How VMC is using knowledge tracing to show radiography students what they know, what they don't, and what to do next.
Nobody wants a linear programme that eats weeks of their time and ends with a quiz. Not students, and not the educators who have to run it.
Yet that is still how much of radiography education is packaged. Every learner starts at module one, moves through the same content at the same pace, and finds out how they did at the end. The student who already understands collimation sits through it anyway. The student who is quietly lost on it keeps moving, because the programme keeps moving.
A straight line treats time as fixed and learning as the variable. We think it should be the other way round: the destination is fixed, and each student takes the shortest safe route to it.
A final quiz tells you what a student got wrong after the teaching is over. By then the gap has had weeks to harden, and there is no time left in the timetable to go back.
It also gives a single score for a bundle of skills. A student who scores 70% might be strong on positioning and weak on exposure factors, or the reverse. The number alone cannot tell you which, so it cannot tell you what to teach next.
This is not a new idea. In 1984 Benjamin Bloom reported that students taught with mastery learning, where each learner gets feedback and corrective work until they reach the standard, performed about one standard deviation above students in conventional classes. Students with one-to-one tutoring plus mastery learning performed about two standard deviations above. Bloom's challenge was to find methods that get close to that result without a tutor for every student.[1] Later reviews suggest the real-world gains are smaller than Bloom's headline figure, but the direction has held: feedback on specific gaps, acted on early, beats a single verdict at the end.
You cannot see what a student knows. You can only see what they do: a correct answer, a well-centred image, a missed anatomical marker. Knowledge is hidden; performance is visible.
A Hidden Markov Model (HMM) is a well-established statistical method for exactly this situation. It estimates a state you cannot observe directly from a sequence of things you can. It has been used for decades in fields such as speech recognition, where the hidden state is the word being spoken and the visible evidence is the sound.[3]
Bayesian Knowledge Tracing (BKT) is a specific, simple HMM built for learning. It was described by Albert Corbett and John Anderson in 1994 and has been used in intelligent tutoring systems since.[2] For each skill, BKT keeps a running estimate of the probability that the student has mastered it. After every attempt it updates that estimate, allowing for two realities of assessment:
The result is not a mark. It is a live, per-skill estimate of what the student knows, which changes as they practise.
Imagine a second-year student, Sam, working on one skill: collimating correctly for an erect occipitomental 30° facial bones view. The model starts with a modest estimate that Sam already has the skill (30%). Here is how the estimate moves over seven attempts in the simulation.
| Attempt | Result | Estimated mastery |
|---|---|---|
| Start | 30% | |
| 1 | Wrong | 19% |
| 2 | Right | 59% |
| 3 | Right | 89% |
| 4 | Wrong (slip) | 57% |
| 5 | Right | 88% |
| 6 | Right | 97% (mastered) |
| 7 | Right | over 99% |
Three things stand out. One wrong answer at the start does not condemn Sam; two correct attempts lift the estimate quickly. A slip at attempt 4 pulls it back, but not to zero, because the model allows for slips. And Sam crosses a 95% mastery threshold at attempt 6, the point at which many tutoring systems treat a skill as learned.
At that moment there is no reason to keep drilling collimation. Sam's time is better spent on the next gap. A linear course would have given Sam the same number of collimation exercises as everyone else.
Figures use illustrative settings (30% starting estimate, 15% chance of learning per attempt, 20% guess rate, 10% slip rate). In practice these are set per skill from real data.
Knowledge tracing is only as good as the evidence it receives. Multiple-choice questions alone give thin evidence about a practical skill like radiography.
That is why we are building our self-assessments around the simulations themselves. Our research platform, CLIO, links each self-assessment to the specific tasks a student performs in simulation: positioning, centring, collimation, exposure selection and image critique. Each action becomes evidence for the skill it demonstrates. CLIO tracks mastery per skill rather than per module, so a student can be strong in one area and still get targeted help in another.
CLIO is active research and development. We have working prototypes and modules in testing with subject-matter expert sign-off, and we are refining the models against real student data before anything reaches customers. We will not put a date on it until the evidence says it is ready.
The aim is not to replace the educator. It is to give the educator a clearer picture, sooner.
The programme stops being a straight line and becomes a map, with each student's position on it visible to them and to you.
We are shaping CLIO with the people who will use it. If you run a radiography programme and want to know more, or want to tell us where your students' gaps usually are, get in touch.
Email sales@virtualmedicalcoaching.com