Match-to-sample (MTS) is one of the most studied procedures in the experimental analysis of behavior. The task is deliberately simple: the child sees a sample and picks, from a set of options, the one that matches it. Behind that simplicity is an extraordinarily powerful mechanism for teaching concepts, language, and relational thinking.
In this article we’ll go through how MTS works, why a handful of trial types can train an open-ended set of relations, and what the procedure actually trains in practice.
This article is the short introduction. If you are putting match to sample into a program and need the trial-by-trial detail — how a trial is built, prompt levels and fading, what to record, and how to read the data afterwards — the complete match to sample guide covers it, and there is a PDF of it.
The procedure
An MTS session is made of many trials. Each trial has three elements:
- A sample, at the top or center of the screen.
- Two or more comparison stimuli below.
- Exactly one of the comparisons matches the sample. The others are distractors.
The child taps the comparison they think is correct. If they’re right, positive feedback follows and the session moves on. If they’re wrong, no reinforcement is delivered and the system re-runs the trial or adjusts difficulty.
At first glance this looks like a “find the pair” game. But the secret is in how the samples and comparisons vary trial to trial. Through that variation, the child doesn’t learn the answer to one specific trial — they learn the relation between sample and correct comparison. Whether that relation then holds with stimuli the child has never seen is what a probe is for: the procedure is built to aim at that, it does not guarantee it on its own.
Why it works
Three reasons make MTS unique:
No prior language required. A child doesn’t need to know how to say “bird” to learn that a photo of a bird matches a pictogram of a bird. This makes MTS accessible to children who don’t yet use spoken language, or who use very little, and at the same time it allows language to be taught from scratch.
Errorless learning is possible. Incorrect options can appear faded at the beginning (more transparent, smaller) so the child succeeds by design. Systematic prompt fading turns that initial success toward real competence, and it is meant to keep repeated early errors from becoming a source of frustration — not to promise there will be none.
It is built to produce generalization. When trained correctly across many exemplars, the child is meant to stop responding to a specific stimulus and start responding to the concept — the difference between memory and understanding. Whether that happened for a given child, and how far it reaches, is a question for a probe, not something the training session can certify on its own.
Five examples: what changes is the relation
Most exercises in Interlaza use this procedure: sample on top, comparisons below, the child picks one. (Not all of them: the app also records the rate and duration of behaviors observed away from the tablet, and has a stimulus-pairing mode in which the child is asked for no response at all. Those are not matching trials and are not measured as such.)
What changes from one MTS trial to the next is the relation between sample and correct comparison. Sometimes that relation is identity, sometimes “it’s the same thing even though it doesn’t look like it”, sometimes “is the opposite of”, “happens before”, “is a kind of”, or “is inside”. MTS is the procedure; the relation is the variable.
Below are five examples, from simplest to most complex.
1. Identity matching
Sample and correct comparison are physically the same image. A photo of a bird matches that same photo of the bird; the distractor is something else. It is the simplest of the five and asks for no notion of category yet: noticing that two things look alike is enough.
2. Non-identical matching (same concept, different exemplar)
Here sample and correct comparison no longer share the same picture: they are the same concept shown two ways. A realistic photo of a bird matches a pictogram of a bird. That rules out the simplest appearance match — but not every visual shortcut on its own, since a photo and its own pictogram can still share an outline or a color. Confirming the child is answering on category rather than a leftover visual cue is what a probe with unrelated images checks.
In the app these are two distinct exercise types, in that order: identity first, non-identical after.
3. Auditory matching (sound → image)
The sample is a sound or a spoken word, not an image. The child taps a speaker, hears “apple”, and picks the apple image from several options. This trains receptive language and prepares the auditory vocabulary base before reading enters the picture.
4. Written word → image
The sample is the written word (no image) and the child picks the matching image. This is exactly the mental relation reading requires: see “apple” and mentally represent the apple. It’s natural reading preparation — no books, no pressure.
5. Association (things that go together)
The sample is a cow, and among the comparisons appears a glass of milk, not another cow. To get it right, the child has to know a relation that is neither identity nor category: cow and milk go together because one produces the other.
It’s worth being clear about what this is and isn’t. It is a functional relation, the same kind as sock→shoe or bird→nest, and it has to be taught like any other. It is not stimulus equivalence, though it is sometimes described that way: equivalence is a much more specific phenomenon, and it is the subject of the next section.
Across these five the pattern is visible: the procedure doesn’t change, the relation does. What comes next is what makes MTS stop being “find the pair”.
Sidman’s derived relations
In the early 1970s, Murray Sidman described something remarkable (Sidman, 1971). If you taught a child just two relations — A → B (the spoken word “apple” matches the photo of an apple) and A → C (the same spoken word matches the written word APPLE) — others showed up afterwards, untrained:
- Symmetry: B → A and C → A — the same two trained relations, reversed.
