Some of the most efficient teaching happens when you get more out than you put in. You teach a few relations directly, and new, untaught responses show up on their own. Those untaught responses are emergent relations, and they are the heart of generative performance.
Why it matters
No program can directly teach every word, match, or sentence a learner will need. If teaching "spoken word goes with picture" and "picture goes with printed word" also produces "spoken word goes with printed word" for free, you have saved trials and built a more flexible repertoire.
Emergent relations also help explain how language and reading grow so quickly. In practice items, you will often read what was taught and what was tested, then name the relation that emerged.
Key ideas
- Emergent means untrained. A relation is emergent when the learner responds correctly to it even though that exact relation was never directly taught or reinforced.
- Most of these relations are built with conditional discriminations. In match-to-sample, the learner sees a sample (A) and picks the correct comparison (B). Trainers usually label stimulus sets with letters: A, B, C.
- Stimulus equivalence has three defining properties (Sidman's framework):
- Reflexivity: matching a stimulus to itself (A goes with A), usually shown as generalized identity matching with new stimuli.
- Symmetry: reversing a taught relation. After learning A goes with B, the learner shows B goes with A.
- Transitivity: linking relations through a shared stimulus. After learning A goes with B and B goes with C, the learner shows A goes with C.
- The combined equivalence test reverses the transitive relation (C goes with A). Passing it requires both symmetry and transitivity, so it is a strong single test that an equivalence class has formed.
- Members of a class are physically unrelated. The spoken word "cat," a cat photo, and the printed word CAT share nothing physical. That is what separates equivalence from stimulus generalization, which depends on physical similarity.
- Functions can spread across a class. If one member gains a function (for example, it becomes a discriminative stimulus or a conditioned reinforcer), other class members may acquire that function without direct training.
- Generative performance also covers new combinations. Through recombinative generalization, a learner taught some combinations of known parts (for example, through matrix training) produces untaught combinations of those same parts.
Definitions
- Emergent relation: a correct stimulus-stimulus relation that appears without direct training or reinforcement of that relation. It is also called a derived relation.
- Stimulus equivalence: the emergence of reflexive, symmetric, and transitive relations among stimuli after some relations are directly taught.
- Equivalence class: a set of stimuli that the learner treats as interchangeable in a given context, even when the stimuli look or sound nothing alike.
- Transfer of function: a function established for one class member also appearing for other class members without separate training.
- Recombinative generalization: correct responding to new combinations of previously learned components.
- Relational frame theory (RFT): a behavior-analytic account that treats derived relational responding as learned, generalized operant behavior. RFT describes relations beyond "same as," such as opposite, more than, and before/after.
Examples from a session
Three stimulus sets, two taught relations
At a clinic, a BCBA works with Rosa, age 8, on early reading. The sets are A (spoken words), B (pictures), and C (printed words).
- Taught A→B: the RBT says "sun," and Rosa picks the sun picture.
- Taught B→C: Rosa sees the sun picture and picks the printed word SUN.
- Tested, never taught: shown the printed word SUN, Rosa points to the sun picture (symmetry, C→B). When she hears "sun," she picks the printed word SUN (transitivity, A→C). Rosa now relates all three forms of "sun" without being taught every pairing.
Generative performance shows up outside the table too. At home, Kwame, age 4, learns to say "big dog" and "little car" while looking at toys. Later, with no teaching, he says "little dog" and "big car." That is recombinative generalization, and it is the logic behind matrix training.
Adults show emergent relations as well. In a vocational program, Lena, age 32, is taught to select the printed price 25¢ when she hears "twenty-five cents" and to select a quarter when she sees 25¢. At a practice checkout, she hands over a quarter when the cashier says "twenty-five cents," a pairing nobody taught her. That is transitivity in a daily-living skill.
Common mistakes / exam traps
- Calling a reversed relation transitivity. Reversing one taught relation (A→B taught, B→A tested) is symmetry. Transitivity needs two taught relations linked by a shared stimulus.
- Calling C→A plain transitivity. When the linked relation is also reversed, it is the combined equivalence test, which needs both symmetry and transitivity.
- Confusing equivalence with stimulus generalization. Generalization depends on physical similarity. Equivalence class members can be completely dissimilar.
- Reinforcing the test trials. If you give differential reinforcement on the untaught relation from the first trial, you cannot tell emergence from new learning. Probe the untaught relations without differential consequences.
- Assuming emergence always happens. Emergence depends on the learner's history and repertoire. Some learners need more support, such as different training structures or more exemplars. Test, then plan from the data.
Symmetry vs. transitivity vs. the combined test
Write out what was taught and what was tested. If the tested relation is simply the reverse of one taught relation, it is symmetry. If it links two taught relations in the same direction, it is transitivity. If it links them and reverses direction, it is the combined equivalence test.
Recombinative vs. response generalization
Both produce untaught behavior, so ask what is new. A new response form to the same stimulus (wiping a table with a sponge after learning with a cloth) is response generalization. Correct responding to a new combination of known parts (following "fold the towel" after learning "fold the shirt" and "wash the towel") is recombinative generalization.
Quick check
During an assessment, Owen, age 5, is shown a photo of a leaf he has never seen before and, without any teaching, selects the identical leaf photo from an array of three. Which property of equivalence does this show?
Related topics
- Recognizing stimulus control (B.12)
- Stimulus vs. response generalization (B.14)
- The verbal operants: mand, tact, echoic, intraverbal, and more (B.19)
- Teaching simple and conditional discriminations (G.6)
- Programming for stimulus and response generalization (G.15)
- Teaching for emergent relations and generative performance (G.19)