# The Spoken Method — Formalized

## Core Thesis
**Understanding = ability to speak about something fluently.** If you can't say it, you don't know it. The method builds verbal fluency around concepts through structured repetition across escalating levels of ownership.

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## The Learning Cycle (per concept)

### 1. PRESENT
Show the thing. Give the learner the explanation in clear, annotated form. They absorb passively. This is the "here's how it works" moment.

### 2. REHEARSE
The learner speaks the explanation back. Not from memory yet — they can see it. The goal is to get the words in their mouth. The app transcribes what they say. They're practicing the *shape* of the explanation.

### 3. HARMONIZE
Test comprehension through choice. Multiple choice, but spoken — the learner says which answer is correct. If wrong:
- Don't give the answer. Ask *why* the wrong answer is wrong.
- Scaffold back: targeted follow-up question about the specific misconception.
- Return to the original question. Let them try again with new understanding.
- Loop until correct.

### 4. RESTATE
"Change octaves." Say the same thing a different way. This is the ownership test. The learner must reformulate — not repeat, not recognize, but *generate* their own version. Multiple valid framings can exist.

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## Structural Principles

### A. Decomposition
Every complex topic breaks into atomic concepts. You never tackle the whole thing at once. Each atom gets its own Present → Rehearse → Harmonize → Restate cycle.

### B. Recombination
After mastering atoms individually, there's a "Full Review" that stitches them back together. The learner must speak about the whole thing — all atoms connected.

### C. Cross-referencing
The same concept appears across multiple problems/contexts. The learner can navigate by concept across contexts, building generalized understanding rather than context-locked knowledge.

### D. Variation ("What If")
Change a parameter. What happens? This tests whether understanding is mechanical (memorized steps) or conceptual (can reason about changes).

### E. Creation
The capstone: learner creates their own example and explains it. This is the highest proof of ownership.

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## The Progression Ladder

```
Absorb → Repeat → Recognize → Reformulate → Transfer → Create
(Present)  (Rehearse) (Harmonize)  (Restate)    (What If)  (Create Your Own)
```

Each rung requires more cognitive ownership than the last. The method doesn't let you skip rungs.

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## Content Structure (3 Levels)

### Level 1: Map
A master class contains 5-6 problems/scenarios. Each is the same core challenge but with different configurations — different setups that change parameters while preserving the underlying concept.

### Level 2: Problem
Each problem decomposes into concept nodes (e.g., Friction, Torque, Acceleration). These form a learning path — a node graph. Each node isolates one concept within that problem's context. Culminates in "Full Review" (all atoms reconnected) and "Create Your Own" (capstone).

### Level 3: Interaction
Inside each concept node, the full learning cycle runs: Present → Rehearse → Harmonize → Restate.

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## Navigation Architecture

### Vertical Axis (Problem-centric)
Sequential problem-by-problem with expandable sub-topics. Hierarchical tree: Problem → Concept → Learning Mode (Rehearse/Harmonize/Restate).

### Horizontal Axis (Concept-centric)
Cross-problem topic filtering. Click a concept label → see that concept across ALL problems. Navigate laterally to build generalized understanding.

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*Origin: Physics teaching app (Mechanics). Designed for domain-agnostic application.*
*Formalized: 2026-03-11*