- Transitivity: C → B, the written word with the photo, which is exactly the trial in example 4 — and which nobody here taught.
- Equivalence: when symmetry and transitivity both hold, the class closes — every one of the nine possible relations among A, B and C now holds, not only the two that were trained.
That is what “equivalence” means technically: not “two things that go together”, and not any single derived relation on its own, but the full, closed set of relations that appears without having been trained, once symmetry and transitivity both hold. And to know whether it happened you have to test it: a few trials on the relation that was not taught, with no help and without telling the child whether they were right. Sidman proposed this as one of the behavioral markers of symbolic thinking: treating arbitrarily related stimuli as if they were “the same”.
The practical implication is the one that matters: a well-designed program can end up with more relations than it taught. How many more, and over what period, depends on the child and the program — there is no number that holds for everyone, and any figure offered without the probe that measured it is a promise, not a finding.
Relational Frame Theory (RFT)
Steven Hayes, Dermot Barnes-Holmes, and collaborators extended Sidman’s work into a broader theory. Relational Frame Theory (RFT) proposes that human language consists of learning families of relations, not isolated relations. Some examples:
- Coordination (same as): A = B = C.
- Distinction (different from): A ≠ B.
- Opposition: A is the opposite of B (hot / cold, tall / short).
- Comparison: A is bigger, smaller, faster, or taller than B.
- Hierarchy: A is a kind of B; B is a kind of C (a dog is a mammal, a mammal is an animal).
- Temporal: A happens before B; A happens after B.
- Spatial: A is on top of B; A is inside B.
- Deictic: I / you; here / there; now / then.
- Causal: A causes B; A follows from B.
Each of these families can be trained and tested with MTS trials. Sidman’s own demonstrations covered equivalence — sameness, essentially the coordination frame; RFT researchers have since studied derived responding across the other frames too, with the evidence strongest for coordination and thinner for some of the rest. Where it has been shown, a trained frame generates derived relations the child applies to new stimuli without additional instruction.
This is what we mean by “infinite relations”: with the right combination of a few trained relations, a child builds a symbolic repertoire that expands exponentially. Each new concept that enters the system opens relations with the ones already there, rather than just joining the list. How many of those actually appear in a given child is, again, a question for the probe.
Varela’s transfer matrix
If MTS and equivalence describe what relations can be trained, Julio Varela and Carmen Quintana asked how to measure exactly when a trained relation transfers to a new context. Their answer is a factorial taxonomy: each trial is defined by four factors —
- Dimension (the domain the matching criterion belongs to — a geometric property, say, rather than a color one).
- Relation (what type of relation is trained: identity, opposition, hierarchy…).
- Modality (a property of the stimulus’s own form — shape, color, size; a morphological axis, not the image/word/sound channel it is sometimes read as).
- Instance (the specific exemplar).
Each factor can be kept Constant between training and the transfer probe, or Variable. Combining the four factors in their two states yields fifteen cells (cell zero, where nothing varies, is not transfer: it’s repetition).
Varela’s own later work adds the image/word/sound axis as its own factor, separate from this four-factor matrix and not part of the original 1995 taxonomy. Interlaza’s implementation keeps that distinction — modality and the sensory channel a stimulus arrives in are tracked as different things, not folded into one label, and the product’s own adaptation of Varela’s terms does not always match a first read of the original papers.
Two warnings, because both are routinely misread. The fifteen cells are a classification, not a difficulty scale: it is not established that cell 5 is harder than cell 4, and in Varela’s own data there are children who score higher on a “later” cell. And the numbering is not an order of application.
What it does give you, and it is a lot, is a precise way to say what was held and what changed between what was taught and what was tested — the question a percent-correct score does not answer. In Interlaza that distinction is what shapes the transfer probes; the research module that reproduces Varela’s full procedure is under methodological review and is not available today.
Why this all matters
Because together, these ideas explain how a child can learn to speak, read, categorize the world, and reason symbolically with relatively few direct trials. MTS is not the minimal unit of all learning — it still rests on prerequisites like attending and basic discrimination — but it is the one procedure underneath all of it, which is what lets so few trial types scale to this many relations.
For a parent, this means that ten minutes of exercises built so the relation is meant to transfer are after something different from ten minutes of “studying isolated words”, and that the way to know whether it actually transferred is the probe, not the impression. For a professional, it means it’s possible to design a program where generalization is planned for from the start rather than added on afterward — though whether it shows up is still a question the probe answers, not the plan. For a researcher, it means the procedure has enough granularity to answer questions that standardized tests never touch.
If you want to see how Interlaza implements these trial types in an adaptive platform, read Why Interlaza helps. If you want to dig deeper into the scientific foundations, the Science page and the introduction article are the next steps.