WisdomForge

Show the Path · Sitting 1

What Is a Proof?

A proof is not a fancy word. It is a path other people can walk, step by step, from what they know to what you are saying.

  • 28 min
  • Talk About It
  • 11–14

Parent briefing · 5 minutes, before they sit

A proof is a path. That is the whole idea. You start somewhere everyone agrees on. You take a step. You show the step. You take another step. You show it. You arrive at the conclusion. If every step is visible and anyone could walk it, the proof holds. If a step is missing or invisible, the proof is broken. The model can produce the conclusion. It cannot always show the path. The student needs to learn that the path is the proof, not the answer.

Hard edges

  • Do not use the word 'theorem' yet. Use 'path.' The vocabulary comes later.
  • Keep it to simple examples: arithmetic steps, a geometric argument, a logic puzzle.

If they say

“The answer is what matters.”
The answer matters for the task. The path matters for understanding. If you only have the answer, you cannot do the next problem. If you have the path, you can walk it again.

Objective

The student can explain what a proof is in plain language: a path of steps from something known to a conclusion, where each step is visible and walkable.

The path

Imagine you tell a friend your house is two blocks from school. They say: prove it. You do not just say 'it is.' You walk the path. Left on Oak. Right on Maple. Two blocks. Here is the door. That is a proof. You showed each step. Your friend could walk it. A mathematical proof is the same thing with ideas instead of streets. You start somewhere everyone agrees. You take a step. You show it. You take another. You show it. You arrive. The path is the proof. The answer is the door. Without the path, the answer is just a claim.

The model's shortcut

A model will give you the answer. 'The sum is 42.' It will not always show the path. It jumps to the door. That is useful if you only need the answer. It is not a proof. A proof is the path. If you cannot walk the path yourself, you have the answer but not the proof. The model is a shortcut machine. Shortcuts are useful. They are not mathematics. Mathematics is the path. The student who confuses the shortcut for the path will have answers and no understanding. The student who knows the difference can use the shortcut when the path does not matter and walk the path when it does.

Big idea

A proof is a path other people can walk. The model gives the door. The proof is the walk.

Try this~14 min total

Walk the path

14 min
  1. Pick a simple math problem you can solve: an addition, a simple puzzle.
  2. Solve it. Write each step as a sentence someone could follow.
  3. Ask: could a friend walk these steps and arrive at the same answer?
  4. Now ask the model the same problem. Does it show the path, or just the answer?
  5. Talk About It: which one is the proof? Which one is the shortcut?

Lesson guide

Ask after you try

After both the student's path and the model's answer.

  1. Ask the model: 'Show me each step.' Compare its path to yours. Did it skip steps? Did it jump? A jump is not a step.
  2. Did they write each step as a walkable sentence?
  3. Did they distinguish the path from the answer?
  4. Did they notice whether the model showed the path or just the answer?

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Talk About It11–14

Currently reading WisdomForge lesson: What Is a Proof?.

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Optional: currently working on WisdomForge sitting: Show the Path — what-is-proof. [v:1:e61e011e]

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You are a WisdomForge young guide sitting beside the lesson "What Is a Proof?". 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 local voice
  • optional image understanding

Ritual reminder

Hint, then example. Talk About It. Chat. Optional local voice-to-text. Optional image understanding.

Fresh profile only. Never clone an adult profile. No child names, photos, or school. Hint-first. User-started. The guide does not make AI safe. You may refuse it.

Dinner table

What path did we walk today, and could someone else follow it?

Sits beside

  • Thinking. Claim and check: the proof is the check. The claim is the door.
  • Science. A hypothesis is a door. The experiment is the path.

Integrity. Do not copy the model's answer and call it your proof. The proof is the path. If you did not walk it, it is not yours.

Next sitting: The Missing Step