CHAPTER XIX

MEASURING RESULTS IN EDUCATION

Efficiency in any line of human endeavor depends upon our ability to evaluate the results which are secured. No one would question the progress which has been made in education during the past hundred years; but one may very justly inquire concerning the efficiency of the work that has been done from the standpoint of the money which has been spent, and the effort and devotion of those who have engaged in teaching. In the mercantile pursuits it has been noted that seven out of every ten failures can be charged directly to a lack of knowledge of facts. Such investigations as we have had in education tend to prove that a like situation is to be found in this field. The failures in education, whether due to a lack of economical use of the funds available, to an inefficient system of organization, or to unintelligent practices in method, are, on the whole, not to be charged to a lack of devotion on the part of those who have given their lives to the schools. Until it is possible to measure the results achieved, the facts of success or failure cannot be established.

Of course, no one would deny that real progress is made by the process of trial and success, both in the art of teaching and in the practice of administration. It is true, too, that we shall have to depend in considerable measure upon demonstration as a means of bringing about improvement in current educational practice. It is none the less true, however, that scientific work in education will furnish the basis for the more rapid elimination of the mistakes in current practice, as well as point the way for improved organization of teaching. The science of education will, in its development, occupy relatively the same position with reference to the art of teaching that the science of medicine occupies with respect to the art of healing. The progress which has been made during the past twenty-five years in the art of farming would never have been possible without the scientific work that has been done in agriculture.

Aside from the fact that we are only beginning to have a profession of education, many other factors have entered to delay the progress in the direction of standardizing our work by means of accurate measurement of the results achieved. One of the most comforting of the fallacies which are at times urged against the attempt to measure results is found in the popular statement that the only criterion by which the success of school work can be measured is found in the ultimate success of the individuals who are subjected to the process. The most inefficient teacher in the most poorly equipped school, if his period of service has been long enough, will point to the success of a few of the boys who once attended that particular school, as proof of the adequacy of the work which is now being done. The failures are never brought to mind. The fallacious reasoning found in such an appeal is all too common in our educational discussion. To take a selected group of individuals, who have, because of native ability, and possibly because of favorable environment, achieved distinction; and to claim that this success is due to our system of education, may be satisfying to our pride, but cannot appeal to our good judgment. The only available measure of the success of the work done in any particular school is to be found in the changes which are brought about in boys and girls, young men and young women, during the period of their school life.

It has been argued, too, that that which is most worth while in education cannot be measured. Those who advance this argument speak continually in terms of “atmosphere,” “spirit,” and the like. There are two replies to be made to this contention. The one is that any power which the teacher has, whether it is called influence, or ability to teach arithmetic, must result in some change in the children who are taught. Another equally valid answer is to be found in the fact that the best teachers of arithmetic, of literature, of geography, of history, and the other studies are, at the same time, the teachers whose influence we value most in the school.

We have been hopeful that the sciences of biology, psychology, sociology, and economics would, in their development, solve the problems of education. No one would deny the significance of the work done in these fields as fundamental to the development of scientific work in education. No one is fully equipped to undertake investigation in the field of education without preliminary training in these fundamental sciences. Progress in the science of education has come, however, through the efforts of those men of sound fundamental training who have attacked the problems of education as such, rather than through the work of the biologist, psychologist, sociologist, or economist. If we should wait for the sciences mentioned to solve our problems, progress would indeed be slow.

Those who are unacquainted with modern statistical methods as applied in the social sciences have at times felt that it was impossible to measure large groups of individuals who differ in ability, in interest, and in environment. It is impossible within the limits of a brief chapter to make clear the validity of such measurement. It may be confidently asserted, however, that the measurement of a large group of individuals is, on the whole, more satisfactory than the attempt to measure a single individual. We can be more sure of the accuracy of our results in comparing two groups of children of a thousand each, than we could in the attempt to measure accurately a single individual with regard to ability in school subjects.

A most persistent objection to the measuring of results comes from those who feel that it is not fair to compare individuals or groups who are not alike in all particulars. They would claim, for example, that we cannot compare children in spelling ability when one group comes from homes in which the English language is spoken, while the other comes from the homes of those who speak a foreign language. It is probable that this objection is due to a belief that measurement will result in a comparison of the present situation without any regard to the growth or development which has characterized the group. If we derive units of measurement in spelling, manifestly the attempt would be to measure the changes which have been brought about in any group in terms of units which are comparable. If group one shows ability ten, having advanced during the year from ability seven, it will be considered just as satisfactory as the advance which has been made in group two, which has moved from ability eight to ability eleven. In other words, the purpose of measurement is never to attempt to make all alike. It is rather to discover differences and the reason for their existence; but most of all to give us some adequate means of determining progress or change.

Let us suppose again, in a matter of business administration, that one school shows a much higher per capita cost than another. This does not prove that one school is more efficiently managed than another. What it does do is to suggest that some adequate reason is to be found for the difference which exists. In like manner, one city may show a much higher cost for janitors’ salaries than does another. This may suggest investigation, but it does not prove that the city with the higher cost for janitors’ service is inefficiently managed or extravagant in its expenditures. It may be that the city that spends a relatively large amount for janitorial service actually gets more per dollar for the money which it spends than does the city with the smaller cost. It is always a purpose of measurement to discover discrepancies and to raise problems.

It has been contended that it is not important to derive scales or units of measurement on the ground that the scientific study of education is significant only in so far as it has to do with a careful investigation of the processes involved in growth. Those who make this contention seem to feel that a careful study of the way in which children come to form habits, to grow in power of reasoning, or in ability to appreciate, will give us the final answer concerning the methods to be employed in teaching. The difficulty with this point of view is that human beings, even though they be trained in investigation, are fallible. The only final test of the success of any method, however carefully derived, and however much of it may depend upon a knowledge of the processes involved in growth in the particular aspect of mental life which is involved, is to be found in the result achieved. Theoretically a method may seem to be perfect, and yet in terms of the results which are secured it may prove to be a failure. If the results are not accurately measured, if we do not derive scales of measurement, we can never be certain of our conclusions with regard to the method to be employed in bringing about any particular type of mental growth or development.

Possibly the one element in the situation which has operated to retard development in the direction of accurate measurement of results, more than any other, is the tendency in education to appeal to authority, and the corresponding lack of devotion to scientific investigation. It is, of course, much easier to solve the problems which one meets by taking the opinion of those who have had experience in the field. No one would deny the value of the judgment of our great educational leaders. The fact remains, however, that these same leaders would be the last ones to place their own opinion in opposition to the results obtained from a careful scientific investigation. Indeed, it is in no small measure due to the insistence of these leaders that we are coming to have adequate investigations with regard to our educational practice.

It has seemed necessary to discuss at some length the objections which have been made against the attempt to measure results in education, rather than to devote more space to a discussion of the work which has already been done. All students of education are familiar with the early work of Rice, and with the later contributions of Thorndike, Ayres, Cornman, and many others who have contributed to the literature of educational investigation. Possibly the most significant piece of work that has been done is Thorndike’s scale for measuring handwriting.[32] We may reasonably hope to have scales derived for the measurement of abilities in other subjects.

In administration, considerable work has already been done with reference to the cost of education, both as regards the relationship of expenditure for education to other expenditures, the question of a proper distribution of money within the educational budget, and of the proper distribution of state school funds.[33] We can, of course, hope for much more significant work in this field as more adequate systems of accounting are introduced and more satisfactory reports are issued. It is noteworthy that in those school systems in which an attempt has been made to check up expenditures carefully, remarkable savings have been made. We have not yet reached the limit of possible reduction of expenditure without the sacrifice of our present efficiency. Much work has been done on problems of school organization, yet the problems of retardation and elimination will be satisfactorily treated only as we secure more accurate records concerning attendance, scholarship, health, promotions, and demotions, such as are provided for by the genetic records now kept in some of our more progressive school systems. The problems of departmental work and individual instruction can never be satisfactorily solved until we measure accurately the results secured under different systems of organization.

Implicit in all of the argument which has been advanced in favor of measuring results is the contention that education means change. If changes are brought about in the children who are being educated, then there must be the possibility of measurement. These changes may take place in habit, in knowledge, in methods of work, in interests and ideals, and in power of appreciation. Probably no one would question the possibility of measuring the change which takes place in the formation of habits. We have quite commonly been willing to measure growth in knowledge by tests which demand that students not only remember facts, but that they show some ability to apply them. Whether or not a student commands a particular method of work can be determined by observation of his method of procedure as well as by the results that he secures. If interests or ideals are changed, there necessarily follows a change in activity. Any real power of appreciation will be accompanied by some change in expression.

The fact that we do not yet have scales or units of measurement which will enable us to evaluate accurately the results obtained in all of the different forms of school activity is not an argument against the possibility of measurement. In any field the development of units of measurement is dependent upon careful investigation, and upon a realization of the imperfection of the units already used. It is only as we insist upon measurement that we can hope to have our units refined. Take for example the problem of grades or marks which are commonly assigned to students as a measure of their efficiency in doing school work. Any investigation of these units will show that there is very great variation in their application by different members of the teaching corps.

The way to bring about a remedy is not to abolish all marks or grades, but rather to study the problem of the proper distribution of marks, and, if necessary, to weigh differently the marks of different instructors. The more imperfect the unit of measure which we now apply, the greater the need for insisting upon accurate measurement.

The first step in the development of scientific inquiry in any field is found in accurate description of the phenomena involved. The demand that we measure results in education is simply a demand that the basis for scientific investigation be made available by means of this accurate description of the situation as it exists. Some investigators in education have already been able to take the further steps in scientific inquiry which have enabled them to foretell with considerable accuracy the results which might be expected in education under given conditions. Further progress is, however, dependent upon that sort of measurement which will discover problems which are not now clearly defined or which have not yet been thought of. Of course, as inferences are made in the light of the problems suggested, there will be still further necessity for accurate measurement. When those who are charged with the responsibility of determining educational policy appeal to fact rather than to opinion, when we are able to evaluate accurately that which we achieve, educational progress will be assured and a profession of education will have been established.

We shall always have most excellent work in teaching done by those for whom scientific investigation, as such, means little. The investigations made will, however, modify the practice of these same teachers through changed demands and because of the demonstration of the validity of the new method of work by those who can appreciate the significance of results achieved by investigators. It is certainly to be expected that open-minded teachers will experiment for themselves and will aid in the work of the expert who must use the schools as his laboratory. Much depends upon the coöperation and good will of all who are engaged in teaching. It is not too much to expect that the spirit of investigation will be found in large measure to characterize those whose privilege it is to provide the situation in which intellectual development is stimulated.

An example of a study involving the coöperation of the pupils, teachers, and supervisory officers of twenty-six separate schools or school systems is Dr. C. W. Stone’s study on _Arithmetical Abilities and Some of the Factors Determining them_. The following quotations from Dr. Stone’s study indicate the type of result which we may hope to get from such investigations.

_In Reasoning_

The scores for the reasoning problems were determined from the results of two preliminary tests—one, giving one hundred 6th grade pupils all the time they needed to do the problems as well as they could in the order as printed (see page 11); and another, giving one hundred 6th grade pupils all the time they needed to do the problems as well as they could in the _reverse_ order from that as printed. The results as tabulated below in table II show that scores for reasoning problems of Grade VI pupils can be very definitely arranged in a scale on the basis of relative difficulty. Just what the scale should be can only be determined by determining the form of distribution and the location of the zero point. From what is known of these the scale of weighting shown in the last column of table II is believed to be the best, and this is the one employed in the computations of this study. However, in order to enable the reader to satisfy himself as to which is the best method, the scores of the twenty-six systems were calculated on each of three other bases—(1) counting each problem reasoned correctly a score of 1; (2) counting each problem reasoned correctly a score based on the ratio of its difficulty as shown in the next to the last column of table II; and (3) counting the scores made on only the first six problems for which presumably all pupils of all systems had ample time. See Appendix, p. 98.

In both reasoning and fundamentals the scores used as a measure of the achievement of a system were computed by combining the scores of one hundred pupils. Where more than one hundred pupils were tested, the papers used were drawn at random, the number drawn from each class being determined by the ratio of its number to the total number tested in the system. Where less than one hundred pupils were tested, the combined scores made were raised to the basis of one hundred pupils.

TABLE II

PRELIMINARY TESTS

REASONING—UNLIMITED TIME

100 Different Pupils Tested Each Time

+=========+==========+===========+=========+============+===========+ |NUMBER OF|% REASONED|% REASONED |AVERAGE %| WEIGHT |WEIGHT USED| |PROBLEMS |CORRECTLY | CORRECTLY |REASONED |ACCORDING TO|AS PROBABLY| | |AS PRINTED|AS REVERSED|CORRECTLY| AVERAGE % | THE BEST | | | | | | CORRECT | | +---------+----------+-----------+---------+------------+-----------+ | 1 | 95 | 92.6 | 93.8 | 1 | 1 | | 2 | 86 | 82.2 | 84.1 | 1.1 | 1 | | 3 | 94 | 89 | 91.5 | 1 | 1 | | 4 | 80 | 83 | 81.5 | 1.5 | 1 | | 5 | 88 | 86 | 87 | 1.1 | 1 | | 6 | 69 | 57.4 | 63.2 | 1.5 | 1.4 | | 7 | 70 | 80 | 75 | 1.25 | 1.2 | | 8 | 29 | 44 | 36.5 | 2.6 | 1.6 | | 9 | 19 | 15.5 | 17.2 | 5.45 | 2 | | 10 | 24 | 27.4 | 25.7 | 3.6 | 2 | | 11 | 17 | 7.5 | 12.3 | 7.6 | 2 | | 12 | 7 | 16.4 | 11.7 | 8 | 2 | +=========+==========+===========+=========+============+===========+

_Precautions observed to make the Scoring Accurate_

The simplicity of the tests made the scoring comparatively easy; and with the observance of the following precautions it is believed that a high degree of accuracy was attained. (1) In so far as practicable, all the papers were scored by a single judge—only two persons being employed on any phase of the work for the entire twenty-six systems; (2) each problem was scored through one hundred or more papers, then the next followed through, etc.; (3) the score for each part of each problem, the errors, etc., were entered on a blank provided with a separate column for each item; (4) where there was doubt as to how the score should be made, the scorer made a written memorandum of how the case was finally decided and this memorandum served as the guide for all future similar cases.

