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A mountain with a path of coloured bricks climbing to a flag and a glowing hint lantern, beside the cover of Escape the Ice Pyramid.

Field Notes

Productive Struggle: Why Getting Stuck Is Part of Learning Maths

4 min read
  • Learning science
  • Hints
  • Study tips

You stare at a puzzle. Nothing fits. It feels like a sign that you are bad at maths. Learning researchers see it differently: some stuck time is where learning happens. But not all of it. Here is what the studies say, and where they stop.

Hard, in a good way

Elizabeth and Robert Bjork use the phrase desirable difficulties for things that make learning feel harder but help it last: spacing practice out, mixing kinds of problem, and testing yourself instead of rereading. They add an important warning: if a learner does not have the background knowledge or skills to respond to a difficulty successfully, it becomes an undesirable difficulty (Bjork and Bjork, 2011).

Three boxes side by side: Too easy, Productive struggle and Too hard, each with a short description.
The useful zone is in the middle, and it moves as you learn.

Even a wrong guess can help

Kornell, Hays and Bjork (2009) gave people questions they could not answer, such as made-up general-knowledge questions, and then showed the answer. A second group saw the question and answer together without guessing first. The guessing group learned the answers better, even though their guesses were wrong. The authors suggest that taking challenging tests, instead of avoiding errors, may be one key to effective learning (Kornell, Hays and Bjork, 2009). Note what happened next in that study: the right answer was shown.

Try first, then be taught

Manu Kapur and colleagues call it productive failure: students attempt a hard problem on a topic they have not been taught yet, usually fail to reach the standard method, and then a teacher builds on their attempts and shows the method. In 2021 Sinha and Kapur combined the results of 53 studies with 166 comparisons, mostly in mathematics and science, in a meta-analysis in the Review of Educational Research. As reported by phys.org, problem solving before instruction tended to beat instruction first.

Two rows of boxes. Teach first: method shown, practise it, test. Try first: struggle, method shown, test.
Both orders include teaching. They differ in what comes first.

The same report states the limits plainly. The approach needs some prior knowledge, it showed smaller benefits for primary school students than for secondary students and undergraduates, and instruction has to follow, showing why the students' own solutions missed the target. Most of the studies covered science, maths and medicine, not every subject. So the research does not say that more struggle is always better.

A hint ladder

None of these studies measured how many minutes to stay stuck, so there is no magic number. The ladder below is our practical suggestion, built on the ideas above: try something real first, take the smallest help that works, and finish by making sense of the answer.

Five steps of a staircase: re-read the rule, try something small, take a nudge, try again, then read the full answer and explain each step.
A hint ladder. Skipping rungs is allowed when you are truly stuck.
  • Set a timer. A few minutes of real trying, pencil moving. Many families pick five to ten for a puzzle, and a younger child may need less. Adjust it to the person.
  • Stuck with no ideas at all? That is the too-hard zone. Take a hint sooner. Frustration without a foothold is not productive.
  • Take the smallest hint first, then try again before reading the next one.
  • Read the full answer when you must, then explain each step in your own words, and come back to a similar puzzle a few days later.
  • For grown-ups helping: ask what they have tried, rather than giving the method.

Where a puzzle adventure fits

Escape the Labyrinth and Escape the Pyramid, Level 1 are puzzle adventure gamebooks, so you do not read them in order. Each chamber is a locked number-pyramid puzzle, and the answer tells you which page to turn to. The Pyramid book has 45 locked chambers and 6 treasure rooms, with hints and full answers in the back; the Labyrinth has 45 chambers and varies the puzzle kind from door to door. In the Labyrinth and the Ice Pyramid, the box at the bottom of each chamber page points to hint and solution pages, so you can take help in small steps. They are puzzle books, not a course, and they will not replace a teacher.

A chamber page of Escape the Ice Pyramid: a drawn ice ramp with a door, the Ice Shards rule, a partly filled number pyramid with loose shards, and a Next Door box that points to hints and the solution by page number.
A chamber page as printed, at low resolution. Nothing is solved.

Books mentioned

Escape the Labyrinth cover

Escape the Labyrinth

A puzzle adventure gamebook with 45 locked chambers. You choose your road, and the puzzle kind changes from door to door.

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Escape the Pyramid, Level 1 (Easy) cover

Escape the Pyramid, Level 1 (Easy)

A puzzle adventure gamebook with 45 locked chambers and 6 treasure rooms, hints and full answers in the back.

View on Amazon
Escape the Ice Pyramid cover

Escape the Ice Pyramid

Go down nine frozen rows through 45 locked chambers. A puzzle adventure gamebook.

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