Stimulus manipulation versus delayed feedback for teaching missing minuend problems to difficult-to-teach students.

The present study evaluated two procedures, Stimulus Manipulation and Delay Feedback Only, for teaching difficult-to-teach students to solve missing minuend problems (i.e., missing number problems starting with a minus sign). The Stimulus Manipulation procedure was directed at establishing the target skill with a minimum of errors. The training consisted of three phases of several steps each. The first phase was designed to establish a nonnumerical response to a prompt, the shape of which was gradually transformed into the final discriminative stimulus. The second phase was designed to extend the control of this stimulus to the numerical operations and to eliminate all supplementary stimuli. The third phase gradually eliminated the originally trained nonnumerical responses. The Delayed Feedback Only procedure included no stimulus manipulation and consisted of the experimenter giving only delayed right.wrong feedback on the solutions. The data indicate that both procedures resulted in all (N = 4) subjects (a) learning to solve the target problems, (b) generalizing this skill to similar, more advanced problems, and (c) maintaining it over multiple intervals of several consecutive weeks. However, systematic differences in error rate and long-term retention across training methods were observed, favoring the Stimulus Manipulation procedure.