✦ Self-Study Module — Architecture

Three layers: what we know, what we can show, and how we decide what's next.

1
Data
The subject and the student

Subject Knowledge Graph

Atomic skills, prerequisites, tiers. One graph per topic. Each skill has lessons (1–3 variants), questions, prediction prompts.

DSE14 Trigonometry — 14 skills
sin
📈
⛓
θ
c²
∿
N
✓
3D
=0
⊥
△
∠
c³
DSE17 Dispersion — 8 skills
x̄
▭
+c
×k
z
μ
?
z₁z₂

Student Model

Per-student, per-topic. Accumulates signals from every interaction. Drives what happens next.

Tracked signals
Skill mastery
ciPre / ciPost
guessRate
ciCalibration
avgTimeOnTeach
avgSessionLen
interactionPref
bounceRate
Teacher overrides
forceTeach
difficultyCeiling
notes
flagCI
→ feeds into →
2
Card Library
12 templates — building blocks of every session
Navigation Learning Assessment Reflection
Topic Select
Navigation
Topic Intro
Navigation
Skill Tree
Navigation
Skill Intro
Navigation
3
Teach
Learning · 3 stages
Returning Student
Learning
?
Question
Assessment · 3-level
Skill Unlocked
Assessment
✓
Topic Complete
Assessment
Milestone
Reflection
Check-in
Reflection
Summary
Reflection
→ selected by →
3
Serving Algorithm
Recommendation engine for learning
Observe

Confidence, accuracy, time, guessing

→
Decide

Which card, skill, variant, format

→
Serve

Render the right card

→
Update

Write back to Student Model

Confident but wrong → route to Teach immediately
High guessRate → more reason-why prompts
Skips teach fast → shorter lessons, jump to practice
Bouncing early → shorter sessions, more milestones
Teacher override → forceTeach, difficulty ceiling
Cold start → defaults, adapt after session 2
Good calibration → trust confidence slider
Prerequisite fail → fallback to skill intro or AI chat
Essai Math · Self-Study Module · Architecture v1 · March 2026 Prepared by Eric San