_What the Scores Measure_

As used in this study the words _achievements_, _products_, _abilities_, except where otherwise qualified, must necessarily refer to the results of the particular tests employed in this investigation. That some systems may achieve other and possibly quite as worth-while results from their arithmetic work is not denied; but what is denied is that any system can safely fail to attain good results in the work covered by these particular tests. Whatever else the arithmetic work may produce, it seems safe to say that by the end of the sixth school year, it should result in at least good ability in the four fundamental operations and the simple, everyday kind of reasoning called for in these problems. It does not then seem unreasonable, in view of the precautions previously enumerated, to claim that the scores made by the respective systems afford a reliable measure of the products of their respective procedures in arithmetic.

_The Data_

The source of the data used to help answer the above questions is some six thousand test papers gathered from twenty-six representative school systems. Copies of the tests may be found in Part I, pages 10 and 11; as may also a statement of conditions under which the tests were personally given by the author, page 13; and the method of scoring, pages 15 to 18.

The achievements are considered from two standpoints—(1) the scores and mistakes of the systems as systems, (2) the scores of individual pupils as individuals.

Table III gives the scores made in reasoning by each of the twenty-six systems, counting all the problems that were solved, and weighting them according to the last column of table II. The Roman numerals used in the left-hand column to designate the systems are those that fell to each system by lot. As seen by the column headed _scores made_, the systems are arranged according to number of scores, _i.e._ system XXIII made three hundred fifty-six points, the lowest score, and is placed first in the table; system XXIV made four hundred twenty-nine points, and is placed second, etc. System V, having made the highest score, is placed last in the table.

ACHIEVEMENTS OF THE SYSTEMS AS SYSTEMS

MEASURED BY SCORES MADE

TABLE III[34] TABLE IV

====================================+=================================== SCORES OF THE TWENTY-SIX SYSTEMS IN | SCORES OF THE TWENTY-SIX SYSTEMS REASONING WITH DEVIATIONS FROM THE | IN FUNDAMENTALS WITH DEVIATIONS MEDIAN. SCORES FROM ALL PROBLEMS | FROM THE MEDIAN. SCORES FROM | ALL PROBLEMS M[35] = 551 | M = 3111 --------+---------+--------+--------+--------+--------+--------+-------- Systems | | | Devia- |Systems | | | Devia- in | | Devia- |tions in| in | | Devia- |tions in Order of| | tions |Per Cent|Order of| | tions |Per Cent Achieve-| Scores |from the| of the |Achieve-| Scores |from the| of the ment | Made[36]| Median | Median | ment | Made | Median | Median --------+---------+--------+--------+--------+--------+--------+-------- XXIII | 356 | -195 | -35 | XXIII | 1841 | -1270 | -41 XXIV | 429 | -122 | -22 | XXV | 2167 | -944 | -30 XVII | 444 | -107 | -19 | XX | 2168 | -943 | -30 IV | 464 | -87 | -16 | XXII | 2311 | -800 | -26 XXV | 464 | -87 | -16 | VIII | 2747 | -364 | -12 XXII | 468 | -83 | -15 | X | 2749 | -362 | -12 XVI | 469 | -82 | -15 | XV | 2779 | -332 | -11 XX | 491 | -60 | -11 | III | 2845 | -266 | -8 XVIII | 509 | -42 | -8 | I | 2935 | -176 | -6 XV | 532 | -19 | -3 | XXI | 2951 | -160 | -5 III | 533 | -18 | -3 | II | 2958 | -153 | -5 VIII | 538 | -13 | -2 | XVII | 3042 | -69 | -2 VI | 550 | -1 | -2 | XIII | 3049 | -62 | -2 I | 552 | 1 | 2 | VI | 3173 | 62 | 2 X | 601 | 50 | 9 | XI | 3261 | 150 | 5 II | 615 | 64 | 12 | IX | 3404 | 293 | 9 XXI | 627 | 76 | 14 | XII | 3410 | 299 | 10 XIII | 636 | 85 | 15 | XXIV | 3513 | 402 | 13 XIV | 661 | 110 | 19 | XIV | 3561 | 450 | 14 IX | 691 | 140 | 20 | IV | 3563 | 452 | 14 VII | 734 | 183 | 33 | V | 3569 | 458 | 15 XII | 736 | 185 | 34 | XXVI | 3682 | 571 | 18 XI | 759 | 208 | 38 | XVI | 3707 | 596 | 19 XXVI | 791 | 240 | 44 | XVIII | 3758 | 647 | 21 XIX | 848 | 297 | 54 | VII | 3782 | 671 | 22 V | 914 | 363 | 66 | XIX | 4099 | 988 | 31 ========+=========+========+========+========+========+========+========

The middle column gives the deviations from the median, which is that measure above and below which one half the cases lie. In this table the median is five hundred fifty-one. These deviations serve to show the differences in scores made; and they are also employed in computing the measures of variability and relationship. The third column is the deviations in per cent of the median. It affords another expression of the difference in size of scores made by the systems.

Table IV reads exactly as III, the scores[37] being those made on all problems of the test in fundamentals. These two tables give some general help on the nature of the product of the first six years of arithmetic work. One very evident fact is the lack of uniformity among systems; another is the lack of correspondence of relative position among the systems in the two tables. With the exception of systems XXIII and XIV, no system occupies the same relative position in the two tables, _e.g._ system XXIV stands second from the lowest in reasoning and eighteenth from the lowest in fundamentals. This fact is more accurately summarized in the coefficients of correlation, table XV, p. 37.

As seen from its heading, table XXII gives the systems in order of achievements. These serial standings are derived from tables III and IV. Reading from the top, system XXIII has an average serial standing of _one_, being lowest in both reasoning and fundamentals; system XXV ranks _three_ in average serial standing, being _fourth_ from lowest in reasoning and _second_ from lowest in fundamentals; the readings for the other systems are similar.

Column Heading Keys: SYS = SYSTEMS A = Average serial standing B = Serial standing in reasoning C = Serial standing in fundamentals D = Serial standing in time expenditure E = Week minutes devoted to arithmetic F = Week minutes devoted to all subjects G = % of time to arithmetic

TABLE XXII TABLE XXIII TABLE XXIV =============+=======================+================================== COMPARATIVE | COMPARATIVE TIME | TIME DISTRIBUTION ACHIEVEMENTS | EXPENDITURE | AMONG GRADES +---+---+----+------+------+----+---------------------------------- | | | | | | | Lower numbers show week minutes | | | | | | | devoted to arithmetic; upper show | | | | | | | % of school time devoted to SYS | | | | | | | arithmetic in each grade | | | | | | +-----+-----+-----+-----+-----+---- A | B | C | D | E | F | G | I | II | III | IV | V | VI -----+---+---+----+------+------+----+-----+-----+-----+-----+-----+---- XXIII| | | | | | | 7 | 6 | 12 | 15 | 15 | 15 1 | 1 | 1 | 14 | 1150 | 9675 | 12 | 100 | 100 | 200 | 250 | 250 | 250 | | | | | | | | | | | | XXV | | | | | | | | 7 | 9 | 10 | 9 | 13 3 | 4 | 2 | 2 | 722 | 8700 | 8 | .. | 100 | 140 | 155 | 130 | 197 | | | | | | | | | | | | XXII | | | | | | | | 8 | 8 | 8 | 7 | 11 4½ | 5 | 4 | 1 | 507 | 7200 | 7 | .. | 90 | 90 | 90 | 90 | 147 | | | | | | | | | | | | XX | | | | | | | 7 | 10 | 12 | 14 | 15 | 15 5 | 7 | 3 | 15 | 1161 | 8200 | 14 | 80 | 113 | 210 | 240 | 265 | 253 | | | | | | | | | | | | XVII | | | | | | | 2 | 12 | 20 | 20 | 24 | 23 7½ | 3 |12 | 21 | 1283 | 7500 | 17 | 27 | 158 | 250 | 258 | 300 | 290 | | | | | | | | | | | | VIII | | | | | | | 2 | 14 | 15 | 15 | 15 | 15 8 |11 | 5 | 18 | 1258 | 9600 | 13 | 25 | 233 | 250 | 250 | 250 | 250 | | | | | | | | | | | | XV | | | | | | | | 11 | 15 | 20 | 17 | 18 8 | 9 | 7 | 16 | 1173 | 8025 | 15 | .. | 147 | 213 | 292 | 250 | 271 | | | | | | | | | | | | III | | | | | | | 10 | 9 | 11 | 11 | 12 | 16 9 |10 | 8 | 6 | 944 | 8025 | 12 | 125 | 125 | 150 | 150 | 165 | 229 | | | | | | | | | | | | XXIV | | | | | | | | | 14 | 17 | 17 | 17 10 | 2 |18 | 7 | 950 | 8775 | 11 | .. | .. | 200 | 250 | 250 | 250 | | | | | | | | | | | | X | | | | | | | | 7 | 12 | 12 | 14 | 18 10 |14 | 6 | 5 | 921 | 8550 | 11 | .. | 88 | 154 | 184 | 216 | 279 | | | | | | | | | | | | I | | | | | | | | 9 | 13 | 14 | 14 | 15 11 |13 | 9 | 9 | 1068 | 9375 | 11 | .. | 130 | 213 | 238 | 238 | 249 | | | | | | | | | | | | IV | | | | | | | 28 | 20 | 20 | 24 | 20 | 23 12 | 4 |20 | 26 | 1854 | 8400 | 22 | 249 | 300 | 306 | 361 | 300 | 338 | | | | | | | | | | | | II | | | | | | | 8 | 12 | 14 | 14 | 15 | 16 13 |15 |11 | 17 | 1247 | 9900 | 13 | 121 | 192 | 217 | 225 | 233 | 259 | | | | | | | | | | | | XXI | | | | | | | 8 | 10 | 10 | 12 | 14 | 13 13 |16 |10 | 4 | 865 | 7650 | 11 | 80 | 100 | 100 | 180 | 210 | 195 | | | | | | | | | | | VI | | | | | | | | 8 | 12 | 18 | 18 | 19 13 |12 |14 | 11 | 1126 | 9000 | 13 | .. | 127 | 177 | 266 | 266 | 290 | | | | | | | | | | | | XVI | | | | | | | 5 | 8 | 13 | 18 | 17 | 16 14½| 6 |23 | 12 | 1127 | 9000 | 13 | 75 | 113 | 187 | 263 | 251 | 238 | | | | | | | | | | | | XIII | | | | | | | | 26 | 23 | 18 | 19 | 19 15 |17 |13 | 25 | 1626 | 8475 | 19 | .. | 388 | 350 | 288 | 300 | 300 | | | | | | | | | | | | XVIII| | | | | | | 6 | 5 | 15 | 20 | 20 | 19 16 | 8 |24 | 19 | 1265 | 8700 | 15 | 75 | 75 | 225 | 300 | 300 | 290 | | | | | | | | | | | | IX | | | | | | | 13 | 15 | 18 | 18 | 18 | 21 17½ |19 |16 | 22 | 1559 | 9000 | 17 | 200 | 225 | 275 | 275 | 275 | 309 | | | | | | | | | | | | XI | | | | | | | | 11 | 15 | 18 | 18 | 18 18½ |22 |15 | 10 | 1130 | 8575 | 13 | .. | 157 | 216 | 250 | 250 | 257 | | | | | | | | | | | | XIV | | | | | | | 15 | 16 | 18 | 19 | 19 | 19 18½ |18 |10 | 23 | 1560 | 8850 | 18 | 225 | 245 | 270 | 280 | 270 | 270 | | | | | | | | | | | | XII | | | | | | | | 6 | 18 | 16 | 19 | 19 19 |21 |17 | 13 | 1148 | 8400 | 14 | .. | 81 | 226 | 255 | 288 | 298 | | | | | | | | | | | | XXVI | | | | | | | 7 | 10 | 10 | 13 | 13 | 17 22½ |23 |22 | 3 | 837 | 7200 | 12 | 80 | 125 | 125 | 150 | 150 | 207 | | | | | | | | | | | | VII | | | | | | | 13 | 19 | 22 | 22 | 22 | 17 22½ |20 |25 | 24 | 1573 | 7800 | 20 | 175 | 262 | 300 | 300 | 300 | 236 | | | | | | | | | | | | V | | | | | | | 8 | 10 | 11 | 12 | 13 | 13 23 |25 |21 | 8 | 971 | 8700 | 11 | 113 | 154 | 167 | 175 | 183 | 179 | | | | | | | | | | | | XIX | | | | | | | 8 | 10 | 17 | 17 | 13 | 20 25 |24 |26 | 20 | 1276 | 9000 | 14 | 125 | 150 | 250 | 250 | 250 | 301 =====+===+===+====+======+======+====+=====+=====+=====+=====+=====+==== .. = no time assigned.

Tables XXIII and XXIV keep the same order of systems and show the time expenditure. The first line of table XXIII reads,—system XXIII ranks fourteenth from the lowest in time expenditure, with 1150 week minutes devoted to arithmetic, 9675 week minutes devoted to all subjects, the 1150 week minutes devoted to arithmetic being 12 per cent of the 9675 week minutes devoted to all subjects. Similarly for the other systems, _e.g._ system XXV with a serial standing in abilities of _three_, and a serial standing in time expenditure of _two_, spends 722 week minutes on arithmetic, and 8700 week minutes on all subjects, arithmetic costing 8 per cent of all the school time. The reader will recognize that the third column, which gives the time devoted to all subjects for one week of each of the first six years, gives the only new data of this table, column two being the same as given in table XXI and the first and fourth columns being derived from the others.

Probably the first essential shown by this table is the lack of correspondence between the serial standing in time cost and the serial standing in abilities; _e.g._ the system with the lowest time cost is found by referring to table XIII to be system XXII, which is seen in table XXII to rank _four and one-half_ in average abilities. Similarly, the system that ranks _fifteenth_ in time cost, ranks _fifth_ in abilities, etc. Another noticeable showing is the wide variability in the _school time_ of the systems. It will be seen to vary from 7200 to 9900 week minutes. This time includes recesses, and it means that lengths of school days vary from an average of four hours to five and one-half hours. And if the names of the systems were given, it would be recognized that almost invariably the longer school hours are accompanied by the least amount of variation in program, such as physical education, field trips, assemblies, etc. Perhaps the other most striking fact of this table is the wide variation in the per cent of time devoted to arithmetic. It varies from 22 per cent for system IV to 7 per cent for system XXII, a difference of more than three to one.

