Chain-of-Thought Prompting and the Reasoning-Model Era
Ask a 2022 LLM a two-step math problem and it blurts a wrong answer in one gulp. Chain-of-thought prompting fixed that by making the model write intermediate steps — the "show your work" trick that jumped GSM8K from 17.8% to 56.9%. This topic covers the discovery, the toolkit (few-shot/zero-shot CoT, self-consistency, verification), the faithfulness caveat, and how prompted CoT grew into RL-trained reasoning models (o1, DeepSeek-R1) that internalize the scratchpad.
01.The Problem: Two-Step Math Needs More Than One Word
Give a 2022-era language model this:
"Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many does he have now?"
Asked for just the answer, the model blurts a number in a single forward pass — and misses. The right path needs two moves: 2 × 3 = 6, then 5 + 6 = 11. The model tried to do multiplication and addition as one reflex.
Why? Because answering directly spends essentially all of its "thinking" on pattern-matching the answer shape, not on the computation. A single next-token prediction has to leap from question to answer in one hop.
So the question becomes
Can a model that produces one word at a time be made to spend words on the middle of the computation?
That is chain-of-thought prompting: letting (and making) the model write out its steps before answering. It produced the largest single prompt-technique capability gain ever measured — and then, in 2024–2025, it quietly stopped being a prompt trick and became a training target. Both halves are this topic.
From Prompted Steps to Trained Reasoning 🧩
From Prompted Steps to Trained Reasoning 🧩
CoT bought capability with tokens in 2022; 2024–2025 reasoning models buy the same capability with RL-trained internal chains and an explicit token budget.
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