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

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Halaman 41

We shall now note more definitely what is implied in the foregoing account — the

constant aiming at a balance or equivalence- ( valens , worth ; æquus ,

The process of adjusting means to end is not simply a process of roughly ...

We shall now note more definitely what is implied in the foregoing account — the

constant aiming at a balance or equivalence- ( valens , worth ; æquus ,

**equal**) .The process of adjusting means to end is not simply a process of roughly ...

Halaman 46

... volume , etc. ; we should simply have to guess how much of one scale would

scale is imperfect if we have no means of defining some unit of the scale in terms

of ...

... volume , etc. ; we should simply have to guess how much of one scale would

**equal**a given quantity of another . Moreover , the measurement within a givenscale is imperfect if we have no means of defining some unit of the scale in terms

of ...

Halaman 49

If , however , the wholes are taken or assumed as

, the operations of multiplication and division may be performed with them . But

this is only because the assumption of

If , however , the wholes are taken or assumed as

**equal**in value , then , of course, the operations of multiplication and division may be performed with them . But

this is only because the assumption of

**equal**( measured ) * It is a great pity that ... Halaman 50

If we are to divide fifteen apples " equally ” among five boys , giving each boy

three apples , this “

) of measure . Much and Many . — The whole falling within a certain limit supplies

...

If we are to divide fifteen apples " equally ” among five boys , giving each boy

three apples , this “

**equal**” distribution assumes the equality of the units ( apples) of measure . Much and Many . — The whole falling within a certain limit supplies

...

Halaman 54

The eye moves along till it has measured , as nearly as we can judge , just as

much space as

performed ; it is pure assumption that the minor act measures an

every time ...

The eye moves along till it has measured , as nearly as we can judge , just as

much space as

**equals**one of the ... number of times the minor act has beenperformed ; it is pure assumption that the minor act measures an

**equal**lengthevery time ...

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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