## 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

and true form of all quantity , number included . The differential of x and the

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 fundamentaland true form of all quantity , number included . The differential of x and the

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

admirable ...

Halaman 69

The simplest

1. ... Or , as it may be otherwise

and the unit of quantity which measures it are homogeneous quantities .

The simplest

**expression**of quantity in numerical terms involves two components :1. ... Or , as it may be otherwise

**expressed**, the unity of quantity to be measuredand the unit of quantity which measures it are homogeneous quantities .

Halaman 75

perceived in the following , where the dots symbolize both times and units of

quantity : a 6 C Measuring by the 3 - feet unit we count it off four times —that is ,

the quantity is

four ...

perceived in the following , where the dots symbolize both times and units of

quantity : a 6 C Measuring by the 3 - feet unit we count it off four times —that is ,

the quantity is

**expressed**by 3 feet taken four times . This is represented by thefour ...

Halaman 77

We measure , for example , a quantity of 20 pounds weight by a 4 - pound weight

, and the result is

in the one

We measure , for example , a quantity of 20 pounds weight by a 4 - pound weight

, and the result is

**expressed**by 4 ... the symbol which denotes measured quantityin the one

**expression**denotes pure number in the other , and vice versa . Halaman 111

( 3 ) The addition , through intuitions , of unequal ( measured ) quantities , which

are thus conceived and

to the development of the times idea . ( 4 ) Continuance of such operations ...

( 3 ) The addition , through intuitions , of unequal ( measured ) quantities , which

are thus conceived and

**expressed**as a defined unity of so many ones , is an aidto the development of the times idea . ( 4 ) Continuance of such operations ...

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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