## The Psychology of Number and Its Applications to Methods of Teaching Arithmetic |

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Halaman 76

damental principle in multiplication known as the law of commutation : the

product of factors is the same in whatever order they may be taken — i . e . , in the

case of two factors , for example , either may be

b is ...

damental principle in multiplication known as the law of commutation : the

product of factors is the same in whatever order they may be taken — i . e . , in the

case of two factors , for example , either may be

**multiplicand**or multiplier ; a timesb is ...

Halaman 113

The

multiplier is always pure number , representing simply the times of repetition of

the derived unit . But from the nature of the measuring process the two factors of ...

The

**multiplicand**always represents a number of ( primary ) units of quantity ; themultiplier is always pure number , representing simply the times of repetition of

the derived unit . But from the nature of the measuring process the two factors of ...

Halaman 114

In multiplication the order is as follows : ( 1 ) The vague or imperfectly defined

magnitude ; ( 2 ) the definite unit of value ( primary unit ) , which has to be

repeated to make the derived ( direct ) unit of measure — the

the ...

In multiplication the order is as follows : ( 1 ) The vague or imperfectly defined

magnitude ; ( 2 ) the definite unit of value ( primary unit ) , which has to be

repeated to make the derived ( direct ) unit of measure — the

**multiplicand**; ( 3 )the ...

Halaman 115

implies division ; the definite unit of measurement which constitutes the

multiplication always implies ratio ; the whole magnitude bears to the unit of

measure a ratio ...

implies division ; the definite unit of measurement which constitutes the

**multiplicand**is always a certain exact ( equal ) portion of some whole . Hencemultiplication always implies ratio ; the whole magnitude bears to the unit of

measure a ratio ...

Halaman 117

The

is as expressed in minor units . It signifies the known value of the unit with which

one sets out to measure ; it is the measuring rod , as it were , which is none the ...

The

**multiplicand**must always be seen to be a Unit in itself , no matter how large itis as expressed in minor units . It signifies the known value of the unit with which

one sets out to measure ; it is the measuring rod , as it were , which is none the ...

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abstract activity actual addition already amount applied arithmetic attention become begin carry cent child clear common complete conception conscious constructive cost counting decimal defined definite denotes digits direct divided division divisor dollar educational equal exact example exercises expressed factor facts feet figures five foot four fractions fundamental given gives groups hundred idea inches interest involved kind learned least less magnitude means meas measured quantity measuring unit mental method mind minor multiplicand multiplication nature necessary objects once operations original practice present primary principle problem psychological pupil rational reason recognition reference relation remainder repeated represents result root seen sense separate simply square stage subtraction taken teacher teaching tens things third tion true unit of measure unity ured vague whole yard