CHAPTER XVIII
THE TEACHER IN RELATION TO THE COURSE OF STUDY
Teachers sometimes look upon the course of study merely as a demand made by those in control of the school system for a large amount of work to be accomplished. The course of study indicates that certain topics in English, arithmetic, nature study, geography, history, industrial arts, and the other subjects of the curriculum are assigned to the grade, and the teacher expects that her pupils will be examined on this work at stated times during the year in order to determine the efficiency of her work and the fitness of the children for promotion. From this point of view, the course of study is an ever present taskmaster, always urging that more work be accomplished. Let us inquire whether this is in reality the meaning of the course of study to the teacher.
In the first place, all will admit that in any system of schools it is necessary to determine somewhat definitely the work to be done by a given grade. If such provision were not made, it would be impossible to transfer children from one school to another, and very difficult for the supervisory force to render help to large numbers of teachers. Then, too, there is an order in the development of subjects, which is necessary both from the standpoint of the subject and from the point of view of the child who is to gain the experience which the subject offers.
It is true that a course of study which is made to fit all of the children of a great city or state must be interpreted liberally, if good teaching is to be done. To this end, our best courses of study demand that a minimum amount of work be done by all teachers, and suggest alternative and optional work to meet the needs of children whose experiences are varied, and whose needs are correspondingly different. In any progressive school system, the capable teacher has opportunity to vary the material presented under the head of the various subjects in such a manner as will satisfy the interests and the problems of the group of children for whose growth she is responsible.
A good course of study will save the teacher much time and energy by the organization of material which it presents. In many of our larger cities a volume of from fifty to two hundred pages has been prepared for each subject. These manuals suggest the order in which it has been found by experience that the topics can best be presented. In many cases a helpful analysis of each large topic from the point of view of presenting it to children is included. Besides this organization of material, references which will prove helpful to the teacher, both from the standpoint of subject matter and of method, are included in our best courses of study. In many cases suggestions for teaching, elaborated at times into complete lesson plans, are given.
In the making of the course of study, the teacher should welcome any opportunity to contribute her knowledge concerning the availability of material or the methods to be used in her grade. Any good course of study should be the joint product of at least three classes of people: the expert in the subject, the expert in supervision and administration of schools, and the expert teacher. The subject matter expert is needed to pass upon the material from the standpoint of fact and from the point of view of one who sees the beginnings of a subject in relation to the whole field. The supervisor has to provide for the proper relation of the different subjects, determines the amount of time to be devoted to the subject, and the general method of procedure in teaching the subject. The teacher needs to advise as to the practicability of the whole scheme. She has in mind a particular group of children with certain experiences, interests, and abilities, and her judgment is probably safer than either of the others as to the availability of any particular topic or phase of the subject. In addition to this service, any group of teachers can give most significant help with respect to the methods which have proved most helpful. Indeed, our courses of study could be made much more helpful if teachers were only asked to give suggestions concerning the organization of material and methods of teaching, which they are so well equipped to offer by reason of their experience in teaching the subject to children. Happily, the practice of inviting the coöperation of teachers in making the course of study is becoming more common in our cities. Any capable teacher who is anxious to participate in the organization of the curriculum will find opportunity to make her contribution.
Possibly there are teachers who, because of the very excellence of the courses of study provided, feel that all that is required for them is to follow blindly the directions given. Instead of considering the course of study as a hard taskmaster, they look upon it as a crutch upon which they lean heavily. For these teachers there is little need for preparation. The course of study and the textbooks have solved the problems of teaching. Let us inquire just what the curriculum of our schools stands for before attempting to decide just what relation the teacher bears to it.
