确认学习：生成式人工智能、代理问题与大学数学中的认知能力
Ascertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics
- University of Cape Town（开普敦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对生成式AI暴露大学数学评估中的代理问题，提出“先构建再委派”与“验证设上限”两原则，以维护认知能力，避免技能萎缩。
AI中文摘要：
几十年来，大学数学以可执行的程序、计算和复现标准证明作为其真正关心的理解的代理，因为程序易于批改而理解则不然。生成式人工智能现在能够执行大部分此类程序。它不仅让学生绕过代理，更暴露了以往被认证的内容中有多少仅仅是代理。这场危机不仅是作弊问题，更是一个代理问题，而解决它迫使学科面对一个长期回避的问题：数学能力中不可简化的人类核心是什么？当部分可执行工作可以被外包时，又该如何构建这种能力？我们设想了两种未来：其一是“置换与再中心化”，即人工智能接管部分执行，教育转向判断、表述和验证；其二是“萎缩”，即过早外包可能侵蚀依赖于先前构建的能力。乐观未来的核心存在一种验证不稳定性：某些监督形式廉价且有界，而另一些则接近构建工作所需的能力。结果是一种设计选择，而非技术宿命。我们不增加模型，而是将应对措施表述为两条原则：先构建再委派，以及让验证设定上限——学生能独立验证人工智能输出的程度，决定了他们可安全委派的范围。我们用一个序列和两个具体问题加以说明，并以一个问题作结：先构建再委派的依赖关系是硬性约束，还是数学教学方式的一种产物？
英文摘要：
For decades, university mathematics assessed executable procedure, computing and reproducing standard proofs, as a proxy for the understanding it cared about, because procedure was cheap to mark and understanding was not. Generative AI now executes much of this procedure. It does not merely let students bypass the proxy; it exposes how much of what was certified was a proxy. The crisis is not simply cheating but a proxy problem, and resolving it forces a question the discipline has long avoided: what is the irreducible human core of mathematical competence, and how can it be built when some of the executable work can be offloaded? We set out two futures: displacement-and-re-centering, in which AI takes over some execution and education moves toward judgment, formulation and verification; and atrophy, in which premature offloading may erode capacities that depend on prior construction. At the heart of the optimistic future is a verification instability: some forms of oversight are cheap and bounded, while others approach the competence required to construct the work. The outcome is a design choice, not a technological destiny. Rather than add a model, we state the response as two principles: construct before you delegate, and let verification set the ceiling: how far a student can independently verify AI output limits what they may safely delegate. We illustrate with a sequence and two worked problems, and close on the question: whether the construct-before-delegate dependency is a hard constraint or an artefact of how mathematics has been taught.
