WisdomForge

Show the Path · Sitting 2

Hunting the Gap

The model is a gap-jumper. It produces answers with invisible holes. The skill is to hunt the gap before you trust the path.

  • 40 min
  • Practice · Reflect
  • 15–18

Parent briefing · 5 minutes, before they sit

This sitting teaches the student to audit the model's solutions the way an editor audits a draft. The model will produce a solution with steps. Some steps will be real. Some will be jumps disguised as steps. The student's job is to hunt the gaps. For each step, ask: 'Does this follow from the previous one? Can I reproduce it on a blank board?' If yes, the step is real. If no, the step is a gap. Fill it yourself or flag it. The model will not flag its own gaps. The student who can hunt gaps will not be fooled by a fluent solution that has holes.

Hard edges

  • Academic integrity: a model solution with gaps you cannot fill is not your proof. You can cite the model's steps you verified. You cannot cite the gaps.
  • Do not let the student think the model is malicious. The gaps are structural, not intentional. The model does not know it is jumping.

If they say

“The model's solution looked fine to me.”
It looked fine because the gaps were dressed as steps. The audit is how you see the costume. If you did not find gaps, either the path was complete or you missed them. Audit again with a harder problem.
“I can't fill the gap, but the answer is probably right.”
'Probably right' is not a proof. If you cannot fill the gap, you have an unsupported step. The answer might be right. The proof is broken. Those are different things. A right answer with a broken proof is a coincidence, not a proof.

Objective

The student can audit a model's mathematical solution for missing steps, identify each gap, and either fill it independently or flag it as unsupported.

The gap audit

A gap audit is simple. Read each step of the model's solution. For each step, ask two questions: 'Does this follow from the previous step?' and 'Can I reproduce this step on a blank board?' If both answers are yes, the step is real. If either is no, there is a gap. Write GAP. Then decide: can I fill it? If you can fill it with your own work, the path holds, and you have made the step yours. If you cannot fill it, the path is broken at that point. Do not trust the solution past the gap. The gap is not a minor inconvenience. It is a structural failure in the proof.

The invisible gap

The most dangerous gap is the one that looks like a step. The model writes 'therefore' or 'so' and jumps. The jump looks like a step because it has the right words around it. But the words 'therefore' and 'so' do not create a logical connection. They announce one. If the connection is not shown, the step is a gap dressed as a step. The student who reads 'therefore' and trusts it has been fooled by the costume. The student who reads 'therefore' and asks 'what follows from what?' has started the audit. The audit is the skill. The model will not perform it for you.

Big idea

The model jumps and dresses the jump as a step. Hunt the gap. Fill it or flag it. A solution with unfilled gaps is not a proof.

Try this~20 min total

Gap audit

20 min
  1. Ask the model to solve a multi-step problem and show its work.
  2. Read each step. For each, ask: 'Does this follow? Can I reproduce it?'
  3. Mark each step: REAL (I can walk it) or GAP (I cannot).
  4. For each GAP, try to fill it with your own work. If you can, it is now yours.
  5. For gaps you cannot fill, write UNSUPPORTED. The solution is broken at that point.
  6. Talk About It: how many gaps did you find? Did the model's solution look complete before the audit?

Lesson guide

Ask after you try

After the gap audit.

  1. Ask the model: 'Show me the step between [line A] and [line B] that I marked as a gap.' If it fills it, compare to your attempt. If it says 'this is a standard technique,' ask: 'Which technique? Show me.' If it cannot name the technique, the gap was real.
  2. Did they mark each step as REAL or GAP?
  3. Did they try to fill each gap independently?
  4. Did they flag unfilled gaps as UNSUPPORTED?

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

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Practice · Reflect15–18

Currently reading WisdomForge lesson: Hunting the Gap.

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You are a WisdomForge emerging guide sitting beside the lesson "Hunting the Gap". The lesson is the text. You are the guide. Hint-first. Do not recite. Do not write the work. Warm, not a friend. If the topic is hard or tender, point to a trusted adult.

Tools on

  • conversation
  • optional parent-approved files

Ritual reminder

Real argument. Practice. Reflect. Chat. Optional narrow search or school files. Not an adult team agent.

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Dinner table

What gaps did we find in a model's solution this week, and did we fill them or flag them?

Sits beside

  • Thinking. Claim and check: the gap audit is the check applied to each step.
  • English. The argument audit in rhetoric is the same skill: check each piece of evidence.

Integrity. Cite the steps you verified. Flag the gaps you could not fill. Do not submit a model's solution as your proof if it has unsupported gaps.

Next sitting: The Model Is a Hostile Reviewer