An adaptive tutoring system's central function is selecting what to present next. That selection rests on a model of the learner, and the differences between systems are mostly differences in how that model works.
The estimate is probabilistic
A student who answers correctly may have understood, guessed, or recognised a superficial pattern.
Systems therefore hold a probability that a skill is mastered rather than a verdict, updating it after each response.
Established methods also carry explicit parameters for guessing and for careless error, so a single wrong answer from a confident student moves the estimate less than a pattern of them.
Difficulty is calibrated against a population
Question difficulty is not assigned by the author but derived from how large numbers of students have performed on it.
That calibration lets the system compare a student's performance against an established scale rather than against the specific items they happened to see.
It also means a new item is unreliable until enough responses have accumulated, which is why platforms are reluctant to change their question banks.
The target is a specific success rate
Selecting the hardest question a student can attempt is not the aim, because constant failure ends engagement.
Systems generally target a success rate high enough to sustain effort and low enough that the work is informative, and the chosen figure is a design decision with real consequences.
Set too high, the student is bored and learns slowly; set too low, they disengage, and the system observes only that they stopped.
Prerequisites are encoded as a graph
Curriculum content is represented as skills with dependency relationships, so failing a topic prompts assessment of what it rests on.
The value of this depends entirely on whether the dependencies are real, and they are usually asserted by subject experts rather than derived from data.
Where a stated prerequisite is not actually necessary, the system sends students backwards through material they did not need, which is a common complaint and hard to diagnose from inside.
Generated questions change the constraint
Systems that generate items rather than drawing from a fixed bank remove the exhaustion problem, since a student can always be given another variation.
They also lose the calibration, because a newly generated question has no performance history and its difficulty is assumed rather than measured.
The current compromise generates variations of calibrated templates, which preserves the difficulty estimate while changing the surface, and it works precisely to the extent that the surface change does not alter the difficulty.