As table XXIV is part of the discussion of factors in time expenditure, its sample readings are given under that heading, page 62.

_The Relation of Time Expenditure to Abilities Produced_

The reader found one indication of the relation, or lack of relation, between time cost and products in tables XXII and XXIII. Each of the three following tables expresses these same facts.

TABLE XXV

COMPARISON OF THE ACHIEVEMENTS OF THE SYSTEMS HAVING LESS THAN MEDIAN TIME COST WITH THOSE HAVING MORE --------------+---------------------------------------------------- | COMBINED SCORES OF THE THIRTEEN SYSTEMS +-------------+------------+------------+------------ |With _less_ |With _more_ |With _less_ |With _more_ |than median |than median |than median |than median | time cost | time cost | time cost | time cost +-------------+------------+------------+------------ | Including home study | Without home study --------------+-------------+------------+------------+------------ Reasoning | 7,519 | 7,893 | 7,277 | 8,135 | | | | Fundamentals | 40,751 | 40,273 | 37,165 | 43,859 --------------+-------------+------------+------------+------------

TABLE XXVI

RATIO OF TIME EXPENDITURES TO ABILITIES[38] ==========+=====================+==================+=================== | AVERAGE RATIOS | REASONING RATIOS | FUNDAMENTAL | | | RATIOS +--------+------------+--------+---------+--------+---------- SYSTEMS | Serial | Time Cost | Serial | Time | Serial | Time Cost |Standing|to Reasoning|Standing| Cost |Standing| to | of | and to | of | to | of |Fundamen- |Systems |Fundamentals|Systems |Reasoning|Systems | tals ----------+--------+------------+--------+---------+--------+---------- IV | 1 | 2.26 | 1 | 3.99 | 4 | .520 XXIII | 2 | 1.92 | 2 | 3.22 | 1 | .624 XVII | 3 | 1.65 | 3 | 2.88 | 7 | .421 XIII | 4 | 1.54 | 4 | 2.55 | 3 | .533 XX | 5 | 1.45 | 7 | 2.36 | 2 | .535 XVIII | 6 | 1.41 | 5 | 2.48 | 13 | .336 XIV | 7 | 1.40 | 7 | 2.36 | 6 | .438 VIII | 8 | 1.39 | 8 | 2.33 | 5 | .457 IX | 9 | 1.353 | 9 | 2.25 | 5 | .457 XVI | 10 | 1.352 | 6 | 2.40 | 18 | .304 XV | 11 | 1.31 | 11 | 2.20 | 8 | .422 VII | 12 | 1.28 | 12 | 2.14 | 9 | .415 XXIV | 13 | 1.24 | 10 | 2.21 | 21 | .270 II | 14 | 1.22 | 14 | 2.02 | 7 | .421 VI | 15 | 1.20 | 13 | 2.04 | 11 | .354 I | 16 | 1.15 | 15 | 1.93 | 10 | .363 III | 17 | 1.05 | 16 | 1.77 | 16 | .331 XII | 18 | 0.943 | 17 | 1.55 | 13 | .336 XXV | 19 | 0.941 | 17 | 1.55 | 15 | .333 X | 20 | 0.93 | 18 | 1.53 | 14 | .335 XI | 21 | 0.913 | 20 | 1.48 | 12 | .346 XIX | 22 | 0.91 | 19 | 1.50 | 17 | .311 XXI | 23 | 0.83 | 21 | 1.37 | 19 | .293 V | 24 | 0.67 | 23 | 1.06 | 20 | .272 XXII | 25 | 0.65 | 22 | 1.08 | 23 | .219 XXVI | 26 | 0.64 | 24 | 1.05 | 22 | .227 ==========+========+============+========+=========+========+==========

The above details are compiled from the scores of individual systems as given in tables III and IV, the median cost being that given in table XXI. As measured by the time used in school, the thirteen systems with less than the median cost stand slightly the better; and as measured by the time including home study, the thirteen systems with more than the median time cost stand somewhat the better. The time used in school is doubtless the more exact measure, but, as shown in table XXI, some systems depend on home study to a considerable extent. Hence both measures are used. The lack of relation indicated in this general way is shown more accurately in the table, page 263, in terms of coefficients of correlation.

The order of systems in this table is determined by the first column, which gives the average serial standing as determined by the ratios of time to products. The right-hand column under each heading gives the ratio of time expenditure to abilities produced, and the left-hand column gives the serial order of that system as measured by the highness of the ratio, _i.e._ highness of cost per unit of product; _e.g._ in system IV the ratio of time to reasoning is 3.99 (see fourth column), the highest ratio in reasoning (determined by dividing the time cost, 1854 week minutes, by 464, the points made in reasoning). The ratio of time to fundamentals in this system is .52; giving an average ratio of 2.26. That is to say, the ratio of time to abilities in system IV is as 2.26 to 1, the highest among the twenty-six systems.

That there is no direct ratio between time expenditure and abilities is again shown by this table. For example, system XXII, which spends the least amount of time (see table XXI), ranks fourth from the lowest in abilities (see table XXII), ranks 25th, that is, next to the highest, in ratio of time cost to abilities produced; and, what is even more striking, system XXVI, which spends third from the least amount of time, ranks third from the highest in abilities and 26th or _highest_ in the ratio of time cost to abilities produced.

That a large amount of time expended is no guarantee of a high standard of abilities may again be convincingly seen by comparing the ratios of the five systems spending the smallest amount of time with the five spending the largest. Of the five spending the least time, the average ratio is .80, which corresponds with the 23d or the 3d from the best in ratio; and of the five spending the greatest amount of time, the average ratio is 1.57, which corresponds with the 4th poorest in ratio.

The last three tables have each shown the decided lack of relationship between time cost and abilities produced, and hence for these systems it is evident that there is practically no relation between time expenditure and arithmetical abilities; and, in view of the representative nature of these twenty-six systems, it is probable that this lack of relationship is the rule the country over.

This is not to say that a certain amount of time is not essential to the production of arithmetical abilities; nor that, given the same other factors, operating equally well, the product will not increase somewhat with an increased time expenditure. What is claimed is that, as present practice goes, a large amount of time spent on arithmetic is no guarantee of a high degree of efficiency. If one were to choose at random among the schools with more than the median time given to arithmetic, the chances are about equal that he would get a school with an inferior product; and conversely, if one were to choose among the schools with less than the median time cost, the chances are about equal that he would get a school with a superior product in arithmetic.[39]

So far, then, as ability in arithmetic means ability to handle such foundation work as is measured by the tests in this study, this “essential” has not _necessarily_ suffered by the introduction of other subjects and the consequent reduction of its time allotment.

One would need to read the whole study to appreciate fully the nature of the investigation. From the pages quoted, however, it must be apparent that: (1) schools and school systems vary greatly in the results which they secure in arithmetic; (2) the excellence of the work done is not directly proportional to the time expended. We will find it necessary to revise our opinions with regard to the organization of school subjects, the allotment of time, the methods of teaching, and the like, in proportion as we have careful investigation in these several fields.

FOR COLLATERAL READING

E. L. Thorndike, _The Principles of Teaching_, Chapter XVI.

APPENDIX

I. THE TEACHING OF ENGLISH IN ELEMENTARY SCHOOLS

BY FRANKLIN THOMAS BAKER, A.M.

I. Historical View of the Subject

=1.= THE CHOICE OF READING MATTER.

1. The school reader an expression of social ideals.

2. German primers and readers of the sixteenth and seventeenth centuries.

3. The “moral tales” of the eighteenth century.

4. The New England Primer.

5. The oratorical and patriotic selections of the early nineteenth century.

6. The school readers of to-day; their general characteristics.

=2.= METHOD.

1. The alphabetic method in use until modern times.

2. New ideas in the sixteenth century and later. Work of Ickelsamer, Basedow, Pestalozzi, Comenius, and Jacotot.

3. Gradual ascendency of the analytic over the alphabetic (or synthetic) method.

4. Recognition of the importance of phonetics, of association of ideas, etc.

REFERENCES: Kehr, _Geschichte des Lese-Unterrichts in der Volksschule_, Gotha, 1889. Fechner, _Geschichte des Volksschullesebuches_, Gotha, 1889. Ford, _The New England Primer_, New York, 1897. Reeder, _Historical Development of the School Reader_, New York, 1900. Hall, _How to Teach Reading_, New York, 1886. _American Journal of Education, Vol. V._, Hartford and London, 1858. Russell, _German Higher Schools_, New York, 1900. Carpenter, Baker, and Scott, _The Teaching of English_, New York, 1903. Huey, _Psychology and Pedagogy of Reading_, New York, 1908.

II. First Steps in Instruction

=1.= MATERIAL.

1. Material should be (1) interesting, (2) literary, so far as possible, (3) adapted to the capacities and tastes of children, (4) of enough difficulty and sufficiently above their own ordinary thoughts to have value as instruction.

2. The best material (1) folk stuff, such as the classic fairy tales, Mother Goose, etc., (2) tales of heroism and sacrifice, (3) poetry of the simpler type, like that of Stevenson and Christina Rossetti.

3. Much of the language work should be free conversation between the teacher and the children about their ordinary experiences.

=2.= METHOD.

1. During the first years much of the literary material must be given orally by the teacher. Oral work is to be held of great importance.

2. Children to be encouraged to commit good things to memory.

3. All reading aloud by the pupils to be done as naturally as possible. Importance of reading by phrases and sentences, rather than word by word.

4. Value of the dramatic element in early work.

5. The conflict between the “word method” and the “sentence method” over. Modern teaching eclectic in method. If any name can be given to the best way, it might be, perhaps, “thought method.”

6. Use of script and print: advantages of each as a first form. Value of printed cards and other devices for drill.

7. Form of type for beginners’ books: not too large; letters to have all differentiating marks _distinct_. Importance of right kind of paper, width of columns, etc. Kinds of pictures most serviceable.

8. When shall writing begin? In general not to be forced on the child in the first year. Arguments for and against this arrangement. Should there be any fixed standard of accomplishment for the first year?

9. Phonetic drill. How many words must be known before it begins? Various plans equally successful. The main thing, perhaps, is to have drill enough to give the pupils _certainty_ in their work, but to keep the drill subordinated to their interest in reading.

10. The order of such drill. “Normal words,” chosen for their meaning, their frequency of occurrence, and their similarity in form to other words either at their beginning or at their end. Many words, however, must be learned without relation to such a scheme.

11. “Normal sentences” those that partially help the reader to the recognition of words; as, “The sun rises in the east, and sets in the west.” For young children, sentences involving the use of repetitive phrases must also be regarded as normal, as in “The House that Jack Built.”

12. In general, both analysis and synthesis to be used in word drill.

13. Importance of securing good habits as to intelligent reading, correct spelling, etc., in the early years. Children can usually do better than they or their elders think they can.

14. Emphasis to be placed upon reading many of the good things over and over, until they are known in whole and in part.

REFERENCES: Bryant, _How to tell Stories to Children_. Carpenter, Baker, and Scott, _The Teaching of English_. Chubb, _The Teaching of English_. Colby, _Literature in Life and in School_. Hall, _How to teach Reading_. Hinsdale, _Teaching the Language Art_. Huey, _Psychology and Pedagogy of Reading_. Arnold, _Reading, How to teach it_. Laurie, _Language and Linguistic Method_. Dewey, “The Primary Education Fetich,” in _The Forum_, May, 1898. Dewey, _The School and Society_. Dye, _Story-Teller’s Art_.

III. The Teaching of Literature

=1.= GENERAL PROBLEMS.

1. Can literature be _taught_? Or can pupils “be taught through literature”? Examples of such educational use of literature.

2. Present aims in teaching literature: entertainment, portrayal of life, acquaintance with the world of thought and feeling as presented in books, cultivation of imagination and sense of beauty.

3. True interpretation implies grasping the central purpose, idea, or feeling of the piece.

4. Various types of literature demand various treatment. Necessity of adapting the treatment to the class.

5. Taste (sense of beauty) developed mainly by contact with good models. Instruction plays a minor part. The love of good reading fostered by judicious selection of material, and by example and influence.

6. How can the habit of good reading be cultivated?

=2.= MATERIAL.

1. The literature chosen must be suitable in its themes, its action, its feeling, its simplicity.

2. Literary histories and biographies: their limited value in elementary work.

3. Scientific and historical material in literature. Literary use of such material not to be confounded with science and history.

4. Pictures and other illustrative material: Sometimes give intuitive basis for desired concepts; sometimes interfere with the imagination.

=3.= METHOD.

1. Reading aloud: its value. Means of securing good results; interest, sense of reality, consciousness of an audience.

2. Analytic study, of content, form, and general literary effects.

_a._ Must be adapted to the pupil’s interest and his stage of development.

_b._ Must yield results of value appreciable by the pupil.

_c._ Effects of too much or too little such study.

3. Correlation of literature with other work possible in limited degree. A matter of class treatment rather than of the general arrangement of the course of study. A problem for the teacher rather than the principal.

4. Treatment of allusions, historical, literary, etc. The need of judicious selection.

5. Treatment of figures of speech, verse forms, new words, etc.

6. Lesson plans: their function and value.

_a._ An outline should control and direct the work, yet be flexible enough to allow freedom on the part of teacher and pupil.

_b._ Introductions: their nature and function. When necessary.

REFERENCES: Carpenter, Baker, and Scott, Laurie, Chubb, Hinsdale, Arnold and Hall, as cited. Scudder, _Literature in Schools_. C. A. McMurry, _Special Method in Reading_. Bates, _Talks on the Study of Literature_. Colby, _Literature in Life and in School_. Adler, _Moral Instruction of Children_.

IV. Study of Certain Typical Books

=1.= NURSERY RHYMES (as _Mother Goose_, Stevenson’s _Child’s Garden of Verses_).

_a._ The nature of their appeal to children in sound, imagery, and ideas.

_b._ Their value in training the ear, the powers of speech, etc.

=2.= GRIMM’ “FAIRY TALES.”

_a._ Their source and relation to other folklore.

_b._ The marvelous, and its effect on children.

_c._ Action, logical sequence, local color.

_d._ Various types of myth.

_e._ The ideal element, poetic justice, etc. Need the harsher elements be omitted?

_f._ Typical lessons.

=3.= “ALICE IN WONDERLAND.”

_a._ Its origin and its place in literature.

_b._ The nature of its reality: based upon things in the child’s world of imagination.

_c._ Its value as humor, as a means of quickening the power of thought.

