Twelve levels, five themes

Difficulty and age are two separate axes here, and no level is named after a school grade — because the same topic arrives at a different age in every country we ship into.

Age sets the look. Placement sets the difficulty.

A parent enters the child's age, and the age chooses the visual theme: how the screen looks, how large the touch targets are, whether Larry is telling a story. A separate adaptive placement of 10 to 15 items chooses the difficulty — per topic, not as one global number.

The two axes are independent on purpose. An eight-year-old who is working on algebra keeps the primary-school theme; nobody is handed an adult interface as a reward for being good at fractions, and nobody is held back by the look of the screen.

The ladder

Twelve difficulty levels, N1 through N12, crossed with five visual themes. Each theme spans a range of levels, and the ranges overlap.

The overlap is deliberate. N3 belongs to both of the first two themes and N6 to two more, so a child who moves fast does not have to leave the theme that fits their age in order to find harder work, and an adult starting over does not land in a screen built for a four-year-old.

The themes carry familiar names because they describe an age and a look — button size, colour, whether there is a story. The levels, which describe the mathematics, carry numbers. That split is the whole point of the next section.

Why no level is called third grade

Because the same topic arrives at a different age depending on the country. Across the school systems this product ships into, formal fractions appear anywhere between ages 6 and 9, negative numbers between 9 and 12, and formal algebra between 10 and 14.

In the United States, formal fraction notation begins in grade 3 and integers in grade 6 under the Common Core, while high-school standards drop the grade-by-grade structure entirely and let states sequence courses differently. In England the same years are one block, Key Stage 2, and Scotland, Wales and Northern Ireland run separate curricula again.

So a level called third grade would be wrong in most of the markets it appears in, and wrong in a way the parent reading it cannot check. We publish the age band and the level number instead, and let the placement decide which level a child actually starts at.

An item is not a challenge

An item is one atomic question, with its answer and its catalogue of named errors — not just that the answer was wrong, but which mistake produced it. A challenge is what the child plays and what scores points, and a challenge is built from one to N items.

That distinction is what decides the clock. A challenge can be a single hard problem or a run of thirty easy ones, so the timer follows the kind of challenge, never the age of the child.

Five modes

Practice mixes problem types on purpose rather than grouping them. In Rohrer and Taylor's studies, interleaved practice made performance worse during the session and doubled it on the next day's test. It is supposed to feel harder while you are doing it.

Which modes run a clock, and why

Ashcraft's experiments are the reason. The same arithmetic problems produced no anxiety-related effect on untimed paper, and a substantial one when the same problems were solved mentally against a clock. The clock is the amplifier — not testing, not being marked, not being wrong.

So the clock appears only where speed is itself the skill being practised: fluency on material already mastered, and a duel somebody chose to enter. It never appears on a problem that takes thinking, and it never appears in the kinder band at all.

One note on sourcing, since this page is public. The best-known claim about timed tests — that they are the direct cause of early math anxiety — had no citation in its original form, and later versions of it cite work about something else. We did not use it. We used the controlled experiments underneath it, which claim less and hold up.

What this page does not claim

Nothing above says this product teaches anyone anything. There is no study behind Math Challenge with a pre-test, a post-test and delayed retention, so there is no such claim to make. What is described here is how the thing is built, and what the evidence behind each choice actually says.

The item bank is not calibrated either. In version one, difficulty is assigned by a human on a 1-100 scale and the placement updates an estimate after each answer; real psychometric calibration waits until every item has 200 to 400 real answers behind it.

Where this comes from

The ladder and the modes are decisions D-002, D-017 and D-018. The evidence is research mc-15 on school ladders across countries, mc-10 on math anxiety and timing, mc-05 on spacing and interleaving, and mc-44 on adaptive placement. All of it is published, including the parts that argue against what we built.