contains descriptions of Prussian lessons reprinted from reports of Stowe, Mann, etc., of about 1840. Especially pp. 49–74.

4. JAMES, WILLIAM. Principles of Psychology. (Henry Holt and Company, 1890.) Vol. I, chap. xiii, and elsewhere. The source of most of the recent criticisms of the theory of proceeding from the simple to the complex.

-5. CALKINS, N. A. Primary

Other works referred to in the text. Object Lessons. (Harper & Brothers, 1862.)

6. GUIMPS, ROGER DE. Pestalozzi, his Aim and Work (D. Appleton and Company, 1890.)

7. Dewey, JOHN, and MCCLELLAN, J. A. The Psychology of Number. (D. Appleton and Company, 1895.)

8. MAYO, ELIZABETH. Lessons on Objects. (London, 1830-1855.) 9. SEELEY, L. Grube's Method of teaching Arithmetic. (Kellogg, 1888.)

10. SMITH, D. E. The Teaching of Elementary Mathematics. (The Macmillan Company, 1900.)