One possible approach comes from the behaviorist theory discussed in Teachers’ perspectives on learning. Irma may persist with the single-digit strategy because it has been reinforced a lot in the past. Maybe she was rewarded so much for adding single-digit numbers (3+5, 7+8 etc.) correctly that she generalized this skill to two-digit problems”in fact over generalized it. This explanation is plausible because she would still get many two-digit problems right, as you can confirm by looking at it. In behaviorist terms, her incorrect strategy would still be reinforced, but now only on a “partial schedule of reinforcement”. As I pointed out in Teachers’ perspectives on learning, partial schedules are especially slow to extinguish, so Irma persists seemingly indefinitely with treating two-digit problems as if they were single-digit problems.
From the point of view of behaviorism, changing Irma's behavior is tricky since the desired behavior (borrowing correctly) rarely happens and therefore cannot be reinforced very often. It might therefore help for the teacher to reward behaviors that compete directly with Irma's inappropriate strategy. The teacher might reduce credit for simply finding the correct answer, for example, and increase credit for a student showing her work”including the work of carrying digits forward correctly. Or the teacher might make a point of discussing Irma's math work with Irma frequently, so as to create more occasions when she can praise Irma for working problems correctly.
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