_d._ What preparation is needed for the appreciation of it?

_e._ Typical lessons.

=4.= “ROBINSON CRUSOE.”

_a._ Its origin and place in literature.

_b._ Fundamental characteristics as a piece of fiction.

_c._ Elements in it that appeal to children, or fail so to appeal.

_d._ Justification of the abridged editions.

_e._ Its relation (1) to the world of romance, (2) to real life.

_f._ How best presented. Typical lessons.

=5.= LONGFELLOW’S “HIAWATHA.”

_a._ Its origin, form, popularity.

_b._ Its qualities, epic and romantic.

_c._ Its treatment of the myth.

_d._ Its value as school reading; parts best suited for this.

_e._ General value of reading about primitive life.

_f._ Relation to handwork, etc.

=6.= HAWTHORNE’S “WONDER BOOK” AND “TANGLEWOOD TALES.”

_a._ Their origin and general literary qualities.

_b._ Romantic coloring given to classic stories; compare Kingsley’s _The Heroes_, and Bulfinch’s _Age of Fable_, and other versions of the myths.

_c._ Different types of myth and fairy story represented.

_d._ Artistic qualities of Hawthorne’s versions; how far can these be shown in the school?

_e._ The ethical element: how treated?

_f._ Typical lessons.

=7.= WHITTIER’S “SNOW BOUND.”

_a._ Its historical value as a presentation of a type of civilization: occupation, pleasures, interests, types of character.

_b._ Its literary value as an ideal treatment of its theme.

_c._ The point of view that of an old man’s retrospect. How far is this appreciable by children?

_d._ The study of this poem involves also attention to structure, diction, allusions, poetic descriptions, and metrical form.

_e._ Typical passages treated in lessons.

=8.= LONGFELLOW’S “EVANGELINE.”

_a._ The poet’s departure from historical fact; its justification.

_b._ The idyllic element; the descriptions.

_c._ The central theme, and its treatment in the first and second parts of the poem.

_d._ The different quality of the two parts; predominance of description and the meditative element in the second.

_e._ Metrical structure.

_f._ What things in the poem can be made especially interesting to young people?

=9.= SCOTT’S “IVANHOE.”

_a._ Its free treatment of historical fact. The difference between historic and poetic truth.

_b._ The historical novel: its general relations to history; to be regarded primarily as literature, not as history.

_c._ The portrayal of ideals and customs of a past age: types of characters; structure (plot) of the book built in accordance with this purpose.

_d._ Difficulties of language, allusions, etc.

_e._ Means of arousing interest in romantic literature. Comparisons with other books commonly read by children.

=10.= SHAKSPERE’S “JULIUS CÆSAR.”

_a._ Historical basis, anachronisms, etc.

_b._ The nature of its appeal to young readers.

_c._ Treatment of verbal difficulties and of the dramatic form.

_d._ The action, the characters, the dramatic motives and situations.

V. Composition

=1.= OBJECT OF TEACHING COMPOSITION.

1. Shall it be “literary,” or aim merely at adequate expression?

=2.= ELEMENTS INVOLVED IN THE PROBLEM: FORM AND SUBJECT MATTER.

1. Importance of subject matter in giving motive and interest, and in determining form.

2. Subjects for composition to include topics from school work and from daily life: to be made _real_, as far as possible. Reality dependent upon interest and the consciousness of an audience.

3. Preparation for the work. Importance of oral treatment, of the gathering and ordering of facts and ideas. Originality not to be expected.

4. Composition units: necessity of training in both sentence and paragraph. Value of outlines, and of drill in sentences.

5. Criticism of written work.

_a._ General aims.

_b._ Means of making criticism effective.

_c._ The object to make pupils self-critical without checking spontaneity.

REFERENCES: Laurie, Hinsdale, Chubb and Carpenter, Baker and Scott as cited above.

VI. Grammar

=1.= HISTORICAL REVIEW.

1. Historical changes in the idea of English grammar.

2. Attempt, in the Renaissance period, to Latinize the grammar of English. Persistence of this point of view.

3. Recent changes due to philological study.

4. What now constitutes English grammar?

5. What problems remain unsolved?

=2.= OBJECTS OF TEACHING GRAMMAR.

1. Various theories: for correctness of expression and for discipline.

2. Modern notions of authority in usage, and of the province of grammar.

=3.= AMOUNT OF GRAMMAR TO BE TAUGHT.

1. How much grammar shall be taught in the schools?

2. What things are of most value?

3. Importance of syntax; of study of forms.

=4.= THE ORDER OF TREATMENT.

1. Syntax or etymology first?

2. A study of the methods of development adopted by some of the representative textbooks.

REFERENCES: Laurie, Hinsdale, Carpenter, Baker and Scott, and Chubb. Liddell, “English Historical Grammar,” _Atlantic Monthly_, Vol. LXXXII. Sweet, _New English Grammar_, Part II. Barbour, _The Teaching of English Grammar_; Goold Brown, _Grammar of Grammars_ (Introduction). Krapp, _Syllabus of English Language and Grammar_ (Columbia University Extension Syllabi, Series A, No. 5).

II. THE TEACHING OF MATHEMATICS IN ELEMENTARY SCHOOLS

BY DAVID EUGENE SMITH, LL.D.

I. The History of the Subject

=1.= ADVANTAGES TO A TEACHER IN STUDYING THE HISTORY OF THE SUBJECT TAUGHT.

=2.= THE EARLY HISTORY OF ARITHMETIC.

=3.= THE GROWTH OF NUMBER SYSTEMS.

=4.= THE DEVELOPMENT OF ARITHMETIC AS KNOWN AT PRESENT.

REFERENCES: Smith, _The Teaching of Arithmetic_, New York, 1909, chap. i; and in general the sections in this syllabus correspond to the chapters in this work. _The Teaching of Elementary Mathematics_, New York, 1900. Ball, _A Primer of the History of Mathematics_, London, 1895, and _A Short Account of the History of Mathematics_, London, 4th edition, 1908. Fink, _History of Mathematics_, translated by Bennan and Smith, Chicago, 1900. Cajori, _History of Elementary Mathematics_, New York, 1896, and _History of Mathematics_, New York, 1893. On Greek Arithmetic see Gow, _History of Greek Mathematics_, Cambridge, 1884.

II. The Reasons for Teaching Arithmetic

=1.= THE ANCIENT POINT OF VIEW.

=2.= CONTENT OF THE PRIMITIVE LOGISTIC, OR ART OF CALCULATION.

_a._ Early counting.

_b._ Early writing of numbers. The development of notations.

_c._ The Influence of the Hindu-Arabic notation.

=3.= CONTENT OF THE EARLY ARITHMETIC, OR THEORY OF NUMBERS.

_a._ Connection with mysticism.

_b._ Contributions of Pythagoras and his school.

_c._ The effect upon modern arithmetic.

=4.= THE REASONS FOR TEACHING IN THE MIDDLE AGES.

_a._ The Church schools.

_b._ The reckoning schools.

_c._ The effect upon modern arithmetic.

=5.= THE REASONS DEVELOPED BY THE RENAISSANCE.

_a._ Influence of commerce.

_b._ Influence of printing. The crystallization of arithmetic.

_c._ The effect upon the subject matter of modern arithmetic.

=6.= THE REASONS OF TO-DAY.

_a._ The practical value. Whatever pretends to be practical in arithmetic should really be so.

_b._ The question of “mental discipline.” The rise of this doctrine. The results of a psychological study of the question. The tangible part of “mental discipline.”

_c._ The interest in the subject for its own sake. The game element of mathematics. The historical development of the science of arithmetic from the primitive game.

REFERENCES: Smith, _The Teaching of Arithmetic_, chap. ii, to the chapters of which no further reference will be made, this syllabus being merely a synopsis of that work. _Teaching of Elementary Mathematics_, pp. 1-70. Young, _The Teaching of Mathematics_, New York, 1907, pp. 41-52, 202-256. On the historical side, consult Fink, _History of Mathematics_, Chicago, 1898. Ball, _Short History of Mathematics_, New York, 1908. Cajori, _History of Elementary Mathematics_, New York. Jackson, _The Educational Significance of Sixteenth Century Arithmetic_, New York, 1906. Branford, _A Study of Mathematical Education_, Oxford, 1908.

III. What Arithmetic should include

=1.= FROM THE PRACTICAL STANDPOINT.

_a._ The utilities of arithmetic overrated. A detailed consideration of the various topics usually studied.

_b._ The effect of tradition upon the matter of arithmetic.

=2.= FROM THE STANDPOINT OF MENTAL DISCIPLINE. DISCIPLINE A MATTER OF METHOD RATHER THAN ONE OF TOPICS.

=3.= FROM THE STANDPOINT OF INTEREST IN THE SUBJECT FOR ITS OWN SAKE.

REFERENCES: Smith, _Teaching of Elementary Mathematics_, p. 19. Young, pp. 23-242.

IV. The Nature of the Problem

=1.= THE GREAT CHANGE IN RECENT YEARS BROUGHT ABOUT BY TWO CAUSES.

_a._ The study of social needs.

_b._ The study of child psychology.

=2.= THE PECULIAR NEEDS OF AMERICA. THE BEARING OF THESE NEEDS UPON THE TEACHING OF ARITHMETIC.

=3.= CHILD PSYCHOLOGY AND THE PROBLEMS STILL AWAITING SOLUTION.

REFERENCES: Smith, _Teaching of Elementary Mathematics_, p. 21. Young, pp. 97-103, 210-218. Saxelby, _Practical Mathematics_, and similar works.

V. The Arrangement of Material

=1.= RECENT CHANGES BROUGHT ABOUT FROM A CONSIDERATION OF CHILD PSYCHOLOGY.

=2.= THE GROWTH OF THE TEXTBOOK.

_a._ The Treviso arithmetic of 1478, and the early arithmetics of Italy, Germany, France, England, and Holland.

_b._ The two-book series.

_c._ The three-book series.

_d._ The extreme spiral arrangement.

=3.= THE MODERN CURRICULUM IN ARITHMETIC.

_a._ Its origin.

_b._ Its present status.

_c._ Improvements to be considered.

REFERENCES: Young, pp. 178-188.

VI. Method

=1.= THE MEANING OF METHOD.

=2.= HOW THE ANCIENTS PROBABLY TAUGHT CALCULATION.

_a._ Various forms of the abacus.

_b._ The abacus at the time of the Renaissance.

_c._ The effect upon arithmetic of abandoning the abacus in western Europe.

=3.= CAUSES OF THE RISE OF THE RULE.

=4.= REVIVAL OF OBJECTIVE TEACHING.

Trapp (1780), von Busse (1786), and Pestalozzi (about 1800).

=5.= THE EARLY FOLLOWERS OF PESTALOZZI.

Tillich (1806), Krancke (1819), Grube (1842).

=6.= TYPES OF LATER METHODS.

_a._ Counting.

_b._ Ratio.

_c._ Extreme spiral.

_d._ Pure concrete work as a basis.

_e._ Pure abstract work as a basis.

=7.= THE EASE AND FUTILITY OF CREATING NARROW METHODS.

REFERENCES: Smith, _Teaching of Elementary Mathematics_, pp. 71-97. Seeley, _Grube’s Method of Teaching Arithmetic_, New York, 1888. Soldan, _Grube’s Method of Teaching Arithmetic_, Chicago, 1878. C. A. McMurry, _Special Method in Arithmetic_, New York, 1905. McLellan and Dewey, _The Psychology of Number_, New York, 1895. Young, pp. 53-150.

VII. Mental or Oral Arithmetic

=1.= HISTORICAL STATUS OF ORAL ARITHMETIC.

=2.= REVIVAL UNDER PESTALOZZI’S INFLUENCE. THE WORK OF WARREN COLBURN IN THIS COUNTRY.

=3.= CAUSES OF THE DECLINE OF THIS FORM OF WORK.

=4.= THE CLAIMS OF ORAL ARITHMETIC UPON THE SCHOOL TO-DAY. THE PRACTICAL AND PSYCHOLOGICAL VIEWS OF THE PROBLEM.

=5.= THE NATURE OF THE ORAL WORK,—ABSTRACT AND CONCRETE.

=6.= THE TIME TO BE ALLOWED TO THE SUBJECT.

REFERENCES: Smith, _Teaching of Elementary Mathematics_, p. 117. _Handbook to Arithmetics_, p. 6. Young, p. 230.

VIII. Written Arithmetic

=1.= WHAT SHOULD BE THE NATURE OF THE WRITTEN ARITHMETIC?

=2.= OBJECT OF THE BUSINESS FORM OF SOLUTION.

=3.= OBJECT OF WRITTEN ANALYSIS.

=4.= NECESSITY OF RECOGNIZING TWO KINDS OF WRITTEN WORK.

=5.= HOW TO MARK PAPERS.

REFERENCES: Smith, _Teaching of Elementary Mathematics_, pp. 121-129.

IX. Children’s Analyses

=1.= THE OBJECT IN REQUIRING ANALYSES.

=2.= WHAT SHOULD BE EXPECTED OF CHILDREN IN THIS RESPECT?

=3.= EXPLANATIONS OF FUNDAMENTAL OPERATIONS. RELATION TO THE FORMAL RULE.

=4.= EXPLANATION OF APPLIED PROBLEMS.

=5.= RELATION TO THE WORK IN ENGLISH.

=6.= THE LIMIT OF PRIMARY WORK, “TWO-STEP REASONING.”

REFERENCES: Smith, _Handbook to Arithmetics_, p. 9. Young, p. 205.

X. Interest and Effort

=1.= STATUS OF ARITHMETIC FROM THE STANDPOINT OF INTEREST.

=2.= DANGER OF OVEREMPHASIS UPON INTEREST.

=3.= LESSENING OF INTEREST WITH THE LESSENING OF EFFORT.

=4.= SAFE BASIS FOR INCREASE OF INTEREST.

=5.= EFFECT OF A GENUINE, SPONTANEOUS INTEREST UPON INCREASE OF EFFORT AND OF POWER.

XI. Improvements in the Technique of Arithmetic

=1.= HISTORY OF THE IMPROVEMENT IN SYMBOLISM.

=2.= HOW THE PRESENT SEEKS TO CARRY ON THIS IMPROVEMENT.

_a._ The difficulties that are met.

_b._ Dangers of too much symbolism.

_c._ The proper criterion for selection.

=3.= THE EQUATION IN ARITHMETIC.

