Contextual control of equivalence-based transformation of functions.

Ten college students learned to sort abstract shapes into three equivalence classes. Then they got lots of practice: the same shapes now told them to press left or right. A red border on the screen meant 'do the opposite of what you learned.'

After many rounds the border color alone controlled whether they kept or flipped their response. The team kept adding new sets of shapes to see if the rule would travel.

Nine of ten adults finally let the border color switch their key press. Four of five still followed the rule when every shape was brand-new.

It took hundreds of trials, but the context cue—not the shapes themselves—ended up in charge.

Allen et al. (2001) ran a similar lab setup but later taught conflicting matches. Their classes fell apart, while Michael’s held firm. The difference: Michael piled on extra exemplars first, showing practice can armor equivalence against future interference.

Frampton et al. (2023) boosted success by letting learners draw their own maps. Together the papers say: either flood the learner with examples or give them a self-made visual—both tricks build sturdy contextual control.

Mason et al. (2025) repeated the idea in rats. A left/right lever rule transferred to new cage lights, but the effect faded fast. The animal data echo Michael’s human finding: transfer happens, yet it’s fragile without enough exemplars.

If you want a client to use a skill only in certain settings, pick a clear context cue and over-teach with many examples. A colored table edge, a specific room, or a badge can signal when to apply the skill and when to hold back. Keep probing with new materials to be sure the context—not the particular objects—controls the response.