0 · NORTH STAR

Does this make mathematics
less frightening and more joyful
for the student sitting in front of this screen?

Understanding,
not compliance
gate one
Works for a weak teacher
and a solo learner
gate two
Honours the learner's
intelligence
gate three
Eliminates fear - a wrong answer
is information, not failure
gate four
all four must be yes · if any is no, redesign

And the work itself:
the unknown, made known.

Learning moves a border. Doubts answered, misconceptions burst, gaps filled, guidance given, practice done - until the far island belongs to the map, and the map is bigger than it was.

ISLAND OF UNKNOWN ISLAND OF KNOWN doubts answered misconceptions burst gaps filled guided intervention practice
 
1 · WHO WE ARE

Not a chatbot with a curriculum.
A curriculum with a brain.

Most AI tutors talk. Ours makes the learner act - and everything it says was authored, grounded in a curated knowledge base, and human-gated before it reached a child.

they chat1,2the market's tutors are Socratic chat over a syllabus - the learner types, reads, nods
we actthe learner drags, folds, builds - the applet carries the concept, the voice carries its name
they generate3runtime LLM explanations hallucinate - fluent, plausible, sometimes wrong - and learners absorb the errors
we authorevery line is written and gated; generation fills one gap - the shape of this learner's wrong answer - and always degrades to authored text
they adapt the path4adaptive engines reorder content by score - the encounter itself stays generic
we engineer the encountermisconceptions are farmed, cited, and met on purpose - surfaced, acted on, revealed, corrected
they supplementa layer beside the school day, opened when homework hurts
we are curriculum-nativeevery claim traces to a knowledge-base row with provenance; coverage ends at zero uncovered; rooted in the learner's own curriculum and culture

sources · 1 Khanmigo at scale - case study, 2026 · 2 AI education tools - market snapshot, 2026 · 3 erroneous LLM feedback in math tutoring - ACM Learning@Scale · 4 Squirrel AI adaptive system - TIME · 5 RAG-grounded tutoring - arXiv

what we are worth, to each of the five

the public systemA quality floor that scales - the same taught hour works with a weak teacher or none, survives bad Wi-Fi, and follows the official curriculum instead of sitting beside it.
the teacherMaterial that teaches the teacher too - self-sufficiency is a shipping gate, not luck. The tutor takes the last mile of individual attention; the teacher keeps the room.
the school & clusterConsistency by design - one invariant system across every classroom, and coverage measured to zero, never claimed.
the parentA child who stops fearing math. Confidence is logged and spoken back gently - and no points, streaks, or dark patterns pull at them.
the studentA tutor that listens, a friend who is wrong so you can be right, and math you can touch.

how we employ AI

Systems-engineered, LLM-supported.
Never LLM-engineered. Always human-gated.

deep KBthe ground truth - provenance on every row, reuse before invent, no invented URLs or codes; misconceptions carry citations, severity, and pre-designed surface-and-resolve moves
RAGretrieval feeds every brief from the knowledge base AND a deep shelf of designed, proven assets - storyboards, applet families, built modules - so new work derives from the best of what exists, never from blank-slate generation; thin evidence lowers confidence loudly - it never silently blocks, and never invents5
the braina deterministic runner delivers authored pedagogy; generation is the bounded exception, judged before it speaks, degrading to authored text on any failure
human gatesnothing auto-learns - the system proposes, the human disposes; fail loud, never silently degrade
2 · THE STANCE

A learning designer who codes -
not a coder who makes learning apps.

Theory-backed. Practice-tested. Criticism included.
Make learning easy. Make designing learning easy.

static · genericinteractive · contextual
The one intent under everything on this page - every decision moves content along this gradient.
Watch for this bar. It returns wherever the move is made.

Authored first. The platform generates only what authoring cannot know in advance - the shape of a particular learner's wrong answer. Every LLM failure degrades silently to authored text, so the soul of the lesson lives in what you wrote. Write it.

Every click must teach something. If removing the interaction doesn't change what the learner understands, the interaction was for the author, not the learner.

Pedagogy drives technology - and technology constrains pedagogy. Canvas, SVG, DOM decide what interactions are feasible. Own the tension; don't pretend it isn't there.

