No" ciphering" or figures used in beginning arithmetic.— To make sure that the child's attention was fixed on the "number ideas" instead of the figures, no figures were used in the problems in the first fifty-five pages of Colburn's book. Thus the child worked approximately 1000 problems (250 concrete and 750 abstract) before being made acquainted with the figures. The number names were all printed in full, thus:

Two and one are how many?

What cost three lemons, at six cents apiece?

What do you understand by one tenth, two tenths, three

tenths, &c, of anything?

Finally, on page 55, the following statement occurred:

Instead of writing the names of the numbers, it is usual to express them by particular characters, called figures.

"One" is written

"Two" is written

I.

2 [etc.].

These quotations show how Colburn, in common with the Pestalozzians, placed great emphasis on getting the number ideas clearly fixed in the child's mind.

Pupils became expert mental calculators.- Colburn said, "The examples are to be performed in the mind, or by means of sensible objects such as beans, nuts, etc." This was recommended primarily in order to secure clearer number ideas. But the performing of the operations mentally instead of on paper also had the effect of developing rapid calculators. In other words, the Pestalozzian methods were very successful in making the number combinations automatic in the pupils' minds. The chief reason for this was the large amount of time saved by omitting the writing process, leaving practically all the time for arithmetical thought. Another reason was the concentration of attention by the children because of the interest excited by the game element in the mental-arithmetic recitations. An example of the results secured in Pestalozzi's own

school is contained in the testimony of a German merchant who visited Burgdorf about 1801. He said:

I was amazed when I saw these children treating the most complicated calculations of fractions as the simplest thing in the world. Problems which I myself could not solve without careful work on paper, they did easily in their heads, giving the correct answer in a few moments, and explaining the process with ease and readiness. (4: 214.)

The widespread influence of Colburn's book has been noted above. During the middle of the nineteenth century mental arithmetic was a very prominent subject in elementaryschool work, and wonder is often expressed that it has disappeared in many schools of the present day. About 1870 another phase of Pestalozzian arithmetic became prominent in the United States under the name of the Grube method. This will be discussed in the next chapter.

Objective and oral methods revolutionized instruction. This chapter has demonstrated the manifold application and the widespread influence of the Pestalozzian principles of objective and oral instruction. The methods of instruction in language, elementary science, home geography, and primary arithmetic were either created or revolutionized by the application of these principles, and in a few decades the work of progressive schools represented an enormous advance over the wasteful mechanical methods which prevailed in the ordinary schools at the beginning of the nineteenth century. But Pestalozzi's influence was not entirely of this beneficial character, and certain pernicious phases of it will be discussed in the next chapter.

BIBLIOGRAPHICAL NOTES

General works to be found in most libraries. Of the general works on Pestalozzi listed below, those by Holman (No. 2), Kruesi (No. 3), and de Guimps (No. 4) are the best for a brief study of Pestalozzian methods. 1. Pestalozzi, H. Leonard and Gertrude. (D. C. Heath & Co.) 2. HOLMAN, H. Pestalozzi, his Life and Work. (Longmans, Green, & Co., 1908.) Pp. 197-283.

3. KRUESI, H., JR. Pestalozzi, his Life, Work, and Influence. (American Book Company, 1875.)

4. GUIMPS, ROGER DE. Pestalozzi, his Aim and Work. (D. Appleton and Company, 1890.) Pp. 412-424, and scattered references.

5. PINLOCHE, A. Pestalozzi and the Modern Elementary School. (Charles Scribner's Sons, 1901.) Pp. 149-275.

Special works.

The following special works are often not available in small libraries, but are important for those who have access to them.

Concerning oral instruction.

Association from 1860 to 1875.

6. Reports of the National Teachers

7. Report of Superintendent Harris of St. Louis, 1870-1871 8. BARNARD, H. National Education in Europe. (C. W. Bardeen, Syracuse, 1854.) Especially pp. 49–74 for descriptions, by American visitors, of Prussian lessons.

9. BARNARD, H. Pestalozzi and his Educational System. (C. W. Bardeen, Syracuse, n. d.) Pp. 405-428 for the report of Oswego methods of 1862. Contains also many papers on object teaching.