A course of study is not so much knowledge to be poured in. Rather it represents possible experiences for which children may have need, experiences which will aid them in the solution of their problems and make possible for them the realization of their purposes. How did all of this knowledge come to be preserved, and how did it happen to be arranged in groups labeled by certain names? Men have preserved from time to time, by handing down by word of mouth or by records made on stone, wood, skin, paper, or other surfaces, knowledge which they have found useful in meeting the problems which confront them. For convenience of reference this knowledge has come to be grouped, and to each group a name has been applied. If we could only remember how we came to have this body of knowledge, how it happened to be thought worth while to preserve the experiences which when grouped together we know as subjects, it might make us a little more judicious in our attempt to acquaint children with their inheritance.
Our schools have all too frequently acted upon the principle that children could assimilate the school subjects without reference to their past experience or their present needs. It has been common to say, teach so much of this or that subject, just as if the child mind was a receptacle to be filled. The difficulty of this attitude toward school subjects is twofold: first, the children fail to gain any appreciation of the experiences involved; and, second, they fail to gain from the process the power of independent thought, or the spirit of investigation which it is the purpose of education to impart.
The doctrine of formal discipline, as commonly interpreted, has been largely responsible for our wrong idea of the meaning of subjects of study. The idea that any study, especially if it proved disagreeable to the pupil, and had no definite relationship either to his past experiences or present needs, would mean most for his education, has not yet entirely disappeared. Aside from the psychological fallacy involved, that ability to do one kind of work would spread or be available for all other kinds of mental activity which we call by the same general name, the devotees of the doctrine ignored the fact that the maximum of activity or hard mental work could be secured only under the stimulus of genuine interest.[30]
Possibly the introduction of the industrial arts[31] and the more rational approach which they demand, may serve to illustrate the method to be used in teaching other subjects. In cooking, for example, we would hardly expect to have a child begin by engaging in an exercise in beating eggs without reference to any problem which required this activity. If children are to learn something of wood and its use in our industries, we commonly expect them to gain some knowledge of the processes involved in the course of the construction of furniture for the playhouse, a flower box for the window, a sled, a checkerboard, or some other interesting project. It is true that the industrial arts lend themselves more readily to the dominant interests of children to do and to make than do most school subjects. If these activities, which are essentially the activities characteristic of our modern civilization, be used to best advantage, they will offer many opportunities for making significant the other subjects.
Any considerable participation in the processes which are fundamental to the great industries cannot fail to arouse an interest in the source of materials, the development of the industry, and a desire to express one’s self with reference to the work which is being done. From the interest in the source of materials grows naturally the work in nature study and geography. The development of the industry takes us back even to the time of primitive man, and history becomes significant. The handling of materials in construction suggests the need of measurement, and arithmetic is provided for. In all of this work there will be a demand for communication, the necessity to learn what others have recorded in books, and the wish to express one’s own experience in oral and written speech. The experiences of people like ourselves, as idealized in literature, will make its appeal in spite of the worst our teaching can do. It is not maintained that all subject matter groups itself naturally around industrial activities, and that these activities should, therefore, form the center of the curriculum; rather, it is sought to emphasize the relationships to the real needs of children and the possibility of utilizing these genuine motives in the teaching of school subjects.
We teach the subjects of the curriculum in order that children may understand their environment, be adjusted to it, and, as President Butler puts it, come into possession of their spiritual inheritance. Out of the work which is done, these same children should gain power to adapt themselves to new conditions and should be equipped to render service in the progress which is yet to be made in our society. Now one’s adjustment to the present environment must be an adjustment to his environment, a solution of his problems as they at present exist. Future adaptability is conditioned by the experience which one has had in making such adjustments. The ability to contribute to the progress in which each should participate is dependent, not so much upon the number of facts one possesses, as upon the attitude of investigation which characterizes him, the respect for truth, and ability to think straight which have been developed by his education. From whatever point of view we approach the problem of teaching our subjects, the answer is the same: meet present situations, solve present real, vital problems, make subject matter meet the needs of the children you are teaching. This analysis of the curriculum makes apparent the important part to be played by the teacher in making available the experiences which the school subjects are organized to present.
