CHAPTER XIX_A brief course in the teaching process

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

+=========+==========+===========+=========+============+===========+

+---------+----------+-----------+---------+------------+-----------+

| 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

--------+---------+--------+--------+--------+--------+--------+--------

--------+---------+--------+--------+--------+--------+--------+--------

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

+---+---+----+------+------+----+----------------------------------

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

+--------+------------+--------+---------+--------+----------

| of | and to | of | to | of |Fundamen-

----------+--------+------------+--------+---------+--------+----------

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.