ifc-0024

1.6 Coaching as typed counter-witness selection

An effective coach does more than label an action incorrect. The coach selects evidence that distinguishes the learner’s current theory from a better alternative. This gives coaching a natural counter-witness semantics.

Suppose the learner considers candidate sketches \(\mathbb S_1,\ldots ,\mathbb S_k\). A pedagogical intervention \(q\) has value when the possible teacher responses separate these candidates:

\[ q^* \in \arg \max _q \operatorname {Discrim} \bigl( p(f\mid q,\mathbb S_1),\ldots , p(f\mid q,\mathbb S_k) \bigr). \]

A tennis coach may exaggerate a motion, physically reposition the learner, contrast two grips, or ask for the same serve from a different stance. Each intervention changes the evidence so that a hidden structural distinction becomes observable.

Teacher corrections can target different components of the sketch:

Correction	Example	Sketch effect
Type correction	“Hold the racket by the grip, not the frame.”	Refines an action’s admissible argument type.
Precondition cue	“Begin the serve behind the baseline.”	Adds a condition to a legal transition.
Invariant cue	“Keep the racket face stable through contact.”	Declares a relation to preserve during a motion.
Segmentation cue	“Recover before preparing the next stroke.”	Introduces a missing subaction or boundary.
Explanatory cue	“This position leaves both sides of the court reachable.”	Connects an instruction to its functional role.
Counterexample	Demonstrate when the usual stroke is inappropriate.	Restricts a rule or introduces a contextual branch.

Table 1.1 A coach can intervene at several distinct locations in an acquired task sketch. Feedback should preserve this type information rather than being collapsed into an undifferentiated scalar reward.

The same correction may update execution and theory simultaneously. The learner can first assimilate it as a local motor adjustment. Repeated failure to transport that adjustment may then reveal a missing type, affordance, or contextual distinction and trigger accommodation.