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A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of “number”. These are the “objectives” of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered.

A series of five experimental conditions were designed to investigate the influence of minimum performance criteria and grade labels on college student academic performance. A college course in abnormal psychology was taught in an individualized manner so that each student could perform on each unit of subject matter in individual performance sessions whenever he wished. In each of the five experiments the minimum performance criteria that had to be attained before progressing to the next unit were varied during the quarter and the resulting changes in performance were recorded. In Experiment I there were no criteria; in Experiments II, III, and IV three levels of criteria (High, Medium, and Low) were varied but all of the criteria defined a course grade of “A”. In Experiment V, the three criteria defined course grades of A, B, and C. The results showed that the criteria controlled performance to a high degree, so that regardless of what quality of performance had been demonstrated previously or was being produced currently, performance was immediately changed to attain new criteria put into effect. Students in Experiment I produced very poor performance compared to the other conditions.

A major purpose of the study was to assess the relative effects of group versus individually contingent free time in modifying student behaviors. Other purposes were to determine the effectiveness of well‐planned lesson activities and tokens without back‐up reinforcers. Eight students in an inner‐city seventh‐grade class of 32 blacks served as subjects. Well‐organized lesson activities and success feedback via tokens did not produce high levels of desirable behavior. In contrast, group and individually contingent free time produced substantially higher levels of appropriate behavior than did the baseline conditions. The group reinforcement procedure appeared to be slightly more effective than individual reinforcement.

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It is commonly understood that the interactions between an organism and its environment constitute a feedback system. This implies that instrumental behavior should be viewed as a continuous exchange between the organism and the environment. It follows that orderly relations between behavior and environment should emerge at the level of aggregate flow in time, rather than momentary events. These notions require a simple, but fundamental, change in the law of effect: from a law based on contiguity of events to a law based on correlation between events. Much recent research and argument favors such a change. If the correlation‐based law of effect is accepted, it favors measures and units of analysis that transcend momentary events, extending through time. One can measure all consequences on a common scale, called value. One can define a unit of analysis called the behavioral situation, which circumscribes a set of values. These concepts allow redefinition of reinforcement and punishment, and clarification of their relation to discriminative stimuli.

Differential reinforcement of compliance with teacher invitations to complete a specific academic task was applied to three extremely negativistic children in a special preschool class. For each child, this technique resulted in clear and useful increases in compliance as it was applied. In addition, the technique produced a greater diversity of sampling the available tasks by all children, enabling them to contact instructional materials they had previously avoided. The reinforcement system, contingent access to free playtime, materials, and a snack, mediated by a token, was thus demonstrated to be an effective contingency. In the case of two children whose compliance was not maximized by differential reinforcement alone, further increases in compliance were produced by combining a 1‐min timeout for noncompliance with the differential reinforcement procedure.