_a._ Object.

_b._ Dangers to be avoided.

=4.= THE PROCESS OF SUBTRACTION AS A TYPE.

_a._ The various historical methods considered.

_b._ The criterion for a selection.

_c._ The claims of the various processes to-day.

=5.= THE PROCESS OF DIVISION AS A TYPE.

_a._ The history of division.

_b._ Present points at issue.

_c._ The probable future.

=6.= PROPORTION AS A TYPE.

_a._ History of proportion and the “Rule of Three.”

_b._ Present symbolism and status.

_c._ Probable future of the subject.

=7.= FUTURE PROBLEMS RELATING TO TECHNIQUE.

XII. Certain Great Principles of Teaching Arithmetic

A summary of the larger principles for the guidance of teachers.

XIII. General Subjects for Experiment

=1.= THE USE OF GAMES.

=2.= CHIEF INTERESTS OF CHILDREN.

=3.= RESULTS OF EMPHASIZING:

_a._ The abstract problem.

_b._ The concrete problem.

=4.= AMOUNT OF TIME TO BE ASSIGNED TO ARITHMETIC.

=5.= RELATIVE AMOUNT OF TIME TO BE DEVOTED TO:

_a._ Oral arithmetic.

_b._ Written arithmetic.

=6.= THE BEST BASIS OF ARRANGEMENT OF AN ARITHMETIC.

XIV. Details for Experiment

Professor Suzzallo’s list of details as set forth in _The Teachers College Record_, January, 1909, p. 43, and in Smith, _The Teaching of Arithmetic_, chap. xiv.

XV. The Work of the First School Year

=1.= ARGUMENTS FOR AND AGAINST NO FORMAL ARITHMETIC IN THIS YEAR.

=2.= THE LEADING MATHEMATICAL FEATURES FOR THE YEAR.

=3.= THE NUMBER SPACE OF THE YEAR.

_a._ For counting.

_b._ For operations.

=4.= THE WORK TO BE ACCOMPLISHED IN ADDITION.

=5.= THE WORK IN THE OTHER OPERATIONS.

=6.= THE FRACTION CONCEPTS TO BE CONSIDERED.

_a._ Part of an object.

_b._ Part of a group.

_c._ The idea of “half as much.”

=7.= DENOMINATE NUMBERS.

=8.= THE QUESTION OF THE USE OF OBJECTS.

=9.= SYMBOLIC WORK AND TECHNICAL EXPRESSIONS.

=10.= NATURE OF THE PROBLEMS OF THIS YEAR.

=11.= THE TIME LIMIT UPON WORK.

REFERENCES: Smith, _The Teaching of Elementary Mathematics_, p. 99. _Handbook to Arithmetics_, p. 11. C. A. McMurry, _Special Method in Arithmetic_.

XVI. The Work of the Second School Year

=1.= THE LEADING MATHEMATICAL FEATURES.

=2.= NUMBER SPACE FOR THE YEAR.

=3.= COUNTING.

_a._ The origin of the “counting method.”

_b._ The extremes to which it may be carried.

_c._ The proper use of counting in teaching.

=4.= THE ADDITION TABLE. RELATION TO COUNTING.

=5.= THE METHOD OF TREATING SUBTRACTION REVIEWED.

=6.= THE MULTIPLICATION TABLE.

_a._ Arguments for and against learning tables.

_b._ Extent of the work for this year.

_c._ Relation to counting.

=7.= DIVISION.

_a._ Relation to multiplication.

_b._ Arrangement of work in short division.

=8.= FRACTIONS.

_a._ Extent of the work.

_b._ Nature of the objective work.

=9.= DENOMINATE NUMBERS.

_a._ Extent of the work.

_b._ Use of the measures. Visualizing the great basal units.

=10.= NATURE OF THE SYMBOLS TO BE CONSIDERED.

=11.= NATURE OF THE PROBLEM WORK.

_a._ Abstract.

_b._ Concrete.

XVII. The Work of the Third School Year

=1.= PECULIAR NECESSITY FOR PREPARATION FOR THIS YEAR’S WORK.

=2.= LEADING MATHEMATICAL FEATURES.

_a._ Beginning of rapid written work.

_b._ Multiplication table completed.

_c._ Most important tables of denominate numbers.

_d._ Work extended to two-figure multipliers and the beginning of long division.

=3.= NUMBER SPACE MAY EXTEND TO 100,000.

=4.= THE ROMAN NUMERALS.

_a._ Extent to which this work should be carried in various school years.

_b._ Historical sketch of the system and of its uses.

=5.= THE COUNTING METHOD FURTHER CONSIDERED. ITS VALUES AND ITS DANGERS.

=6.= THE WRITING OF UNITED STATES MONEY. OPERATIONS.

=7.= SQUARE AND CUBIC MEASURE.

_a._ Extent.

_b._ Nature of objective work.

=8.= SUGGESTIONS AS TO FOUR OPERATIONS.

_a._ Addition. Practical value of checks on all operations.

_b._ Subtraction, as discussed in section XI.

_c._ Multiplication. Should the tables extend to 12 × 12? Devices.

_d._ Division. Algorism considered historically and practically.

_e._ Historical note as to the number of operations.

=9.= EXTENT OF WORK WITH FRACTIONS.

=10.= NATURE OF THE PROBLEMS.

REFERENCES: Smith, _Teaching of Arithmetic_, chap. xvii, p. 73. _Handbook to Arithmetics_, p. 29.

XVIII. The Work of the Fourth School Year

=1.= LEADING MATHEMATICAL FEATURES.

=2.= NUMBER SPACE.

=3.= THE FOUR OPERATIONS.

_a._ Nature of the oral work.

_b._ Criteria for judging written work.

_c._ Speed versus accuracy.

=4.= NATURE OF THE WORK IN COMMON FRACTIONS.

_a._ Historical sketch of various fractions.

_b._ Change in the practical uses of common fractions.

=5.= DENOMINATE NUMBERS.

_a._ What tables are of value? Historical sketch of tables.

_b._ Visualizing the basal units.

_c._ Accuracy in reduction.

=6.= NATURE OF THE PROBLEMS.

REFERENCES: Smith, _Handbook to Arithmetics_, p. 43.

XIX. The Work of the Fifth School Year

=1.= LEADING MATHEMATICAL FEATURES.

=2.= NECESSITY FOR AND NATURE OF PRELIMINARY REVIEW.

=3.= NUMBER SPACE. MODERN TENDENCIES IN USING LARGE NUMBERS.

=4.= NATURE OF THE REVIEW OF THE FOUR OPERATIONS.

_a._ Suggestions for rapid addition and subtraction.

_b._ Checks on multiplication and division.

_c._ Twofold nature of division.

=5.= COMMON FRACTIONS.

_a._ Nature of the theoretical explanations.

_b._ What should be expected of children in this regard.

=6.= DENOMINATE NUMBERS.

_a._ Extent of reductions.

_b._ Nature of the operations.

=7.= HOW TO SOLVE PROBLEMS.

=8.= INTRODUCTION TO PERCENTAGE.

=9.= NATURE OF THE PROBLEMS.

REFERENCES: Smith, _Handbook to Arithmetics_, p. 53.

XX. The Work of the Sixth School Year

=1.= LEADING MATHEMATICAL FEATURES.

=2.= THE GENERAL SOLUTION OF PROBLEMS.

_a._ How the world has solved problems.

_b._ Modern improvements.

=3.= PERCENTAGE.

_a._ Nature of the subject.

_b._ History of the subject.

_c._ Suggestions for treatment.

_d._ The most important applications.

=4.= RATIO AND PROPORTION.

_a._ History.

_b._ Present value, and probable future status.

=5.= NATURE OF THE PROBLEMS.

XXI. The Work of the Seventh School Year

=1.= LEADING MATHEMATICAL FEATURES.

=2.= REVIEW OF OUR NUMBERS. HISTORICAL NOTES.

=3.= REVIEW OF THE FUNDAMENTAL OPERATIONS.

=4.= TYPES OF SUBJECTS TREATED.

_a._ Longitude and time. Origin, value, new features.

_b._ Percentage. What cases are the most important?

=5.= INTRODUCTION OF ALGEBRAIC WORK CONSIDERED. NATURE OF MENSURATION.

=6.= NATURE OF THE PROBLEMS.

XXII. The Work of the Eighth School Year

=1.= LEADING MATHEMATICAL FEATURES.

=2.= NATURE OF THE BUSINESS APPLICATIONS.

_a._ Banking. Extent to which the work should be carried.

_b._ Partial payments. Historical view of the value of the subject.

_c._ Partnership. Value of the historical view.

_d._ Simple accounts.

_e._ Exchange. Wherein its value lies.

_f._ Taxes. Insurance.

_g._ Corporations. Arguments for and against the study of investments.

=3.= THE METRIC SYSTEM.

_a._ Why taught. Historical view.

_b._ Extent of the work.

_c._ Practical suggestions in teaching.

=4.= POWERS AND ROOTS.

_a._ Historical view.

_b._ Present values. Extent of the work.

=5.= MENSURATION.

_a._ Extent to which it should be carried.

_b._ Geometry in the eighth year.

_c._ The formula.

=6.= ALGEBRA IN THE EIGHTH YEAR.

_a._ Historical view. Present values.

_b._ Extent to which it should be carried.

=7.= NATURE OF THE PROBLEM.

=8.= A COMPARISON OF AMERICAN AND FOREIGN SCHOOLS.

III. THE TEACHING OF GEOGRAPHY.

BY RICHARD ELWOOD DODGE, A.M.

I. The Scope and Purpose of School Geography

=1.= SCHOOL GEOGRAPHY A PART OF SCIENCE OF GEOGRAPHY.

Relation of elementary school work to that in secondary school and college.

=2.= DEFINITION OF GEOGRAPHY.

Meaning of this and growth of idea.

_A._ “Study of earth in its relation to life.”

_B._ The emphasis of “causal notion” in school geography.

Rational geography.

=3.= SCOPE OF SCHOOL GEOGRAPHY.

_A._ Possible scope as wide as the subject.

Complexity of subject.

_B._ Practical scope determined by abilities and needs of children, and by necessary sequence of steps in geography study.

_C._ Consequent difficulties for school teachers, even in earlier years.

=4.= SCHOOL GEOGRAPHY MUST BE:

_A._ Unit in each part and as a whole.

Practical reasons for unity.

_B._ Usable at every step.

Importance of this in early grades.

_C._ Closely related to nature work on one hand, and secondary work on the other.

_D._ Based on children’s experiences and earlier knowledge.

=5.= PURPOSE OF SCHOOL GEOGRAPHY TEACHING:

_A._ To teach children geography. Interpretation of this.

Relation of subject to children. Approach to adults’ point of view.

_a._ Knowledge of principles of geography.

_b._ Knowledge of facts that make principles clear.

_c._ Knowledge of facts necessary for daily life.

Other facts that must be included.

_B._ Power.

_a._ To use materials and results gained in classroom and elsewhere.

_b._ To seek out, organize and use new materials.

This suggests method of conducting a portion of class work.

_c._ To think accurately and clearly.

Importance of geography as a means of training in scientific thinking.

REFERENCES: Dodge, R. E., _The Teaching of Geography_, to which no further references will be made, this syllabus being a synopsis of that work. _Teachers College Record_, March, 1901, pp. 3-9. _Journal of Geography_, November and December, 1904; April, 1905; September, 1906. McMurry, C. A., _Special Method in Geography_, chap. i. Geikie, A., _The Teaching of Geography_, chap. i.

II. The Persons involved in School Geography Teaching

=1.= THE DUTIES OF THE SCIENTIFIC GEOGRAPHER.

_A._ Should help make content sound geographically.

He should be source of geography materials.

_B._ Should ascertain that work will insure good training in elements of geography.

Adapted to pupils and valuable as foundation for good later work.

_C._ Should outline method in large so as to produce geographic progress.

_D._ Should assist in substituting good for bad details and help choose between essentials and non-essentials.

=2.= THE OBLIGATIONS OF THE SUPERVISOR OR SUPERINTENDENT.

_A._ Must recognize goal to be reached from standpoint of good geography, and relations of school geography to other phases of geographic education.

_B._ Should accept materials and larger plan of geographer.

Arrange time of schedule.

_C._ Should see that children’s general training is not sacrificed and special training is secured.

_D._ Should insure that work is practical and usable.

_E._ Must see that relations to other subjects are emphasized.

Causal notion again.

=3.= THE OBLIGATIONS AND OPPORTUNITIES OF THE TEACHER.

_A._ Must know more subject matter than he expects to give pupils.

_B._ Must know purposes and scope of course—his part in course as a whole.

Also must know preparation furnished by earlier year’s work.

_C._ Must know relations to other work in the curriculum as a whole and in geography particularly.

_D._ Must know ways subject must be organized and presented to his grade so as best to gain aims desired.

General and special method.

=4.= THE POSITION OF CHILDREN IN REFERENCE TO WORK.

_A._ Meaning of “To teach children geography.”

_B._ The preparation that may be expected in different grades.

_C._ Children’s interest in work.

_D._ Pupils must be trained to work and think.

_E._ Goals are knowledge and power. Importance of rational repetition, of reviews and map work.

REFERENCE: Dodge, _Journal of Geography_, v, p. 385. _The Opportunity of the Geographer in Promoting School Geography._

III. The Organization of a Course of Study

=1.= COURSE AS A WHOLE.

_A._ Must be capable of being judged as good by geographers.

_B._ Must lead to knowledge and power.

_C._ Must be arranged so as to lead from known to unknown along lines of least resistance but not least effort.

_D._ Method of approach of mature mind must not always be followed.

=2.= SOME FUNDAMENTAL CONSIDERATIONS.

_A._ No one course available for all localities.

_B._ Course should start with home geography.

_C._ Should lead next to elementary knowledge of world whole.

_D._ The emphasis to be given to continental work.

Division of work by grades.

_E._ Disadvantages of teaching all continents twice.

The following compromise is suggested as in general workable:

_a._ Twice: North America, United States, Europe, and perhaps portions of Asia.

_b._ Once: Asia, Africa, Australia, and South America.

Present importance of South America.

_F._ Plan of intermediate work should differ from plan of upper grades. “Concentric Circles.”

_G._ The place of physical geography in the course of study:

_a._ Home geography: observational side.

Danger of overemphasis, of giving wrong outlook.

_b._ Intermediate grades: give setting to life side.

