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For parents and teachers

Why this practises maths the way it does

Maths O'Clock is two small, free, ad-free practice games. This page explains the teaching decisions behind them, and points at the research each one rests on, so you can judge whether it suits your child or your class.

Strategies, not flashcards

Children do not get from counting on their fingers to instant recall in one jump. Arthur Baroody's much-replicated account describes three phases: counting, then deriving — working an unknown fact out from a known one — and only then mastery, where the answer simply arrives. The middle phase is where the mathematics actually lives, and it is the phase that flashcard drill skips entirely.

So nothing here is a bare sum with a tip attached afterwards. Every question belongs to one of twenty named strategies, and the strategy is the thing being practised. When your child meets 7 × 9, the app is not testing whether they have memorised 63; it is rehearsing nine groups is ten groups with one group taken away, using 7 × 9 as the vehicle. The same strategy then reappears with different numbers, so what gets stored is the reasoning rather than one particular pair.

Strategies have prerequisites and unlock in order. "Break the fact apart" (7 × 8 as 5 × 8 + 2 × 8) does not appear until equal groups and the fives strategy are both established, because it is built out of them.

Where this comes from. Baroody's phase account of number-fact development; the What Works Clearinghouse's first recommendation, systematic instruction to develop understanding of mathematical ideas, at its strongest evidence tier.

Worked examples that fade, from the back

The first time a strategy appears, the child does not face a blank problem. They see the whole thing worked out, with only the answer missing. Get it right and the last step vanishes. Right again and the next one goes. Eventually the sum stands on its own.

The ladder for 7 × 9
Step shown7 × 10 = 70 · that is one group of 7 too many · 70 − 7 = ?
One hidden7 × 10 = 70 · ?
None7 × 9 — with the strategy still named above it
Fluent7 × 9 — and it now returns on a spaced schedule instead of every session

Two details matter and both are deliberate. The steps are removed from the end backwards, not the front: Atkinson, Renkl and Merrill found backward fading transfers better than forward fading, because the child always works on the step they are most ready for. And a wrong answer puts a step back rather than simply marking the question failed, so the support tracks the child rather than a schedule.

Alongside the ladder, the app periodically asks why does this work? as a question in its own right. In the same research, pairing fading with self-explanation prompts produced medium-to-large gains on both near and far transfer, at no extra time cost — the prompt is what stops a child executing a procedure they cannot explain.

Where this comes from. Atkinson, Renkl & Merrill (2003); the worked-example effect in cognitive load theory; the EEF's finding that analysing worked examples builds understanding of the reasoning rather than just the answer.

Mixed on purpose

A page of twenty multiplication questions teaches a child something unintended: that they do not need to work out which method applies, because it is the same one every time. Interleaved practice — mixing question types so the strategy has to be chosen each time — removes that crutch.

The evidence is unusually clear. In Rohrer and colleagues' randomised controlled trial with seventh-graders, pupils on heavily interleaved practice scored 61% on a delayed test against 38% for those on mostly blocked practice, from the same total amount of work. The recommendation drawn from that line of research is that at least two thirds of practice should be interleaved or spaced.

Each session here opens with a short blocked run of two or three questions on whichever strategy is being introduced — a genuinely new idea does need a moment of consecutive attention — and then interleaves the rest. Measured across sessions, that comes out at roughly three quarters interleaved, with six or seven distinct strategies in a ten-question set.

Where this comes from. Rohrer, Dedrick, Hartwig & Cheung (2020); Rohrer & Hartwig's practitioner guidance on spaced and interleaved practice.

Spaced return

Once a strategy is solid it does not disappear, and it does not come back every day either. It returns after one session, then two, then four, then eight — expanding intervals, the pattern that produces the longest-lasting retention for the least practice. A strategy that goes wrong drops straight back to the next session.

This is why the app is worth ten minutes several times a week rather than an hour once. The schedule only works if the sessions exist.

Pictures that disappear

Ten-frames, number lines and arrays appear while a strategy is being built and drop away once it is fluent. They are not decoration: an array with one column greyed out makes "nine groups is ten groups minus one" something you can see rather than something you are told, and a number line turns 350 − 345 from a borrowing exercise into a visibly tiny hop.

The number line earns its own recommendation at the strongest evidence tier in the 2021 WWC guide, and representations more generally are recommendation three in the same guide. The EEF is careful on one point, which this app follows: representations are scaffolds, and the goal is to remove them.

Where this comes from. WWC (2021) recommendations 3 and 4, both strong evidence; EEF guidance on manipulatives and representations as removable scaffolds.