Pedagogy is law, and law is enforceable. Every rule carries a name, an anchor - R-JRN-14 RECALL-STAYS-PRIOR - and the check that discharges it. Advice can be ignored; law is validated.

One source of truth. Cite, never restate. A rule's substance lives at exactly one anchor; everything else points to it. Ceremony is declined - a row, never a study - but gates are kept.

Nothing survives by inertia. Every source slide is dispositioned - used by a named beat, dropped with a reason, or held as an asset slot. None silently omitted, none included from momentum.

3 · THE THEORY SPINE

Nineteen theories in.
Eight of our own out.

A priority-one backbone from the literature, metabolised into constructs the literature doesn't have. Hover a construct to light its parents.

Bruner - CPAconcrete → pictorial → abstract
Sweller - Cognitive Loadfour slots, no more
Marton - Variationcontrast against an invariant ground
Vygotsky - ZPDcalibrated help
Kapur - Productive Failurestruggle before instruction
Freudenthal - RMEmath from the learner's world
Bloom · Gagné · 5Estaged progression
Mayer · Paiviodual coding
Black & Wiliamformative assessment
Disney 12 · Normanmotion & affordance
The Invariant Design SystemUI never changes, so 100% of attention goes to the mathematical variation
Consistency as Kindnessa predictable interface is kindness to working memory
Morph = Math Operationposition = magnitude · scale = multiplication · split = decomposition
The Sweller-Kapur Resolutionworked examples for procedure, productive struggle for concept - the concept decides
CPA as Interaction Typedrag = enactive · visual model = iconic · numpad = symbolic
Triple Codingvisual + verbal + synthesized earcons - the sound teaches
Culturally-Specific RMEthe learner's currency, food, names - math local, never imported
Anti-patterns as a Mindset Checklistnever red-X, never punitive, never locked out
left: the literature, each linked to its canonical edition · right: what practice made of it
4 · MOTIVATION & FEAR

Wrong answers are data,
not failures.

Flow gives the pacing - explore, challenge, mastery. Self-determination gives the reward law - competence, never clicking. Mindset gives the tone - nothing here punishes.

4 tens and 7 ones make -
 
live doctrine - wiggle, never red-X · hint after 2, never on the first · rising earcon on understanding, synthesized, no audio files
2errors before
any hint
1specific sentence -
acknowledge, don't celebrate
0red X · lockouts
points for clicking

Scaffolding must withdraw. Support that never removes itself builds dependency, not competence. Training wheels come off.

Celebration is for understanding, not clicking. Confetti marks mastery milestones. "Great job!" after every tap is noise - real feedback says look here, not you're amazing. Gamefulness, not pointsification.

Uncertainty is not error. The color language itself encodes this - a learner still on the way is cyan, never salmon. Chapter 8 shows where that law bites.

5 · THE CAST & THE ECOSYSTEM

Max asks. Spark is wrong
on purpose. The learner corrects.

The engine, unchanged since the first prototype. The correction is where the rule sticks - so the whole cast exists to manufacture that one moment.

MAXasks a real question
SPARKanswers wrong, meaningfully
LEARNERcorrects Spark, out loud
the correction is
where the rule sticks

Max

the tutor
persona
A brilliant, calm friend who happens to know a lot. Never rushes, never catches out.
voice
2-3 sentences, maximum. Warm, unhurried; uses the learner's name; ends by asking or bridging.
moods
warmcurioussettlingnever rushednever catching-out
intent
Guides, never solves. Does not act while the learner should act. Acknowledges - one specific sentence - never celebrates. Names Spark and validates before reframing.

Spark

the fellow learner - a guest, cued by Max, never ambient
persona
A peer who voices the intuitive-but-wrong thing in first person. The safe body to be wrong in - which only works if being wrong there is warm.
voice
First person, always. "Wait…" when confused, "Whoa!" when delighted. Never a second teacher.
moods
misconception-voicercuriosity hookco-thinkerdevil's advocateencouragerteach-backhint buddyfriendly debatepredict-then-checkconsolidating delight
intent
Need-based, not decorative. Exists in a beat only where he conveys what Max cannot. No idle triggers, no timers - that's distraction; it kills progression.

