The 85% rule: why most of a child's answers should be wins

A child learns fastest when practice is mostly right and sometimes wrong. The best-known number for "mostly" is 85%, from a 2019 paper that modeled simple learners on two-choice tasks, and the best-known number from a real children's practice system is 75%, from Math Garden. Peabody (peabody.kids) builds every practice round so about 85% of the questions are ones the child already knows, with two new items taught first. It is free through the end of 2026. The 85% is a sensible default, not a measured optimum, and this post explains both the evidence and the limits.

What the 85% rule actually models

Wilson, Shenhav, Straccia and Cohen (2019), writing in Nature Communications, asked a narrow question: for a learner that improves by gradient descent on a binary classification task, what error rate makes learning fastest? Their answer was about 15.87% errors, or roughly 85% accuracy. They checked it on perceptrons, two-layer neural networks and a biologically plausible model of learning. The paper is open access.

Three things are worth saying plainly.

• The learners are mathematical objects, not children.
• The task is two-choice with a clear right and wrong answer.
• The authors say themselves that this is not a prescription for classrooms.

So the 85% rule is a result about a class of learning algorithms. It is a useful anchor because it agrees with what practitioners had already settled on, not because it was measured in a school.

Guessing changes the number

Peabody's questions are three big tap boxes. A child who knows nothing still gets one in three right. That changes what "85% right" means. If raw accuracy is 85% and a third of blind guesses land, the share of questions the child truly knows works out to about 78% (0.85 = 1/3 + 2/3 × p, so p ≈ 0.78). Pelánek (2016), in Computers & Education, gives the standard k-option correction that adaptive systems use for exactly this.

That matters because it puts Peabody's raw target in the same place as the one system that has run this question with thousands of real children.

Math Garden's 75%

Klinkenberg, Straatemeier and van der Maas (2011), in Computers & Education, built Math Garden, a Dutch practice system that rates every child and every item with an Elo score after every answer. Pure measurement theory says the most informative question is one the child has a 50% chance of getting right. Math Garden does not do that. Hofman and colleagues (2018), in the Journal of Intelligence, explain that the system targets a 75% success probability, because failing half the time is unacceptable in something children use every day.

Read across the table and the practical numbers converge: a practice system for children should sit somewhere around three right in four, before guessing is counted.

Bloom's two sigma, and why it did not hold at that size

Any discussion of difficulty ends up at Bloom (1984), in Educational Researcher, who reported that one-to-one tutoring combined with mastery learning moved students about two standard deviations above a conventional class. The number is famous. It has not replicated at that size.

Von Hippel (2024), in Education Next, traces Bloom's figure to two dissertations with small cells and narrow tests, where feedback plus retesting alone accounted for about 1.1 standard deviations. Nickow, Oreopoulos and Quan (2020), in an NBER working paper, pooled 96 randomized trials of tutoring and found 0.37 SD, with reading tutoring strongest in the early grades. VanLehn (2011), in Educational Psychologist, found that software which checks each step of a solution came close to human tutors, at d ≈ 0.76 against 0.79, while software that only marks the final answer managed 0.31. One caution from the research summary this post draws on: which bucket the 0.76 belongs to should be verified against VanLehn's paper itself.

Kraft (2020), also in Educational Researcher, offers the scale to read these by: most education RCTs land below 0.10, and 0.20 on a standardized test is large for anything delivered at scale. By that scale, 0.3 from tutoring is a big deal, and two sigma was never on the table.

The zone of proximal development, in one sentence

Vygotsky (1978), in Mind in Society, called the gap between what a child can do alone and what they can do with help the zone of proximal development. Knowledge Space Theory, the mathematics behind ALEKS, makes the same idea formal: Doignon and Falmagne's "outer fringe" of a knowledge state is the set of things the learner is ready to learn next. In adaptive practice the zone is wherever the chance of a right answer sits around 75% to 85%. That is what the targets above are approximating.

How Peabody builds a round

AI writes the stories; code decides the rest. The practice brain in Peabody is ordinary code, and a round, called a deck, is built like this.

