Abstract

Three-year- to seven-year-old children were asked to make a solution for the math problems. In order to solve them subjects should use six additive or subtractive operations as follows: (1) Simple Addition (a+b=?), (2) Simple Subtraction (a-b=?), (3) Adding Amount (a+?=b), (4) Subtracting Amount (a-?=b). (5) Added Amount (?+a=b), and (6) Subtracted Amount (?-a=b). Experimenters gave the questions to subjects through two procedures: (1) Pictorial presentation with verbal explanation (2) Numerical presentation with printed materials (cards on which equations such as "3+?=5" were written). When the numerical presentation, several stages for solving the equations were found: (I) Wrong Solution, (2) Adding given digits for any equations, (3) Can do Simple Addition, (4) Can do both Simple Addition and Simple Subtraction, (5) Can do Adding Amount and Subtracting Amount, (6) Can solve all the equations. When pictorial and verbal procedures, almost all the 3-year-old children can do both Simple Addition and Simple Subtraction. The stages found from the analyses of the data from the pictorial and verbal procedures were reconfirmed. Origins and developmental trends of additive and subtractive abilities were discussed.