Nearly 100 school teachers, researchers, students and educators from around the world gathered online to confront a deceptively simple question: how do you know when a student has really understood a piece of physics? The workshop, titled «How Do You Know They Understood?», used a question about nuclear half-lives to expose how difficult that judgment can be.
Participants were given three possible answers to a question about radioactive decay. The first was scientifically the most accurate, treating decay statistically: for a large population of nuclei, the proportion that will decay can be predicted, but not the exact decay time of any individual nucleus. The second and third answers contained increasing misconceptions, treating half-life deterministically as if each nucleus carried its own internal clock. Only 44% of the audience chose the correct answer, while 33% picked the second and 22% the third.
The split revealed a deeper problem. A correct calculation, a correct statement and a model that captures the physics are not necessarily the same thing. A participant from Hungary focused on the mathematical demands of the topic, while another joining from Canada noted that a student might struggle with calculation yet still grasp something essential: radioactive decay lets us predict a population while leaving the decay time of any single nucleus unpredictable.
That exchange made the problem feel much less tidy. Physics gives students many routes to the right answer. Some arrive through pattern recognition, spotting a familiar problem type and reusing a method or following a calculation procedure without being able to explain why it works physically. They may calculate two half-lives correctly while still imagining that each nucleus carries an internal clock.
The workshop's organizer described this as a «diagnostic asymmetry» of success: educators tend to investigate how students get wrong answers more deeply than the routes they follow to get right ones. The trouble is that a student might get the right answer while the reasoning behind it falls apart when the situation changes. In other words, they might be right without having understood any physics.
To address this, participants tried a different tactic: creating questions deliberately designed to make the hidden physics visible. If a student says a patient becomes radioactive after an X-ray, what would have to change in the patient's nuclei for that to be true? The question forces reasoning through the distinction between irradiation, contamination and activation. Similarly, a student who understands radioactive decay should be able to move between words, a decay graph and a statement about a population of nuclei while keeping the same probabilistic picture.
By the end of the session, the method had been reduced to three moves: diagnose, respond, recheck. The organizer described it as a simple diagnostic approach for testing how robust the evidence of understanding is, rather than a general model of how students learn. The final move — change something physically meaningful and ask again — proved the most persistent.
The workshop began with a question about which students had understood half-lives best and ended with a question the organizer now wants to ask whenever a student gives exactly the hoped-for answer: what needs to change before we can trust that this understanding will be passed on? Perhaps one of the most revealing moments in a physics lesson comes just after the correct answer, when educators decide whether the model has earned their confidence.
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