Larger facts only.

_c._ Upper grade: basis of work.

Not to be taught as a topic by itself but as a means to an end.

_H._ Emphasis of industries and commercial side.

_I._ “Following interests of children,”—best meaning of phrase. Value and dangers.

Recent interest in industrial education places a renewed obligation on geography to be practical and to be free from fads.

Developing interest. Temporary and permanent interests.

REFERENCES: _Teachers College Record_, March, 1901, pp. 9-15. McMurry, C. A., _Special Method in Geography_, chap. ii. Redway, J. W., _New Basis of Geography_, chap. x. Bagley, W. C., _Function of Geography in Elementary Schools_, _Journal of Geography_, Vol. III, p. 222. Dodge, Richard E., “Some Suggestions Concerning a Course of Study in Geography,” _Journal of Geography_, vii, pp. 7-14.

IV. Home Geography and World Whole

=1.= CERTAIN GENERAL CONSIDERATIONS.

_A._ Home geography not a subject or a division of geography, but a method of approach to field as a whole,—cannot have a uniform course for all places.

_B._ Method of procedure must be from known to unknown through analysis of experiences of pupils.

_C._ Work should not call for knowledge of distant places.

_D._ Lessons should become more intensive and scope more extensive.

_E._ Topics should be taken up in definite sequence so far as possible.

_F._ Definitions, if any, to be summaries at close of developed points and not points of departure.

_G._ Units developed to be good geography units which may be used as basis for comparison over world. Heat, storms, woods, for instance, are not good units. Crossroads or city corners good units.

_H._ Local history to be brought in as much as possible.

Should be intimately related to geography and may often be point of departure.

_I._ Importance of observation of local conditions.

Reasons for giving a certain place to processes of earth change.

=2.= TOPICS IN HOME GEOGRAPHY.

_A._ Social:

_a._ Simple life groups and relations.

(1) Home, village, city, etc. (2) Needs and means of communication. (3) Need for government. Form not to be included. (4) Reasons for trade. Simple illustrations. (5) Industrial features. (6) Universality of similar features over world.

_B._ Earth:

_a._ Forms of landscape as related to life.

_b._ Forms of drainage as related to life.

_c._ Soils and their use. Classification a minor matter.

_d._ Simpler atmospheric phenomena.

_e._ Direction and distance.

_f._ Maps.

_g._ Gravity.

=3.= TOPICS OFTEN INCLUDED.

_A._ Suitable to few localities: Volcanoes, mountains, ocean.

_B._ Not geographical:

_a._ Name and functions of officers of local government.

_b._ Building of a house or mechanical details of any trade.

_c._ Topics in geology such as formation of coal, marble, etc.

_C._ Beyond powers of pupils.

_a._ Form of earth, relation of bodies in solar system.

_b._ Rotation and revolution of earth.

_c._ Theory of storms.

=4.= SUMMARIES:

_A._ Must be simple and easily drawn from previous work.

_B._ Must be of such a nature that they can be expanded as years go on without overturning base learned in earlier years.

_C._ Examples of good summaries:

_a._ Wind is air moving horizontally.

_b._ River is a stream of water and detritus flowing through the land.

_D._ Examples of bad summaries:

_a._ A lake is a body of water surrounded by land.

_b._ Mountains are high elevations of land.

_c._ A divide is the high land which separates two rivers.

_d._ A river is a stream of water which flows into the sea.

_e._ Hollow places in the land filled with water are called lakes.

_f._ A swamp is a tract of land soaked with water.

=5.= SOME SIMPLE UNITS OF HOME GEOGRAPHY TO INDICATE BASIS OF CHOICE OF TOPICS.

_A._ The home:

_a._ Simplest group of individuals which illustrates essentials of larger groups.

_b._ A unit of government: need of government in home and in any group.

_c._ Division of labor in home illustrates a world truth as to relations of individuals and groups.

_B._ Groups of homes.

_a._ Country four corners.

_b._ Village.

_c._ City.

_d._ Location of such cities as Vienna, Constantinople, Chicago.

_C._ Simpler surface features.

_a._ Why important,—travel over, seen as landscape.

_b._ Why emphasize landscape and not forms first?

_c._ Plains,—why most important? Life relation to.

_d._ Rolling lands.—Relations to life.

_e._ Mountain regions.—Relations to life (should, in many localities, be deferred to later work).

REFERENCES: _Teachers College Record_, March, 1901, pp. 15-17. Davis, W. M., “Home Geography,” _Journal of Geography_, p. 1. Geikie, A., _The Teaching of Geography_, chap. ii. McMurry, C. A., _Excursions and Lessons in Home Geography_.

=6.= FIRST KNOWLEDGE OF WORLD WHOLE.

_A._ Expansion of home geography outward to ocean.

_a._ How to present form of earth—relation to home, necessities and luxuries.

_b._ Parts of earth that may be related to home in developing knowledge of world whole, based on experience of pupils.

(1) Northern North America and Europe—furs. (2) Southern North America—bananas, woods, cacao. (3) Northern South America—India rubber, coffee, Brazil nuts. (4) Southern South America—hides, and meat products. (5) West Central Europe—embroideries, wine, cheese. (6) Southern Europe—olives, cork. (7) Southeastern Asia—tea, silks, spices, fire-crackers. (8) Central Africa—ivory, palm oil. (9) Southern Africa—diamonds. (10) Southwestern Asia—rugs. (11) Australia—wool.

=7.= HOW TO LEAD UP TO CLIMATE OF WORLD.

_A._ Points to be brought out:

_a._ Direction and distance in time.

_b._ Similarity of purpose of life. Food, clothing, shelter.

_c._ Different ways of doing things amid different conditions.

Homes, dress, travel, kinds of food, natural food, weather conditions.

_d._ Interrelation of peoples.

_B._ Points which may be neglected:

_a._ Overmuch detail, _i.e._ Details of home life or occupations. Scenery.

_b._ Curious and unimportant customs. Slanting eyes. Personal customs.

REFERENCES: Farnham, A. W., “Oswego Geography Course,” _Journal of Geography_, v, p. 109. _Teachers College Record_, March, 1901, pp. 17-20, 24-27.

V. The Point of View and Method of Approach in Intermediate Work

=1.= PURPOSES.

Knowledge of more important Continents and Countries, lives of people and reasons therefor.

_A._ Knowledge of facts of everyday life. Consequences to causes,—physical features in the large as points of departure for giving setting. Follow political divisions because of practical advantage.

_B._ Industrial interrelations of regions to be brought out.

_C._ Causal location and non-causal location. Picturesque side and how secured. Permanent location in visual image. Temporary location for clearness and practice. Memory work in location.

_D._ “Methods” of approach:

_a._ “Concentric”—disadvantages.

_b._ “Journey”—when valuable—disadvantages.

_c._ “Type” method. What this means in a large way.

_d._ “Map drawing” method.

_e._ Value of reversing method in upper grammar grades.

_E._ The place of method.

_a._ Advantages and disadvantages of following a “method,” centered about a personal point of view.

_b._ Value of subordinating “methods” to method.

REFERENCES: Bagley, W. C., “Geography in Intermediate Grades,” _Journal of Geography_, iv, p. 299. _Teachers College Record_, March, 1901, pp. 29-35.

=2.= THE SO-CALLED TYPE METHOD.

_A._ What is a type? “A type is that individual of a species or genus which contains the largest number of features which are characteristic of the species or genus as a whole.”

_B._ Types must be good geographic units, and not mere instances. The essentials of a good geographic unit.

_C._ A typical instance is not:

_a._ The most involved or striking example.

_b._ The most interesting example.

_D._ Why types cannot easily be selected in geography. Advantages and difficulties of using types.

_a._ Examples of good types.

_E._ Ways in which teaching by types is actually used in various texts and courses of study.

_F._ Teaching by “types” does not readily lead to the bringing out of political features; leads to overmuch detail and overemphasis of non-essentials.

REFERENCE: McMurry, C. A., _Special Method in Geography_, chap. ix.

VI. Industrial and Commercial Geography

=1.= PRESENT EMPHASIS OF INDUSTRIAL AND COMMERCIAL GEOGRAPHY.

_A._ Reasons for that emphasis: practical and educational.

_B._ Industrial geography deals with the geography underlying the principal human occupations: that is, the reason for the occurrence of industries in given localities.

_C._ Commercial geography deals with the elementary principles of trade and commerce, and includes a study of geography of great regions of production and demand, with causes. Emphasizes interrelation of commercial areas and reasons for same.

_D._ Industrial geography should be emphasized in intermediate years; commercial geography in the upper grades.

_E._ Industrial geography should include the study of groupings of peoples according to occupations and lead up to a knowledge of the simpler reasons therefor. These groups are agriculture, grazing, lumbering, mining, manufacturing, commerce, and “scenic centers.”

_F._ Geography does not call for study of technique of industries, and should not include special study of details of industries. Futility of studying processes. Geographic side includes the reasons for industry and not the manner of it. Technique is largely result of human invention and is not geographic except possibly where some invention has revolutionized an industry and greatly changed relations of peoples to their geographic surroundings.

_G._ Geography underlying agriculture, grazing, and lumbering as examples of geographic influences.

_H._ Commercial geography should be based on knowledge of industrial and physical geography of earlier years, and should be a part of regional geography—not a special topic. It should include study of routes of trade, areas of supply and consumption of _chief_ foods, textiles, manufactured products, raw materials, etc., and relative status of chief commercial nations, and reasons.

_I._ Difficulties in teaching commercial geography are due to modernness of subject, constant changes involved, lack of illustrative materials and to difficulties of securing proper materials for class study.

_J._ Some recent successes in teaching commercial and industrial geography. The development and purposes of commercial museums for schools.

REFERENCE: _Teachers College Record_, March, 1901, pp. 29-35.

VII. The Basis of Work in the Upper Grades

=1.= GEOGRAPHY IN UPPER GRADES SHOULD BE FOUNDED ON GOOD WORKING KNOWLEDGE OF ELEMENTARY PRINCIPLES OF GEOGRAPHY.

_A._ These principles should be elaborated summaries or generalizations of earlier work, and should be developed only so fully as is necessary for clearness and for future good work.

_B._ Physical geography not as an end, but as a means to an end.

_C._ Life consequences to be made prominent as illustrations at every step.

=2.= THIS WORK SHOULD INCLUDE:

_A._ Earth’s shape—simple proofs and effects.

_B._ Earth’s motions—results.

_C._ Elements of climate and weather as related to earth’s motions with effects. Importance of climate.

_D._ Simpler land forms and influence on life. Drainage.

_E._ Simpler features of oceans and oceanic movements as related to commerce and trade. Tides need not be elaborated.

_F._ Distribution of plants as related to causes, especially climate.

_G._ Distribution of animals as related to causes. This topic should be treated briefly.

_H._ Races of men and their distribution as related to climate and food supply.

_I._ Elements of commerce causally developed.

_J._ Elements of political geography—including meaning of nation, of boundary, origin of boundaries, exchange of consuls, ministers, etc.

=3.= TOPICS WHICH MAY BE OMITTED:

_A._ Causes of tides.

_B._ Condition of interior of earth.

_C._ Causes of mountain growth.

_D._ Details of glaciation.

_E._ Geological development of continent.

=4.= METHOD IN LARGE.

_A._ Work should be developed, as far as possible, as result of map work and personal observations.

_B._ Principles should be illustrated as widely as possible to show general importance.

_C._ Some topics may readily be studied in association with study of Africa or Australia, and thus training may be given in working from causes to consequences, as preliminary to later use of definite causal order.

REFERENCE: Redway, _New Basis of Geography_, chap. viii.

VIII. The Topical Method in Upper Grades

=1.= GENERAL AGREEMENT IN REFERENCE TO TEACHING CONTINENTS IN UPPER GRADES FROM CAUSES TO CONSEQUENCES.

_A._ Principles should be used as basis of work.

_B._ Work should be largely based on map study, especially maps of climate, physical features, distribution of trade routes, peoples, industries, etc.

_C._ Work should not be too stereotyped,—that is, order of procedure should not always be the same.

_D._ Training should be given in reasoning and in use of reference books, texts, atlases, etc.

_E._ Topical method means to work from larger, simple, general features, out to more detailed, special and complex conditions. Possible modifications and advantages. Using an imaginary continent.

=2.= AN EXAMPLE OF TOPICAL ORDER: THE LARGER FEATURES OF NORTH AMERICA.

_A._ Location:

_a._ By latitude and longitude.

_b._ In reference to ocean.

_c._ In reference to other continents.

_d._ In reference to wind systems.

_B._ Larger surface features:

_a._ Cordilleran Highland.

_b._ Appalachian Highland.

_c._ Atlantic Coastal Plain.

_d._ Great Central Plain.

_e._ Height of Land.

_f._ Influence and extent of glaciation.

_g._ Consequent lines of drainage:

(1) Arctic drainage. (2) Pacific drainage. (3) Atlantic drainage.

(_i_) Direct. (_ii_) By St. Lawrence. (_iii_) By Gulf of Mexico.

_C._ Coast line:

_a._ Compare east and west coast as to:

(1) General form. (2) Number of harbors. (3) Availability of harbors. (4) Nearness to foreign ports.

_D._ Climate:

_a._ Position in reference to wind systems.

_b._ Summer and winter distribution and range of temperatures.

_c._ Relation to ocean and ocean currents.

_d._ Chief modifications due to surface.

_e._ Three climatic divisions: east coastal, west coastal, and interior.

_f._ Rainfall in each as related to agriculture.

_g._ The growing season conditions in each.

_E._ Vegetation:

_a._ Chief vegetation regions as related to climate and surface.

_b._ Distribution and characteristic features of tundra, forests, steppes, and deserts.

_c._ Significance of vegetation distribution.

_F._ Animals: Briefly as related to climate and vegetation.

_a._ Domestic.

_b._ Wild.

_G._ Mineral products: As related to surface.

_H._ People: Distribution of people as related to surface, climate, drainage, coast line, and products. (Follow this by summary of United States as related to North America, and then by New England, following order given and extending to occupations and commerce. Bring out location of leading cities causally.)

_I._ Summarize continents by comparative study of reasons for commercial development of principal nations and of distribution of great world products.

REFERENCES: Farnham, A. W., “Oswego Geography Course,” _Journal of Geography_, v, p. 211. Hotchkiss, C. W., _Journal of School Geography_, ii, p. 41. Reudiger, W. C., “Suggestions for Geography Teaching in Upper Grades,” _Journal of Geography_, iv, p. 433.