Naming the mistake

A red cross tells a child they are wrong. It does not tell them what they did. When the app recognises a specific error, it names it:

The child answersWhat the app says
19 × 9 = 209You added a group. Nine is ten groups minus one.
46 + 9 = 56That is 46 + 10. You still have to take one back.
7 × 8 = 35You did one part. Both parts have to be added together.
247 rounded to 250Check the halfway point again — it was closer the other way.

Teaching guidance is consistent that misconceptions need addressing directly, with examples and non-examples, because children will otherwise defend and repeat them. A generic "not quite, try again" leaves the faulty rule perfectly intact.

The timer question, honestly

You will find a "Beat the clock" toggle in the grown-ups panel, switched off. It would be easy to justify that by citing only one side of the evidence, so here is both.

On one side, the 2021 What Works Clearinghouse guide's sixth recommendation is, at its strongest evidence tier, to regularly include timed activities as one way to build fluency in mathematics. That is not a fringe position and it deserves stating plainly.

On the other, a substantial literature associates timed testing with the onset of maths anxiety, and shows that anxiety consumes the very working memory a child needs for reasoning — with the effect falling hardest on children who have the most working memory to lose.

These are less contradictory than they look. The WWC means brief, low-stakes, self-competitive activities, where a child races their own previous score inside a supportive classroom. The anxiety research is largely about high-stakes, public, graded tests. The gap between them is the setting, not the stopwatch.

Which is why the default here is off. A child practising alone at a kitchen table has the stopwatch but not the teacher keeping it light, and the app cannot tell the difference between excitement and dread. If racing the clock genuinely motivates your child, turn it on — that is a defensible reading of the evidence, and it is why the toggle exists rather than being omitted.

Where this comes from. WWC (2021) recommendation 6, strong evidence, on one side; Boaler and the maths-anxiety literature on working memory under time pressure on the other. The default is a judgement about unsupervised home practice, not a claim that the evidence is one-sided.

What to expect, including the awkward part

Your child will get more questions wrong here than on a conventional drill app, at least at first, and their session scores will look worse. This is not a bug and it is worth understanding before you conclude the app is too hard.

Choosing a strategy is harder than repeating one, so mixed practice depresses performance during practice while improving it on a later test. That is precisely the 61%-versus-38% gap: the group that looked worse while practising was the group that had learned more. Robert Bjork's term for this family of effects is desirable difficulties — conditions that slow visible progress and increase real progress. If you want a single thing to watch instead of the score, watch whether your child can say why their method works.

The grown-ups panel (the cog, top right of the maths game) shows every strategy with its phase — New, Building, or Fluent — how many steps of scaffolding are still showing, and accuracy. That is a truer picture of progress than a percentage, and it tells you what to talk about over the kitchen table.

Sessions are ten questions and take five to ten minutes. Little and often beats long and rare, both for the spacing schedule and for a nine-year-old's patience.

The strategies in full

For teachers who want to know what is covered, and parents who want the vocabulary the app uses so it matches what you say at home.

AreaStrategies
AddingPairs that make ten · Doubles · Near doubles · Bridge through ten · Pairs that make 100 · Add ten, then adjust
Taking awayCount up to take away · Back through ten · Take ten, then adjust
Place valueSplit into place values · Multiplying by ten
MultiplyingEqual groups · Turn-around facts · Double it again (×2, ×4, ×8) · Five is half of ten · Nine is ten take one · Threes and sixes · Break the fact apart
DividingDivision is multiplying backwards
EstimatingRounding to the nearest

There is no year group or grade attached to any of this, on purpose. The app finds each child's level from a short placement round in the first session and moves each strategy independently, so the same page suits a six-year-old on ten-frames and a ten-year-old breaking apart 8 × 7.

And the clock game

The Tick Tock Quest follows the same spirit for telling the time: reading analogue clocks, quarter past and quarter to, minutes past and to, elapsed time, am and pm, and 24-hour time — with a drag-the-hands mode, because setting a time is a different skill from reading one and children are often fluent at one and lost at the other.

Privacy, cost and classroom use

There are no accounts, no sign-up, no analytics, no advertising and no tracking of any kind. Your child's name, stars and progress are stored in that browser's own storage on that one device and never leave it — which also means progress does not follow them from the tablet to the laptop, and clearing site data clears it. Nothing is ever sent to us, because there is no us to send it to: the whole thing is static files.

It is free with no catch, and free to use in a classroom, on a whiteboard, or as homework. No attribution needed. If it is useful to your school, just use it.

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References

Summarising research is not the same as conducting it. These are the sources the design leans on; where they disagree, as they do on timing, this page says so rather than picking the convenient side.