Show the Path · Sitting 4
Reproducibility Is the Standard
A proof you cannot reproduce is a proof you do not own. The blank board test is the standard for whether the path is yours.
- 40 min
- Practice · Reflect
- 15–18
Parent briefing · 5 minutes, before they sit
This sitting makes the blank board test the standard. The student works with the model on a proof. Then they close everything and reproduce the full proof on a blank board. If they can, the path is theirs. If they cannot, the path was the model's, and they followed it. The standard is not perfection. It is reproducibility. A mathematician who cannot reproduce their own proof does not own it. The student who adopts this standard will never confuse following for understanding.
Hard edges
- Academic integrity: a proof you cannot reproduce is not your proof. You can cite the model's help, but you cannot submit it as your own work.
- Accommodations: a reader or extra time is access, not a ghost. The blank board test is about the student's understanding, not their speed.
If they say
- “I don't need to reproduce it. I understood it.”
- Understanding while following is real. It is not the same as reproducing. The blank board test is the difference. If you can reproduce it, you own it. If you cannot, you understood it while it was in front of you. That is a different thing. Both are useful. Only one is mastery.
- “In the real world, I can just look it up.”
- You can look up the steps. You cannot look up the understanding. The steps are on the internet. The path in your hands is not. The blank board test is how you know which one you have.
Objective
The student can reproduce a complete proof on a blank board after working with a model, and explain why reproducibility is the standard for mathematical understanding.
The standard
In mathematics, reproducibility is the standard. A proof is yours if you can reproduce it. A proof is the model's if you cannot. The blank board test is the check: close everything, take a blank page, reproduce the proof. If you can, the path is in your hands. If you cannot, the path was in the model's hands and you were reading over its shoulder. Both are useful experiences. Only one is understanding. The student who adopts reproducibility as the standard will always know the difference. The student who does not will confuse following for owning for the rest of their education.
What the test reveals
The blank board test reveals exactly which steps you own and which you followed. You might own steps 1 through 3 and lose the path at step 4. That is useful data. Step 4 is the step you need to relearn. The model can help you relearn it. Then you take the blank board test again. If you can reproduce step 4 this time, you own it now. The test is not a grade. It is a diagnostic. It tells you where the path is yours and where it is not. Then you fix the gaps. The test is the map of your understanding.
Big idea
Reproducibility is the standard. A proof you cannot reproduce is not yours. The blank board test is the map of what you own and what you followed.
Try this~22 min total
Full blank board
22 min- Work with the model on a proof at your level. Walk the path.
- Close everything. Blank page. Reproduce the full proof.
- Mark each step: OWNED (I can do it) or GAP (I cannot).
- For each GAP, study the step with the model. Then close and try again.
- When you can reproduce the full proof, write: REPRODUCIBLE. The path is yours.
- Talk About It: which steps were hardest to reproduce? What did that reveal?
Lesson guide
Ask after you try
After the blank board test.
- Show the model the gaps you found. Ask: 'Help me understand the step I could not reproduce.' Study it. Then close the chat and try again. The second blank board is the real test.
- Did they reproduce the full proof on a blank board?
- Did they mark each step as OWNED or GAP?
- Did they relearn the gaps and try again?
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Dinner table
What proof did we reproduce on a blank board this week, and where were the gaps?
Sits beside
- English. Voice you can reproduce: the exam-hall test. Same standard.
- CS. Code you can explain: the same standard for programming.
Integrity. A proof you cannot reproduce is not your proof. Cite the model's help. Do not submit a proof you cannot reproduce on a blank board as your own.