The science behind Math Workout

Built on research

Math Workout is built around science. Each workout is designed around a well-studied idea from the science of learning, such as retrieval practice, spaced repetition, worked examples or working memory, and we show you the research behind it, with links to the papers.

We write these pages for curious players, for parents choosing what their child plays, for teachers who want to know why a game is built the way it is, and for families looking for activities for people living with dementia. Doc keeps it light, and the references let you check every claim.

Our standards

• Every science claim links to its published source.
• Every reference is checked against its official record and its abstract before it goes on a page.
• Every research number comes from a cited source.
• We keep the pages up to date and fix mistakes fast: tell us at support@mathworkout.app.

What decades of research show

Some of the strongest findings in all of learning science sit behind Math Workout's workouts.

Quizzing yourself works. A meta-analysis of practice testing found that practice tests helped learning more than restudying and every other comparison condition,¹ and a large review of ten study techniques rated practice testing and spreading practice out over time as the two most useful.² That is why every workout asks you to answer from memory.

Spacing works. A synthesis of 317 experiments found that spreading practice out beats cramming it together.³ That is why the Progress review brings each fact back after a gap, sooner when it is shaky and later when it is secure.

Practice improves what you practise. An independent review of brain training research found plenty of evidence that training improves performance on the trained tasks,⁴ and a large second-order meta-analysis found that working memory training improved performance on memory tasks.⁵ Math Workout trains a skill you use every day: mental arithmetic.

Mental arithmetic works the brain. A meta-analysis of brain imaging studies found that calculation tasks draw on a network in the parietal lobes and on distinct areas of the prefrontal cortex for different operations,⁶ and as children and adults gain arithmetic skill, brain activity shifts toward parietal areas that specialise in arithmetic.⁷ In a randomised controlled study in Japan, healthy adults aged 70 to 86 who solved basic reading and arithmetic problems every day for six months improved their scores on tests of frontal lobe function and processing speed.⁸

Games help people learn. A meta-analysis of studies with school and college students found that digital games significantly improved learning compared with lessons without games.⁹

And the right level of challenge matters. Children who practised with an adaptive math program at higher success rates attempted more problems and improved their math more,¹⁰ and intelligent tutoring systems raised test scores by a median of 0.66 standard deviations over conventional teaching.¹¹ That is the thinking behind our patent-pending Math Adapt AI.

How we choose research

We start with peer reviewed papers, and with reviews and meta-analyses that pool many studies, because they give the clearest picture. We use recent work where it exists, and the original study where it matters, for example the first test of an idea.

Every reference is checked before it goes on a page: we look up its DOI in Crossref to match the authors, year, title and journal, check for corrections and retractions, and read at least the abstract, so that each sentence says what the paper found.

Each science page shows the date its science was last checked, and we check every page again at least once a year.

How to read a reference

A reference tells you who did the research, when, what it is called and where it was published. Here is how to read one:

Spotted a mistake?

Email support@mathworkout.app with the page and the reference, and we will check it.