The Reasoning Revolution: From Chain-of-Thought to Adaptive Thinking, and What It Changes for Marking, Maths and Science

A mathematics teacher used AI for a first pass on Form 3 simultaneous equations. Every final answer was right and the feedback read well, until she reached step three: the model had dropped a negative sign while rearranging, then two steps later made a second error that happened to cancel the first. A student copying that working would learn a wrong method and believe it was correct. This was the signature failure mode of 2024-era models — and while the reasoning models of 2026 have made it much rarer, they have not eliminated it.

The biggest change in models over two years is not that they are cleverer. It is that thinking before answering became the default. For schools that shifts three things: how usable marking is, how trustworthy maths and science explanation is, and the shape of the bill.

Plain-language mechanics: from blurting out to drafting first

Early language models behaved like a student called on in class: asked a question, they started talking immediately and worked it out as they spoke. Fast, but liable to take a wrong turn halfway through anything multi-step.

Chain-of-thought was the first fix: add "think step by step" to the prompt and the model would write out its working before giving the conclusion. The reason it worked is unglamorous — the model predicts one token at a time, so writing the intermediate steps gives it a scratchpad that every later step can see.

Through 2024 and 2025 that scratchpad moved backstage: the model generates internal reasoning the user never sees, or sees only in summary, and then produces the final answer. OpenAI's o1, o3 and o4-mini were the first mainstream models to work this way. On 20 January 2025 DeepSeek-R1 published an equivalent reasoning model with open weights, showing the capability was not the preserve of the largest labs. On 24 February 2025 Anthropic's Claude 3.7 Sonnet exposed extended thinking as a switch, the milestone that popularised the approach.

2026 brought the third stage: adaptive thinking. The model no longer waits for a human to decide whether to think; it judges whether the question warrants it and for how long. In staffroom terms: the first generation thought only when told, the second gave you a thinking switch, and the third decides by itself while you supply only a rough steer.

Head-to-head: the four "how long to think" dials

The table below describes design as published in September 2026 documentation. It is not a performance ranking.

Three points deserve care:

• Effort is behavioural guidance, not a hard ceiling. Anthropic's documentation says it directly: at lower effort the model will still think when a problem is hard enough, and the actual hard limit is max_tokens. A school cannot lower effort and call the cost guaranteed.
• Thinking tokens bill at output rates. Google labels the column "Output price (including thinking tokens)". Since flagship output is typically five times input ($10 against $50 on GPT-6 Astra), reasoning effort is the easiest cost to lose control of in 2026.
• "Think step by step" is obsolete. OpenAI's reasoning best practices state that such prompting may not help reasoning models and can sometimes hurt. Rather than teaching the model how to think, state the task, output format and constraints. This changes how prompts should be written; see the prompt engineering course.

What actually changed in three teaching scenarios

Marking: from feedback-shaped text to rubric-aligned feedback

The commonest problem with 2024-era AI feedback was vagueness: "content is adequate, structure could be improved". It had not genuinely compared the work against a rubric; it had generated text that looked like feedback.

Reasoning models changed that. Before answering, the model works through the rubric criterion by criterion, locates the corresponding sentences in the student's work and then decides a mark. The practical difference is that feedback starts quoting specific sentences from the student's own text, and score consistency across repeated runs of the same rubric improves markedly. That is what moved AI marking from an interesting demo to something that belongs in a staffroom.

One line has not moved: marks still require teacher review before release. Better rubric alignment does not mean the model understands this class, or knows what was emphasised in last week's lesson.

Maths: it shows its working, and the working can still be wrong

Reliability on multi-step calculation has improved noticeably, and models can now format intermediate steps so they drop straight into a worksheet. That is particularly useful for differentiated teaching: ask for the same problem worked at three levels of difficulty.

But the teacher in the opening paragraph still has her problem, just less often: a model can produce a complete, orderly derivation that reaches a wrong conclusion. Because the steps are tidy, the error is now harder to spot than it used to be. Our guidance is specific: any worked solution going to students must be checked step by step, not only at the final answer.

Science: better explanation, no fewer factual errors

Multi-step causal explanation — why this happens, what changes if we alter a condition — is where reasoning models help science teaching most. But keep two things apart: reasoning improves getting from the known to the unknown; it does not make the model know more. It will still misremember experimental values, textbook editions and the unit sequencing of the Hong Kong curriculum, in exactly the same confident tone.

Limits and blind spots: four things reasoning does not fix

One, reasoning does not correct facts. Knowledge cutoffs remain, and they differ: 30 April 2026 for GPT-6 Astra, 1 February 2026 for Grok 4.6, January 2026 for Claude Sonnet 5. No amount of thinking reaches past the cutoff. Where current facts matter, the answer must come from the school's own knowledge base — see the school knowledge base.

Two, reasoning does not fill gaps in local knowledge. Hong Kong curriculum codes, EDB circular numbers and full school names are thin in any training corpus, and reasoning only makes the wrong content look better organised.

Three, latency is a real classroom cost. While the model thinks, the student waits. Fifteen seconds is enough to lose the attention of a Form 3 class, which is why a student-facing chat interface should not run at high effort across the board.

Four, the cost curve is non-linear. Moving from medium to xhigh can double output tokens, and output costs five times input. An integration without routing can burn a month's budget on a single batch marking run. Any school wiring up the API directly should set usage caps first.

One more thing worth saying plainly: thinking content is usually invisible or summarised. That affects traceability — you can see the final answer and the stated justification, but not the model's full internal derivation. Audit records should therefore preserve the input, the output and the model settings rather than assuming the reasoning can be reconstructed later.

Actionable guidance: a routing rule and a prompt framework

Routing rule — the platform should do this automatically, and the school should know it is happening:

A four-part prompt framework for the reasoning era:

1. Role and context: "You are a Hong Kong secondary mathematics teacher writing for Form 3 students."
2. Task: one sentence on what to produce. Do not instruct it how to think.
3. Output format: the exact fields, counts and language required.
4. Constraints: the most important part — flag uncertainty rather than filling gaps, use Traditional Chinese and Hong Kong usage, do not give the answer away.

An example:

You are a Hong Kong secondary mathematics teacher writing for Form 3 students.
Task: produce the full worked solution to the simultaneous equations problem below, with one sentence after each step stating the purpose of that step.
Output: a step table (step / operation / purpose), followed by the three errors students most commonly make.
Constraints: write in Traditional Chinese using Hong Kong terminology; every step must be independently checkable; if the problem lacks data, write "insufficient data" rather than assuming values.
[paste the problem]

The last line is what matters: requiring every step to be independently checkable drops the teacher's review cost from redoing the work to scanning it line by line.

Takeaway

The reasoning revolution moved AI from fast and shallow to slow and accurate, and handed the "how long to think" decision to the model itself. For schools the genuine gain is that marking and maths and science explanation have finally become usable. The genuine risk is that an orderly wrong answer is harder to catch than a messy one, and that cost creeps upward with thinking depth.

The right response is neither switching reasoning off nor turning it all the way up, but routing by task and keeping a teacher checkpoint in front of anything that reaches a student. For how the platform handles this layer, see the feature overview; for how the four vendors differ elsewhere, see the US provider head-to-head.