The method of the recitation

Front matter

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H^tt QJoUege of Agriculture

At a^amtll InlaetBitg Strata, Sf. 5.

Preface

The Method of the Recitation has sprung out of school-room work, and is designed to be a practical application of the principles of method to the various problems of class-room instruction. It is an effort to bring together and to organize the various principles that control skilful teaching.

It is based fundamentally upon the inductive-deductive thought movement in acquiring and using knowledge.

This organized plan of laying out recitation work was first projected by the thinkers of the Herbart school in Germany. For more than thirty years they have been developing and applying it under the - title " The Formal Steps of Instruction " {Die formalen Stufen des Unterrichts). Formerly Dr. T. Ziller at Leipzig was a leader in the movement, and more recently Dr. W. Rein at Jena. They worked out their theory and applied it with proficiency to a large variety of topics in different studies, thus showing the flexibility of leading principles under various forms of application.

vii

VIU PREFACE

The Method of the Recitation is based upon the principles of teaching which were expounded and illustrated in the work of Herbart, Ziller, and Rein. At the same time, the authors hope to have shown in the body of the work that we have to do here with principles recognized by teachers in every land, and that there is no thoughtless imitation of foreign methods and devices. While our debt to German thinkers for an organization of fundamental ideas is great, the entire discussion, as here presented, springs out of American conditions ; its illustrative materials are drawn exclusively from lessons commonly taught in our schools. In fact, the whole book, while strongly influenced by Herbart's principles, is the outgrowth of several years' continuous work with classes of children in all the grades of the common school.

The Method of the Recitation may be regarded as Part II of the broad subject of Method of which the "General Method," published earlier, is Part I. The latter book is a discussion of the leading principles of education as they bear on the school curriculum, and is designed to be preliminary to the definite treatment of recitation work.

The final test of the value of any such effort to organize the recitation must be found in the worth of the actual lessons worked out in accordance with

PREFACE IX

its principles. Two chapters, II and XI, are given up to such typical lessons. Each topic or lesson unity treated requires several or even many recitation periods for its completion.

The authors have divided the work nearly equally between them, Chapters I, II, except the illustration " In unity is strength," Chapters IX, X, XI, and XIII, except the parable of the tares, being written by C. A. McMurry. Chapters III, IV, V, VI, VII, and VIII, Chapters XII and XIV by F. M. McMurry.

The present edition has been completely revised and supplied with marginal topics for better use as a text-book. Considerable additions have been made to the original edition and some changes made in the division and arrangement of chapters.

Contents

CHAPTER PAGS

I. Variety versus Uniformity in Methods of

Instruction i

Chapter I Variety Versus Uniformity In Methods Of Instruction

There has been a long-standing dispute among teachers whether or not the processes of instruction must conform to any fixed and uniform regulatives. Among scholars, and even among teachers, many have been sceptical of anything like a definite science of education.

At the first glance, the broad field of education Reasons foi presents a medley, — many and varied studies, chil- 40^3^^^"" dren of all ages and capacities, and teachers of science of

education,

nearly every quality and description. There are many sorts of schools, and great diversity of purpose and method even in schools of the same kind. In high schools, for example, there are general and business courses, classical and scientific courses, but teachers are at variance as to the best methods of instruction even in the classical course, to say nothing of the different standpoints of teachers of classics and of natural science. What is still more discouraging, the very sciences upon which pedagogy claims

Universal principles of method the basis of a science of education.

to be based, psychology and ethics, lie as much in the field of controversy as pedagogy itself. In the midst of this endless variety and fluctuation in the theory and practice of teaching, it is not strange that many educated people, even teachers, take a sceptical attitude toward scientific method, and regard each person as a law unto himself.

This tendency to discredit a science of education is indicated by our use of the term method. There is scarcely a more common word in the teaching profession, and it is frequently employed in the plural form, a practical admission not of one and only one right method, but that their number is legion, Also some of the most common watchwords of our profession point in the same direction, "Freedom and originality," " The teacher is born, not made," " Make your own method."

