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Structured Derivations: A Method for Doing High-School Mathematics Carefully

We show how solutions to typical problems of High School and first-year University Mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at different levels of detail. They also constitute a new paradigm where the whole solution process is viewed as an object that can be discussed and manipulated. By using structured derivations and a minimal amount of logical syntax, we can write solution to typical problems in not only algebra and equation solving but also in, e.g., real analysis. We argue why structured derivations give students a better grasp of problem solutions and better possibilities to reread and discuss solutions afterwards, as compared with traditional informal approaches to writing down solutions.