The research behind Interlaza

A child gets it wrong three times in a row and pushes the tablet away. What those three attempts practised is the wrong answer, and the frustration came with it. The alternative is to set the screen up so the child is right from the first trial, then withdraw that help as they start answering alone.

Errorless learning (Terrace, 1963) is a teaching strategy that structures the environment so that students make few or no errors during acquisition. Rather than presenting full-difficulty trials from the outset, the procedure fades stimulus supports gradually — ensuring the student experiences success at each stage before supports are removed.

INTERLAZA uses a configurable distractor fading procedure (3 phases by default): distractors begin at low opacity and gradually increase to full visibility across phases. After any error, difficulty drops immediately back one phase — protecting against the frustration and emotional responses that errors can produce in young children. Crucially, each concept tracks its own phase independently, so mastery of one concept never artificially inflates or deflates difficulty on another.

Mueller et al. (2007) reviewed the errorless learning literature for children with pervasive developmental disorders and confirmed the approach as best practice for this population. The frustration-free progression through success — rather than through repeated correction — is particularly important for maintaining motivation and approach behavior toward learning tasks.

There is a card with a strawberry on the table and two options below it. The child touches the strawberry twenty times running. They may have compared the cards, or they may have learned that touching the strawberry makes a pleasant sound happen. The score is identical either way.

A matching-to-sample procedure only formally affords relational learning. Functionally, most such tasks can be solved by what Emilio Ribes calls a coupling contact — recognizing an object and repeating a gesture. If the correct answer is always the same thing, or the pairing never varies, the child can reach 100% without comparing anything. Recognizing the same stimulus, in Ribes' words, "is simply a repetition pattern".

INTERLAZA is built so that this cannot happen silently. Roles rotate — every object appears as sample, as correct option and as distractor, chosen least-used-first rather than at random, because a stage is only a few dozen trials and chance alone will happily leave one object in a fixed post throughout. Concept sets are spread across the values of the dimension being trained, so no single value becomes a fixed datum. And the relation is held constant while everything else changes, which is what makes comparison the only route to being right.

Accuracy under feedback still proves nothing about the kind of contact reached — Ribes is explicit that "accurate performance is not sufficient to identify the type of functional contact developed". So every stage closes with a transfer probe: the trained dimension is replaced (color → size) with novel objects, prompting is off, and the learner is not told whether they were right. Early stages, which train no dimension, instead change the exemplar — the answer is redrawn as a pictogram rather than a photograph, so a correspondence bound to the concept survives while one bound to a single image does not.

Probes do not score and do not gate progression. Expect performance to fall: that fall is the measurement, and it reports how much of the earlier accuracy rested on repetition.

A child is taught two things: that the spoken word "dog" goes with a photograph of a dog, and that the same spoken word goes with the written word dog. With nothing further taught, they match the photograph to the written word. Nobody taught them that pair.

In 1971, Murray Sidman described this: teaching a small number of conditional discriminations can give rise to relations nobody taught. Train A→B and B→C, then test: many students go on to match A→C (transitivity), C→A, B→A, and C→B (symmetry) — without any explicit instruction on those pairs, and the test is what shows it. Stimuli that have never appeared together during training act as if they belong to the same equivalence class.

Sidman and Tailby (1982) formalized three defining properties of equivalence: Reflexivity (A matches A), Symmetry (if A→B then B→A), and Transitivity (if A→B and B→C then A→C). Training just two conditional discriminations can be followed by four untaught relations — the symmetry pairs B→A and C→B, the transitive A→C, and the equivalence relation C→A — and when they appear, the student behaves as if all three members of the class are interchangeable. This is why match-to-sample training is a gold standard for teaching language concepts in applied behavior analysis.

INTERLAZA builds on this paradigm. The core exercise levels (identity → symbolic → auditory) are based on Sidman's training sequence, while the equivalence probe module tests all three equivalence properties without feedback. The procedure is the point: train two relations, then test whether the other four emerge, rather than assume they did.

A child is right five times running with two options on screen. How much confidence does that deserve? Five correct coin flips in a row happen once in thirty-two tries. What is needed is a way to put a number on that confidence and update it on every answer.

Bayesian Knowledge Tracing (Corbett & Anderson, 1995) is a probabilistic model that estimates a student's mastery of a concept in real time. After each trial response, the model applies Bayes' theorem to update P(mastery) — the probability that the student has acquired the underlying knowledge — accounting for the possibility of lucky guesses and careless errors. Four parameters govern the model: P(L₀) initial mastery, P(T) probability of learning on any given trial, P(G) guess rate, and P(S) slip rate.

The result is a dynamic mastery estimate that responds to actual performance patterns rather than simple trial counts. A student who answers correctly three times in a row but has shown fragile performance previously will have a lower P(mastery) than one who has been consistently accurate — and the algorithm adjusts accordingly. When P(mastery) exceeds 0.95, INTERLAZA advances difficulty; when it drops below 0.40 or errors cluster, difficulty decreases. This creates individualized learning trajectories for each child and each concept, without requiring instructor manual adjustment.

INTERLAZA uses BKT as the primary mastery criterion for advanced exercises, and also to drive adaptive difficulty adjustment (adding or removing comparison stimuli) and errorless learning phase transitions. Per-student parameter adaptation (Yudelson et al., 2013) is on the development roadmap, which will further improve the model's precision for individual students.

A child already has "the same color" with photographs. What happens if you ask for "the same size"? And if you keep the color but swap the photographs for drawings? They look like the same question and they are not: each one checks something different about what the child learned.

