An answer with no visible reasoning is a rumour: it might be true, but nobody — including you, three weeks later — can tell why. In this course the reasoning is the work. Derivations, optimizations, and models built from data all live or die on whether a reader can follow the chain, and showing it is a concrete skill with named parts.
The four-part habit on paper
- Restate — one line saying what the problem actually asks, in your own words. “Find when the velocity is zero” is a different job from “find when the object returns to its start” — half of all wrong answers are right answers to a misread question.
- Reason — the steps in order, with a word about why each move is legal. “The quotient rule applies only where the denominator is nonzero, so we note and treat it separately” beats a bare arrow — and in an optimization, the why is the product: the derivative set to zero finds candidates, and the sentence that checks them against the endpoints is the step that makes the answer true.
- Units — carried through every line, not sprinkled on at the end. A The Speed Camera answer should arrive in kilometres per hour; a Smooth Landing descent rate in metres per second, and its comfort in metres per second squared; a vector’s magnitude should say what it measures. Units that arrive wrong have found your error for you.
- Answer sentence — a full sentence a stranger could read on its own: “The car was travelling 63 km/h as it passed the camera, so the ticket stands.” A boxed answers nothing by itself.
At the whiteboards
One rule does most of the work: the person holding the marker writes only other people’s ideas. It forces reasoning out loud — you cannot write what nobody has said — so every line on the board has already survived one listener. And cross out rather than erase: a corrected line is a record of thinking, which is what the board is for, as Mistakes Are Data argues at length.
The checklist
- Could someone follow this without me standing beside it?
- Is there a why beside every non-obvious step?
- Do the units survive from the first line to the last?
- Does it end in a sentence answering the actual question?
- Are my crossed-out attempts still visible?