WisdomForge

Show the Path · Sitting 6

The Full Path

Walk, write for a reader, check with the model, reproduce on a blank board, report. One full mathematical path, end to end. That is the capstone.

  • 40 min
  • Practice · Reflect
  • 15–18

Parent briefing · 5 minutes, before they sit

This is the emerging capstone. The student runs the full cycle: solve, write for a reader, submit to the model's hostile review, reproduce on a blank board, report. The output is one proof that survived three tests: the reader test, the model's review, and the blank board. The proof is the capstone artifact. It is the proof that the student can show a path others can walk in the age of the machine that gives the answer.

Hard edges

  • The proof must survive all three tests. If it fails one, the student fixes it and retries. The capstone is the proof that passed.
  • Academic integrity: the proof is the student's. The model is cited as a reviewer. The blank board is the student's own reproduction.

If they say

“This is too much work for one proof.”
The first time, it is. The capstone is the investment. The second proof will be faster. The third will be a habit. The capstone is the proof that the skill exists. After that, the skill is yours.
“The model can write a better proof.”
It can write a smoother proof. It cannot write a proof that passes your blank board test. It cannot write a proof that a peer walks. It can write a proof that a reader follows, but the path is the model's, not yours. The capstone is the proof that is yours.

Objective

The student can run the full proof cycle on a real mathematical problem, produce a readable proof that survives a model's hostile review and a blank board test, and write a one-paragraph report.

The three-test proof

The capstone proof passes three tests. The reader test: a peer can walk it. The model's hostile review: the model found the weak steps and the student fixed them. The blank board test: the student can reproduce it without notes. A proof that passes all three is a proof. A proof that passes one or two is a draft. The student who runs the cycle and passes all three has produced something the model cannot: a path that is owned, verified, and reproducible. That is mathematics in the age of fluency.

Big idea

The capstone proof passes three tests: the reader, the model's review, and the blank board. A proof that passes all three is a proof the model cannot replace.

Try this~30 min total

The three-test proof

30 min
  1. Pick a problem at the edge of your skill. Walk it. Write each step for a reader.
  2. Test 1: Show a peer or family member. Can they walk it?
  3. Test 2: Ask the model for a hostile review. Fix the weaknesses it finds.
  4. Test 3: Close everything. Blank board. Reproduce the proof.
  5. Write the report: 'Problem: [X]. Path: [steps]. Reader: [passed/stuck at Y]. Model review: [found Z, fixed]. Blank board: [reproduced/gaps at W]. Verdict: [proof/draft].'
  6. If draft, fix and retry. If proof, keep it. It is the capstone artifact.

Lesson guide

Ask after you try

After the three-test proof.

  1. Show the model the final proof. Ask: 'Could you write this proof yourself, without me?' If it says 'yes,' ask: 'Show me.' Compare. If its proof is different, the difference is the model's path versus yours. Both might be correct. Only one is yours.
  2. Did the proof pass all three tests?
  3. Is the report honest about which tests passed and which needed fixes?
  4. Can the student name what the three-test proof has that a model answer does not?

8 turns left this sitting. User-started only. Never on page load.

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Practice · Reflect15–18

Currently reading WisdomForge lesson: The Full Path.

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Dinner table

What proof did we build this week, and did it pass all three tests?

Sits beside

  • Science. The full measurement protocol is the same structure: design, measure, calibrate, report.
  • Thinking. The full rhetorical audit is the same structure: ethos, pathos, logos, frame, missing voice.

Integrity. The report cites the model as a reviewer, the peer as a reader, and the blank board as the reproduction test. The proof is the student's. The citations are honest.

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