Our pedagogy seems to have fallen into a condition similar to that in which philosophy found itself in the time of the Sophists. Each man's judgment was counted as good as another's. Each man was the measure of all things, and though two men differed radically, both might be right in their judgments. The Sophists were sceptical of any universal standard of truth.

But Socrates, who followed the Sophists, sought in the individual's thinking, when properly guided, a universal principle of truth, so that all men when they think logically and soundly must agree. He

VARIETY VERSUS UNIFORMITY 3

was in search of a uniform mode of thinking which would have universal validity. Pedagogy likewise is in search of universal principles of method in learning, based not upon the subjective whim of the teacher, but upon the common law of mental action which is universal with children and students, in fact with all human beings. And the extent to which such universal principles of method are discovered, determines the extent to which there is a science of education.

The question is this : Is there any essential, natural process upon which a uniform method of treating the varied school subjects can be based ? As already said, to outward appearance there seems to be no such process; there seem to be no principles that may serve as a guide for all persons in teaching all subjects. But we should not be discouraged by appearances. The fact that even good teachers show an infinite variety of individual and personal traits, and that studies differ greatly in subject-matter, is no proof that there is not a common mode of procedure for instruction. We remember that everywhere in nature and in society is variety and apparent confusion; fundamental laws do not stand out so as to be easily detected by careless observers. They lie deep and must be searched out by patient examination and labor. In the study of trees and flowers no scientist is -deceived by the multiplicity and variety of forms. It is the habit of his mind to reduce all varieties to common structural forms and simple classes.

Hence, while there is a large element in teaching that is always variable, according to the branch of study and the differing personality of teacher or pupils, may there not be essential uniformity ; some great underlying principles of method ? Economy of Could these principles be discovered, no one would prhicipies. deny their value ; we are not so enamoured of indi vidual freedom as to refuse submission to rational, regulated processes.

Definite and valuable principles of action, while they check one's freedom along foolish lines, guide effort into the channels of efficiency. Too much freedom becomes positively oppressive. Whether travelling over a continent or through a field of thought, erecting a mansion, or developing a high moral character, whoever would keep his bearings and work forward to an important end, must have a guide. Whether it be a compass, a model, or an ideal, he must look to it continually for direction. Any one engaged in a work so important and difficult as teaching is much in need of fixed principles which outline for him the ideal of method. If convinced that no one method is right, that no ideal can be set up, he is like a sea captain who is persuaded that whatever course he may choose for his vessel is at least possibly good. He acknowledges the possession of no standard of excellence, and sees chiefly fog in his

VARIETY VERSUS UNIFORMITY 5

chosen course. He is subject, therefore, to half-hearted action, for energy and encouragement are not born of uncertainty and confusion.

No one, therefore, will object to a search for the unity that may underlie the variety of good methods in teaching.

Our text-books supply us with a definite formula- The uniform, tion of methods of teaching. They are generally j^teL^booL^ constructed out of the experience of the better teachers and in conformity with those traditional ideas and practices which are common to the great body of instructors. The examination and comparison of our most widely used text-books in grammar, arithmetic, history, geography, reading, etc., will show a uniformity in at least one very important respect.

It may be said that our text-books in English grammar are built on a single plan. As surely as an ordinary dwelUng has parlor, sitting room, and kitchen, so grammar has orthography, etymology, and syntax. This is one kind of uniformity ; namely, that of leading topics in the subject-matter. But, what is more to our purpose, the general truths contained in these materials are singled out as the central aim of study. In grammar everything culminates in the definitions and rules, whose complete mastery gives us the scientific grasp of the structure and meaning of language. In most books even the method of reaching the rules and definitions is stereotyped. Definitions, examples, and applications constitute the regular order in the treatment of every topic. Green's grammar is an Dlustration. Some of the more recent books have modified the order of topics and have adopted an inductive method of treatment ; but under all changes the definitions and principles expressing the functions of the parts of speech and the syntactical relations of the elements of the sentence have remained the central aim of instruction.

