WisdomForge

Show the Path · Sitting 5

Proof as a Social Act

A proof is a social act: you write a path so others can walk it. The model writes for itself. You write for the reader. The reader is the test.

  • 40 min
  • Practice · Reflect
  • 15–18

Parent briefing · 5 minutes, before they sit

This sitting teaches the student that proof is social. Mathematics is not a private act. It is a public path. You write so others can verify. The model writes for itself. The student writes for the reader. The reader is the test: a peer, a model used as a reader, or a teacher. The proof that only the writer can follow is a note. The proof a reader can walk is mathematics. The student who adopts this standard will write proofs that communicate, not just calculate.

Hard edges

  • Academic integrity: the proof is yours if you wrote it. If the model wrote it and you copied, it is the model's proof, not yours.
  • The model as a test reader is different from the model as a writer. The student must use it to test, not to write.

If they say

“I don't need to write for others. I understand it.”
You understand it for yourself. That is a note. A proof is for the reader. If you cannot write it so another person can follow, you have a private understanding, not a public proof. Mathematics is public. Write for the reader.
“The model can just write the proof.”
It can. That proof is the model's, not yours. It is written for the model's pattern, not for your reader. Use the model as a test reader. Write the proof yourself. The proof that is yours is the one you wrote for a reader.

Objective

The student can write a proof that a peer could follow, use the model as a test reader, and explain why proof is a social practice, not a private one.

Mathematics is social

Mathematics is not done in private. A proof is written for a community. The community verifies it. If the community cannot follow it, the proof is not accepted. This is not a school rule. It is how mathematics works. The model writes proofs that skip steps because it does not have a reader. It has a pattern. The student who writes for a reader is doing mathematics. The student who writes for themselves is keeping notes. The difference is the reader. Write for the reader. Use the model as a test reader. Use a peer as a real reader. The proof that survives both is a proof.

The model as a test reader

The model can be a test reader. You write the proof. You show the model. You ask: 'Could a peer follow this? Where would they get stuck?' The model finds the gaps. You fill them. This is different from asking the model to write the proof. The model as a reader tests your proof. The model as a writer replaces your proof. Use it as a reader. Never use it as a writer. The student who knows the difference is doing mathematics with a tool. The student who does not is outsourcing their thinking.

Big idea

Proof is social. Write for the reader. Use the model as a test reader, never as a writer. The proof that survives a reader is a proof.

Try this~22 min total

Write for a reader, test with the model

22 min
  1. Write a proof on a problem at your level. Write for a peer, not for yourself.
  2. Show the model. Ask: 'Could a peer follow this? Where would they get stuck?'
  3. Fill the gaps the model finds. Rewrite the proof.
  4. Show a real peer or family member. Can they walk it?
  5. Write: SOCIAL PROOF (a reader can walk it) or PRIVATE NOTE (only you can follow it).
  6. Talk About It: what did the model catch as a reader that you missed as a writer?

Lesson guide

Ask after you try

After the proof is written and tested.

  1. Show the model the proof. Ask: 'Could a peer follow this?' If it says 'yes, it is clear,' ask: 'Where would they get stuck?' If it finds a gap, fill it. The model is a reader, not a writer. Use it to test, not to write.
  2. Did they write for a reader, not for themselves?
  3. Did they use the model as a test reader?
  4. Did the proof survive a real reader (peer or family member)?

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Practice · Reflect15–18

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Dinner table

What proof did we write for a reader this week, and did it survive the test?

Sits beside

  • English. Writing for the reader is the same skill in essays and proofs.
  • Science. A methods section is a proof for other scientists. Same social standard.

Integrity. Cite the model as a test reader if it found gaps you fixed. The proof is yours. The review is the model's. The citation is honest.

Next sitting: The Full Path