Concerning elementary science. - See above, No. 7.

9a. HUXLEY, T. H. The Advance of Science in the Last Half Century. (D. Appleton and Company, 1898.) Also in same author's Methods and Results, chap. ii. A brief attractive discussion of the topic.

Nature study. 10. See the Nature Study Review (1905), particularly the first volume.

Geography.—11. GAGE, W. L. Life of Carl Ritter. (Charles Scribner's Sons, 1867.) One of the best books in English from which to gain an appreciation of the relation between the work of Basedow and Pestalozzi, and of the scientific and pedagogical development of a subject. The second chapter (pp. 16-43) gives a very good account of Salzmann's school at Schnepfenthal.

12. RITTER, CARL. Comparative Geography. (American Book Company, 1865.) The introduction contains a discussion on the teaching of geography, and the condition of the subject as a science.

13. RITTER, CARL. Geographical Studies. (American Book Company, 1861.) Pp. 13-22, a brief sketch of Ritter's work, by Gage.

14. GUYOT, ARNOLD. Geographical Teaching. (Charles Scribner's Sons, 1867.) Good exposition of principles with sample lessons.

15. GUYOT, ARNOLD. Geographical Series, Introduction. (New York and Chicago, 1866.) Preface gives fundamental principles.

16. PHILLIPS, C. A. Development of Methods of Teaching Modern Elementary Geography, Elementary School Teacher, 1910. Vol. X, pp. 427-439, 501-515.

17. SCHERER, H. Geographie; also Geographieunterricht. (Wunderlich, Leipzig.) Two volumes of a very valuable series. The series contains a volume on the development of the science of each subject geography, mathematics, etc.; also a companion volume on the development of the teaching of each subject.

Concerning arithmetic.

18. COLBURN, WARREN. First Lessons in Arithmetic on the Plan of Pestalozzi. (Houghton Mifflin Company, 1821.) Edition of 1863 practically same as original except the title. Revised and enlarged edition of 1884 contains, in an appendix, the original preface and a memoir of Colburn.

19. UNGER, F. Die Methodik der praktischen Arithmetik. (Teubner, Leipzig, 1889.) The best history of the teaching of arithmetic. Pp. 175-198 discusses Pestalozzi and German followers.

Other books referred to in the chapter. 20. PARKER, F. W.. Talks on Teaching. (Kellogg, 1891.)

21. Teachers College Record, 1891. Vol. XII.

22. BARNARD, H. American Journal of Education, 1858. Vol. V, p. 55. Contains a memoir of Woodbridge.

CHAPTER XVI

PESTALOZZIAN FORMALISM; DEGENERATE OBJECT TEACHING; SIMPLE TO COMPLEX 1

Main points of the chapter.

1. Certain formalized Pestalozzian methods have exerted a pernicious influence on elementary-school practice. 2. Hence Herbert Spencer accepted Pestalozzi's general principles but rejected his formal methods and specific devices.

3. Pestalozzian object teaching often degenerated into memorizing a list of adjectives. Dickens satirized such methods.

4. Pestalozzi and Spencer assumed that the natural process of learning consisted in building up complex wholes from unanalyzable elements, that is, proceeding from the simple to the complex.

5. Consequently Pestalozzi advocated the organization of an alphabet or graduated series of exercises for each subject, which was to be learned as the first step in studying the subject.

6. This principle was the basis of (1) the synthetic, alphabet-syllablespelling method in teaching reading; (2) of the straight-line, curved-line, etc., method of beginning drawing; and (3) of the Grube method of teaching arithmetic.

7. Recently psychologists have maintained that the natural method of learning is not as stated in 4 above, but that the child's experience begins as a big, blooming, buzzing confusion," and that he learns by analyzing complex wholes as far as may be necessary for practical purposes, and then reconstructing more or less organized wholes.

Pernicious elements in Pestalozzianism.-The Pestalozzian methods described in the preceding chapters were a reaction against the formalism of words, which dominated the elementary schools at the beginning of the nineteenth century. This reaction was, for the most part, of permanent benefit to the elementary schools. But there were tendencies to formalism,

1 Special supplementary reading: Herbert Spencer, "Education," chap. ii. See above, p. xxiii, for further directions.