IX. The Use of Maps and Textbooks

=1.= ADVANTAGES OF A TEXT:

_A._ Outlines a course of study when none better is available.

_B._ Gives clear definitions and summaries.

_C._ Gives second exposition of subject matter of value to pupils who gain best impression through the eyes.

_D._ Shows relative values of different parts of subject.

_E._ Furnishes text, maps, and illustrations for study.

_F._ Gives chance for training in how to study.

_G._ Gives means of holding children responsible for certain work.

=2.= HOW TO USE TEXT:

_A._ Text should be servant of teacher, and not the teacher a slave of text.

_B._ Text used _before_ recitation in association with outline or series of map questions where nature of materials or other conditions do not permit development. Advantages of assigning lessons in certain grades.

_C._ Text used _in_ recitation to give training in how to study in intermediate grades.

_D._ Text used _after_ recitation as means of summary and review in much of home geography and in certain parts of upper grade work. Teachers here use materials of book as “texts” or points of departure.

=3.= THE USE OF MAPS.

_A._ Maps fundamental in geography.

_B._ Maps only clear and accurate means of representing certain classes of facts. Examples of such facts.

_C._ Essential points to be kept in mind in map use.

_a._ Cardinal directions indicated by meridians and parallels.

_b._ Top of map is not necessarily north.

_c._ Scale is necessary for getting ideas of distance and area.

_d._ Each map has special symbols adapted to special purpose of map.

_e._ First maps studied should be maps of local region shown in a horizontal position and properly oriented.

_D._ Maps of most service in texts and classroom:

_a._ Political maps in all grades.

_b._ Physical maps of large areas only give relative conditions. Cannot give exact representation of country. Dangers in physical and relief maps.

_c._ Climatic maps: annual, seasonal, special. Winds and heat belts.

_d._ Vegetation maps in upper grades.

_e._ Product and commercial maps as related to vegetation, climate, and surface.

REFERENCES: Redway, J. W., _New Basis of Geography_, chap. ix. Calkins, R. C., “The Text, the Course of Study and the Teacher,” _Journal of Geography_, iv, p. 164. Brown, Robert M., “Map Reading,” _Journal of Geography_, iv, pp. 273-288.

X. The Relation of Geography to Other Subjects in Curriculum

=1.= PLACE OF GEOGRAPHY.

_A._ Geography is considered by some as fundamental subject in curriculum, as it gives basis for study of human activities.

_B._ Geography is rather an important subject to be studied in connection with other subjects so as to produce best results from curriculum as a whole.

_C._ Coöperation between subjects does not mean parallelism in teaching or disorganization on one subject because of temporary possible cross relations to other subjects.

_D._ Unity of course of study as whole in any subject of more value than temporary mutual relations between subjects.

_E._ Geography closely related, in many ways, to nature study, history, language, and arithmetic.

_F._ Geography may contribute to and receive help from industrial subjects.

=2.= GEOGRAPHY AND NATURE STUDY.

_A._ Simpler elements of geography should be included sanely in nature study of Grades I, II, and III.

_B._ Geography in Grade III and perhaps IV should be based on nature study of earlier years. Simpler aspects of home geography should be taught before Grade III.

_C._ Geography contributes to nature study knowledge of conditions influencing distribution of plants and animals, elements of weather, soils, slopes, drainage, simple land forms, distance, and other conditions affecting problems of food, clothing, and shelter.

_D._ Geography gives application to nature study in upper grades, summarizes distribution of animals and plants, and gives regional basis to nature study.

_E._ Nature study contributes to geography knowledge of plants and animals and their ecological relations, physics and chemistry of soils, water, etc., as related to agriculture, grazing, and lumbering.

_F._ Topics of doubtful value in nature study or elementary geography.

_a._ Formation of coal, marble, and rocks, and similar topics.

_b._ Minerals, except in localities where minerals may be found.

_c._ Earth’s motions and similar large topics which cannot be studied through observation.

=3.= GEOGRAPHY IN ITS RELATION TO HISTORY.

_A._ Geography finds its best applications in history.

_B._ Geographic influences _vs._ geographic controls in history.

_C._ Geography deals with the relation between physical environment and life in all its phases. History deals with the interpretation of human movements.

_D._ Hence history finds its basis largely in geography both in reference to large facts and smaller details. Examples.

_E._ Suggested order of studying geography and history in the different grades. History should aid in making political geography understandable.

=4.= GEOGRAPHY IN ITS RELATION TO ARITHMETIC.

_A._ Problems in area, distance, time, averages, proportion, etc., may well be developed through use of facts of geography.

_B._ Graphic method of representing comparisons in geography should be developed in arithmetic.

_C._ Latitude and longitude to be developed in geography and applied in arithmetic.

=5.= GEOGRAPHY IN ITS RELATION TO LANGUAGE.

_A._ Geography finds much of its material in literature and its largest means of expression in language.

_B._ Geography should give landscape setting to poetry and prose.

_C._ The study of literature should include material which is geographically sound.

_D._ Much geography is not expressed in good literary form, and much literature is geographically unsound.

REFERENCES: McMurry, C. A., _Special Method in Geography_, chap. viii. Allen, L. R., “Correlation of Geography and History,” _Journal of Geography_, ii, p. 404. Woodice, Florence A., and Brown, Robert M., “An Experiment with Geography and History with a Sixth Grade,” _Journal of Geography_, vii, pp. 1-7.

XI. Geography and Expression Work

=1.= EXPRESSION.

_A._ Chief and most important forms of expression are oral and written expression.

_B._ Danger and unfairness of considering expression work to be merely handwork.

=2.= CHIEF WAYS IN WHICH HAND WORK CAN BE USED IN GEOGRAPHY.

Through map drawing, map filling, sand or chalk modeling, and freehand drawing.

_A._ Modeling:

_a._ A means to an end of value if done skillfully and easily.

_b._ Dangers in representing scale and slopes.

_c._ Should involve small area as to details or merely general features of a large area. First work in modeling should be devoted to features that children may observe as wholes.

_B._ Map Drawing:

_a._ Too time-consuming as a rule.

_b._ Difficulties of projection and scale.

_c._ Over-refined product should not be called for.

_d._ Children’s maps are a bad basis for visualization.

_C._ Map Filling:

_a._ Makes use of best base map available and same base map for all.

_b._ Excellent means of review as test of knowledge gained.

_c._ Relative value of flat and relief outline maps.

_D._ Freehand Drawing:

_a._ An accessory to geography work, not a way of making confused objects or relations clear.

_b._ Value of slope sketching, of simple landscape work, and of map coloring.

_c._ Hand work may borrow ideas and details from geography but adds little to value of geography as a subject.

XII. Equipment in Geography Teaching

=1.= NECESSITY OF EQUIPMENT.

Maps, globes, and illustrations. Costly single pieces of apparatus to be avoided.

_A._ Maps:

_a._ Every schoolroom should contain the following wall maps:

(1) Mercator map of world. (2) Map of North America or United States. (3) Map of continents to be studied.

_b._ Maps should be chosen for demonstration and recitation work and not for study.

_c._ Hence should be clear, capable of being seen across the room, not overcrowded with details: rivers and cities not overemphasized.

_d._ Upper grades should have physical map of United States and Europe for use in history and geography.

_e._ The use of United States Geological Survey Topographic Maps.

_f._ Use and means of securing weather maps.

_g._ Blackboard outline maps,—value and use.

_h._ Difficulties of securing certain much desired wall maps.

_B._ Globes:

_a._ One 10 or 12 inch political globe available in every room.

_b._ Globe to be of a size to be easily handled.

_c._ Political globe should be up-to-date; not overcrowded.

_d._ Blackboard globes,—how used.

_e._ Small physical or political globes for individual use.

_f._ The use of relief globes.

_C._ Apparatus:

_a._ Avoid large pieces and geographical diagrams.

_b._ Standard thermometer, barometer, compass, and wind vane to be available.

_c._ Special pieces available for special purposes.

_D._ Illustrations:

_a._ Includes photographs, cuts from magazines, slides, stereoscopic views.

_b._ Necessity of scheme for selection, classification, and storage of materials.

_c._ Value of a few good illustrations as compared with a host of poor illustrations.

_d._ Relative advantages of pictures, slides and stereoscope for special purposes.

_e._ Mechanical difficulties incident to class use of illustrations.

REFERENCES: Redway, J. W., _New Basis of Geography_, chap. xi. “Equipment for Geography Teaching,” _Journal of Geography_, v, pp. 242-250. Whitbeck, R. H., “Practical Work in School Geography,” _Journal of Geography_, iii, pp. 374-379. Emerson, P., “Field Work in the Class-Room,” _Journal of Geography_, i, pp. 54-57, 81-98.

XIII. The Geographic Preparation of a Teacher of Geography

It is neither possible nor desirable to have every grade school teacher a specialist in geography.

_A._ The scope of work analyzed.

_a._ Larger portion of work will be the geography of continents in earlier or later grades.

_b._ Small portion of work will be development of principles of physical and life geography.

_c._ The principles will be expected to be used in continental work.

_B._ The requisite training of a teacher must then include:

_a._ Some study of larger principles so as to make these principles usable in all grades.

_b._ Special study of one or more continents so as to give point of view and method of studying a region causally.

_c._ Training in use of maps, especially atlas and text maps, weather maps and United States Geological Survey Topographic Maps.

_d._ Knowledge of larger principles underlying geography teaching in the grades and study of special difficulties in each phase of elementary school work. Knowledge of subject matter is an essential basis for study of methods of teaching.

_e._ These requisites suggest the necessary content and order of procedure in geography courses in training classes.

_C._ Desirable training that teachers should be encouraged to secure.

_a._ Knowledge of geography beyond the minimum outlined above and sufficient to make them independent workers and possibly investigators in some phase of geography.

_b._ Good knowledge of history of United States and Europe.

_c._ Knowledge of elements of anthropology, economics, and biology, particularly along ecological lines.

_d._ Knowledge of modern industrial problems in the United States, particularly along lines of agriculture, manufacturing, commerce, and conservation of forests and water supply.

_D._ Opportunities for securing training in geography.

_a._ Larger and better normal schools and many colleges and universities now include well planned courses in geography.

_b._ Teachers in service will find splendid opportunities for geography work at the summer schools of colleges and normal schools. Also in some cases in certain phases of the subject, work may be secured in extension and correspondence courses.

_c._ Teachers seeking summer school opportunities should go to institutions that have summer terms, and not, as a rule, merely to summer institutions. Geography cannot be adequately taught without equipment, and only those institutions which are in operation the year round can have adequate equipment.

SELECTED REFERENCE LIST FOR TEACHERS

_General_:—

_Longman’s Gazetteer._ Longmans. The authoritative pronouncing and spelling gazetteer of the world. Contains excellent brief descriptions of all important places.

_Lippincott’s Gazetteer._ A recent authoritative volume containing excellent brief descriptions of all places of any importance.

_Andree’s Hand Atlas._ Velhagen and Klasing, Leipsig. Recent reference atlas containing excellent climatic maps and maps showing distribution of peoples, religions, plants, animals, etc.

_Stieler’s Hand Atlas._ Perthes, Gotha. The leading reference atlas.

Mill, _International Geography_. Appleton. The best single volume reference book on general and regional geography.

_Stanford’s Compendia_ (reissue). Stanford. The leading reference books on the several continents. Two volumes each on Asia, Australia, North America, Central and South America, Africa and Europe.

_Regional Geography._ Appleton. Accurate, readable, helpful volumes of first importance. Includes volumes on Britain and the British Seas, Central Europe, India, The Nearer East, and North America.

Herbertson, _Senior Geography_. A very useful volume summarizing geography of several continents in a causal order. Especially helpful for Europe.

Mill, _Hints to Teachers and Students on the Choice of Geographical Books for Reference and Reading_. Longmans. A very helpful reference list with brief comments on the individual references. Gives general and special references. A new edition appeared early in 1909.

_The Teaching of Geography_:—

Geikie, _The Teaching of Geography_. Macmillan. A very suggestive book on the essentials of good geography teaching.

McMurry, C. A., _Special Method in Geography_. Macmillan. Discusses the scope of geography and outlines a course emphasizing the teaching by types.

Redway, _New Basis of Geography_. Macmillan. Interesting and helpful for teachers in upper grades who need to teach continents from the practical standpoint.

_Physical Geography_:—

Mill, _Realm of Nature_. Scribners. A very valuable and simple book on physical and mathematical geography and on biogeography.

Davis, _Physical Geography_. Ginn & Co. An authoritative secondary school text, particularly helpful in reference to the land features.

Davis, _Elementary Meteorology_. Ginn & Co. The leading English book on weather and climate.

Ward, _Practical Exercises in Elementary Meteorology_. Ginn & Co. Very helpful to teachers who have to deal with weather phenomena.

Gilbert and Brigham, _Introduction to Physical Geography_. Appleton. An interesting, authoritative, and well illustrated secondary text on physical geography.

Tarr, _New Physical Geography_. The Macmillan Company. One of the newest and best high school books.

Salisbury, _Physiography_. Henry Holt & Company. Most inclusive and best illustrated volume available. An indispensable library reference volume.

Harrington, Mark W., _About the Weather_. Appleton. Very helpful for teachers in elementary grades.

Dodge, _Reader in Physical Geography for Beginners_. Longmans. Small volume on physical geography, available as an introduction to the subject.

_Biogeography_:—

Ratzel, _History of Mankind_ (3 vols.). Macmillan. A very comprehensive book on the races of mankind, the first volume being particularly valuable for its consideration of the problems of race distribution.

Wallace, _Island Life_. Macmillan. Classic book on animal distribution from geographic standpoint.

Guyot, _Earth and Man_. Scribners. One of the older books, and hence not written from a modern standpoint: but still invaluable for presenting the relation of earth features to life.

Herbertson, _Man and His Work_. A. and C. Black. A very usable and interesting small volume, showing the manner of life of people living in different vegetation regions and amid different surface conditions.

Lyddeker, Hutchinson and Gregory, _Living Races of Mankind_. Hutchinson & Co. Two splendidly illustrated volumes on the races of men, simple, and popularly written.

_Commercial Geography_:—

Adams, _Commercial Geography_. Appleton. An accurate, well ordered, and almost indispensable book on commercial geography. Maps and diagrams are very numerous and helpful for the teacher.

