Reported is a comparison of the School Mathematics Study Group (SMSG) and Suppes' approaches to teaching informal geometry in grades three and four. Twenty-eight classes (617 students) were randomly assigned to an SMSG, Suppes, or control group. The students were from lower to middle socioeconomic backgrounds and measured at or below national achievement norms. Achievement was measured by a criterion pretest-posttest-retention test. At grade 3, posttest and retention test means of the Suppes group were significantly higher than those of the SMSG group. At grade 4, the posttest mean of the SMSG group was significantly higher than that of the group taught by the Suppes approach. With the grades combined, the Suppes group outperformed the SMSG group significantly on both posttest and retention test means. (RS)