An examination of a score of the best arithmetics in use will show a striking uniformity in the series of important topics treated. The following series is very familiar : the four fundamental operations, factoring, common fractions, decimals, compound numbers, percentage, ratio, proportion, involution, and evolution. But this external uniformity of subject-matter is only a sign of that deeper-lying uniformity which aims at the development and use of fundamental principles. The elementary general truths of arithmetic lie at the basis of all the important topics handled. The solution, analysis, and explanation of problems are simply means for bringing the important principles clearly to light. When the principles can be explicitly stated and intelligently applied, the essential aim of arithmetic has been reached. In most books even the method of procedure in mastering the rule is the same, first one or two simple problems worked out and explained, then the rule, followed by a series of applications growing more complex and difficult.

VARIETY VERSUS UNIFORMITY 7

In algebra and geometry the essential principles which constitute the framework of these studies are still more strikingly prominent as the aim of study. While the methods of approach to principles vary somewhat, the definitions, theorems, and propositions, when finally reached, are formulated in nearly the same language.

In mathematics, therefore, as in grammar, instruction centres in the principles to be understood and applied. All variations in method, whether inductive or deductive, are different modes of presenting these generalizations.

A comparative study of the leading commonschool geographies will show a similar agreement in aim. No study is richer in the abundance and variety of concrete material than geography, but the books follow a strong traditional tendency and are really modelled on a single plan. Not only the outline of leading topics is the same, such as mathematical geography, physical features of the continents, the political divisions and populations, the chief occupations, as agriculture, commerce, mining, and manufacturing, but in these topics the chief purpose is to give a distinct emphasis to the general truths which underlie all the variety of geographical detail.

Some of these truths, for example, are the following : soil comes from rock ; slopes are necessary for drainage, and drainage for farming; mountains greatly influence temperature and rainfall; the

S METHOD OF RECITATION

roads of a country are an index of its civiliza. tion ; great cities owe their growth largely to the advantages of their location for transpcittation ; coal and iron ore are the two most important mineral products ; climate and occupation greatly affect the char, acter of a people. The location of points, the fixing of boundaries, etc., are of use, to be sure, but interest in geography centres primarily in such truths as these.

In history every important event is typical or representative in character, setting forth a truth common to many other events, or reappearing in the lives of many persons. In Hamilton's life and thinking as a statesman the notion of a strong central power of government was potent. This idea appears, also, in other statesmen, as in Webster, Washington, and Lincoln, and has gradually become an idea common to all patriotic Americans. The building of the old national road was a particular event, but it illustrated the principle of the right of the federal government under the constitution to make internal improvements. So every event in history, that is worth learning, helps point the way to a more general truth. History, therefore, has a large number of general truths in store, and it is the deeper, broader meaning of these general ideas which we seek, through particular events, to disclose.

This statement may be accepted without committing one's self in favor of a philosophy of history, such as that presented in Hegel's noted work bearing that

VARIETY VERSOS UNIFORMITY 9

title. One may properly believe that sufficient data for the broadest, deepest truths concerning human progress are wanting, so that history cannot reveal such truths, even to advanced students ; but one may still feel convinced that it is the purpose of history to present general truths' of a lower order, as those just suggested.

Beginning reading is a study in which the mastery and use of arbitrary symbols play a very important part; yet there is a small nucleus of generalization upon which the study is organized. In good reading final consonants are enunciated with distinctness; soft tones are heard; and the voice is modulated in accordance with the thoughts expressed. It is such abstract statements as these that the learner must comprehend and apply before he can read well.

Finally, even spelling contains its rules. But these, you say, are partly useless because of their numerous exceptions. True ; and that is one of the reasons why spelling fails to receive the respect accorded to other studies. Its want of reliable rules deprives it of scientific content, and it is regarded by many persons as an evil, though a very necessary one. It is not a full study.

In these various studies, therefore, we find the tendency predominant to concentrate effort upon the mastery of essential general truths. What is the reason for such uniformity ? Is it simply blind custom, or have we been working out, consciously or unconsciously, a fundamental principle in education ?

