Ask for the working, then check it

A conclusion cannot be checked; a chain can

If a model tells you the answer is 4.2 kJ, you have one thing to verify and no way to verify it short of doing the problem yourself. If it gives you six steps, you have six small things to verify, most of which take seconds, and an error anywhere is usually visible.

This is the practical reason to ask for working. There is a second reason: models are measurably more accurate when they produce intermediate steps. Generating reasoning before the answer improves performance on multi-step problems, and the effect is large enough that it is now built into how most assistants respond by default. Asking for the steps improves the answer and gives you something to inspect. It costs one clause.

Work through it step by step. State each assumption as you use it. Give the final answer last, on its own line.

Steps are not proof

Here is the honest limitation, and it matters. A chain of reasoning produced by a model is also generated text. It reads as the derivation that produced the answer; it is a plausible derivation written alongside it. Research on this (often discussed as the faithfulness of chain-of-thought) repeatedly finds cases where the stated reasoning does not match what actually drove the answer, including cases where a model given a hint changes its answer to match the hint while producing a chain that never mentions it.

So visible working buys you two real things:

1. Checkability. You can find the wrong step yourself.
2. Accuracy. Step-by-step generation does better on multi-step problems.

It does not buy you a guarantee that the reasoning shown is the reasoning used. Do not treat a plausible chain as verification. Treat it as a document to audit.

How to audit a chain quickly

You rarely need to check every step. Three passes, in order, catch nearly everything:

Units and dimensions. In any physical or engineering problem, carry the units through. If joules appear where you expected joules per second, the error is upstream of that line and you can stop reading. This one check catches an enormous proportion of numerical errors and takes about fifteen seconds.

Magnitude. Is the answer the right size? A drug dose of 4 grams where you expected milligrams, a distance of 300 metres where you expected kilometres, a probability of 1.4. Estimate roughly before you look at the answer so you have something to compare against.

The joint. Most wrong chains are right for several steps and then make one unjustified move: a cancellation that requires a term to be non-zero, an approximation applied outside its range, a rule from one case used in another. Find the step where the difficulty of the problem actually lives and read that one properly.

Make it show the assumptions separately

A useful variation:

Before solving, list every assumption the solution will rely on. Then solve. Then say which assumption, if wrong, would change the answer most.

This surfaces the thing you actually need to check. In coursework, the assumption list is often worth more than the answer: it is frequently exactly what the marker is looking for, and it is the part students omit.

The re-derivation test

The strongest cheap check: cover the chain and redo the step you are least sure about yourself. If you can reproduce it, it is right and you have practised. If you cannot, either it is wrong or you have found the thing you need to learn. Both outcomes are useful, which is unusual for a check.

This is also the point where a lot of the learning happens. Reading somebody else’s correct derivation teaches you very little. Regenerating one step of it teaches you a lot, for the reasons in the fluency lesson.

For non-numerical subjects

The same move works outside the sciences, in a different vocabulary.

• Set out the argument as numbered premises and a conclusion before writing the paragraph. Then check whether the conclusion actually follows, and whether any premise is doing work it cannot support.
• Which of these claims is contested among historians, and by whom? Then check that the contest is real.
• Which sentence in this paragraph carries the most weight, and what would have to be true for it to hold?

In every case you are converting a smooth output into a set of joints you can test individually. That is the whole technique.