Abstract

This study was carried out to investigate that underlying mental operations of the use discounting (and augmentation) principles are special kinds of additive (and subtrad abilities as reverse operations (x+a=b -> x=b-a: x-a=b -> x=b+a). In study, three-year- to five-year-old children were asked to make a solution quantity, math, and attribution problems. Six kinds of math problems (simple addition, a+ simple subtraction, a-b=?: adding amount, a+?=b: subtracting amount, a-?=b: added amount ?+a=b: subtracted amount, ?-a=b), two kinds of quantity problems (tee using clay and the other using water) which treat added quantity arcs subtracted quantity, and two kinds attribution problems (discounting and augmentation) were administrated. Major findings study oars as follows: (1) Adding and subtraction seem to be developed simultaneously discounting and augmentation principles appear to be used at the same time. (2) Over half the three- or four-year-old children and almost all the five- or six-year-old children use discounting and augmentation principle. (3) Results support the hyphothesis that opera of added or subtracted amount is underlying operation for the use of discounting augmentation principle.