1. About 30 questions, about 85% of them items the child already knows. Most answers should be wins.
2. Due reviews come first. A known item comes back for review on a growing schedule, and anything due is asked before anything new.
3. Then the items still being learned, the ones answered right only with a hint, or right after a miss.
4. Then at most two new items per deck, and no more than four new per day in each subject. Each new item is taught before it is asked, then rehearsed a few questions later. New items never have a timer.
5. A miss comes back three questions later. Not at the end of the round, when it would be forgotten, and not immediately, when it would be copied.
6. A probe card about once every 40 answers. It measures only and moves no level.

Two rules keep the round from tipping into frustration. If the child misses two of the last five questions, no more new items are added this round. If they miss three, the game is told to ease. Wrong answers cost tempo, never a life, and the pay is a point for a first-try unhinted right answer, a quarter after a miss or hint, nothing for a wrong one.

A child who is cruising, with everything seen already solid, gets the next six items in order as stretch items without a lesson. A thin deck climbs until the child misses, which works as placement. A child with more than two items in the learning pile gets no stretch at all.

Every answer is three big boxes with near-miss distractors, and when the word is the answer Peabody says it rather than printing it above the boxes.

What this does not show

• 85% is a default, not a measured optimum. Nobody has run the experiment that finds the best share of known items for a five-year-old tapping boxes. The number is chosen because the modeling result, the Math Garden target and the guessing correction all land in the same neighborhood.
• Wilson's rule is about one kind of learner on one kind of task. Applying it to a child learning that 7 + 8 = 15 is an analogy, and the authors said so.
• Peabody has not been tested in a trial. The rules above are inspectable and the research numbers belong to the studies that produced them. Nothing here is a claim about what Peabody does to a child's scores.
• Performance during practice is a poor guide to learning. Bjork and Bjork (2011) call the conditions that feel harder but teach more "desirable difficulties". A round that is 85% wins is easy on purpose, so Peabody also spaces reviews across days and keeps a few items hard.
• Peabody counts; it does not fit a model. A rung is passed on counts and shares (80% of what was seen solid), not on an Elo rating. That is simpler to read and cruder than Math Garden.

What a parent can do

Watch for the two bad ends. If every answer is a win and your child is bored, the deck needs new items; Peabody will offer stretch items on its own, but a word from you helps. If more than one in four answers is a miss, step the level down rather than the pressure up. The grown-up view shows which items are known, learning or missed, and which books ran too easy or too hard, in plain words with no scores for the child. Start free and the first round will show you the shape of it.

Learn more elsewhere

• Bjork and Bjork on desirable difficulties: the researchers who coined the term explain why harder practice often works better.
• NSW CESE: cognitive load theory: the clearest free explainer of why the right help depends on what a learner already knows.
• The Learning Scientists: free posters and bookmarks on six study strategies, from cognitive psychologists.

For about seventy more, checked and sorted by who they're for, see where to learn about AI.

Questions parents ask

Is the 85% rule a real finding?

Yes, with a narrow scope. Wilson and colleagues (2019) showed that for simple learning algorithms on two-choice tasks, learning is fastest at about 85% accuracy. It has not been measured in children, and the authors did not present it as a classroom rule.

Why not make practice harder so my child learns more?

Because a child who fails half the time stops. Math Garden, which has run the question with real children, targets 75% success for that reason. Difficulty that a child cannot overcome is not a desirable difficulty.

Does Peabody ever push beyond the 85%?

Yes. A child whose seen items are all solid gets six untaught stretch items in order, and a thin deck climbs until the child misses. A struggling child gets no stretch. The share is a default that bends with the last few answers, not a fixed quota.

Does Bloom's two sigma mean tutoring software is worthless?

No. It means the famous number was too big. Pooled randomized trials of tutoring land around 0.3 standard deviations, which is large on Kraft's (2020) scale, and VanLehn (2011) found step-by-step tutoring software close to human tutors in the studies he reviewed.