Proceeding from simple to complex. Favored by Spencer.The second large group of formalized Pestalozzian practices resulted from the extreme application of the principle that in the process of instruction the teacher should proceed from the simple to the complex. The validity of this principle will be discussed later in this section. It is open to a variety of interpretations. Thus Herbert Spencer states it as the first of the Pestalozzian principles which he would "defend in its entire extent," but rejects the practices which Pestalozzi described for its application. Spencer defended the principle in these words:

That in education we should proceed from the simple to the complex is a truth which has always been to some extent acted upon; not professedly, indeed, nor by any means consistently. The mind grows. Like all things that grow, it progresses from the homogeneous to the heterogeneous; and a normal training system, being an objective counterpart of this subjective process, must exhibit the like progression. Moreover, regarding it from this point of view we may see that this formula has much wider applications than at first appears. For its rationale involves not only that we should proceed from the simple to the combined in the teaching of each branch of knowledge, but that we should do the like with knowledge as a whole.

Pestalozzi desired to mechanize instruction. With Pestalozzi this principle was bound up with his desire to mechanize instruction. Describing his work in the second school in which he taught at Burgdorf (1799), Pestalozzi said:

I once more began crying my ABC from morning to night. . . . I was indefatigable in putting syllables together and arranging them in a graduated series; I did the same for numbers; I filled whole notebooks with them; I sought by every means to simplify the elements of reading and arithmetic, and by grouping them psychologically, enable the child to pass easily and surely from the first step to the second, from the second to the third, and so on. The pupils no longer drew letters on their slates, but lines, curves, angles, and squares. (6: 179.)

Shortly after this, when Pestalozzi was explaining his experiments to a visiting French-Swiss official, the latter said, "I see, you want to mechanize instruction." 'He had hit

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the nail on the head," said Pestalozzi, "and supplied me with the very word I wanted to express my aim and the means I employed." (6: 183.)

Later Pestalozzi said that he meant that he desired to psychologize instruction; but the fact remains that what he really did was to reduce much of instruction to a mechanical routine by application of the principle of proceeding from the simple to the complex.

Would organize an alphabet of every subject.

In one

of Pestalozzi's last publications, "The Song of the Swan," he said:

I now came to consider the idea of elementary education from the point of view of means of instruction. From its very nature, it demands the general simplification of its means, which simplification was the starting-point of all the educational labors of my life. At first I desired nothing else, but merely sought to render the ordinary means of instruction for the people as simple as to permit of their being employed in every family. And so in every branch of popular knowledge or talent, I set to work to organize a graduated series of exercises, the starting-point of which was within everybody's comprehension, and the unbroken action of which, always exercising the child's powers without exhausting them, resulted in a continuous easy and attractive progress, in which knowledge and the application of knowledge were always intimately connected. (6: 375.)

Pestalozzi said that these graduated series of exercises would make teaching so easy that "schools would gradually almost cease to be necessary, so far as the first elements are concerned."

Thorough mastery of each step required. — Closely connected with the practice of using a minutely graduated series in each subject was the emphasis on the mastery of each step or element before proceeding to the next. This notion of thoroughness was another factor in establishing mechanized routine among the Pestalozzians.

The influence of these principles in the teaching of subjects in the elementary schools was very great, particularly in the case of reading, arithmetic, drawing, writing, and form study.

From simple to complex in teaching reading; synthetic method. In the teaching of reading the influence of Pestalozzi was to fix and stereotype the synthetic method of beginning with long drills on the letters, and then proceeding to syllables, words, phrases, etc. The first steps in this alphabet-syllable-spelling method of teaching reading Pestalozzi described in these words:

The spelling-book must contain the entire range of sounds of which the language consists, and portions of it should be repeated daily in every family. . . . No one imagines to what a degree the attention of infants is aroused by the repetition of such simple sounds as ba, ba, ba, da, da, da, ma, ma, ma, la, la, la, etc.

