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 four basic trial types can train infinite relations, and what the procedure actually trains in practice.
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. And that relation transfers to new stimuli they have never seen.
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 pre-verbal children and to those with limited verbal repertoires, 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 into real competence. No accumulated frustration.
It generates generalization. When trained correctly across many exemplars, the child stops responding to a specific stimulus and starts responding to the concept. That’s the difference between memory and understanding.
Four examples: what changes is the relation
Every exercise in Interlaza uses the same procedure: sample on top, comparisons below, the child picks one. What changes from trial to trial is the relation between sample and correct comparison. Sometimes that relation is identity, sometimes equivalence, 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 four examples, from simplest to most complex.
1. Identity matching
Sample and correct comparison are the same concept across two exemplars. A realistic photo of a bird matches a pictogram of a bird. This trains the child to recognize the category “bird” regardless of the specific exemplar.
2. 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.
3. 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.
4. Equivalence (a derived relation)
This is where it gets interesting. 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 the derived relation “cows produce milk”. And, as we’ll see in the next section, this is a relation nobody taught the child directly — it emerges from having trained categories and properties separately.
This last type is where MTS stops being “find the pair” and becomes symbolic thinking.
Sidman’s derived relations
In the late 1960s, Murray Sidman discovered something extraordinary. If you taught a child that A → B (an image matches a word) and A → C (the same image matches a sound), the child spontaneously developed:
- Symmetry: B → A and C → A, without extra training.
- Transitivity: B → C and C → B.
- Equivalence: a full set of bidirectional relations among A, B, and C.
These relations were not trained. They emerged on their own. Sidman demonstrated that this is one of the behavioral markers of symbolic thinking — the ability to treat arbitrarily related stimuli as if they were “the same”.
The practical implication is enormous: every well-designed MTS trial trains, indirectly, many relations that never explicitly appear in a session. That’s why three to four weeks of structured practice produce vocabulary gains that isolated material can’t match.
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. And, as Sidman showed, once trained, they generate 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 multiplies the available relations, doesn’t just add to them.
Varela’s transfer matrix
If MTS and equivalence describe what relations can be trained, Julio Varela and Claudia 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 (what property varies: shape, color, size, function).
- Relation (what type of relation is trained: identity, opposition, hierarchy…).
- Modality (visual, auditory, written…).
- 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 distinct transfer levels (level zero, where nothing varies, is not transfer: it’s repetition). Each level describes a different kind of generalization.
This is not academic curiosity. It lets you know, trial by trial, what kind of generalization a child has achieved and which is still missing. It’s the most precise tool available for measuring transfer in conceptual learning, and it’s the basis of Interlaza’s research module.
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 a trick. It’s the minimal unit of learning that scales.
For a parent, this means that ten minutes of well-designed exercises can have a disproportionately larger effect than ten minutes of “studying isolated words”. For a professional, it means it’s possible to design programs that produce generalization by default, not as an extra. 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 four types of trial 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.