{"course":{"slug":"ai-for-students","title":"AI for Students","url":"https://addaly.com/learn/ai-for-students","level":"beginner","track":"work"},"lesson":{"slug":"ask-for-the-working","title":"Ask for the working, then check it","url":"https://addaly.com/learn/ai-for-students/ask-for-the-working","position":12,"of":73,"minutes":8,"answer":"Ask for steps because they improve accuracy and give you something auditable, then audit with units, magnitude and the one difficult joint.","keyIdea":"Ask for steps because they improve accuracy and give you something auditable, then audit with units, magnitude and the one difficult joint, never treating the stated reasoning as proof that it is what produced the answer."},"body":{"format":"markdown","text":"## A conclusion cannot be checked; a chain can\n\nIf 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.\n\nThis 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.\n\n> Work through it step by step. State each assumption as you use it. Give the final answer last, on its own line.\n\n## Steps are not proof\n\nHere 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.\n\nSo visible working buys you two real things:\n\n1. **Checkability.** You can find the wrong step yourself.\n2. **Accuracy.** Step-by-step generation does better on multi-step problems.\n\nIt 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.\n\n## How to audit a chain quickly\n\nYou rarely need to check every step. Three passes, in order, catch nearly everything:\n\n**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.\n\n**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.\n\n**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.\n\n> Figure: Auditing a chain, about two minutes. Steps: 1. Units (Carry them down every line and cancel. Joules where you wanted joules per second means the error is above that line.); 2. Magnitude (Estimate roughly before you look. Grams where you expected milligrams. A probability of 1.4.); 3. The joint (Find the one step where the difficulty of the problem actually lives, and read that step properly.); 4. Re-derive (Cover the chain and redo the step you trust least. Either it holds, or you have found the thing to learn.). A conclusion gives you one thing to verify and no way to verify it. Six steps give you six small ones, most of which take seconds. None of this proves that the reasoning shown is the reasoning that produced the answer, and research on the faithfulness of these chains keeps finding cases where it is not. Visible working is a document to audit, not a guarantee.\n\n## Make it show the assumptions separately\n\nA useful variation:\n\n> Before solving, list every assumption the solution will rely on. Then solve. Then say which assumption, if wrong, would change the answer most.\n\nThis 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.\n\n## The re-derivation test\n\nThe 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.\n\nThis 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.\n\n## For non-numerical subjects\n\nThe same move works outside the sciences, in a different vocabulary.\n\n- *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.\n- *Which of these claims is contested among historians, and by whom?* Then check that the contest is real.\n- *Which sentence in this paragraph carries the most weight, and what would have to be true for it to hold?*\n\nIn every case you are converting a smooth output into a set of joints you can test individually. That is the whole technique."},"check":{"question":"Why is a step-by-step chain from a model not evidence that the reasoning shown is the reasoning that produced the answer?","options":[{"text":"Because the temperature setting randomises intermediate steps more than final answers.","correct":false,"tempting":"Invents a mechanism; sampling applies uniformly across the output, and a stable chain can still be unfaithful."},{"text":"Because models generate the final answer first and then write a justification backwards to fit it.","correct":false,"tempting":"Overstates the mechanism into a specific claim that is not generally true; generation is left to right, and the steps do genuinely improve accuracy."},{"text":"Because the chain is generated text written alongside the answer, not a record of what produced it.","correct":true},{"text":"Because chains are usually copied from training examples of similar problems rather than computed for this one.","correct":false,"tempting":"Treats the model as retrieving a stored solution; it is generating one, which is why the chain adapts correctly to a novel problem's numbers."}]},"prev":{"slug":"give-it-the-source","title":"Give it the source","url":"https://addaly.com/learn/ai-for-students/give-it-the-source"},"next":{"slug":"follow-ups-that-find-the-weak-joint","title":"Follow-ups that find the weak joint","url":"https://addaly.com/learn/ai-for-students/follow-ups-that-find-the-weak-joint"},"authorship":"Founder and series editor: Dr Mustafa Mun. Written by AI models to a written standard. Exam keys checked blind by a second model: 3,665 of 3,666 agreed. Academic review invited.","review":{"status":"Draft, open for academic review"},"cite":"Addaly (2026) 'Ask for the working, then check it', in AI for Students. Edited by M. Mun. Addaly. Available at: https://addaly.com/learn/ai-for-students/ask-for-the-working (Accessed: 13 October 2026).","licence":{"name":"CC BY-NC-SA 4.0","url":"https://creativecommons.org/licenses/by-nc-sa/4.0/"},"reader":{"schema":1,"title":"Ask for the working, then check it","courseTitle":"AI for Students","module":{"index":2,"slug":"asking-well","title":"Asking well"},"answer":null,"keyIdea":"Ask for steps because they improve accuracy and give you something auditable, then audit with units, magnitude and the one difficult joint, never treating the stated reasoning as proof that it is what produced the answer.","hero":{"kind":"figure","figure":{"t":"figure","label":"Figure","figure":{"type":"flow","steps":[{"label":"Units","detail":"Carry them down every line and cancel. Joules where you wanted joules per second means the error is above that line."