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Develops mathematical understanding through examples, visualization, and analogy
Passed 26 of 26 test cases with the skill, and 25 of 26 without it.
1 fixed25 passed either way0 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
A test case the skill fixed. Same model, same prompt, with and without the skill.
Why does the Laplace transform convert differential equations into algebraic equations? Provide a structured understanding breakdown: restatement, concrete e^(-2t) transformation example with numbers, ASCII time vs s-domain mapping sketch, simple constant function simplification, spring-mass frequency analogies, intuition summary, and verification step.
| Checked | Without skill | With skill |
|---|---|---|
| Computes the explicit Laplace transform 1/(s+2) for the concrete function e^(-2t). | Missed | Passed |
The instructions your model reads when the skill loads.
Trigger on phrases like:
Use before computation to establish understanding (Polya's "understand the problem" phase).
Guide through Mason's specializing-generalizing cycle:
Ask: "Can you state the problem in your own words?"
Ask: "What would a concrete example look like?"
Ask: "What form should the answer take?"
Ask: "Can you draw a picture or diagram?"
test cases passed, vs 25 / 26 without
More skills from the same source and nearby in the registry, with their headline benchmark lift.