The spelling book contained all the possible combinations of vowels and consonants for such drill. After these had been mastered, words were to be learned by spelling them. As was the case in Salzmann's school, Pestalozzi provided large movable letters to be inserted in a frame by the teacher as a means of class instruction. These methods were copied in the Prussian schools which were described in Professor Stowe's report to the Ohio legislature in 1839. After telling how the children were drilled on the elementary sounds of letters and syllables till they were mastered, Stowe said:

They were now prepared to commence reading. The letters are printed in large form on square cards; the class stands up before a sort of rack, the teacher places one upon the rack . . . [and says], What letter is that? [Pupils answer] H. He places another. What letter is that? A. I now move these two letters together, thus: HA. What sound do these letters signify? Ha. [And so on, adding a letter at a time, the teacher proceeded until he had formed hard, hard fist, hard fisted, hardfistedness.] (3: 52.)

In the next higher grade the reading proceeded as follows according to Mr. Stowe :

The sentence is first gone through with in the class, by distinctly spelling each word as it occurs; then by pronouncing each word distinctly without spelling it; a third time by pronouncing the words and mentioning the punctuation points as they occur [and so on until the sentence

is finally read with expression]. Thus one thing is taken at a time, and pupils must become thorough in each as it occurs, before they proceed to the next. (3: 52.)

In the Oswego schools, similar synthetic methods were used, but with special emphasis on the phonic values instead of the names of the letters.

Study of form, drawing, and writing.— Applying the general principle of reducing each subject to its elements, Pestalozzi maintained that the elements of drawing and writing are lines and geometrical figures of various sorts, and that long drill in these elements as arranged in his "alphabet of form" should be the first step in instruction. These practices were copied in England and America.

The elements of form with which the children were to be made acquainted occupied sixty pages in N. A. Calkins's Primary Object Lessons" (1861), one of the best of the numerous books on object teaching published in America about the time of the Oswego movement. This included instruction about corners, sides, straight and curved lines, plane and curved surfaces, right, acute, and obtuse angles, equilateral and right-angled triangles, perpendicular, horizontal, and parallel lines, the square, rhomb, and parallelogram, pyramids, prisms, cubes, circles, semicircles, circumferences, arcs, center, radius, diameter, cylinders, cones, spheres, hemispheres, and ovals. Calkins's book was largely an imitation of Miss Mayo's, which included, in addition to the above, the tetrahedron, octahedron, pentagonal dodecahedron, icosahedron, rhombic dodecahedron. All of this was to be taught in infant or primary schools and was partly correlated with the teaching of drawing.

The teaching of drawing was to begin with the making of these geometrical figures, starting with various kinds of lines, etc. Spencer, while defending the principle of proceeding from the simple to the complex, said that he wholly disapproved of this "formal discipline in making straight lines

and compound lines." A drawing book constructed on these principles he denounced as "the most vicious in principle" which he had seen.

Writing was taught in connection with drawing in the Pestalozzian methods. The letters were analyzed into straight, curved, and slanting lines, into acute and obtuse angles, etc., and drill given on these before proceeding to write letters, words, and phrases.

Thorough mastery of elements in arithmetic; Grube method. In the preceding chapter the improvements that had been made in the teaching of arithmetic by applying the Pestalozzian principle of sense perception were discussed in connection with Warren Colburn's "First Lessons," which was published in Boston in 1821. The Pestalozzian principle of reducing each subject to its elements and requiring thorough mastery of each element before taking up the next was also very influential as applied to the teaching of arithmetic. This application was emphasized by a German, Grube (1816-1884), in a work published in 1842. Grube was not original in his system of teaching arithmetic. He copied a number of Pestalozzi's characteristic ideas, notably the sense-perception basis, as well as ideas from other sources. The essential characteristic for our present purposes, and the one by which the system is most commonly known, is the practice of considering each number as an individual, and mastering all the possible operations with it, namely, addition, subtraction, multiplication, and division, before taking up the next number. This differs radically from the common practice of first teaching counting, sometimes up into the millions, then addition of all numbers, then subtraction, then multiplication and division. Inasmuch as Grube began with the number one, which was mastered before proceeding to number two, and so on up to ten, counting was definitely eliminated. The first year was spent on the numbers from one to ten, and the first three years on the numbers up to one hundred.