12.4 Procedures That Promote Emergent Relations and Generative Performance

Teaching Less, Learning More

Tasks B.15 and G.11 concern emergent relations (responses that appear without being directly taught or reinforced) and generative performance (correct responding to new combinations or situations). Section 3.3 defined reflexivity, symmetry, and transitivity. This section turns those properties into instructional procedures. The practical payoff is efficiency: carefully chosen teaching produces many more skills than were taught.

Equivalence-Based Instruction (EBI)

Equivalence-based instruction uses matching-to-sample (section 12.2) to teach a small set of arbitrary relations among stimuli and then tests for the relations that should emerge if the stimuli form an equivalence class.

Designing an EBI Program

1. Choose the stimulus sets. Example for early reading: A = spoken word ("cat"), B = picture of a cat, C = printed word cat. Example for college statistics: A = a term, B = its definition, C = an example graph.
2. Choose a training structure.
   • Linear series: teach A-B and B-C.
   • One-to-many (sample-as-node): teach A-B and A-C.
   • Many-to-one (comparison-as-node): teach B-A and C-A. All three can produce equivalence; programs choose based on which relations are easiest to teach and which matter most for the learner.
3. Teach the baseline relations to mastery with reinforcement and error correction, mixing classes so the learner must attend to the sample (for example, cat, dog, and pig sets taught together).
4. Test without reinforcement. Present probe trials for the untaught relations (symmetry: B-A, C-B; transitivity: A-C; equivalence: C-A) without feedback. Reinforcing test trials would teach the relation directly and you could no longer tell whether it emerged. Keep baseline trials (with reduced reinforcement) mixed in so the learner stays engaged.
5. Remediate if needed. If a relation fails to emerge, review the baseline relations, add training on a missing relation, or change the training structure, then retest.

Counting the Payoff

In the reading example, teaching 2 relations (A-B and B-C) can yield 4 untaught relations (B-A, C-B, A-C, C-A) plus reflexivity for each stimulus. As class size grows, the number of emergent relations grows much faster than the number taught: adding a fourth member (D = sign) by teaching just C-D can produce relations between D and every other member.

Sidman (1971) worked with an adolescent with severe intellectual disability who could already match spoken words to pictures. After he was taught to match spoken words to printed words, he matched printed words to pictures and read the words aloud, relations that were never directly taught. Reviews of EBI with college students have found it efficient for teaching course concepts such as statistics and neuroanatomy.

Related Generative Repertoires

• Naming (bidirectional naming): when hearing an object's name, saying the name, and selecting the object become integrated, a learner who is taught only to tact an object can also select it when asked, or vice versa. Multiple-exemplar instruction across listener and speaker responses is used to establish this repertoire.
• Derived relations beyond sameness: relational frame theory extends equivalence to other relations (opposite, more than, before and after). If "A is more than B" and "B is more than C," the learner can derive "C is less than A."

Matrix Training and Recombinative Generalization

Recombinative generalization is responding correctly to new combinations of previously learned components. Matrix training arranges teaching to produce it:

Teaching only the diagonal (push car, roll ball, drop block) can lead the learner to perform or name the untaught combinations ("roll car," "drop ball"). Matrix training has been used for actions with objects, early grammar, play, and preliteracy skills (for example, Axe & Sainato, 2010). Overlapping arrangements (teaching a few more cells) help when the diagonal alone does not produce full recombination.

Multiple-Exemplar Instruction and Generalized Operants

Multiple-exemplar instruction (MEI) teaches a response across many varied examples so that a general repertoire emerges, not just specific stimulus-response pairs. Teaching imitation of many different actions produces generalized imitation (section 3.4); teaching many "Show me ___" items across materials produces generalized instruction following. MEI is also how generative performance is built: after enough exemplars, the learner responds correctly to examples never taught.

Example: Teaching Coin Values

A teacher wants a student to name coin values, select coins by value, and match written prices to coins. Instead of teaching every combination, she defines three stimulus sets for each coin: A = the coin, B = the spoken coin name ("quarter"), and C = the written value ("25 cents"). She teaches B-A (select the quarter when hearing "quarter") and B-C (select "25 cents" when hearing "quarter") with reinforcement until both are mastered, mixing pennies, nickels, dimes, and quarters so the student must attend to each sample. She then runs unreinforced probes for A-C (match the coin to "25 cents") and C-A (match "25 cents" to the coin). Because this one-to-many structure uses the spoken name as the node, the student can now show coin-to-value relations that were never taught directly, saving many teaching sessions.

Practical Guidelines

• Choose stimuli that are socially meaningful (reading, money, safety signs, course concepts).
• Teach baseline relations to a high criterion before testing.
• Run test probes in extinction and mix in maintenance trials.
• Graph emergent relations separately from taught relations so you can see what the instruction produced.
• If relations do not emerge, change the procedure; do not simply keep testing.

Common Exam Traps

• Reinforcing test trials. Then the relation was taught, not derived.
• Calling a taught relation emergent. Only relations never directly reinforced count.
• Confusing transitivity and symmetry. Symmetry reverses a taught relation (B-A after A-B); transitivity links two taught relations through a shared stimulus (A-C after A-B and B-C).
• Confusing stimulus generalization with recombinative generalization. Stimulus generalization is responding to physically similar stimuli; recombinative generalization is new combinations of learned parts.