CONTENTS
.
1. Aims .........
2. Guiding Principles ..........
Outline By Grades:
Grade One ........
Grade Two.
Grade Three ......
Grade Four .....
Grade Five ............
Grade Six ...............
Grades Seven and Eight ..........
4. Games and Drill Devices ......
5. General Bibliography
......
V
.


AIMS
The work in the elementary school should provide for:
1. Speed and accuracy in computing with numbers arising in com-
mon business, industrial, and social practices.
2. Ability to solve the ordinary problems arising in business, social,
and industrial activities.
3. An understanding and appreciation of the common social, indus-
trial, and business fields in which computation with numbers arises.
GUIDING PRINCIPLES
I. In the Selection and Organization of Subject Matter
1. “The selection of the subject matter for the course of study
and the relative emphasis which it receives there, should
be determined by its relative importance in social life.”
- McMurry
2. “The arithmetic of the elementary school should deal with prob-
lems and practices which arise in real life.” — Thorndike
3. “The school should favor real situations, should present issues
as life will present them.” — Thorndike
4. “For the elementary school the content of arithmetic to be
selected is that which is of direct use in the common daily
needs of life in the measurement of quantities and values.”
- Bonser
5. "Interpretive knowledge in arithmetic for the elementary
grades should include such numbers and number relation-
ships as are found in current usage.” — Bonser
II. In Methods of Teaching
1. The content of problems in arithmetic should be true, i. e., the
situation described in the problems should be a real situation.
2. The processes which the problem requires should be those which
life requires.
The computations required should be those which are useful in
real life.
4. The number facts, processes, and principles should be connected
at the time of learning with those life situations which utilize
them.
5. The answers to problems should have real significance in the
number situation being studied.
os
DEK


5.
6.
7.
The recitation period shorúc be user requently to observe chil-
dren at work in order to discover meconomical habits which
are not revealec in finished results.
The recitation period shouc be a times a "clearing house for
the discussion of inciriana difficulties.
The recitation perioc showIC DE Used to teach children bow to
study aritmetic.
Lengthy vertal explanations of problems solved correctly
shond be aroidec.
The teacher shonic endeavor in the recitation as well as in the
study period to incricuabize instruction.
8
9.
OUTLINE BY GRADES
GRADE ONE
The work of this grade should be entirely incidental and informal No
time should be given tonumber work as sort on the program but the teacher
should utilize all the activities of the grade in which quantitative facts and
relationships are needed, for the purpose of estabishing in the child's mind
the number concepts, both in their serial and collection meaning, and the
ratio idea as it is needed in simple measurments for construction work of
various sorte.
Some of the natural situations in the school room which utilize numbers
are:
1. Estimating the number of milk bottles needed each day and buying
tickets
2. Counting money for banking
3. Counting, and estimating materials, such as scissors, paper, chairs,
etc., needed in various school activit.es
4, Keeping records of attendance, books read, reading vocabulary, etc..
5. Finding pages in a book
6. Telling time
7. Keeping height and weight charts
8. Playing games
9, Buying school supplies
10, Building with blocks
11, Measuring with paper, wood, cloth, etc. for construction work
12. Playing house, store, post-office, etc.
13. Making gardens and planting seeds
14. Giving a party or picnic


2 2 2 2 3 3 3 3 4
4 6 6 7 4 5 6 7 5 and the reverse
Column addition without carrying, three and four addende,
one and two place numbers
Meaning of and -- , "Hum" and "adding"
4. Subtraction
Combinatione. the reverse of the addition combinations
Subtraction of two place numbers without "borrowing."
Meaning of , "wubtracting", "subtract", and "difference"
6. Fractions
Meaning of two equal parts
Meaning of 14. V. V. 14 of concrete things
6. Measures
Telling time
Measuring with inches
Adding and subtracting cents
Meaning of
Meaning of *
7. Problems
Mimple one step problems about child experience with mum.
1. Notation and numeration
Continue work of first Semester,
2. Counting
Count hy 'N
Count odd and even numbers by 2'
%. Addition
Combinations
2 2 % % 4 4 4 4 6 7 8 9
% 9 % 90.7 % 9 6 7 8 ) and the reverse
6 6 6 6 6 6 6 7 7 %
0.7 % 97 % 9 % 9 %) and the reverse


