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