You attempt a problem. You get it wrong. You open the worked solution, read it top to bottom, and every line makes sense. You close it feeling that the gap is repaired.
Two weeks later the same question, lightly disguised, defeats you again. Nothing was repaired. What happened in between is one of the best-documented failures in learning science, and it has a name.
The fluency illusion
Reading a correct solution is easy, and the ease is the problem. Cognitive psychologists call it the illusion of fluency: we judge how well we know something by how smoothly it processes, and a well-written solution processes very smoothly indeed. Every step follows from the last. Nothing is confusing. That smoothness gets misread as competence.
But recognising a step as correct and being able to produce it are different operations. Recognition runs on the solution in front of you; production runs on retrieval from memory, with a blank page. You have practised only the first, then graded yourself on the second.
This is why re-reading is the most popular study method and one of the least effective. It generates confidence faster than it generates skill, and confidence is the thing that stops you from practising more.
You didn't lose the whole solution — you lost one line
Here is the part that matters practically. When a worked solution defeats you, it is almost never all of it.
Nine of the twelve lines are moves you already own. Somewhere around line four there is a substitution you would not have thought of, or a constraint pulled from the problem statement you had not noticed was usable, or a standard form you did not recognise. That is the line. Everything after it reads fine because you have been handed the thing you were missing — which is exactly why reading forward feels like understanding.
Reading the solution as a block hides this. The one line you needed is buried among eleven you didn't, and the average feeling across the twelve is "yes, that makes sense".
So the practical question is never "did you understand the solution". It is: which line would you not have produced yourself? Almost nobody asks it, because a block of text does not invite the question.
Meeting the solution one line at a time
Rhovecs does not hand you the solution as a block. It reveals it one step at a time, and the final answer stays hidden until the last step is out — so the panel cannot be skimmed to the bottom for the number.
That single constraint changes what you do. You meet each line on its own, before you have seen where it leads, which is the only moment at which you can honestly tell whether you would have got there. Line four either lands or it doesn't, and it lands or doesn't in isolation, not softened by the eight lines after it that made everything look inevitable.
Every revealed line carries one action: I don't follow this. Pressing it explains that line, and only that line — what move it makes, why it is legal, and why it is the natural thing to do at that point in the derivation. It does not restate the line, and it does not re-walk the solution. One line is the whole job.
There is no withholding. You have already attempted the problem and already failed it, so there is nothing left to protect: the explanation does not turn into a question, does not ask what you think, and does not coach. That posture is deliberate. Socratic questioning has its place before an attempt; after one, it is just friction between you and the thing you came for.
If the explanation raises another question, you can ask one follow-up on that step and get a direct answer.
Why every student gets the same explanation
The explanation for a given line is written once and then served to everyone who presses that button on that line.
This is a design choice with two consequences worth stating. The first is economic: because one explanation is shared rather than generated per student, its marginal cost is effectively zero, which is why the whole surface is available on every plan rather than sold as a premium extra. Explaining a line of Physics should not be a paid tier.
The second consequence is about honesty. A shared explanation cannot reference your attempt, your answer, or your mastery record, because it is the same text for a student who missed line four and a student who missed line nine. It explains the mathematics, not you. Elsewhere in the system your record is used heavily — it is what selects your next problem — but an explanation of why a substitution is legal is a fact about the substitution.
The explanation is generated by a language model, and it is constrained tightly: it is grounded in the stored, human-reviewed solution for that specific problem, and it explains one indexed line of it. It is not free-form tutoring, and it is not inventing mathematics on the spot.
Pressing "I don't follow this" is also recorded as a signal in its own right, whether or not the explanation had to be written fresh. A line that consistently stops students is telling us something about that solution, not just about those students.
What this does not do to your record
Opening the solution is not a neutral act inside the mastery model, and the article on how Rhovecs decides what you practise next covers the accounting: an attempt where you viewed the solution scores nothing toward mastery. It is excluded entirely.
That is not a punishment. It is the only consistent position. Mastery is a record of what you can produce unassisted, and an attempt where the method was handed to you is not evidence about that. Letting it count would make the number kinder and useless.
What follows the walkthrough instead is the repair: the mistake is classified, and a short set of problems is assembled around the specific technique that broke — not more of the chapter. You get another chance to produce the line yourself, which is the only thing that ever moves the score.
Reading the solution is not the learning. It is the moment before the learning, correctly aimed.