Is it not the latter ? Whether conscious of it or not,

text-book makers have been laboring for the nearest

approach to a scientific statement and arrangement

of general truths that each of the studies would per-

^ mit. And while there has been much glib talk about

/freedom and originality in teaching, the text-books

^have held the great majority of teachers in a well-

^ defined routine ; have led them to do practically the

J same things, and in essentially the same way.

The striking similarity that marks each large class of text-books is one of the most noticeable characteristics of our education, and is in clear contrast to that variety of methods discussed at the beginning of this chapter. Education gravitates into these channels of generalized knowledge as surely as rivers work their way through the lowlands. Even in a democratic country where each community is free to adopt its own system and method of education, where no hierarchy of learned men in any way officially directs the educational policy, we see an almost universal tendency toward uniformity, based upon the broad scientific principles of any study.

General If now we find that the ground for this uniformity

Itarting-point ^^ really a scientific idea, not only widely recognized, method™f'''° ^^^ ^^^*^ ^^ psychology, we may fix a starting-point instruction, for a sound pedagogy. The mastery of the general truths of a study must remain the direct purpose of instruction in each branch of knowledge. These

VARIETY VERSUS UNIFORMITY II

truths are what are known in psychology as general notions or concepts. They are the centres around which the knowledge of any subject is grouped and classified. It is the mastery of these rules and principles, and the ability to apply them, that are constantly aimed at in all the best school work. From an examination of the psychologies we detect that the treatment of the precept and the concept (the particular and the general notion) furnishes two leading chapters of mental science. The process of learn- "' ing as explained by all the psychologies culminates'' in the general notion or concept. Psychology sup-' plies, therefore, a strong support to our conclusion as to the basis of scientific method.

It would not be difficult to show that all the higher studies, as history, science, language, medicine, law, etc., become organized under general notions or principles ; in fact, the definition of science is " generalized, classified knowledge."

In the history of philosophy also the general notion plays a r61e not less important than in these other subjects. From the days of Socrates and Plato on, inductive and deductive reasoning have set the general notion as the centre of all thinking — as the thing aimed at in induction, and as the basis of all true deduction. When Herbert Spencer, therefore, calls his most fundamental book " First Principles," he has in mind those general truths which he at the basis of his entire system of thought.

In conclusion, we find that the general notion is a ''pivotal centre of discussion not only in elementary ''' and higher studies of all sorts, but also in the great ' fields of psychology and philosophy.

It is not claimed that the method by which general notions have been worked out in our text-books is uniformly correct and valid. This is a question that we are not called upon to settle at this point. Whether or not an inductive or deductive approach to general truths is the correct one, we can leave for further >/ consideration. But one leading aim of instruction in . every important study is a mastery, in the full sense, -■ of its general truths. Without this basis no method of instruction has any validity. It may be that the method by which this aim can be best realized has been so thoroughly misinterpreted and misapplied that we have approached a uniformity of error in our methods of teaching. It may be that definitions and abstract formulae have been set too much in the forefront of every lesson, and also that systematically formulated knowledge has been forced prematurely into lower grades. Yet it is a great step in the right direction to have fixed clearly the aim of instruction, to have determined the goal toward which all proper mental movement tends. Assuming that our conclusions thus far are justified, we may move on to a discussion of the essential steps in a correct method of instruction.

Chapter II Illustrative Lessons Showing The Processes Of Reaching General Truths

In the first chapter, having located the goal of instruction in general notions and in their proper use, the question, how to reach them, now becomes paramount. In the present chapter a number of lessons is worked out to illustrate the different processes in vogue for mastering general truths. In each example two different methods are presented : first, that common to many of our text-books and to the usual practice of teachers ; and second, the fuller inductive and developing method now followed in some schools.

The purpose of this chapter is not only to show the two ways of reaching a comprehension of such truths, but also to suggest other important phases of recitation work. In the discussions of recitation method which follow, these lessons may be kept in mind as illustrating the principles under treatment.

The lessons are taken from different studies, — arithmetic, geography, literature, natural science, and history. They recognize generalizations as the goal of instruction, but leave open the question as to

>3 whether or not any further principles of method may be found in the treatment of these various materials.