The courses of study may present much that is helpful in the organization of material, the suggestions for teaching may be gathered from the experience of many teachers, and still the great problem of making these subjects vital to children remains as the work of every teacher. Motives which grow out of the experience which children have already had must be sought. The material to be presented will be significant in the experience of these children only when they approach it in order to satisfy their real needs. Aside from the possibility of finding in one of the subjects, as, for example, the industrial arts, a motive for other work, the school situation itself presents many opportunities for discovering real needs to children.
The school festival, school parties for parents, fairs and sales, the general assembly, excursions, gardening or other industrial activity, plays and games, have in the hands of skillful teachers provided a compelling motive for a great variety of school work. The author would not deny the power of intellectual interest, but he knows, as does every other teacher, that with children in the elementary school this motive is only gradually developed. The teacher who is alert to find some real need for the computations of arithmetic; who gives a genuine opportunity for oral or written expression; who appeals to the desire to use the knowledge gained in history and geography by means of the historical festival, the article in the school paper, and the like, as well as to the curiosity of the child; who allows children to make real things which satisfy their individual or collective needs in the industrial arts,—is the teacher who is teaching school subjects in the way that will mean most in the education of her pupils.
The demand that the teacher vitalize the curriculum does not lose sight of the necessity for drill, or of the demand that children know, as a result of their education. As a matter of fact, the more vital the experiences, the more apparent it becomes to both teacher and pupil that the fixing of knowledge or the acquiring of skill is a necessary condition of present efficiency and of future progress. The children who have the most genuine need for the multiplication table will be the first to learn it. If you are to read to a whole school and want to have them enjoy with you the selection which you are to interpret, you will have the best possible reason for good expression. History means something, if you really need to know the history of a period in order to reproduce accurately its language, manners, dress, and the like in your festival. The mistake which at times has been made by enthusiastic teachers of neglecting the drill side of the work, has not been due to any difficulty which the situation presented from the standpoint of the children who are engaged in meaningful activities.
The teacher may not expect all children to gain equally in command of the experiences represented by the course of study. For her there must literally be courses of study for each subject, in that she must adapt her work in so far as is possible to individual needs. The office of teacher may well be exalted, for it is the teacher who must, because of her insight, provide for the needs of each child committed to her care, and in rendering this service provide society with its greatest asset, a truly educated human being.
For Collateral Reading
S. T. Dutton and D. Snedden, Administration of Public Education in the United States, Chapter XVIII.
Exercises.
The selections from courses of study are quoted by Dr. C. W. Stone in his monograph on Arithmetic Abilities and Some Factors Determining them. In Dr. Stone’s study the pupils in twenty-six schools or school systems were tested. One of the problems raised had reference to the excellence of the course of study. The selections quoted represent a variety in excellence such as one will find in the courses of study prepared in any subject.
Study these selections from the following points of view:—
1. Do any of them give too little information to the teacher concerning the work required in the grade?
2. Do any of them restrict the work of the teacher unduly?
3. Which do you consider the best course of study?
4. Are any of these statements so complete as to relieve the teacher of the necessity of reorganizing the work for her own class?
5. How would you modify any of these courses of study in order to make it more valuable to teachers?
6. Indicate possible maximum, minimum, and optional work in the third-grade work in arithmetic.
SELECTIONS ILLUSTRATING GENERAL EXCELLENCE
From each of two systems ranking among the lowest five in course of study.
3 B. Speer work. Simple work in addition and subtraction, following the plan in the Elementary Arithmetic.
3 A. Primary Book. First half page 26, second half page 41.
Grade III, Number
Exercises, mental and written, in addition, subtraction, multiplication, and division of numbers.
The processes will be explained.
The multiplication table up to 12 will be made by the pupils and thoroughly committed to memory.
Drill in rapid addition.
Notation and numeration to five periods.
Table of weights, United States and English money. Problems in all tables learned.
