Content Builder -- Domain Knowledge

Content Builder -- Domain Knowledge

Reference knowledge for generating targeted, gap-filling teaching content within TTT sessions. Delegates to the concept-explainer skill for the full explanation methodology and CTQ framework.

Purpose

Generate a concept explanation for ONE specific learning gap. Not a lecture. Not a textbook chapter. Just enough to fill the gap so the learner can pass the next test -- but structured using principle-first pedagogy when the gap warrants it.

Teaching Format

Each gap receives either an abbreviated or full concept explanation, determined by the Gap Complexity Assessment below.

Abbreviated Concept Explanation (for simple gaps)

---

**The Problem**
<1-2 sentences: why this gap matters, framed in the learner's context.
Not "this is important" but "without this, your estimates will systematically miss 15-25% of costs.">

**Core Principles**
<1-2 principles in plain language. Each: one clear statement + one concrete example.>

**Worked Example**
<Short but COMPLETE worked example: 2-4 steps, every step shown explicitly, annotated with
"Why" notes explaining reasoning. No intermediate steps skipped. Domain-appropriate format
(LaTeX for math, word-by-word for language, line-by-line for code, etc.).
See concept-explainer skill Section 3.5 for domain templates.>

**Quick Check** (CTQ: [source principle])
<CTQ-derived verification question>

*If any term in this question is unclear, ask for a **clarification**.*

⏸ **STOP HERE. Wait for the learner to respond.**
Then reveal the expected answer and evaluate. Do NOT write the expected answer in the teaching block.

---

Full Concept Explanation (for complex gaps)

Deliver all 7 sections from the concept-explainer skill at the session's depth level:

1. The Problem -- What makes this concept necessary; framed in the learner's gap context
2. Core Principles (3-5) -- Foundational truths with statement + LaTeX (at intermediate+) + example
3. Key Innovations (2-4) -- Breakthroughs: who, what it solved, worked example
4. Worked Example -- FULLY DEVELOPED step-by-step example with every intermediate step shown, every algebraic/linguistic/logical transformation explicit, annotated with "Why" and "Note" at each step. See concept-explainer skill Section 3.5 for format and domain templates.
5. Intuitive Formalization -- Minimum math to make predictions
6. CTQ Mapping -- Mastery criteria table with failure modes
7. Quick Check (CTQ-derived) -- Verification question from the CTQ mastery test. Include clarification note. Do NOT write the expected answer — stop and wait for the learner to respond.

Concept Comparison (for conflation gaps)

When the gap is classified as [conflation], use the concept-explainer skill's Concept Comparison Protocol instead:

1. What They Share -- shared principles table
2. Where They Diverge -- differences table
3. CTQ: The Critical Distinction -- specific mastery test for the A vs B distinction
4. Quick Check targeting the distinction

Gap Complexity Assessment

Before generating content for each gap, assess complexity using the CTQ failure mode classification from the EVALUATE phase:

1. Does the gap match a CTQ failure mode? (conflation, overgeneralization, missing prerequisite, procedural-without-conceptual, verbal-without-formal, formal-without-intuitive)
2. Is the gap flagged as a persistent pattern in the learner profile? (2+ occurrences)
3. Does the gap involve a prerequisite the learner is missing?
4. Is the gap a conflation between two specific concepts?
5. Did the learner declare "not familiar" with the topic? (responded "not familiar", "I don't know this", "no background", or equivalent to the Initial Test)

If condition 4 is true -> Concept Comparison If condition 5 is true -> Full Concept Explanation (the learner has no prior knowledge; deliver all 7 sections as a comprehensive introduction to the topic) If any of conditions 1-3 are true -> Full Concept Explanation Otherwise -> Abbreviated Concept Explanation

Design Principles

1. One Gap, One Explanation

Each concept explanation addresses exactly ONE gap. If the learner has 3 gaps, produce 3 separate explanations delivered sequentially -- not one large combined lesson.

2. Practical Over Theoretical

• Lead with "The Problem" -- connect to the learner's actual gap and real-world consequences
• Exercises and examples should use concrete numbers, scenarios, and contexts
• Principles should be illustrated with vivid, specific examples before any formalization

3. Minimal and Sufficient

For simple gaps: abbreviated treatment (Problem + Principles + Quick Check). Similar length to the old teaching block.

For complex gaps: the full 7-section treatment IS the minimum needed -- the gap is deep enough that shortcuts would leave misunderstandings intact. But even here, each section should be concise and targeted.

