A Learning World
How to play
- Pick a world from the front page:
- The Orchard Below the Wall: the first build. Separate stations along a road (a bridge, a counting gate, a thrown stone, a locked door).
- The Long Vale: one skill built up in chapters. Each chapter ends at a gate you open by using its idea.
- The Ways: one problem, three paths. Described below.
- Click the view to look around · W A S D to walk · arrow keys also look.
- E interacts with whatever you are looking at · Enter submits an answer.
- N toggles night · Tab shows the design notes behind each station.
- The warp menu (top bar) jumps between areas. It exists for testing and is marked in the log.
- Answers are checked by computation at runtime, not against stored answer keys. A record of your actions stays in your browser; the Log button downloads it, and nothing is sent anywhere.
- Most on-screen text is placeholder wording. The mathematics is exact.
An example: designing a component as a tool for thought
Tools for thought are simple mechanisms built on something known about how people learn, packaged so they can be reused. Spaced repetition is the familiar one: it takes a single finding, that memory fades on a schedule and that review timed to that schedule strengthens it, and turns it into a tool (cards plus a scheduler) that works for any content. The Ways is an attempt at the same kind of tool for a different target: not remembering, but diagnosing and repairing understanding inside a multi-step skill.
The design, concretely:
- The problem: factor 2x² + 7x + 6. It is chosen because the leading coefficient forces the general rule: find two numbers that multiply to a·c and add to b. Students often only half-know it.
- The choice: at a trailhead, three paths, each marked with a rule for the two numbers: multiply to 12, add to 7 (correct; it uses a·c); multiply to 6, add to 7 (the a = 1 habit carried over); multiply to 7, add to 6 (the two roles swapped). The wrong rules are not random distractors. Each is a documented, common misunderstanding, so the choice itself reports what the student currently thinks.
- The consequence: choosing a path means walking into it, and each path plays the chosen rule out honestly. On the a = 1 path the rule keeps working: a pair exists, and the split of 7x checks out. It fails only at the grouping step, where the parentheses refuse to match. That is exactly where this misconception actually breaks, and the student watches it break instead of being told.
- The repair: minimal by design. A quick a = 1 problem confirms what the student does know. One connection is made: the product target was a·c all along; with a = 1 it merely looked like c. Then the original problem is asked again. The path leads back to the trailhead, and the re-choice, not the repair, is the real test.
- The record: every choice, answer, and timing is logged: which path was taken, how long the decision took, whether the repair carried back to the original problem.
The pattern (wrong options designed to diagnose, consequences that appear where the misunderstanding really breaks, a minimal repair, a return to the choice) does not depend on 3D or on games. The same component could run as a worksheet, a branched video, or a conversation. The world version adds one thing: the structure of the solution becomes a space you move through, and remember as a place.
Memory: the carvings
When you answer a station correctly, its stone is carved: an inscription appears beside it with one more piece of insight about the idea. The reward for being right is more information. A reader who already knew it confirms their understanding; a reader who did not gets the idea stated once, plainly, at the moment they earned it.
Every carving is also written to a memory kept in your browser (nothing is sent anywhere). Carvings fade: strength drops over minutes for now, a placeholder schedule until the real model, tuned by difficulty and performance, replaces it. A faded carving clouds to dots and withholds its insight until it is read again. Reading a carving restores it and counts as a review. Fading never locks anything; it clouds assistance and nothing else.
The Carvings button in any world opens the Still Place: a quiet ring where everything you have carved stands as a stone, whichever world it came from. Reading a stone there is the same review. Fading plus review is the raw mechanism of spaced repetition; here it lives as a place you visit rather than a card queue.
Other components here follow other findings the same way: practice stations for revision, and honest instruments whose readings degrade when a skill fades. Spaced repetition, worked examples, retrieval practice: the aim is a shelf of such mechanisms, each small, each grounded, each reusable across content.