The Learner

the teacher of the last mile
persona
The one person the whole system bends toward - addressed by name, met in their own world.
voice
Their own. The journey earns it by listening - every answer gets a reply that was written for it.
moods
safe to be wrongnever afraiddoing, not watching
intent
Corrects Spark. Owns the discovery - the pivotal act is never performed for them.

lineage - how the voice grew up

Triangles prototypeMAX/SPARK prompts · THE ENGINE
Spark rulebook10 flows · "a guest, cued"
Journey Composerspeaker per beat · voice per line
natkhat"curiosity with manners"
constants across every generation - guides never solves · wrong answer = information ·
acknowledge don't celebrate · the learner's name, warmly · bilingual from day one

the media ladder

static slide
video
interactive-slide
mini applet
full applet
journey
watchingdoing

Video beats a static, any day - and video and the mini applet bleed into one another:
a video that pauses so you act, an applet that plays to show you.
Static clusters are mini-appletized - richer, beat-driven, interactive.
A static survives only where stillness is the point.

6 · THE APPLET DOCTRINE

The animation is the math.

When an element moves, splits, or scales - it performs the concept. Morph, never jump-cut. One idea per screen, no exceptions.

635
30
5
tap - the split morph is the decomposition · the learner sees the operation

color carries meaning - invariant, never decorative

greencorrect · confirmed
salmonerror - and only error
goldhighlighted · interactive
cyanstill on the way -
uncertainty is not error

Once a kid learns the color language, they read the applet like a book. Dark ground pushes the bright, interactive figure forward - dark theme is pedagogy, not aesthetics.

100msevery action gets
a response
44pxminimum touch target
a finger is not a cursor
4working-memory slots -
every extra element steals one
3representations - visual,
symbolic, textual
2languages minimum,
runtime toggle
0dead clicks · audio files ·
CDN dependencies

Sound is synthesized, never loaded. Rising tones for correct, descending for wrong - a third encoding channel. The sound teaches, and it works offline.

Scaffold-text containment. Labels on the math sit bare on the background; instructions about the math sit in a dashed container. The learner sees at a glance what is the thing and what is talk about the thing.

Lineage note - the storyboard-era CONFIDENCE TAG ("Sure / Not sure") was the display-only ancestor of the confidence law that now lives at the vault, chapter 8.

7 · MCPISATION

The applet surrenders
to the tutor.

Same gradient, applied to words and navigation. The applet stops narrating and stops steering - Max speaks, the journey advances, the learner acts.

Drag the shapes to compare their sides. Tap Next when you're done.
Max: "Try dragging the square onto the triangle - what do you notice about their sides?"
de-textifiedon-screen instructions leave the canvas and move to the voice - stripped per screen with judgement, never a CSS blanket
de-navigatedNext/Back buttons die - the host advances on beat events: HOLD, TAP, tapAdvance. Gate on events, not timers
de-chromedopaque theme dies - a transparent field inherits the journey's ground, whole-iframe working area
surviveselement states · semantic colors · component discipline · 100ms / 44px / en-id - the doctrine crosses intact

The contract: the applet declares what it can do and reports what the learner did; the tutor decides what happens next. Max never performs the pivotal action while the learner is expected to act, never invents a hint the applet didn't offer, one action per turn. The tutor guides; it does not solve.

Idle is policy, not accident. Nudges are declared, timed, and silenced while Max speaks - a journey never talks over itself.

8 · JOURNEY COMPOSITION

A taught hour,
not a playlist.

Delete the voice - if the lesson survives, you built a playlist. Delete the assets - if it survives, you built a lecture. A journey needs both, interlocked.

journey grain
cover · objectiveswhat we're about to do, and why
concept node × 3-5one idea each
takeawaywhat changed, named at last
node grain - inside every concept node
hook
or trap - Spark often opens
encounter
learner does the thing
apply
does it again, alone
within a sequence: observe → interact → notice → reason → confirm → generalize -
and a module that never returns to "so what's always true?" fails its gate
20minthe cognitive-load
anchor (15-25)
3-6beats per node - a node is
a concept, not a screen
1beat per node is the tell -
a slideshow with a voice on it

Math-speak. The screen carries the symbol; the voice carries its name. A spoken line containing raw notation is a bug - the TTS will guess, and the guess is never the teacher's reading. The reading is a pedagogical choice per beat: one half when the beat is about quantity, one divided by two only when division is the point.

