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

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Halaman ix

Mental arithmetic becomes in their psychology " the discipline for the pure reason

, ” although as a matter of fact the three

neither of them employed in mathematical reasoning W. T. HARRIS .

WASHINGTON ...

Mental arithmetic becomes in their psychology " the discipline for the pure reason

, ” although as a matter of fact the three

**figures**of the regular syllogism areneither of them employed in mathematical reasoning W. T. HARRIS .

WASHINGTON ...

Halaman 59

The former method , that of symbols , is illustrated in the old - fashioned ways—

not yet quite obsolete - of teaching addition , subtraction , etc. , as something to

be done with “

...

The former method , that of symbols , is illustrated in the old - fashioned ways—

not yet quite obsolete - of teaching addition , subtraction , etc. , as something to

be done with “

**figures**, ” and giving elaborate rules which might guide the doer to...

Halaman 60

The child simply takes , for example , the

operations with them , which are dignified by the names addition , subtraction ,

multiplication , etc .; he knows very little of whạt the

...

The child simply takes , for example , the

**figures**3 and 12 , and performs certain “operations with them , which are dignified by the names addition , subtraction ,

multiplication , etc .; he knows very little of whạt the

**figures**signify , and less of the...

Halaman 104

Because of the rhythmic character of multiplication such forms of it as can be

objectively presented in simple constructions — the putting together of triangles ,

squares , cubes , etc. , to make larger or more complex

...

Because of the rhythmic character of multiplication such forms of it as can be

objectively presented in simple constructions — the putting together of triangles ,

squares , cubes , etc. , to make larger or more complex

**figures**, of dimes to make...

Halaman 116

The sole interest which attaches to it is external , as arising from the mere

manipulation of

figuring ” work may be interesting ; but this interest is re - enforced , transformed ,

when ...

The sole interest which attaches to it is external , as arising from the mere

manipulation of

**figures**. Under an interested teacher , indeed , even the pure “figuring ” work may be interesting ; but this interest is re - enforced , transformed ,

when ...

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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