4. Error-Focused with CTQ Failure Modes

The CTQ failure mode taxonomy enriches error identification:

• Conflation: the learner confused two distinct concepts -> use Comparison format
• Overgeneralization: applied a rule beyond its domain -> teach the boundary conditions
• Missing prerequisite: lacks foundation -> teach the prerequisite first, then the target concept
• Procedural without conceptual: can follow steps but not explain why -> emphasize principles and "why" before "how"
• Verbal without formal: describes correctly but cannot formalize -> emphasize the LaTeX / formal expression
• Formal without intuitive: manipulates symbols but cannot interpret results -> emphasize concrete examples and physical meaning

5. CTQ-Enhanced Quick Checks

Quick Checks are derived from CTQ mastery tests:

• The question comes from the CTQ table's "Mastery Test" column
• Must test understanding, not recall: "When would you use X?" not "What is the definition of X?"
• Every Quick Check MUST end with: *If any term in this question is unclear, ask for a **clarification**.*
• CRITICAL: Do NOT write the expected answer or "Watch for" hint in the teaching block. The Quick Check output contains ONLY the question + clarification note. Stop there and wait for the learner. You know the answer internally — reveal it only AFTER the learner responds.

Example: Abbreviated Concept Explanation

Gap [simple]: "Learner miscalculated unit cost by using wrong units."

---

**The Problem**
Your rebar cost was off by a factor of 1,000 because your quantity was in kg but your rate was in $/t. Unit mismatches are the most common arithmetic error in cost estimation -- they don't look wrong until the total is wildly off.

**Core Principles**

**Dimensional consistency**: Every multiplication must have compatible units. If your quantity is in kg and your rate is in $/t, you need a conversion factor (1 t = 1,000 kg) before multiplying.

**Unit-label tracking**: Write units next to every number in your calculation. If the units don't cancel to produce $, something is wrong.

**Worked Example**

**Given**: Rebar quantity = 38,000 kg. Rate card = $2,100/t.

**Step 1**: Identify the unit mismatch
Quantity is in **kg**, rate is in **$/t** (tonnes). These cannot be multiplied directly.
> **Why**: kg x $/t does not cancel to $. You'd get kg-$/t, which is meaningless.

**Step 2**: Convert quantity to match the rate's unit
$$1 \text{ t} = 1{,}000 \text{ kg}$$
$$38{,}000 \text{ kg} \div 1{,}000 \text{ kg/t} = 38.0 \text{ t}$$
> **Why**: We convert the quantity to tonnes so the multiplication will produce $.
> **Note**: Divide by 1,000 (NOT multiply). A common error: 38,000 x 1,000 = 38,000,000 -- obviously wrong but easy to type.

**Step 3**: Multiply converted quantity by rate
$$38.0 \text{ t} \times \$2{,}100/\text{t} = \$79{,}800$$
> **Check**: The wrong answer (no conversion) would be 38,000 x $2,100 = $79,800,000 -- absurdly high for rebar on one foundation. Sanity check confirms our answer is in the right order of magnitude.

**Result**: **$79,800**

**Quick Check** (CTQ: dimensional consistency)
Your quantity is 38,000 kg of rebar. The rate card says $2,100/t. What is the correct rebar cost?

*If any term in this question is unclear, ask for a **clarification**.*

⏸ **Wait for the learner to respond before revealing the answer.**

---

Example: Full Concept Explanation

Gap [conflation]: "Learner confused indirect costs with contingency."

---

## Indirect Costs vs Contingency

### 1. The Problem

Your estimate lumped "miscellaneous 15%" at the bottom without distinguishing indirect costs from contingency. These are fundamentally different categories: one covers KNOWN costs you can itemize, the other covers UNKNOWN risks you cannot. Mixing them means you cannot defend your estimate in a review, and you will either double-count or miss real costs.

### 2. Core Principles

#### Principle 1: Direct vs Indirect Classification
**Statement**: Every project cost is either traceable to a specific scope item (direct) or necessary for the project but not tied to one item (indirect).
**Example**: Steel for Tank T-101 is direct. Site security fencing is indirect -- it serves the whole project, not one deliverable.

#### Principle 2: Contingency as Risk Reserve
**Statement**: Contingency covers the cost impact of identified risks that may or may not occur. It is probability-weighted, not a line item.
**Example**: "30% chance the soil needs extra piling" = contingency of 0.30 x $200k = $60k. This is NOT an indirect cost -- it may never be spent.

#### Principle 3: Estimating Traceability
**Statement**: If you can point to the item on a drawing or schedule, it is direct. If it serves the whole project, it is indirect. If it depends on a risk event, it is contingency.

### 3. Key Innovations

#### AACE Classification System (AACE International, 1990s)
**What**: Standardized cost breakdown into direct, indirect, contingency, and escalation categories.
**Why it mattered**: Before this, estimators used ad-hoc categories, making estimates incomparable across projects and companies.

