Stimulus manipulation versus delayed feedback for teaching missing minuend problems to difficult-to-teach students.
Gradual stimulus shaping beats simple delayed feedback for teaching missing-minuend problems, cutting errors and boosting retention.
01Research in Context
What this study did
The team compared two ways to teach missing-minuend math problems. One group got stimulus shaping: the worksheet slowly changed from easy prompts to the final form. The other group got plain worksheets plus delayed feedback at the end.
They used an alternating-treatments design so each learner tried both methods. The kids were labeled “difficult-to-teach,” but no diagnosis was given.
What they found
Stimulus shaping cut errors and the kids kept the skill longer. Delayed feedback worked, just not as well. Both groups learned, but shaping won on accuracy and maintenance.
How this fits with other research
Mosk et al. (1984) showed the same thing three years earlier: shaping beat traditional prompting on every score for kids with ID doing visual-motor tasks. Rutter et al. (1987) now extends that win to math facts.
White et al. (1990) later repeated the pattern with sight words—fading with stimulus similarity cut errors in half versus a standard prompting hierarchy. The 1987 study sits in the middle of this chain, proving the rule holds across tasks and learners.
Dougherty et al. (1994) looks like a contradiction at first—they praise immediate feedback, not delayed. But they compared immediate versus delayed correction, while the 1987 study compared shaping versus delayed feedback. The lesson: give feedback right away, and also shape the stimuli; the two tactics work together, not against each other.
Why it matters
If a child is stuck on math facts, don’t just tell them the right answer later. Change the worksheet itself—start with the answer visible, then fade it out. You’ll see fewer errors today and better scores next week.
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Join Free →Fade the math worksheet: first sheet shows the subtrahend in gray, next sheet hides it, final sheet looks like the test.
02At a glance
03Original abstract
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.
Research in developmental disabilities, 1987 · doi:10.1016/0891-4222(87)90008-4