pivot

name	pivot
description	Use when pivoting a finalized learning sheet's task and examples to a new real-world context, or when scrutinizing its reasoning for logical gaps
argument-hint	[week-number]

Pivot Learning Sheet

Week number is provided as $ARGUMENTS. Replace N below with the week number.

Inputs

Read these files before starting:

1. weekN/N.learning-sheet.typ — the finalized sheet to pivot
2. Relevant textbook/*.md chapters (check coursedesign/schedule.typ for assigned textbook sections)
3. week1/1.learning-sheet.typ — reference for how task boxes and examples are structured (skip if pivoting week 1 itself; use templates/week-template/N.learning-sheet.typ instead)

Concern 1: Creative — Pivot Task & Examples

Step 1: Catalog what exists

Extract from the current sheet:

• The task box (motivating problem, code snippet, closing question)
• Every worked example tied to the task context (not pure math examples — only those that reference the real-world framing)
• The opening bridge paragraphs connecting task to theory
• The "Back to the task" section at the end
• All AI prompts (#badge-broader and #badge-deeper) that reference the task context

Step 2: Propose 2-3 alternative task framings

Generate candidate motivating tasks for the same theory. Each must be:

• A different real-world context (e.g., plagiarism detection, DNA analysis, network protocol validation, data compression)
• Genuinely interesting — a student should want to solve it
• Naturally connected to the week's theory — the theory should actually solve the task, not be a forced fit

Brainstorming-style presentation: Before presenting options, write a short analysis of the current task's strengths and weaknesses (e.g., which of the week's big ideas it covers vs. misses). Then present candidates using AskUserQuestion with markdown previews. Each option must include:

• A concrete task box preview (the actual text students would see, including code snippet)
• A coverage checklist showing which of the week's key concepts the framing naturally connects to (✓/✗)
• Strengths and weaknesses in the option's description field

Include the current task as one option (in case the user wants to keep it and only do the reasoning audit).

Step 3: Rewrite each creative item with the user

Walk through each cataloged item from Step 1 one by one. For each item:

1. Show the user the current version (quote the relevant lines)
2. Present your proposed rewrite using the chosen task framing
3. Use AskUserQuestion to let the user approve, request changes, or skip

Process items in this order:

1. Task box (problem statement + code snippet + closing question)
2. Opening bridge paragraphs
3. Each worked example tied to the old context (one at a time)
4. Each AI prompt that references the old context (one at a time)
5. Any Part-opening sentences that reference the old context (one at a time)
6. "Back to the task" / summary section

Only apply each edit after the user approves it. If the user requests changes, revise and re-present before moving on.

Do NOT change:

• Definitions, theorems, proofs
• Pure math examples (not tied to the task context)
• Section structure or ordering

Concern 2: Deep Reasoning — Flag Logical Gaps

Independently from the pivot, scrutinize every non-trivial reasoning chain in the sheet. This includes formal proofs, but also informal arguments like "a stack reverses, so PDAs can't do X" or "this is equivalent to Y because...".

For each argument, ask:

• Does each step follow from the previous one?
• Are there hidden assumptions?
• Is any claim stated without justification?
• Could a careful student poke a hole in this reasoning?
• Are edge cases handled?

Output and confirmation

1. Present the full audit using this format:

## Reasoning Audit: Week N

### Argument 1: [name] (lines NN-NN)
- **Claim:** [what is being argued]
- **Status:** sound / has gap / uncertain
- **Gap (if any):** [what's missing or hand-wavy]
- **Suggestion:** [how to fix or strengthen]

### Argument 2: ...
(repeat for each non-trivial argument)

### Summary
- X/Y arguments are sound
- Gaps found: [list]

2. List non-sound items — collect all arguments with status "has gap" or "uncertain" into a numbered checklist for the user.

3. Confirm each item one by one — for each non-sound item, use AskUserQuestion with markdown previews to present:

   • The claim and the identified gap/concern in the question text
   • Options with before/after previews: "Apply fix" option shows the proposed new text in its markdown field; "Skip (no change)" option shows the current text in its markdown field
   • Explain why this matters (what a careful student might notice) in the option description

   Only apply fixes the user approves. Process items sequentially (one AskUserQuestion per item).

Workflow

1. Read the sheet and textbook chapters
2. Run Concern 2 (reasoning audit) first — report findings, then confirm fixes one by one
3. Run Concern 1 (creative pivot) — propose alternatives, get user choice, rewrite
4. Output: the pivoted .typ file + the reasoning audit report