The purpose of this study was to determine the effect of using externally paced testing upon cognitive achievement and attitudes of college freshmen who were administered externally paced programed instruction material in mathematics. Three groups, each containing equal numbers of students representing three characteristics work rates, were administered 271 frames dealing with permutations, combinations, and probability at three different externally controlled rates. Each of the nine treatment groups was randomly divided into three smaller groups and presented immediate posttests at three different externally controlled rates. Retention tests were given three weeks later under the same externally paced conditions. An analysis of covariance was performed with SAT mathematics and verbal scores used a covariates. Where significant differences were found among the adjusted mean scores, the Scheffe multiple comparison test was used. There was no significant difference in test scores for students who used different natural working rates and for subjects subjected to three externally controlled teaching rates. Students administered posttests under an average rate had significantly greater scores (P less than .05) than students who used a fast controlled rate. There were no significant interactions of any combinations of natural pacing rates, controlled teaching rates and controlled testing rates. (Author/JP)