"Adaptive learning" is a marketing umbrella covering several genuinely different technical approaches โ€” and knowing roughly how they work makes it much easier to tell a real one from a relabelled worksheet. None of it is magic. Each approach makes a specific, checkable claim about what it's tracking and how it decides what to show a student next.

Item Response Theory: scoring the question, not just the student

Item Response Theory (IRT) is the statistical backbone behind most computerised adaptive testing. Instead of just counting how many questions a student got right, IRT estimates two things at once: the student's underlying ability, and each question's own difficulty and "discrimination" (how well that question distinguishes strong from weak students at that ability level).

Once a question bank has these estimates, the system can pick, in real time, the single next question that will tell it the most about a student's true ability โ€” usually one they have roughly a 50% chance of getting right given the current estimate. Get it right, the ability estimate rises and a harder item is selected next; get it wrong, it falls and an easier one follows. This is the mechanism behind most serious adaptive testing, including exam-style placement tests.

Bayesian Knowledge Tracing: tracking mastery of one specific skill

Bayesian Knowledge Tracing (BKT), developed by Corbett and Anderson in 1994, works differently. Rather than estimating one overall ability number, it tracks a probability โ€” for one specific skill at a time โ€” that the student has actually mastered it, updating that probability after every attempt using four parameters: the chance they already knew it, the chance they'll learn it from this attempt, the chance they'll guess correctly without knowing it, and the chance they'll slip up despite knowing it.

Once that mastery probability crosses a threshold (often around 95%), the system moves the student on to the next skill. This is closer to how a good human tutor thinks โ€” "has this specific student actually got this specific skill down" โ€” than IRT's broader ability estimate, and it's the technique behind well-known systems like Carnegie Learning's Cognitive Tutor.

Knowledge-space theory: mapping what's logically possible

ALEKS, a widely used maths platform, takes a structurally different approach called knowledge-space theory. Rather than a single difficulty number, it models an entire domain as a knowledge space โ€” the combinations of skills that are logically achievable given prerequisite relationships (you can't master solving equations with fractions before you can add fractions, for instance). A short adaptive assessment โ€” typically 25-30 questions โ€” locates a student's exact position within that space, identifying not just "how hard should the next question be" but specifically which skills, out of everything logically reachable from here, are ready to be learned next.

What Duolingo actually does (and the myth worth correcting)

It's commonly repeated that Duolingo uses a chess-style Elo rating system for difficulty. The more accurate picture: Duolingo's placement testing uses genuine IRT, and its internal difficulty engine โ€” known as Birdbrain โ€” uses a logistic-regression method inspired by IRT to jointly estimate exercise difficulty and learner proficiency, aiming for what its engineering team calls "Goldilocks difficulty." Separately, a model called Half-Life Regression predicts how quickly a specific learner will forget a specific item, driving when it resurfaces for review โ€” a decay model, not a difficulty model. Worth knowing if you've heard the Elo claim repeated as fact: it's a reasonable shorthand, but not literally what's running under the hood.

Why the differences actually matter to you as a parent

These aren't interchangeable techniques dressed up differently โ€” they answer different questions. IRT answers "how able is this student, broadly, right now." BKT answers "has this student mastered this one specific skill." Knowledge-space theory answers "given everything logically achievable, where exactly does this student sit, and what's next." A product built on any of these, implemented well, is doing real, checkable work. A product that can't explain which (if any) of these it's doing is a reasonable place to be sceptical โ€” see the questions worth asking before trusting the label.

FAQ

How does adaptive learning software actually decide what to show next?

Most systems use Item Response Theory (estimates ability, picks the next question to maximise information), Bayesian Knowledge Tracing (tracks mastery probability of a specific skill), or knowledge-space models (maps logically achievable skill combinations and locates the student within them).

Is 'adaptive learning' one single technology?

No โ€” it's an umbrella term covering distinct underlying mechanisms that behave quite differently from each other, all commonly marketed under the same word.

Does Duolingo use an Elo chess rating system?

Not exactly. Its placement testing uses Item Response Theory, and its difficulty engine (Birdbrain) uses logistic regression inspired by IRT, with a separate Half-Life Regression model for spacing reviews.

Duke Harewood ยท founder, aitutors.me ยท Updated 11 Jul 2026.