Square and cubic measure. Troy and apothecaries’ weights. Principles of multiplication.
From the system standing best in course of study.
Grade III B
Scope: Review the work taught in preceding grades. (This review may require from four to six weeks.)
Addition and subtraction of numbers through twenty. Multiplication and division tables through 4’s. Give much practice upon the addition of single columns. Abstract addition, two columns; the result of each column should not exceed twenty. The writing of numbers through one thousand. Roman notation through one hundred. Fractions ½, ¼, and ⅓. The object of the work of this grade is to make pupils ready in the use of the simple fundamental processes.
Book: Cook and Cropsey’s New Elementary Arithmetic (for use of teacher), pp. 1 to 46.
The chief difficulty in the work of this grade is in teaching the arithmetical forms as applied to concrete processes. Pupils should know very thoroughly the work given on pages 1 to 23, Cook and Cropsey’s Arithmetic, before any new forms are taught. They have up to this time used the arithmetical signs and the sentence, and have stated results only. New forms for addition and subtraction are first applied to concrete processes on page 24. No other forms should be taught until pupils are very familiar with these. A drill should be given showing that these two forms are identical and that we must first know what we wish to use them for, if applied to problems. Write
9
2
upon the board and indicate your thought by the signs + and -.
| 9 | 9 | 9 | apples | 9 | apples |
| + 2 | - 2 | + 2 | - 2 | ||
| 11 | 7 | 11 | 7 | apples |
Pupils should be very familiar with these forms before any written concrete work is given.
When the new form for multiplication is introduced, this drill should be repeated:
| 9 | 9 | 9 |
| + 2 | - 2 | × 2 |
| 11 | 7 | 11 |
Nothing new should be added to this until pupils can use these forms without confusion.
When presenting the new forms for division and partition the same method may be used, but pupils should use the form for division some weeks before using the same form for partition. It is not necessary to use the division form for partition until the last four weeks of the term, and not even then, if there seems to be any danger of confusion in using the same form for both processes. The terms division and partition should not be used. The terms measure and finding one of the equal parts can be easily understood. Pupils should be able to read arithmetical forms well, before any use is made of these forms in their application to written concrete work.
All concrete problems should be simple and within the child’s experience.
Grade III A
Scope: 1. Review the work of Grade 3 B.
2. Abstract addition of three columns. Subtraction, using abstract numbers through thousands. Addition and subtraction of United States money. Multiplication and division tables through 6’s. Multiplication and division of abstract numbers through thousands, using 2, 3, 4, and 5 as divisors. Addition and subtraction by “endings” through 2 + 9, last month of term. Writing numbers through ten thousands. Roman notation through one hundred. Fractions ½, ¼, and ⅓.
3. Application of fundamental processes to simple concrete problems, of one step.
4. Measures used—inch, foot, yard, square inch; pint, quart, gallon; peck, bushel; second, minute, hour, day, week, month, year. Use actual measures.
Books: (In hands of pupils) Walsh’s New Primary Arithmetic, pp. 1 to 68.
(For teachers’ use) Cook and Cropsey’s New Elementary Arithmetic, pp. 46 to 85, Article 105.
Even with only the work of a single grade to judge from, one has no difficulty in recognizing the wide difference in the excellence of these courses. As may be seen from Table XXVIII, page 73, in the rating they stand about thirty steps apart, i.e. the one from which the third illustration was taken has a score of 65, while the others have scores of 32 and 39, respectively.
SELECTIONS ILLUSTRATING EXCELLENCE IN DRILL AND IN CONCRETENESS
From the system ranking next to the best in drill.
Grade III B
I. Objective.
1. Work.
a. Fractions. Review previous work. Teach new fractions; 7ths, 10ths, and 12ths.
b. Notation, numeration, addition and subtraction of numbers to 1000.
c. Liquid and dry measures.
d. United States money.
e. Weights.