},{"label":"Magnitude","detail":"Estimate roughly before you look. Grams where you expected milligrams. A probability of 1.4."},{"label":"The joint","detail":"Find the one step where the difficulty of the problem actually lives, and read that step properly."},{"label":"Re-derive","detail":"Cover the chain and redo the step you trust least. Either it holds, or you have found the thing to learn."}],"title":"Auditing a chain, about two minutes","caption":"A conclusion gives you one thing to verify and no way to verify it. Six steps give you six small ones, most of which take seconds. None of this proves that the reasoning shown is the reasoning that produced the answer, and research on the faithfulness of these chains keeps finding cases where it is not. Visible working is a document to audit, not a guarantee."},"alt":"Figure: Auditing a chain, about two minutes. Steps: 1. Units (Carry them down every line and cancel. Joules where you wanted joules per second means the error is above that line.); 2. Magnitude (Estimate roughly before you look. Grams where you expected milligrams. A probability of 1.4.); 3. The joint (Find the one step where the difficulty of the problem actually lives, and read that step properly.); 4. Re-derive (Cover the chain and redo the step you trust least. Either it holds, or you have found the thing to learn.). A conclusion gives you one thing to verify and no way to verify it. Six steps give you six small ones, most of which take seconds. None of this proves that the reasoning shown is the reasoning that produced the answer, and research on the faithfulness of these chains keeps finding cases where it is not. Visible working is a document to audit, not a guarantee."}},"blocks":[{"t":"h2","id":"a-conclusion-cannot-be-checked-a-chain-can","runs":[{"text":"A conclusion cannot be checked; a chain can"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"quote","runs":[{"text":"Work through it step by step. State each assumption as you use it. Give the final answer last, on its own line."}]},{"t":"h2","id":"steps-are-not-proof","runs":[{"text":"Steps are not proof"}]},{"t":"p","runs":[{"text":"Here is the honest limitation, and it matters. A chain of reasoning produced by a model is "},{"text":"also","i":true},{"text":" 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."}]},{"t":"p","runs":[{"text":"So visible working buys you two real things:"}]},{"t":"ol","start":1,"items":[[{"text":"Checkability.","b":true},{"text":" You can find the wrong step yourself."}],[{"text":"Accuracy.","b":true},{"text":" Step-by-step generation does better on multi-step problems."}]]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"how-to-audit-a-chain-quickly","runs":[{"text":"How to audit a chain quickly"}]},{"t":"p","runs":[{"text":"You rarely need to check every step. Three passes, in order, catch nearly everything:"}]},{"t":"p","runs":[{"text":"Units and dimensions.","b":true},{"text":" 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."}]},{"t":"p","runs":[{"text":"Magnitude.","b":true},{"text":" 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."}]},{"t":"p","runs":[{"text":"The joint.","b":true},{"text":" 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."}]},{"t":"h2","id":"make-it-show-the-assumptions-separately","runs":[{"text":"Make it show the assumptions separately"}]},{"t":"p","runs":[{"text":"A useful variation:"}]},{"t":"quote","runs":[{"text":"Before solving, list every assumption the solution will rely on. Then solve. Then say which assumption, if wrong, would change the answer most."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"the-re-derivation-test","runs":[{"text":"The re-derivation test"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"for-non-numerical-subjects","runs":[{"text":"For non-numerical subjects"}]},{"t":"p","runs":[{"text":"The same move works outside the sciences, in a different vocabulary."}]},{"t":"ul","items":[[{"text":"Set out the argument as numbered premises and a conclusion before writing the paragraph.","i":true},{"text":" Then check whether the conclusion actually follows, and whether any premise is doing work it cannot support."}],[{"text":"Which of these claims is contested among historians, and by whom?","i":true},{"text":" Then check that the contest is real."}],[{"text":"Which sentence in this paragraph carries the most weight, and what would have to be true for it to hold?","i":true}]]},{"t":"p","runs":[{"text":"In every case you are converting a smooth output into a set of joints you can test individually. That is the whole technique."}]}],"check":{"question":[{"text":"Why is a step-by-step chain from a model not evidence that the reasoning shown is the reasoning that produced the answer?"}],"options":[{"text":[{"text":"Because the temperature setting randomises intermediate steps more than final answers."}],"correct":false,"tempting":[{"text":"Invents a mechanism; sampling applies uniformly across the output, and a stable chain can still be unfaithful."}]},{"text":[{"text":"Because models generate the final answer first and then write a justification backwards to fit it."}],"correct":false,"tempting":[{"text":"Overstates the mechanism into a specific claim that is not generally true; generation is left to right, and the steps do genuinely improve accuracy."}]},{"text":[{"text":"Because the chain is generated text written alongside the answer, not a record of what produced it."}],"correct":true,"tempting":null},{"text":[{"text":"Because chains are usually copied from training examples of similar problems rather than computed for this one."}],"correct":false,"tempting":[{"text":"Treats the model as retrieving a stored solution; it is generating one, which is why the chain adapts correctly to a novel problem’s numbers."}]}],"order":[0,1,2,3],"why":null},"prev":{"slug":"give-it-the-source","title":"Give it the source","minutes":9},"next":{"slug":"follow-ups-that-find-the-weak-joint","title":"Follow-ups that find the weak joint","minutes":8}}}