The Layered-Explanation Prompt

A companion template for Learning with AI: A Framework for Students, Instructors, and Universities. See Part I, “Ask for help, not replacement.”

Use this when a concept sits above your current level and a single explanation is not getting you unstuck. It asks the AI to explain the same idea at three depths at once, so you get an entry point, a working understanding, and a sense of where the idea leads.

The prompt

Paste this, then name your concept and your course:

Explain [concept] three ways, for a student in [course / level].

1. Everyday analogy. Explain it with a plain analogy, no technical terms, as you would to someone who has never taken this subject.
2. At my level. Explain it as it would be taught in my course, using the terms and notation I am expected to know.
3. One step deeper. Explain it one level beyond where I am now, so I can see what it connects to and where it leads.

After the three explanations, give me two or three short questions I can use to check whether I actually understand it, and do not include the answers yet.

How to use it well

The three levels are not the finish line. They give you a way in; the understanding is yours only when you can produce it without the AI in front of you.

1. Read all three levels before deciding which helped. Often the gap between two levels is where the idea finally clicks, not any single explanation on its own.
2. Answer the check questions with the window closed. If you cannot, you have found what to work on next, which is the point.
3. Then rebuild the idea in your own words, a few sentences, a diagram, or a worked example from memory. This is the step that turns a good explanation into something you know.
4. If a level still does not land, go back one level. A hint that keeps missing usually rests on an idea underneath it. Make that idea solid first, then climb back up.

A worked example

Concept: eigenvectors. Course: first linear-algebra course.

• Everyday analogy. Some directions in a stretch or push do not turn; they only get longer or shorter. Those special directions are the eigenvectors, and how much they stretch is the eigenvalue.
• At my level. For a matrix A, an eigenvector v satisfies A v = λ v: applying A scales v by the number λ without changing its direction. You find them by solving det(A − λI) = 0 for the eigenvalues, then solving for each v.
• One step deeper. When a matrix has a full set of independent eigenvectors, you can write it as A = P D P⁻¹, which turns hard repeated operations like Aⁿ into easy ones on the diagonal matrix D. This is why eigenvectors show up everywhere from differential equations to the stability of systems.

Check questions: Why does an eigenvector keep its direction under A? What does an eigenvalue of 0 tell you about the matrix? Can you give a 2×2 matrix and one of its eigenvectors from memory?

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This template is for your own study. Treat any AI explanation as a draft to verify, not a source to cite, and follow your course’s policy on when AI use is permitted.