用1934个学习原子构建数学课程，实现自动组题与能力评估。
Atom Learning Model (ALM): how a real classroom got tokenised
- 将757页教材拆分为1934个可操作的学习原子，按4616条前置关系排序。
- 系统自动生成6648道题，每题成本仅26便士，准确匹配学生能力水平。
- 无需人工标注，验证了学习路径的自动化可行性，适合教育技术研究者。
原子学习模型（ALM）将英国GCSE及进阶数学课程的757页材料转化为1934个学习原子，每个原子代表一个可执行的学习步骤，并通过4616条机器生成的前置依赖关系进行排序。问题由一组原子及其子结构构成，学生能力以0到1之间的分数表示每个原子的掌握程度，题目适配性仅需一次算术运算判断，无需调节难度参数。所有原子、链接和题目均由机器生成，无人工干预。读取757页材料花费55英镑，构建整个系统耗资615至1230英镑。在七周内，系统为两所英国中学的373名学生生成6648道题目，每题成本26便士。四项测量结果出乎意料：成本主要来自链接而非文本；语言模型对题目难度的评分与实际掌握度的相关性仅为-0.0123；当答题时间从三秒增至七秒时，学生停止作答；部署中未出现超过两步前置依赖的问题，这恰好是核心假设可被检验的关键点，因此该假设未被证伪，也未被证实。
原文摘要 · Abstract (English)
The Atom Learning Model (ALM) tokenises a school curriculum. 757 pages of GCSE and Further Mathematics material were read by machine into 1,934 atoms, each one thing a learner can do in a single step, ordered by 4,616 machine-written prerequisite links. Both sides of a lesson are then expressed in that one structure: a question is a set of atoms plus everything beneath them, a child's ability is a score between 0 and 1 on every atom of the same graph, and whether a question suits a child is arithmetic over one index, with no difficulty parameter fitted for either side. Nobody wrote an atom, a link or a question. Reading the 757 pages cost £55, building the whole structure cost between £615 and £1,230, and against it the system composed 6,648 questions for 373 children in two English secondary schools over seven weeks, at 26p per composed question. Four measurements went against expectation. The cost is in the links, not the pages. The composer's own difficulty label has a rank correlation of -0.0123 with measured facility, so a language model shown a question cannot say how hard it is. Children stop working when a mark takes seven seconds instead of three. And the deployment never served a question deeper than two prerequisite steps, which is exactly where the central premise becomes testable, leaving it unfalsified rather than confirmed.
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