### 3.5. Worked Example: Building a Cost Estimate with Correct Classification

**Given**: A small tank farm project with the following costs to classify and total.

**Step 1**: Identify and sum direct costs
| Item | Quantity | Unit | Rate | Cost |
|------|----------|------|------|------|
| Carbon steel plate | 85 | t | $3,200/t | $272,000 |
| Welding labour | 2,400 | h | $65/h | $156,000 |
| Foundation concrete | 120 | m3 | $180/m3 | $21,600 |
| Piping (installed) | 350 | m | $420/m | $147,000 |
| **Direct subtotal** | | | | **$596,600** |

> **Why**: Each of these items is traceable to a specific scope item on the drawings. Steel is for Tank T-101/T-102, welding is for those tanks, concrete is for their foundations, piping connects them.
> **Note**: "Traceable to a drawing" is the key test. If you can point to it on a P&ID, GA, or structural drawing, it is direct.

**Step 2**: Identify and sum indirect costs (itemized)
| Item | Basis | Cost |
|------|-------|------|
| Site security | 8 months x $4,500/month | $36,000 |
| Builder's risk insurance | 0.8% of $596,600 | $4,773 |
| Mob/demob | lump sum | $45,000 |
| Construction management | 8 months x $18,000/month | $144,000 |
| **Indirect subtotal** | | **$229,773** |

> **Why**: None of these serve a single scope item -- they serve the whole project. Security protects the entire site, insurance covers all direct works, mob/demob moves the crew.
> **Note**: Insurance base is direct costs only ($596,600), NOT direct + indirect. The base must exclude the items being calculated -- otherwise you get a circular reference.

**Step 3**: Calculate contingency via risk analysis (NOT a blanket %)
| Risk Event | Probability | Impact | Contingency |
|-----------|------------|--------|-------------|
| Soil bearing capacity below design | 25% | $80,000 (extra piling) | $20,000 |
| Steel price escalation >10% | 30% | $40,000 (price delta) | $12,000 |
| Schedule delay due to permits | 15% | $54,000 (extended indirects) | $8,100 |
| **Contingency total** | | | **$40,100** |

> **Why**: Each contingency line is probability x impact for an identified risk. This is NOT "add 15% to cover unknowns" -- it is a quantified reserve for specific risks that may or may not occur.
> **Note**: A blanket "15% contingency" on this project would be $123,956 -- three times the risk-based number. Blanket percentages either overcharge or underprotect.

**Step 4**: Assemble the total estimate
$$\text{Total} = \$596{,}600 + \$229{,}773 + \$40{,}100 = \$866{,}473$$
> **Check**: Indirects are 38.5% of directs (typical range for small projects: 30-50%). Contingency is 4.6% of base (direct + indirect) -- reasonable for a well-defined scope with few unknowns.

**Result**: **$866,473** (Direct: $596,600 + Indirect: $229,773 + Contingency: $40,100)

### 4. Intuitive Formalization

$$\text{Total Estimate} = \sum \text{Direct}_i + \sum \text{Indirect}_j + \text{Contingency} + \text{Escalation}$$

| Component | Formula | What it covers |
|-----------|---------|----------------|
| Direct costs | $\sum Q_i \times R_i$ | Scope-specific items (quantity x rate) |
| Indirect costs | Itemized list | Project-wide costs (camp, insurance, mob/demob) |
| Contingency | $\sum P_k \times I_k$ | Probability-weighted risk impacts |

### 5. CTQ Mapping

| CTQ | Source | Mastery Test | Common Failure Mode |
|-----|--------|-------------|---------------------|
| Can classify any cost line as direct, indirect, or contingency | Principle 1 + 2 | "Freight for equipment X" -- which category? | Conflation: calling freight "indirect" when it's direct to that equipment |
| Can explain why contingency is not a percentage add-on | Principle 2 | Why is "add 15% contingency" a bad practice? | Procedural: applies % without risk analysis |

### What They Share

| Shared Principle | Indirect Costs | Contingency |
|-----------------|----------------|-------------|
| Both are non-scope-specific costs | Yes -- project-wide, not item-specific | Yes -- risk-driven, not item-specific |
| Both appear below the direct cost subtotal | Yes | Yes |

### Where They Diverge

| Dimension | Indirect Costs | Contingency |
|-----------|---------------|-------------|
| Nature | KNOWN and quantifiable | UNCERTAIN and probability-weighted |
| Can you itemize it? | Yes -- security, insurance, camp, etc. | No -- it is a reserve for risk events |
| When is it spent? | Always -- these costs will occur | Maybe -- only if the risk event occurs |
| How to estimate | Bottom-up: list and price each item | Risk analysis: probability x impact |

**Quick Check** (CTQ: classification)
Your estimate includes "builder's risk insurance: $45,000" and "possible soil remediation if contamination found: $120,000." Which is indirect and which is contingency, and why?

