Instructional research is reviewed where teaching failures have produced students who seem to be less able to use learning skills or had less access to knowledge in some domain than before they were taught. Three general types of "mathemathantic" (i.e. where instruction "kills" learning) effects are hypothesized, theoretical explanations for each effect are examined and representative studies in each area are described. The three types of effects described are where instruction serves to: (1) substitute learning procedures (e.g. novel learning strategies are hypothesized to interfere with the learning of higher general ability learners and inadequate learning strategies are provided to those with lower general ability); (2) impose less desirable motivational goals on learners (e.g. when teaching methods lead constructively motivated learners to believe that failure avoidance has replaced achievement directed goals and, conversely, when defensively motivated students believe that achievement directed goals have replaced the opportunity to avoid failure); and (3) substitute student control for system control over instructional method (e.g. by allowing lower cognitive load instructional methods to be chosen by high general ability, constructive students and/or by allowing higher cognitive load methods to be chosen by defensive students who have low general ability). A four-page bibliography and an outline of situations when mathemathantic effects are more probable are attached. (Author/JAZ)