Chisholm, _Commercial Geography_. Longmans. The most inclusive volume in the English language. Contains excellent abstracts of general geography of each country in a good causal order.

_Periodicals_:—

_Journal of Geography._ Published by Teachers College, New York City. Only journal in the country devoted to teaching of geography.

_Geographical Teacher._ Phillips, London. Similar in scope to above journal and contains much of value to American teachers.

_National Geographic Magazine._ Washington, D. C. Leading popular journal of geography in country.

_Geographical Journal._ London. Leading strictly geographical journal in English-speaking world.

IV. THE TEACHING OF HISTORY

BY HENRY JOHNSON, A.M.

I. What History is

=1.= THE WORD “HISTORY” MAY DENOTE:

_a._ Past facts themselves.

_b._ Traces left by past facts.

_c._ The study which investigates such traces.

_d._ The knowledge thus obtained.

_e._ An account or narrative in which such knowledge is embodied.

=2.= THE SOURCES OF HISTORICAL KNOWLEDGE.

_a._ Primary sources.

1. Material remains—roads, buildings, tools, weapons, clothing, any material object shaped by man or associated with his life on the earth.

2. Reports of conditions and events made by actual observers. Such reports may be oral, written or printed, pictorial.

_b._ Secondary sources—reports or accounts based upon primary sources.

_c._ Accounts based upon other accounts in varying degrees of removal even from secondary sources.

_d._ Existing sources relate to fragments only of man’s total experience in the world.

=3.= HISTORICAL CRITICISM—THE FOUNDATION FOR THE DETERMINATION OF PARTICULAR FACTS RELATING TO THE PAST.

_a._ External criticism—investigation of the origin and transmission of sources; a study of form, language, writing. Is the material remaining authentic? Who was the author of the document? What did he say?

_b._ Internal criticism—investigation of the content of sources. What did the author mean? Are his statements true?

_c._ The need of historical criticism finds daily illustration in the schoolroom, in ordinary conversation, in the newspapers.

_d._ Historical criticism first formally applied by the Greeks. Not fully developed until modern times.

=4.= HISTORICAL SYNTHESIS—PUTTING THE FACTS TOGETHER INTO A BODY OF ORGANIZED KNOWLEDGE.

_a._ The chronological order—facts arranged according to time of occurrence.

_b._ The geographical order—facts arranged according to place of occurrence.

_c._ The logical order—facts arranged according to their intrinsic nature.

_d._ One order used exclusively.

=5.= HISTORY AS AN ACCOUNT OR NARRATIVE.

_a._ The subject embraced.

1. A single person.

2. A single people—whole known period or a part of it.

3. The whole world—universal history.

_b._ General conceptions of history writing.

1. A narrative of memorable events. Aim, mainly to please. Content determined by taste of authors and their public. Epic poets and story-tellers early contributors. Classical type fixed by Herodotus, the “father of history.”

2. A collection of precedents supposed to be useful to statesmen, generals, and others. Aim, didactic. Content determined by the kind of examples or lessons needed. But these, according to early conceptions, to be valuable must be true to the facts. Facts largely political and military. A conception introduced by Thucydides and developed by Polybius.

3. Scientific history. Aim, to exhibit the past as it was and to explain how it came to be what it was. Content determined by what is regarded as significant in illustrating the idea of development in human affairs.

_c._ These general conceptions correspond roughly to stages of human culture.

_d._ History generally regarded merely as a branch of literature up to 1850.

_e._ Side by side with scientific histories, works of the older types are still being produced.

REFERENCES: Langlois and Seignobos, _Introduction to the Study of History_, pp. 63-70, 211-231, 296-321. Bernheim, _Einleitung in die Geschichtswissenschaft_, pp. 5-13, 33-43, 72-78. Fling, _Outline of Historical Method_, pp. 5-124. Robinson, _History_, Columbia University Press, 1908. Rhodes, in _Atlantic Monthly_, Vol. LXXXV, pp. 158-169. Winsor, in _Atlantic Monthly_, Vol. LXVI, pp. 289-297.

II. The Problem of Adapting History to Children

=1.= SPECIAL GUIDANCE SOUGHT IN THE “NATURAL” TASTES AND INTERESTS OF CHILDREN.

_a._ These determined by experiment.

_b._ Sometimes regarded as a final criterion.

_c._ Reinforced by the culture epoch theory.

_d._ Conclusion: “The childhood of history for the child, the boyhood of history for the boy, the youthhood of history for the youth, the manhood of history for the man.”

_e._ The conclusion interpreted.

1. Facts to be selected and arranged according to their cultural stages and not according to time or place of occurrence.

2. Manner of treatment to accord in general with the conception of history first developed by the race.

3. Scientific history thus excluded.

_f._ General comment: Important to distinguish between the natural tastes and interests of children and the cultivated intelligence of children.

=2.= APPROACH FROM THE SIDE OF HISTORY.

_a._ Kinds of historical facts.

1. Facts relating to physical appearance of men and their material environment.

_a._ Possibility of direct appeal to the senses.

_b._ The simplest illustration of change in the world.

_c._ Material aspects of the past sufficiently unlike those of the present to be interesting.

2. Facts relating to what men did.

_a._ Direct sense appeal not applicable.

_b._ Only actions now in progress can be observed.

_c._ With these as a basis actions in progress in the past more or less readily imaged.

_d._ That action appeals to children an axiom of history teaching.

3. Facts relating to thoughts and feelings of men, the motives that moved them to do or to say.

_a._ Known only through deeds and words.

_b._ Real understanding of the past measured by pupil’s ability to enter this inner life of history.

_c._ Important to recognize difficulties and limitations.

_d._ The mental states of a Clovis, a Charlemagne, a Napoleon, or even of a cave-man, an Indian, a pioneer, largely beyond the experience of children and of most adults.

4. In each of these groups the simplest facts relate to particular objects, particular acts, thoughts, feelings.

5. Collective facts, facts relating to social groups, to institutions, to general causes that act in history, much more difficult.

_a._ How represent a wave of prosperity? a panic? a revolution? society itself?

_b._ Such expressions made intelligible by resolving them, so far as possible, into their concrete elements.

_b._ The kinds of facts enumerated common to literary, didactic, and scientific history.

_c._ Degree of difficulty presented by a given type of facts not essentially different for different kinds of history.

_d._ A principle of grading thus suggested as applicable to one kind of history as to another.

1. Any facts readily visualized possible material for school history.

2. Clear visualization a factor in stimulating interest.

3. Clear visualization of the man, the act, the situation, a necessary key to his mental states.

4. Elementary history, therefore, to be largely descriptive and narrative, to be made up of concrete examples rather than generalized knowledge.

_e._ Time and place relations essential to the conception of any fact as historical. As difficult for one kind of history as for another.

_f._ Special conditions imposed by scientific history.

1. Facts in palpable conflict with present knowledge not to be regarded as historical.

2. Facts to be characteristic of persons, peoples, places, periods; not exceptional, abnormal, bizarre.

3. Facts to be so presented as to exhibit relations, cause and effect, continuity.

4. Facts to be so presented as to arouse some consciousness of how we know what we know about the past and why we do not know more.

5. These conditions quite possible to meet within the limits suggested by the principle of grading already set forth.

REFERENCES: _Teachers College Record_, November, 1908, pp. 1-25. Bernheim, in _Neue Bahnen_, Vol. X, pp. 265-300, 337-357. Seignobos, _L’Histoire dans l’Enseignement secondaire_, pp. 3-25. Muzzy, in _Association of History Teachers of the Middle States and Maryland_, 1906, pp. 13-28, especially 17-19. Channing, in _North Central History Teachers’ Association_, 1907, pp. 14-18. Laurie, in _School Review_, Vol. IV, pp. 655-660. Salmon, in _Year Book Society for Scientific Study of Education_, 1902, pp. 47-54; McMurry, in same, 1903, pp. 47-51. _American Historical Association_, 1905, pp. 135-145. Hinsdale, _How to Study and Teach History_, pp. 42-52, 67-74. Rice, in _Educational Review_, Vol. XII, pp. 169-179; Burnham, in same, Vol. XXVII, pp. 521-528. Peabody, in _National Education Association_, 1893, pp. 284-285. Barnes, _Studies in Historical Method_, pp. 57-105. Mace, _Method in History_, pp. 255-308. Suzzallo, in _Teachers College Record_, May, 1904, pp. 11-19; Marker, in same, pp. 20-33.

III. The Question of Aims and Values

=1.= THE FAITH OF EDUCATORS IN THE UTILITY OF HISTORY ATTESTED BY PROGRAMS IN THE SUBJECT FOR EVERY GRADE OF INSTRUCTION FROM THE KINDERGARTEN TO THE UNIVERSITY.

=2.= CURRENT DISCUSSIONS CONFUSING.

_a._ Aims sometimes defined without reference to the nature of history. History then repudiated wherever it happens to interfere with “the uses of history.”

_b._ Aims sometimes inconsistent with each other.

_c._ Little to indicate that one of the aims of historical instruction is to teach history.

=3.= AIMS COMMONLY PROPOSED.

_a._ Discipline—training of the memory, the imagination, the judgment.

_b._ Culture—“enriching the humanity of the pupil.”

_c._ Inspiration—furnishing ideals of conduct, patriotism, social service.

_d._ Practical knowledge—teaching pupils how to act in the present.

_e._ The illumination of other studies, especially literature and geography.

_f._ The cultivation of a taste for historical reading.

_g._ The explanation of the present—nothing in the world to-day really intelligible apart from its history.

=4.= SPECIAL MODERN EMPHASIS UPON THE SOCIAL VALUE OF HISTORY.

_a._ An application of a general point of view in education.

_b._ Special demands upon history.

1. Must show in the form of concrete examples what society is and how it works.

2. Must “give a vivid and intense realization of social duties and obligations.”

=5.= PERTINENT QUESTIONS.

_a._ Are the aims proposed in fact promoted by a given kind of instruction?

_b._ Are they promoted as effectively as they might be by some other kind of instruction?

_c._ Are they the most useful of the possible ends that history might serve?

=6.= OBSERVATIONS AND EXPERIMENT NEEDED TO FURNISH DATA FOR ANSWERS.

REFERENCES: McMurry, _Special Method in History_, pp. 1-17. Kemp, _Outline of Method in History_, pp. 104-113. Barnes, _Studies in Historical Method_, pp. 106-121. Lloyd, in Spencer, _Aims and Practice of Teaching_, pp. 141-148. Rice, _History and Literature_, pp. 3-26, 149-166. Woodward, in _Essays on Teaching of History_ by Maitland and others, pp. 69-78. Hinsdale, _How to Study and Teach History_, pp. 2-17. Bourne, _Teaching of History and Civics_, pp. 77-92. _Year Book, Herbart Society_, 1898, pp. 25-56. Snedden, in _Journal of Pedagogy_, Vol. XIX, pp. 259-268. _Proceedings, National Education Association_, 1892, pp. 348-352; 1894, pp. 397-412; 1895, pp. 139-142, 306-308; 1896, pp. 410-413. Report, _Committee of Seven_, pp. 158-162. Kirk, in _Education_, Vol. XVI, pp. 15-18; Crawford, in same, Vol. XXII, pp. 281-286; McMahon; in same, Vol. XXIII, pp. 109-114. Langlois and Seignobos, _Introduction to the Study of History_, p. 331. Lea, in _American Historical Review_, Vol. IX, pp. 233-246. Harrison, _Meaning of History_, pp. 1-23. _Teachers College Record_, November, 1909, pp. 55-56.

IV. The History Program for the Elementary School

=1.= THE PREPARATORY PERIOD—THE FIRST THREE OR FOUR YEARS.

_a._ Myths, fairy tales, fables, Oriental, Greek, Roman, later European. Some use of American folk lore.

_b._ Simple biographies from American or world history. May or may not be arranged chronologically.

_c._ Stories connected with anniversaries, birthdays, Thanksgiving, Christmas.

_d._ Stories from the Bible.

_e._ Stories of primitive life.

_f._ Stories of inventions.

_g._ Stories from local history.

_h._ Various studies of a geographical or sociological character.

_i._ Several or all of these types of material may be represented in a single program.

_j._ Some schools carry this kind of work into higher grades.

=2.= THE INTERMEDIATE STAGE—FIFTH AND SIXTH YEARS.

_a._ Beginnings of textbook instruction.

_b._ More attention to chronological order and geological setting.

_c._ Subject: ancient history, the Middle Ages, English history, American history. Chief emphasis on American history.

_d._ Material usually biographical.

_e._ Some schools begin this stage of work in the fourth year.

=3.= THE LAST TWO YEARS.

_a._ Subject usually the United States.

_b._ The subject often divided.

1. Colonial period for the seventh year.

2. Later period for the eighth year.

_c._ Some schools have English history in the seventh year.

_d._ Civics frequently combined with history, especially in the eighth year.

_e._ Occasionally some Greek and Roman or general European history in one or both of these years.

=4.= THE PROGRAM PROPOSED BY THE COMMITTEE OF EIGHT.

First grade: Indian life. Explanation of holidays.

Second grade: Indian life. Holidays. Local history.

Third grade: Heroes of other times. Holidays.

Fourth grade: Historical scenes and persons in American history, colonial period.

Fifth grade: Historical scenes and persons in American history continued. Great industries of the present.

Sixth grade: European background of American history.

Seventh grade: American history to the Revolution. European background continued.

Eighth grade: The United States since the Revolution. Great events in European history.

REFERENCES: Bourne, _Teaching of History and Civics_, pp. 72-74, 106-114, 353-365. Reports of Committees: _Committee of Ten_, pp. 163, 177-181; _of Fifteen_, pp. 62-67; _of Twelve_, pp. 171, 174-175; _of Seven_, pp. 162-172; _of Eight_, pp. 1-91; Salmon, in _Year Book, Society for Scientific Study of Education_, 1902, pp. 31-60. McMurry, _Special Method in History_, pp. 18-33, 238-268. Kemp, _Outline of Method in History_, pp. 133-263. _Elementary School Record_, Vol. I, No. 8, pp. 199-216. Rice, _History and Literature_, pp. 27-74. Magnusson, in _New York Teachers Monographs_, March, 1903, pp. 90-97. Greene, _History in the Kindergarten. Warfield, in Education, Vol. XIV, pp. 1-5. Gordy and Twitchell, Pathfinder in American History_,