2. Objects and Devices.
a. Counting frame.
b. Splints, disks for fractions, etc.
c. Shelves.
d. Liquid and dry measure.
e. United States money.
f. Scales.
II. Abstract.
1. Work.
a. Counting to 100 by 2’s, 10’s, 3’s, 4’s, 9’s, 11’s, 5’s, beginning with any number under 10; counting backwards by same numbers, beginning with any number under 100.
b. Multiplication tables. Review tables already studied. Teach 7 and 9.
c. Drill in recognizing sum of three numbers at a glance; review combinations already learned; 20 new ones.
2. Devices.
a. Combination cards, large and small.
b. Wheels.
c. Chart for addition and subtraction.
d. Fraction chart.
e. Miscellaneous drill cards.
f. Pack of “three” combination cards.
Prince’s Arithmetic, Book III, Sects. I and II.
Speer’s Elementary Arithmetic, pp. 1-55.
Shelves: See II A.
Combination Cards: large and small. These cards should contain all the facts of multiplication tables 3, 6, 8, 7, and 9. As:—
| 7 × 1 | 2 × 7 | 7 ÷ 1 | 21 ÷ 3 | |
| 1 × 7 | 7 × 3 | 14 ÷ 2 | 21 ÷ 7, | etc. |
| 7 × 2 | 3 × 7 | 14 ÷ 7 |
For use of these cards, see directions in I B.
Wheels for Multiplication and Division:
See directions under II A.
Chart for Adding and Subtracting:
For directions, see II B and II A.
Add and subtract 2’s, 3’s, 4’s, 5’s, 9’s, 10’s, 11’s, 12’s, 15’s, and 20’s.
Fraction Chart shows, ½, ¼, ⅛, ⅓, 1/6, 1/9, 1/12.
Miscellaneous Drill Cards:
For directions, see I A.
“Three” Combination Cards:
For use, see I A.
Grade III A
I. Objective.
1. Work.
a. Fractions previously assigned.
b. Notation, numeration, addition, subtraction, multiplication, and division of numbers to 1000.
c. Long and square measures.
d. Weights.
2. Objects and Devices:
a. Counting frame.
b. Splints, disks for fractions, etc.
c. Shelves.
d. Scales.
II. Abstract.
1. Work.
a. Counting to 100 by any number from 2 to 12, inclusive, beginning with any number under 10; counting by same numbers backward, beginning with any number under 100.
b. Multiplication tables—all tables.
c. Drill in recognizing sum of three numbers at a glance; review combinations already learned; 20 new ones.
2. Devices.
a. Combination cards—large and small.
b. Wheels.
c. Chart for adding and subtracting.
d. Chart for fractions.
e. Miscellaneous drill cards.
f. Pack of “three” combination cards.
Prince’s Arithmetic, Book III, Sects. III to VI, inclusive.
Speer’s Elementary Arithmetic, pp. 56-104.
Shelves: See II a.
Combination Cards: large and small. The cards should contain all the facts of the multiplication tables 11 and 12, also the most difficult combinations from the other multiplication tables. As:—
| 12 × 1 | 12 ÷ 1 | 24 ÷ 2 |
| 1 × 12 | 12 ÷ 12 | 24 ÷ 12, etc. |
| 12 × 2 | 12 ÷ 2 | |
| 2 × 12 | 12 ÷ 3 |
For use of cards, see directions in I B.
Wheels for Multiplication and Division:
See directions under II A.
Chart for Adding and Subtracting:
For directions, see II B and II A.
Add and subtract 6’s, 7’s, 8’s, 13’s, 14’s, 16’s, 17’s, 18’s, and 19’s.
Review other numbers under 20.
Chart for Fractions shows all fractions already assigned.
Miscellaneous Drill Cards:
For directions, see I A.
From the system ranking best in concreteness.
