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Experimental conditions were designed to examine students' sensitivity to scheduled contingencies and accurate or fallacious rules as these variables influence performance during computer-generated math problems. Experimental subjects were provided: scheduled contingencies followed by extinction, follow-up extinction, and a rules condition promulgating accurate or fallacious rules for accessing reinforcement. Control subjects did not have access to rules; however, sensitivity to direct-acting contingencies was measured during response independent reinforcement. Performing with accurate rules and scheduled contingencies, most experimental subjects correctly answered math problems at accelerated rates and extended durations. Also, providing fallacious rules during response independent reinforcement induced high rates and extended durations of superstitious responding. However, for most students response independent reinforcement, without rules, was insufficient to induce such behavior. Evidence from this study suggests that maintenance of high rate superstitious responding requires exposure to a fallacious rule in conjunction with making contact with response independent reinforcement. Implications from this study support the theory that superstitious behavior may become self-sustaining by precluding one's opportunities to contact the null effects of not performing in accordance with fallacious rules. Ramifications regarding interactions between verbal fallacies and coincidental reinforcement are discussed.