The Addition of Fractions

In first learning to add fractions, one method of the arithmetics is fairly illustrated by the following: — What is the sum of 3%, ^f , and \% ?

Process : /^ + M + it = ^F^ = f f = ^if • What is the sum of \\, \%, ^|, and ^ ? What is the sum of |, ^, and {^ ?

Since unlike fractional units cannot be added, re-

fduce the fractions 4, A. a-nd

28 33 91 43 15^' *° ^ common denomit7 + ¥t + f¥ = ft=it?- nator and then add the

resulting fractions.

After ten or a dozen problems the following rule is given : —

" To add fractions, reduce the fractions to a common denominator, add the numerators of the new fractions, and under the sum write the common denominator."

The following more detailed process is suggested for consideration : —

How shall we add fractions whose denominators are unlike }

What fractions have you already learned to add } Try these, \ and |. | and |. ^ and ^. Can you

ILLUSTRATIVE LESSONS I5

add \ and ^ ? What change is necessary before adding them? Why not add them in the same way as the others ? How can you add one bushel and one peck ? Change the bushel to pecks. Add two yards and one foot. What change was necessary in both examples ?

Add J and f ^ = |. | + 1 = |. Illustrate this with a square divided into fourths and eighths. Add f and ^^. Add ^ and |. What was done in all these cases before adding .■' How shall we add ^ and ^ ? How can you change the two fractions so that they will be alike, that is, have the same fractional unit.' Change them to twelfths. One-third equals how many twelfths .' One-fourth equals how many twelfths ? i + i = -^ + A = 1^- Illustrate this with a sheet of paper folded into thirds, fourths, and twelfths.

Add I and J. What is the common fractional unit? Itis^. |4-|=-^V-h^ = ^.

|and^ = ? i + ^=U + ^ = U=-^^- Notice, now, what was done in each of these problems : J + i, f + i and I -f 3^. The fractions in the first were changed to twelfths, in the second to tenths, and in the third to twentieths. Was the value of the fractions changed? But in each example the fractions were changed to a common fractional unit, or a common denominator. What was done to the numerators ? In each fraction they were changed to correspond with the change in the denominator. Then, in adding, the numerators were added.

Make a rule for adding fractions that will cover all the cases so far worked : —

"To add these fractions, change the fractions to equivalent fractions having a common denominator. Add the numerators for a new numerator and use the common denominator for the new denominator."

To acquire skill and accuracy in this kind of addition : —

1. Add oral problems as follows : —

2. For written work add such as these : —

3. Add mixed numbers as follows : —

Trade Centre in the Northwest — Minneapolis as a Type

This topic may be treated in two ways, briefly, as in the geographies, or in a fuller inductive manner. One of our grammar school geographies says : —

" Minneapolis, which adjoins St. Paul, so that the two are called the 'Twin Cities,' manufactures more flour than any other city in the world, its capacity being 40,000 barrels a day. The two cities have had a remarkably rapid growth."

Tilden's " Commercial Geography," which is very much fuller on this topic than the regular geographies, says: —

"Minneapolis, on the Mississippi at the Falls of St. Anthony, is the greatest flour-milling city in the world, and one of the greatest lumber markets and lumber-manufacturing centres in America. The yearly output of the flour mills is nearly 10,000,000 barrels. Of this about one-third is shipped to foreign countries, constituting about one-fourth of the total flour export of the United States. In manufacturing this flour the Minneapolis mills grind about 45,000,000 bushels of wheat annually. The Pillsbury ' A ' mill is the largest flour mill in the world, having a daily capacity of 7500 barrels. The saw and planing mills of Minneapolis have an annual output of the value of ^10,000,000, and the lumber is manufactured into barrels, boxes, cars, wagons, and many other products, aggregating a value twice as great. In the decade 1 880-1 890 the population of Minneapolis increased nearly fourfold."

The following is a much fuller treatment of Minneapolis in its important relations to the Northwest, such as would require several recitations : —

We will inquire into the causes which make Min- Minneapolis neapoHs an important city.

