The Key Ring: How to Practise

You solved thirty problems from section 4.2, and you solved them confidently, almost without errors. On the test the same kind of problem comes up — and you sit there not even knowing where to start.

Nothing was forgotten. It's just that in section 4.2 you never had the main part of the work: choosing the method. It was written in the heading.

The key and the key ring

Imagine you're learning to open doors, and you have a teacher.

A considerate teacher does this: leads you to a door and hands you the right key straight away. You insert it, turn it, the door opens. Thirty doors, thirty keys, thirty successes. The feeling: I know how to open doors.

Then the teacher leaves and hands you a ring of forty keys. The door is the same one. And now it turns out that the skill you'd been training was "insert and turn." The work reality demands starts earlier: look at the lock and pick the right key off the ring.

That's the gap between practice as taught and practice as needed. One problem type in a row is a teacher passing you keys. Confidence grows; the skill that matters isn't trained at all.

The textbook hands you the key. Life hands you the ring.

Mixing versus blocking

The approach where you hammer through one problem type in a row is called blocked practice. The approach where types are mixed and the order is unpredictable is interleaving. The difference in results is dramatic and has been confirmed many times.

Doug Rohrer and Kelli Taylor (2007) taught students to compute the volumes of four obscure solids. One group practised in blocks: all the problems on one solid, then all on the next. The other group did the same problems mixed together. During practice the blocked group looked markedly better — about 89% correct against 60% for the mixed group. But on the delayed test a week later the picture flipped, and by an enormous margin: 63% correct for the mixed group against 20% for the blocked one.

Nate Kornell and Robert Bjork (2008) repeated this with entirely different material: students learned to recognise painters by style. Some were shown each artist's works in a block, others were shown them shuffled. Mixing won again. And the most interesting part — after the experiment almost every participant was convinced the blocked order had been better for them. Feeling and result diverged even where the result was already known.

The mechanism is exactly the one from the article on illusions of competence. Blocks give you smoothness: the method is already in hand, all that's left is to apply it. Mixing forces you to decide afresh each time which key to take — and that unpleasant effort of choosing is the skill being trained.

The key that jammed

Blocked practice has one more side effect — it accustoms you to a single key so thoroughly that you stop seeing the others.

In the 1940s Abraham Luchins ran the classic water jar experiment. Participants were given a series of problems: how to measure out a required volume of water using three vessels of different capacities. The first problems could be solved only one way, a fairly cumbersome three-step method. People found it and applied it successfully time after time.

Then they were slipped a problem solvable by that same cumbersome method but also, trivially, in two moves. Most participants didn't notice the simple solution and kept doing three steps. Some were given a problem where the old method no longer worked at all — and they declared it unsolvable.

This is the Einstellung effect: a successfully drilled method becomes a rut from which the alternatives aren't visible. Experience turns from an advantage into blinkers. It's exactly why a newcomer sometimes solves the problem a team has been stuck on for a week: they aren't holding the key that jammed.

The practical conclusion: when a problem won't move, ask separately not "how do I apply my method" but "what other approach exists at all." And mix problem types — that's the best prevention against ruts.

Practice at the limit, not in comfort

The second big question is not only what to mix, but how hard to go.

Anders Ericsson, who studied experts in music, sport and chess, described the notion of deliberate practice. Four features distinguish it:

work on what you can't do yet, rather than repetition of what's mastered;
a specific narrow goal for the session, not "play a bit" or "study a bit";
fast feedback — you see immediately whether it worked;
immediate correction of the error, not "I'll sort it out later."

Put simply: you have to practise on locks that resist. The scales you can already play add nothing; that one bar that fell apart adds everything.

It's worth naming the limits of this idea too, because it's often presented in absolute form. A meta-analysis by Brooke Macnamara and colleagues (2014) showed that the amount of deliberate practice explains only part of the differences between people — a noticeable part in games and music, a far smaller one in professions and education. So "ten thousand hours" is neither a guarantee nor a universal law. But the direction is right: how you practise matters more than how much.

The polished key trap

Last, about where diligent people's time goes.

Overlearning is continuing to drill what you've already mastered within the same session. A little of it is useful: it takes the skill to automaticity. Beyond that it adds almost nothing, and Rohrer and Taylor showed that even the gain you do get fades quickly — it's far more profitable to take the same time and scatter it across several days.

The temptation is understandable: solving familiar problems is pleasant, and every success confirms your competence. That's how an hour of study turns into polishing a key that already opens. The real work is in the awkward problems you can't do yet.

In practice

Mix problem types. Not "twenty differentiation problems," but ten mixed from different sections in random order. Ready-made exercise sets almost always come in blocks — shuffle them yourself.

Practise choosing the method separately. Take a list of problems and, without solving them, just determine for each: which tool is needed here and why. That trains the very move textbooks don't give you.

Look for where it breaks. Don't start a session warming up on the familiar; start by finding the weakest spot. Once you've located it, work right there, in short repeats with checking.

Set a narrow goal for the session. Not "I'll do some physics," but "I'll work out why I mix up components in inclined-plane problems." A goal like that can be checked at the end.

Change the approach periodically. If you're solving with the same method for the third time in a row, ask yourself separately: is there a shorter one? That's prevention against a jammed key.

Check yourself

Close the article and answer in your own words:

Which skill goes untrained when you solve one problem type in a row?
Why did the blocked group in Rohrer and Taylor's experiment look better during practice and worse on the test?
What did Luchins's water jar experiment show, and how does it apply to your practice?
What are the four features of deliberate practice?
Why is polishing what you've already mastered a poor use of study time?

In short

Blocked practice hands you the key ready-made: you train applying a method but not choosing it.
Interleaving feels harder and looks worse in the moment but produces several times better results on a delayed test — and almost nobody believes this about themselves.
The Einstellung effect: a successful method turns into a rut from which simple solutions aren't visible.
Deliberate practice sits at the edge of your ability, with a narrow goal, fast feedback and immediate correction. How you practise matters more than how much.
Overlearning is a pleasant imitation of work. Polishing a key that already opens is pointless.
The textbook hands you the key. Life hands you the ring.