7 Drill should be motivated.
a. The learner should recognize the value of the fact to be
learned.
b. Number facts should be put to use as soon as they are
learned.
C. Each number fact should be associated at the time of
learning with other number facts to which it is most
closely related.
d. The child should be stimulated to an interest in his own
progress.
8. Drill should be distributed in harmony with the laws of learn-
ing. The common errors which Thorndike points out are
as follows:
a. Giving too much practice at the first learning.
b. Leaving too long intervals with no practice.
c. Leaving number facts in too great isolation.
9. Reviews should not be mere repetition of facts learned, but
should provide for increased facility, and comprehension of
facts, computations, and processes.
10. Number games are valuable in motivating drill. The following
principles should guide in their use:
a. Choose those games which give a maximum amount of
arithmetic drill and do not detract from the number
fact or principle involved.
b. Choose those games in which the computations are not so
involved as to destroy the game element.
C. Manipulate the game so that each child will get the max-
imum amount of practice.
d. Manipulate the game so that the weaker children will get
more drill than the stronger ones.
11. Drill periods should be short.
IV. In the Conduct of the Recitation
1. The recitation period should be devoted largely to teaching
and testing rather than to drill.
2. Work done correctly during the study period should not be
repeated in the recitation.
3. Typical errors of the group made during study period should be
discussed during the recitation period.
4. Errors not common to the group should be taken up with the
pupils individually.


5. The recitation period should be used frequently to observe chil-
dren at work in order to discover uneconomical habits which
are not revealed in finished results.
6. The recitation period should be at times a "clearing house" for
the discussion of individual difficulties.
7. The recitation period should be used to teach children how to
study arithmetic.
8. Lengthy verbal explanations of problems solved correctly
should be avoided.
9. The teacher should endeavor in the recitation as well as in the
study period to individualize instruction.
OUTLINE BY GRADES
GRADE ONE
The work of this grade should be entirely incidental and informal. No
time should be given to number work as such on the program but the teacher
should utilize all the activities of the grade in which quantitative facts and
relationships are needed, for the purpose of establishing in the child's mind
the number concepts, both in their serial and collection meaning, and the
ratio idea as it is needed in simple measurments for construction work of
various sorts.
Some of the natural situations in the school room which utilize numbers
are:
1. Estimating the number of milk bottles needed each day and buying
tickets
2. Counting money for banking
3. Counting, and estimating materials, such as scissors, paper, chairs,
etc., needed in various school activit.es
4. Keeping records of attendance, books read, reading vocabulary, etc..
5. Finding pages in a book
6. Telling time
7. Keeping height and weight charts
8. Playing games
9. Buying school supplies
10. Building with blocks
11. Measuring with paper, wood, cloth, etc. for construction work
12. Playing house, store, post-office, etc.
13. Making gardens and planting seeds
14. Giving a party or picnic


2
2
I ON
2 3 3 3 3 4
4 5 6 7 5 and the reverse
Column addition without carrying, three and four addends,
one and two place numbers
Meaning of + and =, "sum” and “adding"
4. Subtraction
Combinations — the reverse of the addition combinations
Subtraction of two place numbers without “borrowing"
Meaning of —, "subtracting”, “subtract”, and “difference”
5. Fractions
Meaning of two equal parts
Meaning of 1/2, 1/6, 1/3, 1/4 of concrete things
Measures
Telling time
Measuring with inches
Adding and subtracting cents
Meaning of ¢
Meaning of $
7. Problems
Simple one step problems about child experiences with num-
bers
Second Semester
1. Notation and numeration
Continue work of First Semester.
2. Counting
Count by 3's
Count odd and even numbers by 2's
3. Addition
Combinations
I or I ON
i vor 1
2 2 3 3 4 4 4 4 6 8 9
8 9 8 9 6 7 8 9 6 7 8 9 and the reverse
- - - - - - - - - - - -
5 5 5 5 6 6 6 7 78
89 7 8 9 8 9 9 and the reverse
- -


