## The Psychology of Arithmetic |

### From inside the book

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Page xi

... are at present forced to think somewhat vaguely in terms of mental functions,

like "ability to read the vernacular," "ability to spell common words," "ability to add,

sub- tract,

Introduction: The Psychology of the Elementary School Subjects.

... are at present forced to think somewhat vaguely in terms of mental functions,

like "ability to read the vernacular," "ability to spell common words," "ability to add,

sub- tract,

**multiply**, and divide with integers," "knowledge of the historyIntroduction: The Psychology of the Elementary School Subjects.

Page xii

tract,

States," "honesty in examinations," and "appreciation of good music," defined by

some general results obtained rather than by the elementary bonds which

constitute them. The psychology of the school subjects begins where our

common sense knowledge of these functions leaves off and tries to define the

knowledge, interest, power, skill, or ideal in question more adequately, to

measure improvement in it, ...

tract,

**multiply**, and divide with integers," "knowledge of the history of the UnitedStates," "honesty in examinations," and "appreciation of good music," defined by

some general results obtained rather than by the elementary bonds which

constitute them. The psychology of the school subjects begins where our

common sense knowledge of these functions leaves off and tries to define the

knowledge, interest, power, skill, or ideal in question more adequately, to

measure improvement in it, ...

Page 1

CHAPTER I THE NATURE OF ARITHMETICAL ABILITIES ACCORDING to

common sense, the task of the elementary school is to teach: — (1) the meanings

of numbers, (2) the nature of our system of decimal notation, (3) the meanings of

addition, subtraction,

of certain common measures; to secure (5) the ability to add, subtract,

and divide with integers, common and decimal fractions, and denominate

numbers, ...

CHAPTER I THE NATURE OF ARITHMETICAL ABILITIES ACCORDING to

common sense, the task of the elementary school is to teach: — (1) the meanings

of numbers, (2) the nature of our system of decimal notation, (3) the meanings of

addition, subtraction,

**multiplication**, and division, and (4) the nature and relationsof certain common measures; to secure (5) the ability to add, subtract,

**multiply**,and divide with integers, common and decimal fractions, and denominate

numbers, ...

Page 4

A study of these original methods shows that

counting, and not from addition as nearly all textbooks treat it.

counting. When children count by 4's, etc., they accent the same as counting

gymnastics or music. When a child now counts on its fingers it simply_reproduces

a stage in the growth of the civilization of all nations. I would emphasize again

that during the counting period there is a somewhat spontaneous development of

the ...

A study of these original methods shows that

**multiplication**was developed out ofcounting, and not from addition as nearly all textbooks treat it.

**Multiplication**iscounting. When children count by 4's, etc., they accent the same as counting

gymnastics or music. When a child now counts on its fingers it simply_reproduces

a stage in the growth of the civilization of all nations. I would emphasize again

that during the counting period there is a somewhat spontaneous development of

the ...

Page 10

... real situation supporting them. 1. At 70 cents per 100 pounds, what will be the

amount of duty on an invoice of 3622 steel rails, each rail being 27 feet long and

weighing 60 pounds to the yard ? 2. A man had property valued at $6500. What

will be his taxes at the rate of $10.80 per $1000? 3.

fourteen hundred-thousandths by one hundred nine millionths, and divide the

product by five hundred forty-five. 4. What number

265| ? 5.

... real situation supporting them. 1. At 70 cents per 100 pounds, what will be the

amount of duty on an invoice of 3622 steel rails, each rail being 27 feet long and

weighing 60 pounds to the yard ? 2. A man had property valued at $6500. What

will be his taxes at the rate of $10.80 per $1000? 3.

**Multiply**seventy thousandfourteen hundred-thousandths by one hundred nine millionths, and divide the

product by five hundred forty-five. 4. What number

**multiplied**by 43f will produce265| ? 5.

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### Common terms and phrases

ability to add adding addition answers arith arithmetical ability arithmetical functions arithmetical learning average better bonds boys cents child column common common fractions computation connections cost counting Courtis Test cream cheese decimal fractions decimal notation deductive deductive reasoning difficulty divide division Divisor drills Educational Psychology element elementary school equal example exercises facts figures four functions girl give given grade greatest common divisor habits hundreds improper fractions improvement inches integers interest knowledge large numbers least common multiple less long division manipulation meanings of numbers measure metic mixed numbers multiplication overlearning percent pounds principle problems psychology pupil quarts quotient reasoning relation response result score situations solve sort square subtraction Swiss cheese tables task taught teacher tenth textbooks things thinking Thorndike tion two-place understanding United States money words write yards

### Popular passages

Page 61 - Multiplication is the process of taking one number as many times as there are units in another.

Page 42 - Solve as many of the following problems as you have time for; work them in order as numbered : 1. If you buy 2 tablets at 7 cents each and a book for 65 cents, how much change should you receive from a two-dollar bill?

Page 42 - How many pencils can you buy for 50 cents at the rate of 2 for 5 cents? 5. The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 a pair. What was the total cost of uniforms and shoes for the nine?

Page 42 - A girl spent one-eighth of her money for car fare, and three times as much for clothes. Half of what she had left was 80 cents. How much money did she have at first?

Page 45 - STEP 13 (12.9) A school in a certain city used 2516 pieces of chalk in 37 school days. Three new rooms were opened, each room holding 50 children, and the school was then found to use 84 sticks of chalk per day. How many more sticks of chalk were used per day than at first? Answer. STEP 14 (14.2) A girl spent V& of her mony for car fare, and three times as much for clothes.

Page 35 - You will be given eight minutes to find the answers to as many of these addition examples as possible. Write the answers on this paper directly underneath the examples. You are not expected to be able to do them all. You will be marked for both speed and accuracy, but it is more important to have your answers right than to try a great many examples.

Page 132 - How much practice should be given to arithmetic ? How should it be divided among the different bonds to be formed ? Below a certain amount there is waste because the pupil will need more time to detect and correct his errors than would have been required to give him mastery. Above a certain amount there is waste because of unproductive...

Page 171 - The third means used to facilitate analysis is having the learner respond to situations which, pair by pair, present the element in a certain context and present that same context with the opposite of the element in question, or with something at least very unlike the element.

Page 45 - In the blank space below, work as many of the following examples as possible in the time allowed. Work them in order as numbered, entering each answer in the "answer" column before commencing a new example.

Page 43 - Do not work the following examples. Read each example through, make up your mind what operation you would use if you were going to work it, then write the name of the operation selected in the blank space after the example. Use the following abbreviations: Add.