GENERAL AIMS 137 



" Discovery, through observation of the number fact to 

 be taught; drill, to fix the fact in mind; application of the 

 fact to the experiences of the children and to relations that 

 they can readily grasp, is the order of instruction usually 

 followed in taking up the formal study of number. At this 

 time the utmost skill of the teacher is required to know the 

 content of the child's mind. When the child says that 4 

 and 3 are 7, for instance, has he imaged 4, 3, and their sum, 

 7 ? Does he see clearly the relation that 4 and 3 bear to 7 

 or has he, parrot-like, repeated a sentence without meaning 

 to him? Every pupil is led to discover the combinations 

 and separations for himself, again and again, until he knows 

 them. During this stage of the work the figure processes 

 are kept in the background, and the number fact is dis- 

 covered, applied, and emphasized. Figures are then intro- 

 duced with good old-fashioned drill to fix the facts. 



" Training in the instantaneous recognition of the unit 

 groups, 2, 3, 4, and 5, is continued. Clear mental images 



are formed. By this grouping the pupils 

 Imaging 



are led (assisted by objects whenever neces- 

 sary), to image 6 as 3 and 3; 7 as 5 and 2; also as 3 and 

 4; 8 as 4 and 4, and as 5 and 3. Subtraction is imaged as 

 readily as addition. The same process of imaging in 

 groups, followed by persistent drill, is used in taking up the 

 work in multiplication, division, and partition. 



" As soon as four or five combinations are learned, col- 

 umn addition is begun. In this work great care is taken 



by the teacher in preparing exercises, as no 

 Addition combination is presented that the children 



have not already learned. The work in 

 counting and writing numbers is continued within reason- 



