The purpose of the study was to compare the results obtained from a group of fourth-grade students taught to add and subtract rational numbers through the use of field postulates and other properties of whole numbers with fourth-grade students taught by a standard method using objects and the number line. Eight classes of 30 students each participated; the classes were assigned treatments at random and provided four replications for the study. The experimental groups studied 30 investigator-prepared lessons, while the control group used a legally adopted text. All students were given standardized tests of IQ and of arithmetic skills. Two forms of a criterion test in performance on the addition and subtraction of fractions were developed, validated, and administered. Results showed the experimental course to be more effective than the standard method, that subjects with higher IQs tended to make greater gains than those with lower IQs within each treatment group, and that within each treatment group there were significant differences among mean gain performance of achievement subgroups. (Author/DT)