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

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Halaman vii

In the differential calculus ratio is most adequately expressed as the fundamental

and

differential of y are ratios . The authors of this book have presented in an

admirable ...

In the differential calculus ratio is most adequately expressed as the fundamental

and

**true**form of all quantity , number included . The differential of x and thedifferential of y are ratios . The authors of this book have presented in an

admirable ...

Halaman ix

The

the importance of arithmetic which prevails in our elementary schools . As if it

were not enough that the science of number is indispensable for the conquest of

...

The

**true**psychological theory of number is the panacea for that exaggeration ofthe importance of arithmetic which prevails in our elementary schools . As if it

were not enough that the science of number is indispensable for the conquest of

...

Halaman 3

This does not mean that there is any opposition between reflection and

observation . There can not be observation in the best sense of the word without

reflection , nor can reflection fail to be an effective preparation for observation .

This does not mean that there is any opposition between reflection and

**true**observation . There can not be observation in the best sense of the word without

reflection , nor can reflection fail to be an effective preparation for observation .

Halaman 4

... freedom — to say this is simply to proclaim that the problem of education is

essentially an ethical and psychological problem . This problem can be solved

only as we know the

the ...

... freedom — to say this is simply to proclaim that the problem of education is

essentially an ethical and psychological problem . This problem can be solved

only as we know the

**true**nature and destination of man as a rational being , andthe ...

Halaman 5

To know these things is to be a

the essential qualifications of the

ethics can take education out of its purely empirical and rule - of - thumb stage .

To know these things is to be a

**true**psychologist and a**true**moralist , and to havethe essential qualifications of the

**true**educationist . Briefly , only psychology andethics can take education out of its purely empirical and rule - of - thumb stage .

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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