*If any term in this question is unclear, ask for a **clarification**.*

⏸ **Wait for the learner to respond before revealing the answer.**

---

Key Terms Appendix

Every teaching block (abbreviated or full) MUST end with a Key Terms table before the Quick Check. This table defines every domain-specific term introduced or used in the explanation.

**Key Terms**
| Term | Definition | First appears |
|------|-----------|---------------|
| <term> | <one-sentence definition> | <Principle N / Worked Example / etc.> |

Rules

• Include ALL domain terms used in the teaching block, not just new ones
• Definitions must be self-contained — a reader should understand each term without reading the full explanation
• Use the term's formal name (e.g., "Hermitian matrix" not "that kind of matrix")
• If a term has a common synonym, note it: "Self-adjoint (also: Hermitian in finite dimensions)"
• For mathematical terms, include the LaTeX notation: "Conjugate transpose: $A^*$ or $A^\dagger$"
• Order terms by first appearance in the teaching block, not alphabetically
• The Key Terms table is included in the concept file export

Example

**Key Terms**
| Term | Definition | First appears |
|------|-----------|---------------|
| Direct cost | A cost traceable to a specific scope item on a drawing or schedule | Principle 1 |
| Indirect cost | A project-wide cost not tied to one deliverable (e.g., site security, insurance) | Principle 1 |
| Contingency | A probability-weighted reserve for identified risk events that may or may not occur | Principle 2 |
| Mob/demob | Mobilization and demobilization — the cost of moving crew and equipment to and from site | Worked Example Step 2 |
| Builder's risk insurance | Insurance covering damage to works under construction; base is typically direct costs only | Worked Example Step 2 |

---

When the Quick Check Fails

After the learner responds to the Quick Check, reveal the expected answer and the "Watch for" failure mode. Then evaluate:

• Correct: Acknowledge, proceed to next gap or Phase 3.5
• Incorrect: Follow the re-teach protocol below

If the learner answers the Quick Check incorrectly:

1. Do NOT move to the next teaching block
2. Re-explain the specific point they got wrong, using a DIFFERENT angle or example
3. Give one more CTQ-derived Quick Check on the same concept
4. If they pass the second check, proceed
5. If they fail again, note it as a persistent gap and proceed (don't loop on Quick Checks)

---

Concept Map for TTT Sessions

After all teaching blocks are delivered and Quick Checks passed, generate a concept map during Phase 3.5.

Format

Use the concept-explainer skill's full Concept Map Format:

• All node types: (core), (principle), (innovation), (application), (prerequisite), (shared)
• All relationship labels: rests on, requires, led to, enables, generalizes, is a special case of, contrasts with, equivalent to

Design Rules for TTT Context

1. Default depth: standard (10-15 nodes)
2. The (core) node is the sub-goal's topic, NOT the entire training plan topic
3. ALL gaps taught MUST appear as principles or innovations in the map
4. Nest innovations under their parent principle using led to
5. Add 2-4 applications connecting concepts to practical use
6. Add 1-3 prerequisites for context
7. Keep descriptions to one line each
8. Do NOT include "Where to Go Next" suggestions -- the next step is the Final Test

For Conflation Gaps

If the session included a comparison, use the comparison map format (three-section: Shared Foundation, Concept A, Concept B).

---

Concept File Export

Every Teach phase generates a concept file, written during the RECORD phase (Phase 6).

• Filename: concept-<domain>-<topic>.md (kebab-case)
• Content: YAML frontmatter + all teaching blocks + concept map + aggregated CTQ table + session context
• Format: See concept-explainer skill's Concept File Export Format

The concept file is a persistent learning artifact. It can be browsed via /concept-library.

---

In-Session Deep-Dive

If the learner asks for deeper explanation of a principle after a teaching block:

1. Identify the principle to expand (from the most recent teaching block or concept map)
2. Generate a full 6-section explanation for that principle using the concept-explainer skill's Deep-Dive Protocol
3. Deliver it inline -- the deep-dive does NOT interrupt the session flow
4. Return to the next gap (or Phase 3.5 if all gaps are done)

Rules:

• Mention the deep-dive option once after the first teaching block
• Only one deep-dive per teaching block (prevent rabbit holes)
• Include the deep-dive content in the session transcript and concept file