Julio Varela and Carmen Quintana's transfer taxonomy classifies how learned discriminations transfer to new situations by varying four independent factors: Dimension (what property is relevant), Relation (the matching criterion), Modality (the morphological property it is read on), and Instance (the specific stimulus objects used). Each factor can be Constant (K) or Variable (Var) between training and test, producing 15 distinct transfer types. The 15 rows are a classification — Varela's own data shows difficulty does not track how many factors vary.

The practical insight is real but bounded: you can teach a child to match red circles to red squares (training) and then systematically test whether that learning survives a change of shape, of criterion, or of the objects themselves. Of the 15 cells, published research has reproduced five conditions, always in second-order matching to sample — the rest of the grid remains taxonomy, not finding.

What INTERLAZA takes from this work is the verification idea: mastery is only claimed when learning survives instances the child never practised. The dedicated Varela research module is temporarily withdrawn while it is rebuilt to reproduce the published protocols faithfully — this page presents the taxonomy as a historical classification under methodological review.

Read the full guide: the 4 factors and the 15-type taxonomy →

A child is told that one coin is worth more than another. Without ever having compared them, they pick the first when asked for the one worth more — and they also know the second is worth less. They related the two coins by what someone said about them, not by how they look.

Relational Frame Theory (Hayes, Barnes-Holmes & Roche, 2001) extends stimulus equivalence to a much richer repertoire of relations. Where Sidman showed that stimuli can be learned as equivalent (same as), RFT demonstrates that humans learn to apply arbitrarily applicable relational responding across many frame types: not just coordination (sameness), but also distinction (different from), opposition (opposite of), comparison (more/less than), hierarchy (part of/contains), temporal, spatial, and deictic (perspective-taking) frames.

Relations in RFT are governed by two types of contextual cues: Crel — a cue that specifies the type of relation (e.g., "opposite of" vs. "same as") — and Cfunc — a cue that selects which function of a stimulus is relevant in a given context (e.g., size, temperature, category). This Crel/Cfunc structure is what makes language so flexible: the word "more" changes the relational frame, and the context determines whether we're comparing size, quantity, or temperature.

INTERLAZA incorporates multiple RFT frame types — coordination, distinction, opposition, and comparison — with configurable Crel cues and Cfunc dimensions. Peer-reviewed research across clinical populations (Dunne et al., 2014; Gibbs & Tullis, 2021) confirms that these frame types are trainable and clinically meaningful — not just theoretical constructs.

An instructor changes one thing about the session and wants to know whether it helped. Answering that takes a measurement before, a measurement after, and a measure that means the same thing both times. Without those, all that is left is the impression that the session went better.

Applied Behavior Analysis (ABA) is the scientific discipline that studies behavior as a function of its environment and applies those findings to socially significant problems. Its roots are in B. F. Skinner's experimental analysis of behavior — The Behavior of Organisms (1938) laid out the operant framework, and Verbal Behavior (1957) extended it to language as learned functional classes (mand, tact, echoic, intraverbal). Sidney W. Bijou then carried the operant program into child development: Child Development: A Systematic and Empirical Theory (Bijou & Baer, 1961) reframed development itself as progressive interactions between the child and the environment, and Bijou's later work on experimental studies with typically developing and atypically developing children became the template for modern behavioral learning research. Baer, Wolf and Risley (1968) then defined the seven dimensions that still guide ABA practice today: applied, behavioral, analytic, technological, conceptually systematic, effective, and generality.

For INTERLAZA, ABA contributes the core mechanics that the platform relies on every session: operationally defined target behaviors, discrete-trial teaching, prompting and prompt fading, differential reinforcement, systematic data collection, and mastery criteria. Match-to-sample itself is a conditional discrimination procedure native to this tradition — which is why the trial structure, reinforcement schedules, and phase transitions in the platform map directly onto standard ABA protocols (Cooper, Heron & Heward, 2020).

ABA gives the platform its measurement and teaching machinery: what a trial is, how to reinforce, how to fade, how to score mastery, and how to generalize. The interbehavioral lens in the next section gives the platform its conceptual vocabulary — what counts as a stimulus in the first place.

The same photograph of a dog can ask a child for very different things: find another one like it, point to it on hearing the word, or pick it out among several animals when asked which one has four legs. The photograph has not changed; what it does in each task has.

Where standard ABA treats the stimulus as a relatively stable environmental event, Kantor's (1959) interbehavioral field theory reframes it as a functional role that emerges during the interaction between an organism and its environment. The same physical object can serve completely different stimulus functions depending on context, history, and the organism's current state. The unit of analysis is not the response to a stimulus, but the full behavioral field in which the two are inseparable.

This distinction underlies INTERLAZA's three-layer data model: Concepts represent abstract ideas (e.g., "dog" as a category). Instances are concrete representations — specific images, sounds, or words that instantiate a concept. Stimuli are the functional roles those instances play during a particular trial — sample, comparison, correct, incorrect. A JPEG of a dog is not a stimulus. It becomes one when it is presented to a child in a specific trial context with a specific relational function.

This precision matters clinically. When a child fails to respond correctly, the question is not "which image was wrong?" but "which stimulus function failed to control the response?" Varela (2008) extends this framework into a full interbehavioral account of intelligent behavior — the theoretical foundation for the transfer matrix module. ABA and interbehaviorism are complementary here: ABA tells us how to teach a trial; interbehaviorism tells us what a trial actually is.