Mathematics: If the children are actually doing work which has social value, they must gain accurate knowledge of the activities in which they are engaged. They will keep a record of all expenses for materials used in the school, and will do simple bookkeeping in connection with the store which has charge of this material. In cooking, weights and measures will be learned. The children will also keep accounts of the cost of ingredients. Proportions will be worked out in the cooking recipes. When the children dramatize the life of the trader, in connection with history, they have opportunity to use all standards of measurements. Number is demanded in almost all experimental science work; for instance, the amount of water contained in the different kinds of fruit, or the amount of water evaporated from fruits under different conditions (in drying fruits). All plans for wood work will be worked to a scale and demand use of fractions. When the children have encountered many problems which they must solve in order to proceed with their work, they are ready to be drilled on the processes involved until they gain facility in the use of these. The children should be able to think through the problems which arise in their daily work, and have automatic use of easy numbers, addition, subtraction, multiplication, short division, and easy fractions.
As one reads these two samples of excellence he must find that each is so excellent in its one strong feature that it is not good; that work according to either must suffer; that what each needs is what the other has. Such a synthesis is represented in the next illustration.
A Combination of Excellences
September. 1. Measure height, determine weight. From records determine growth since September, 1905. 2. Learn to read thermometer. Make accurately, scale one fourth inch representing two degrees on paper one inch broad. Find average temperature of different days of month. Practice making figures from 1 to 100 for the thermometer scale. Count 100 by 2’s. 3. Make temperature chart. 4. Measure and space calendar, making figures of size appropriate to inch squares. Learn names of numbers to 30. 5. Make inch-wide tape measure for use in nature study, number book and cubic-inch seed boxes. 6. Review telling time. A. In addition to above; analyze numbers from 11 to 40 into tens and ones. Walsh’s Primary Arithmetic to top of page 10.
October. Problems on calendar,—number of clear, of cloudy, and of rainy days in September. Compare with September, 1905, 1904, 1903, 1902; temperature chart and thermometer; height and weight. Lay off beds for tree seeds; plant the same. Make envelopes for report cards. Drill on combinations in the above. Make rod strings and hundred-foot strings for determining distance wing seeds are carried from plants. Practice making figures from 1 to 100 for thermometer scale. Develop table of tens. A. In addition to the above analyze numbers from 40 to 50 into tens and ones. Primary Arithmetic, pp. 10-22. Teach pupils to add at sight.
November. From wall calendar count number of clear days, of cloudy days, and rainy days in October. Compare with September; with October of 1905, of 1906. Find average daily temperature; 8.30 A.M., 1 P.M. What kind of trees grow fastest? Measure growth of twigs of different kinds of trees. Compare this year’s growth with that of last year and of year before last. Compare rate of growth of different kinds of trees, as oak, willow, Carolina poplar, and elm. Develop table of 5’s from lesson with clock dial; review 2’s and 10’s. Practice making figures from 1 to 100 for the thermometer scale. Learn words representing numbers as well as figures. Make seed envelope. A. Analyze numbers from 60 to 65 into tens and ones. Primary Arithmetic. B, pp. 17-26; A, pp. 39-49.
Last six weeks of first term.—Continue finding average daily temperature. From wall calendar count number of clear, of cloudy, and of rainy days in November. Compare with November, 1906, 1905. Continue measurements on growth of trees. Drill on telling time from clock dial. Practice making figures from 1 to 100 for thermometer scale. Continue learning words representing numbers. Review tables of 2’s, 5’s, 10’s; learn table of 3’s. Primary Arithmetic. B, pp. 27-40. Analyze numbers from 11 to 30 into tens and ones. Primary Arithmetic. A, pp. 49-61. Analyze numbers from 66 to 100 into tens and ones. In January review all facts in number book. Drill on tables.
(Only the first one half of the third year’s course shown.)
The system from which this last selection is taken had the following remarkable rankings: 3d best in general excellence, 2d best in concreteness, and 5th best in drill. And as measured by the tests of this study, this system stood 4th from the best in abilities, and spent a little less than the medium amount of time.