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

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Halaman vii

... view which makes unity a qualitative instead of a quantitative idea are sure to

appear in the methods of solution adopted . Pupils studying music by the highest

method learn thoroughly those combinations which

... view which makes unity a qualitative instead of a quantitative idea are sure to

appear in the methods of solution adopted . Pupils studying music by the highest

method learn thoroughly those combinations which

**involve**double counterpoint . Halaman viii

They furnish little , if any , training in thinking the ratio

number . The psychology of number requires that the methods be chosen with

reference to their power to train the mind of the pupil into this consciousness of

the ...

They furnish little , if any , training in thinking the ratio

**involved**in the very idea ofnumber . The psychology of number requires that the methods be chosen with

reference to their power to train the mind of the pupil into this consciousness of

the ...

Halaman 24

In the simple recognition , for example , of three things as three the following

intellectual operations are

forming one connected whole or group — that is , there must be a recognition of

the three ...

In the simple recognition , for example , of three things as three the following

intellectual operations are

**involved**: The recognition of the three objects asforming one connected whole or group — that is , there must be a recognition of

the three ...

Halaman 25

Part of the difficulty of performing the abstraction which is required to get the idea

of number is , accordingly , that this abstraction is complex ,

the difference which makes the individuality of each object must be noted , and ...

Part of the difficulty of performing the abstraction which is required to get the idea

of number is , accordingly , that this abstraction is complex ,

**involving**two factors :the difference which makes the individuality of each object must be noted , and ...

Halaman 30

It appears to be forgotten that he may and should perform many operations and

reach definite results by implicitly using the ideas they

ideas can be explicitly developed in consciousness . If facts are presented in their

...

It appears to be forgotten that he may and should perform many operations and

reach definite results by implicitly using the ideas they

**involve**long before theseideas can be explicitly developed in consciousness . If facts are presented in their

...

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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