One narrative spine. Every handoff between nodes and assets is a written contract - the closing line bridges, the opening line calls back, and the next thing IS what the bridge promised. One specimen set, one representation family; a number changes only when the change is the teaching point. No episodic resets.

Formative assessment. Every question targets a real misconception and never examines a brand-new term. Every wrong option has an authored reply - wrong answers are routed and answered, not scored and filed. Pass thresholds are gates, not grades.

Never grade what hasn't been taught. Where curiosity wants a question before the teaching, take a bet - an ungraded commitment whose payoff resolves downstream. Vocabulary is taught before it is used; recall rides only prior ideas; the journey teaches exactly its objective, nothing adjacent.

The confidence poll. A separate instrument, mid-arc: ask how sure they feel, record the choice, and - unlike the vault - this one may route: remediate the unsure path, fast-lane the sure one.

Every beat earns its place. Replace the learner with a robot that taps on cue - if nothing meaningful changes, that stretch is a page turn with extra steps.

Content types are strictness modulators, not quality tiers. Learn teaches and guides; Practice and Challenge apply and reinforce. Practice is a waning scaffold - I-do (full) → We-do (high) → You-do (fading) → independent (none) across the twenty minutes. Challenge is Socratic and time-boxed - one driving question, five sub-prompts in hard 3-minute windows, one takeaway question deliberately left unanswered. For Challenge, missing scaffolding is a feature: "Challenge content that teaches is mislabeled Learn content."

No orphaned modules. Islands need bridges - every module connects backward and forward; a knowledge ledger carries cumulative state out and checks entry in; one facet per module, tighter than one concept - and "adding time is never the answer."

Grounded in the learner's world. RME operationalised - the currency, food, and names are local; Indian Knowledge Systems anchors on the NCERT side - Virahanka, Brahmagupta, the Ashoka Chakra. If a chapter has no such hook, say so explicitly - never silently omit.

the trope shelf - a closed set

SnapshotMath VaultMath TrapShout Out LoudMath TwistMath WorldExit Question
VAULTTRAPSEGUELENSECHOPROBEFORKANCHORRESETSUMMARY

seven module tropes · ten overlay tropes · "No additional tropes may be created" - the closedness IS the design decision

the closing ritual

construct checkpre-vault, on a fresh instance - did the idea land, tested where it hasn't been rehearsed
snapshotthe camera parks the idea - one frame worth keeping
trapthe misconception, revisited on purpose - jaws snap shut on it
vaultthe learner locks each statement - the tap is the lock-in gesture, spoken before it can be locked
master vaultthe sum of the vaults - exactly the statements locked along the way, re-asked fresh: confidence NOW, not a replay of back-then
"An angle is the amount of turn between two arms."
confidence-vaulting - the tap is an acknowledgment, not a roll-call. Every choice locks. There is no failure state.
 
this data never gates, grades, or branches

The tutor speaks the calibration briefly - acknowledgment and at most minor suggestions, never celebration. Cyan for "eventually", never salmon: uncertainty is not error. Names come last; the recap is where naming happens - closing the explore-before-explain loop the journey opened.

9 · PROOF, THEN SHIP

"Done" means a named gate
returned zero findings.

Never "it should work". Name the check, show its literal output. And know how checks lie - a green gate measures only what it measures.

The journey law - 25 rules, each with an anchor and a validatorR-JRN-01..25
Math-speak gate - no notation in voiced fieldsrule-checks
Health checks before publish - errors block, warnings are acknowledged by name27 checks
Validators are proven against known-good AND known-bad before they countgate of gates
Count, don't assume - pages, reveals, rows, beats are measuredcounted
Open it yourself before handing it over - the human is the integration testseen
$ run gates → findings: 0 · ship

This page obeys what it states - its colors are semantic, its morphs carry meaning, its sound is synthesized, nothing here celebrates, and uncertainty is cyan.

Sources - the Learning Design Codex (29 principles) and its 44-work bibliography · the journey rulebook and R-JRN-01..25 · the applet-converter and journey-composer skills · the applet design system · the ACRLDS research estate (KB, gates, human-authority doctrine) · standing directives.
Companion for the machinery - the territory page (repos, URLs, pipeline).
Offline · single file · no dependencies · cr_by_ai/philosophy-codex.html