Joshua Biro reports from an online workshop he held to find out how we know if a student has really understood a piece of physics
How do you know when a student has really understood a piece of physics? That was the simple premise behind a recent online workshop I organized, attended by almost 100 school teachers, researchers, students and educators from around the world.
To explore the topic, I posed a question about nuclear half lives, to which I gave three possible answers. The first answer was scientifically the most accurate, with the second and third containing increasing misconceptions about their meaning.
The task for the audience was to say which response they thought showed the strongest understanding.
The first (correct) answer treated radioactive decay in a statistical way. For a large population of nuclei, we can predict the proportion that will decay, but not the exact decay time of any individual nucleus. The other two answers treated half-life more deterministically, as if each nucleus carried its own lifetime.
We found that 44% of the audience picked the first answer, with 33% going for the second and 22% for the third.
Understanding their understanding
Delegates then considered the matter a little more deeply. We know that a correct calculation, a correct statement and a model that captures the physics are not necessarily the same thing. So to decide which answer showed that a student had gained a true understanding of the underlying science, we had to say what evidence we were looking for.
One participant from Hungary focused on the mathematical demands of the topic. Another, joining from Canada, pointed out that a student might struggle with calculation and still grasp something essential: radioactive decay lets us predict a population while leaving the decay time of any single nucleus unpredictable. The exchange made the problem feel much less tidy.
By then, the title of the workshop – “How Do You Know They Understood?” – had become the problem itself.
We know that physics gives students many ways to arrive at the right answer. Some do it through what is essentially pattern recognition – spotting a familiar type of problem and then either reusing a method that worked before or following a calculation procedure, but without being able to explain why it works physically. They may even calculate two half-lives correctly while still imagining that each nucleus carries an internal clock.
We tend to investigate how students get wrong answers more deeply than the routes they follow to get the right solutions
Joshua Biro
I have come to think of this as a “diagnostic asymmetry” of success. We tend to investigate how students get wrong answers more deeply than the routes they follow to get the right solutions. Trouble is, a student might get the right answer but the reasoning they used to get there might fall apart when the situation changes. In other words, they might be right but haven’t actually understood any physics.
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So the participants tried a different tactic. They created questions that are deliberately designed to make the hidden physics visible. If, for example, a student says that a patient becomes radioactive after an X-ray, what would have to change in the patient’s nuclei for that to be true? Suddenly, the distinction between irradiation, contamination and activation has to be reasoned through.
The same idea works when the physics appears in a different form. 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, I had reduced the method to three moves: diagnose, respond, recheck. It is a simple diagnostic approach for testing how robust the evidence of understanding is, rather than a general model of how students learn.
That final move has stayed with me: change something physically meaningful and ask again. I began the workshop by asking which students had understood half-lives best, and I left with a question I now want to ask whenever a student gives me exactly the answer I hoped for: what do I need to change before I 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 we decide whether the model has earned our confidence.