Polymath
Polymath
Method
Polymath is a practice for range across the arts and sciences. Each field has a skill tree, a mastery score, and a review date. The standard is visible. The schedule carries the review.
The mechanics below are ordinary findings in learning research. They are built into the sessions, not left as advice on a poster. The seed questions are written and checked. They are not generated.
You answer before you see an explanation. Roediger and Karpicke (2006) found that taking a test improved later recall more than restudying the same material. The attempt is the study. The explanation is what you get after you have tried to remember.
A skill comes back after a delay, and the delay grows when the day went well. Cepeda, Pashler, Vul, Wixted, and Rohrer (2006) reviewed the spacing effect: practice spread over time beats the same practice massed into one sitting, if what you care about is later recall.
The scheduler is SM-2, the SuperMemo 2 algorithm published by Wozniak (1990). A passing day sets the next gap to 1 day, then 6 days, then the previous gap multiplied by an ease factor. Ease starts at 2.5, moves with the quality of the day, and does not fall below 1.3. The interval for today is computed from the card as it stood this morning, so answering ten questions does not stack ten intervals. A weak day resets the count of successful reviews and brings the skill back tomorrow. A later model such as FSRS could replace the ease factor. This version stays with SM-2 because the steps are short enough to test.
Today mixes fields, and it will not place the same field twice in a row while another field is still in the set. Rohrer and Taylor (2007) found that shuffling problem types improved later test scores, even though practice felt less smooth. The mix is the desirable difficulty, not a decoration.
Each skill has a SmartScore from 0 to 100. It is not a percent correct. Correct answers add fewer points as the score climbs. Misses cost more near the top, and an easy miss costs more than a demanding one. Only demanding questions can finish the last stretch, so a run of easy items cannot reach 100. Bloom (1968) argued for mastery learning: stay with an objective until the performance is actually secure, and make that standard visible. Eighty is proficient here. One hundred is mastered.
IXL's SmartScore behaves this way in public descriptions. Their exact formula is not published. The table is the formula this app uses.
| Score | Emerging, correct | Demanding, correct | Emerging, miss |
|---|---|---|---|
| 0 | +12 | +20 | -3 |
| 50 | +7 | +13 | -6 |
| 90 | +1 | +5 | -12 |
| 98 | +0 | +1 | -14 |
The score cannot fall below 0 or rise above 100, so a miss at 0 changes nothing.
Spacing, interleaving, and retrieval feel slower than rereading. Bjork (1994) argued that these difficulties improve long-term learning when the learner can still succeed. The worked example is the other half of that idea: help is present while you are new, and it leaves as you get stronger.
Each skill opens with a fully worked example while the score is under 35. Sweller and Cooper (1985) showed that studying worked examples can beat unguided problem solving for novices in algebra. Renkl, Atkinson, Maier, and Staley (2002) showed that fading those examples into problems to solve supports the handoff. After 35, the example remains available, and it is no longer shown first.
Some items ask you why before they show the explanation. Pressley, Symons, McDaniel, Snyder, and Turnure (1988) found that answering "why" questions helped people learn confusing facts. Dunlosky and colleagues (2013), reviewing study techniques, rate elaborative interrogation as useful, and rate practice testing and distributed practice higher still. Practice testing and distributed practice carry the method. The why prompt is the additional step.
After a set, and on the Connections page, you link a concept in one field to a concept in another, in your own words. Gick and Holyoak (1983) showed that people carry a solution to a new problem more reliably when they have formed a schema across examples, rather than treating each case as a one-off. The note is stored on this device. The app does not grade the prose.
Game keeps an ability estimate for each field, and one estimate across all of them. A correct answer on a hard question raises the estimate more than a correct answer on an easy one. A miss on an easy question lowers it more than a miss on a hard one. The chance of a correct answer depends on the gap between your ability and the question's difficulty. That is a one-parameter Rasch model.
Points use the same gap. Before you answer, the number shown is what a correct answer is worth for you. A question above your estimate pays more. A question below it pays little. A wrong answer scores zero. Questions are chosen where the model expects you to succeed about two times in three, and they are mixed across fields.
A correct answer pays the coffer from those same points. A low stake pays brass coins. A moderate stake pays silver coins. A high stake pays a gold coin. Only a stake well above your estimate pays one stone, and each field has its own: lapis lazuli for mathematics, labradorite for physics, malachite for biology, carnelian for history, moonstone for philosophy, jade for economics, and obsidian for the arts. Ten brass coins exchange for one silver coin, and ten silver coins for one gold coin, when you pay. Stones are not exchangeable. They buy the premium pieces and the extra rooms, so a field you have not stretched shows up as a stone you do not yet have. The gold coin is the metal. A gold trophy still means a field is mastered.
Placement is optional: two or three questions in each field, harder after a correct answer and easier after a miss. Answers in ordinary practice move the same estimates and the same coffer.
These are the works the mechanics rest on. Nothing in the list was invented for this page.