. 7. Giving problems which include unnecessary data
The following principles are quoted from the 18th Year Book of the
National Society for the Study of Education and from Thorndike's
New Methods in Arithmetic and Thorndike's Psychology of Arith-
metic. They should be observed in teaching the subject matter of
the grade.
1. In column addition, grouping digits to make 10 or some other
convenient number is not helpful.
2. The Austrian or additive method of subtraction is not super-
ior to the "take away" method.
3. In borrowing it is better to increase the subtrahend by one
than to decrease the minuend.
4. After the initial stage of practice, drill upon the fundamental
combinations should be given by means of examples.
5. Counting backward by 2's, 3's, 4's is an aid to subtraction.
6. It is unwise to use the common crutch of writing the min-
uend or subtrahend changed when "borrowing” takes
i .. place.' .
7. To prevent counting in addition from becoming a fixed
habit, the teacher should use ""hidden" addition and should
force · speed. “ (Hidden addition means addition where
real objects are presented but where they are hidden dur.
ing the act of adding, so that the pupil must think the
Citate numbers and add them.). Asi :
8. Using +,-, or x as a sign of what you are to do in com-
putations seems inadvisable.
in! 9. Writing the number to be carried in addition should be per-
mitted.
10. The number which causes most difficulty is 0. It should be
read "no,” “not any," or "zero." There are two main rea-
sons for zero difficulties. First, 0 is peculiar arithmetic-
ally in that it has a separate set of habits of its own, such
as 0 in column addition, neglect it; any number minus zero
is unchanged; 0 times a number equals 0; any number times
O equals 0; 0 divided by any number equals 0; second, the
operations with 0 are not uniform.
VI. Outcomes
1. Automatic control over all fundamental addition, subtraction,
multiplication, and division combinations
2. Intelligent command of the language necessary in understand-
ing and using the subject-matter of the grade
17


3
2
Subtract: 80413
46349
Multiply: 67496982
40968
Add: 1842
2287
4940
3694
1738
2429
1365
5506
1179
Divide: 275) 75625
I oor A voor Hoco er
5034 X 3278
25 = 5/8
3321/2 = 12
1213 • 134
6. A knowledge of the fields of social activity in which the subject-
matter of the grade functions
7. The well established habits of checking answers, of estimating
results and using abbreviated methods
8. An interest in his progress and an increasing sense of responsi-
bility for his own drill processes
9. Ability to use the textbook with ease as a guide to study
10. Ability to understand problems involving the fractions and
measures outlined in the subject-matter and ability to compute
readily with any of them
V. References
Text: Arithmetic Essentials—Drushel-Noonan-Withers, Book Two,
Part One
The Thorndike Arithmetic, Book Two, Part One, Chapters 1 and 2
Everyday Arithmetic—Hoyt and Peet, Intermediate, Part Three,
Chapters 1, 2, 3, 4, 5, 7, and 8 .
Efficiency Arithmetic—Chadsey-Smith, Intermediate, Part One,
Chapters 1, 2, 3, 5, and 6
GRADE SIX
I. Outline of Subject-Matter
First Semester
1. Notation and Numeration
Reading and writing numbers to billions
2. Four Fundamentals
Speed and accuracy tests
29


• Profit and Loss
Simple interest
Trade discount
Common and decimal fraction equivalents
Second Semester
1. Four Fundamentals
Speed and accuracy tests
2. Fractions
Speed and accuracy tests
3. Measures
Continued practice
Terms to be known, "point,” "line," "straight line," "curved
line," "angle," "perpendicular," "parallel," "right angle,"
"horizontal," "vertical," "rectangle," "triangle," "circle”
Board measure
Cubic measure
Cord Wood
English pound
French franc
German mark
4. Problems
Equation continued
5. Decimals
Continued practice
6. Business Forms
Continue forms used in first semester
7. Percents
Applications of percentage in taxes, insurance, and simple
interest
Grade Eight
First Semester
1. Four Fundamentals
Speed and accuracy tests
Short cuts
2. Fractions
Speed and accuracy tests
36


The child is required to give orally the remainders, subtracting 0
from each number in the first row, 1 from each number in the second row,
2 from each number in the third row, etc. When writing remainders, a
whole group write remainders only to rows designated by the teacher.
The value in this lies in the fact that all pupils in the group are not only
working, but working independently.
MULTIPLICATION DRILLS
Efficient work in multiplication requires the ability to multiply and
add quickly. To cultivate this ability the following device was used:
7
4
x
0
and
X
oer HA H coc O
00 voor A CON
The child begins with 4 X 7 and 1, 4 X 2 and 1, 4 X 8 and 1, etc.
until he has finished the column. He then begins again with 4 x 7 and 2,
4 X 2 and 2, 4 X 8 and 2, etc. Any digit may be used in the multiplier.
There is one matter which must be guarded, however: No number added
should be greater than the multiplier less one, since this situation is never
met in an actual example. For instance, in multiplying by 4, 3 is the
largest number ever carried and to require a pupil to add a number such
as 8 would be wasteful drill.
SHORT DIVISION DRILL
It is just as important that pupils be drilled upon the giving of
quotients and remainders as upon the division tables. The chart printed
below was used almost daily by teachers in the fourth, fifth, and sixth
grades in overcoming slow and inaccurate work in naming quotients and
quotients and remainders.
51