Where is it and what have you heard about it.' Why is it sometimes called the flour city .' What is meant by the "Twin Cities".' Recall Hennepin's trip on the upper Mississippi and what you know of the Falls of St. Anthony. Can you tell something of the wheat fields and pineries of Minnesota ?

St. Paul was an important trading-point and the capital of the state before Minneapolis had a beginning. Why should MinneapoUs spring up only ten miles away and soon become larger even than St. Paul? The great water-power of the Falls is the first answer. How can water from a river be used to run a mill ? Where have you seen a mill run by water-power.? Describe the water-wheel, the dam, and mill-race. At Minneapolis the water is carried by a channel on the west side of the falls under the great mills where it drops forty feet to the large turbine wheels at the bottom, turning them and with them aU the machinery of the mills.

Lumber. Along the upper Mississippi and its branches in

northern Minnesota are large pine forests. How could the pine logs be brought to the sawmills at Minneapolis? Some of the early settlers moved northward into the pineries, cut down the trees in winter and sent them floating down the streams to the sawmills at Minneapolis. Soon large lumber companies were formed with big sawmills at the Falls, and owning extensive pine lands in the North. In the winter time they sent scores of men to the logging camps to get out the logs and float them down in springtime to the mills. With the mills at Minneapolis came the families of the mill companies and of the workmen, and thus a flourishing town sprang up at the Falls. Great lumber yards with their stacks of boards stretched along the river.

Some of this lumber would be used in building up Minneapolis, but where would most of it be sent ?

The farmers were rapidly settling up the prairie regions of the Northwest. Locate these prairies on the map. In what directions from Minneapolis would most of the lumber be sent ? For two or three hundred miles to the west, southwest, and northwest from Minneapolis the whole prairie land was rapidly taken by settlers. How could this lumber be gotten best to the new farms and villages } At first wagons were used, but soon railroads were built across the prairies, from St. Paul and Minneapolis, and car-loads of lumber were sent out to the towns and distributed by merchants to the farmers. As the lumber business grew the whole upper Mississippi with its tributaries became a network of streams and logging camps, collecting logs for the mills at Minneapolis. Closely connected with the sawmills were the planing mills for preparing dressed lumber, sash, doors, moulding, etc. Factories were also built for the manufacture of furniture, barrels, wagons, and agricultural implements. All these products were distributed by the railroads over the broad prairie regions of southern and western Minnesota, Iowa, the Dakotas, and Nebraska. In short, Minneapolis, by reason of its favorable position on the river and its water-power, soon became the chief centre of the lumber business of the Northwest, collecting logs from the pine lands of the North, working them up into lumber, furniture, etc., and distributing them to the broad area of prairie states. How would the prairie farmer pay for the lumber

(Vheatand and other goods coming from St. Paul and Minnoi °'^' apolis ? What is the leading crop of the Northwest ?

It was soon found that the prairies were well adapted to the growth of wheat and other small grains. In a few years the prairies, with the rich valley of the Red River of the North, became one of the largest wheatproducing districts in the world. How would the farmers get their wheat and other grains to Minneapolis ? The water-power at the Falls was soon found to be more valuable for flour mills than for sawmills. In the lumber mills the sawdust supplied abundance of fuel for the furnaces, so that they did not need the water-power, and hence the latter was used for running the great flour mills that were now built at the Falls. The same railroads which distributed lumber to the prairies collected the wheat. In 1871 only two car-loads of wheat were received in Minneapolis. In 1887 the Great Western road alone brought 33,000,000 bushels of wheat to the elevators at Minneapolis. In 1896 250,000 barrels of flour were ground here in a single week. In what directions would this immense quantity of flour be shipped and marketed .' What lake ports would receive much of it for shipment by water ? Notice on a railroad map the important railroad lines from the Twin Cities to Duluth, Milwaukee, and especially to Chicago. Much of this flour is shipped to Illinois, Ohio, etc., much to Pennsylvania, New York, and New England, and whole cargoes to Liverpool and Hamburg.