Researchers once sat students down with worked-out physics solutions and recorded everything they said while studying them. The students who went on to solve problems successfully, and the students who went on to fail, opened those worked solutions about equally often. Nine times out of twelve problems for the successful group. Ten out of twelve for the unsuccessful one.
So the thing that separated them was not whether they looked at the answer. It was what they did while looking.
The study is from 1989. I still think it is the most useful thing anyone has written about this, because of how it reframes the problem. Opening the solver is not what goes wrong. What goes wrong is that reading a solution has a right way and a wrong way, most of us default to the wrong one, and nobody gets taught the difference.
The difference is how you enter the solution
The detail in Chi and colleagues' data is where this gets practical.
The unsuccessful students, when they got stuck, went back to the worked example and started reading from the first line. They did this just over four times per problem, and each time they read about thirteen lines. They were re-reading the whole thing, repeatedly, hoping it would land.
The successful students almost never did that. They went straight to one particular equation, read a line and a half, checked the single thing they wanted to check, and got out again. Their commonest move was what the researchers called compare-and-check, holding one step against their own work, and they did it over three times as often as the weaker group.
Total episodes of looking at the example: 2.7 per problem for the good students, 6.7 for the poor ones. The weaker students spent more time in the solution and got less out of it, because re-reading a correct answer feels productive and produces almost nothing.
There is your first rule, and it is entirely mechanical. Do not scroll a solution from the top. Know the specific step you are stuck on, go to that step, and get out.
Attempt it first, and let the attempt fail
The order matters more than anything else in this article, and there is a clean experiment on it.
Manu Kapur randomly assigned 75 ninth-graders to learn standard deviation two ways. One group was taught the method and then solved problems. The other group tried to solve the problems first, alone and unaided, and was taught afterwards. Same teacher, same materials, same total time. Only the order changed.
On procedural questions, plugging into the formula, the two groups were identical: 9.24 against 9.47 out of ten, with a p-value of .896. If all you want is to execute a method, order does not matter.
Everything else diverged sharply. On conceptual understanding the attempt-first group scored 6.33 against 3.84. On transfer to novel problems, 5.37 against 3.11. Those are very large effects, and they were replicated in a second study in the same paper.
One more finding is worth sitting with. The attempt-first students reported significantly more mental effort. It felt harder to them, and it worked better. If your study method feels comfortable, that is information, and not the good kind.
Being honest about the limits: a meta-analysis of 53 studies puts the average benefit at a more modest 0.36, and the authors note the effect reverses for younger children in second through fifth grade. For a secondary or college student learning a new maths topic, though, the direction is well supported: struggle first, then look.
Say out loud why each step is allowed
Once you are in the solution, one habit does most of the work.
In the 1989 study, the successful students generated an average of 15.3 genuine explanations of the physics while studying an example. The unsuccessful students managed 2.8. The correlation between how many explanations a student produced and how well they later solved problems was 0.81, which for this kind of research is enormous.
They were not reading harder. They were doing something different in kind: stopping at each line and working out why that line was allowed to follow the one before it.
You can get most of this with a prompt so small it barely counts as work. Atkinson, Renkl and Merrill tested it on high-school students in advanced algebra: after each worked step, name the principle that step used. That was the whole intervention.
Near-transfer scores climbed from 0.29 to 0.53. Far transfer went from 0.23 to 0.41. Both of those are large effects. And the time cost? Study time was 32.95 minutes without the prompts and 30.85 with them, a difference that means nothing statistically. As the researchers put it, the technique "requires no additional instructional time."
So: after each step the solver shows you, say what rule that step used. Not what it did. What rule permitted it. If you cannot name the rule, that is the step you did not understand, and you have just located it precisely.
Then take the steps away, from the bottom up
The same paper tested how to wean yourself off worked solutions, and the answer is not to stop cold.
Their sequence, called backward fading, runs across four problems: the first is fully worked, the second omits the last step, the third omits the last two, and the fourth is a plain problem you do alone. You lose the solution gradually, from the end backwards.
This beat the obvious alternative of alternating a full example with a full problem. It also beat forward fading, where you remove the first steps instead. Removing the last step first works better, and it makes intuitive sense: the closing move of a problem is the one you can most easily reconstruct from context.
In practice, with a solver, that means your second problem of a set should have you covering the final line before you read it and trying to produce it yourself. Then the last two lines. Then the whole thing.
The protocol
- Attempt first, alone, and expect to fail. The failed attempt is doing work.
- Identify the exact step you are stuck on before you open anything.
- Enter the solution at that step. Do not read from the top.
- Name the rule that permits each step you read. If you cannot, that is your gap.
- Close it and reproduce the step from nothing.
- On the next problem, cover the last line and produce it yourself. Then the last two.
- Do a fresh problem of the same type with nothing open.
None of this takes longer than what you are already doing. The Chi data is blunt about that: the weaker students spent more total time inside the worked example than the stronger ones did. You are not being asked to work more. You are being asked to stop re-reading.
What this actually costs you
About ninety seconds a problem, and the discomfort of being wrong on purpose before you get help.
That second part is the real barrier, and I do not want to pretend otherwise. Attempting first means sitting with not knowing, at eleven at night, with a deadline. Every instinct says open the solver now. The research says that instinct is optimising for how the session feels rather than for what you can do next month, and that gap between feeling prepared and being prepared is exactly what an exam measures.
None of this makes using a solver dishonest. Whether it is permitted is a separate question with its own answer, and I have written elsewhere about where that line sits. This is the narrower question of whether the thing works. On that the evidence is unusually clear. It works when the solution comes after your attempt and gets read a step at a time. It does nothing whatsoever when you scroll it from the top.
If you want to practise the mechanics, pick a topic you half-know and run one problem through a full step-by-step solution, naming the rule behind every line as you go. It takes about three minutes, and it will tell you very quickly which lines you were previously just watching go past.