CoLearn: An Agentic Tutor that Learns its Learner
in a Human–AI Co-Learning LoopCoLearn：一种在人机共学循环中学习其学习者的代理导师

Kailai He Zhihao Wu Linhai Zhang Runcong Zhao Yulan He Jiazheng Li Affiliation: King’s College London Affiliation: hekailai@gmail.com , {zhihao.wu, linhai.zhang, runcong.zhao, yulan.he, jiazheng.li}@kcl.ac.uk

Abstract摘要

Good tutoring adapts to the individual: it tracks what a learner knows, notices why they go wrong, and asks the next question that will help most. Most deployed tutoring tools instead serve fixed item banks and treat a wrong answer as a single bit of signal. We present CoLearn, an interactive, agentic tutor that supports an iterative tutoring loop: the learner practises, and the system builds an evidence-grounded memory of the learner’s mastery and misconceptions. This memory is updated as evidence accumulates and is used to generate the next personalised question. CoLearn has three components: (i) a persistent learner-state memory that updates per-topic mastery with a soft-evidence variant of Bayesian Knowledge Tracing, where a large language model acts as a continuous observation function; (ii) adaptive question generation that targets the learner’s weakest topic and recurring misconceptions; and (iii) an evidence view that makes personalisation visible and testable through live progress visualisation and blind A/B comparison. In blind A/B evaluation, questions conditioned on this memory are preferred over non-personalised ones $68$ – $69\%$ of the time, and in persona simulations with hidden ground-truth mastery the agent’s belief converges toward the learner’s true mastery.优秀的辅导能够因材施教：它会追踪学习者的知识掌握情况，注意他们出错的原因，并提出最能提供帮助的后续问题。然而，大多数已部署的辅导工具往往提供固定的题库，并将错误答案仅视为一个简单的信号。我们提出了 CoLearn，这是一种交互式的代理导师，支持迭代辅导循环：学习者进行练习，系统则建立一个基于证据的学习者掌握情况和误解记忆。该记忆会随着证据的积累而更新，并用于生成下一个个性化问题。CoLearn 包含三个组件：(i) 一个持久化的学习者状态记忆，通过贝叶斯知识追踪（BKT）的软证据变体更新各主题的掌握程度，其中大语言模型充当连续观测函数；(ii) 针对学习者最薄弱主题和反复出现的误解的自适应问题生成；(iii) 一个证据视图，通过实时进度可视化和盲测 A/B 对比，使个性化过程变得可见且可验证。在盲测 A/B 评估中，基于该记忆生成的问题在 68%–69% 的情况下优于非个性化问题，并且在隐藏真实掌握程度的角色模拟中，代理的信念会收敛于学习者的真实掌握水平。

1 Introduction1 引言

Good teaching is not the scoring of answers as right or wrong. A long tradition in learning science treats genuine learning as conceptual change: the learner gradually replaces a faulty understanding with a more accurate one (Piaget, 1952; Smith III et al., 1994), so a wrong answer is informative. It exposes the specific misconception the next round of teaching should address (Tatsuoka, 1983), where earlier behaviourist accounts recorded only whether a response was correct (Thorndike, 1913). Good instruction also meets each learner where they are, pitching the next task into the gap between what a student can do alone and what they can do with help (Vygotsky, 1978; Bloom, 1984; VanLEHN, 2011; Li et al., 2023; Li et al., 2024b; Li et al., 2025; Wong et al., 2026), which requires continuous diagnosis of the learner’s present understanding (Black and Wiliam, 1998; Li et al., 2026). The ideal tutor, in short, maintains a progressively refined account of each learner’s understanding and misconceptions and acts on it. However, a human teacher who could continuously diagnose every student is unrealistic and expensive.优秀的教学不仅仅是给答案打分。学习科学中有一个悠久的传统，即将真正的学习视为概念的转变：学习者逐渐用更准确的理解取代错误的理解（Piaget, 1952; Smith III et al., 1994），因此错误的答案是有信息量的。它揭示了下一轮教学应解决的具体误解（Tatsuoka, 1983），而早期的行为主义观点仅记录反应是否正确（Thorndike, 1913）。良好的教学还应因材施教，将后续任务设定在学生独立完成与辅助完成之间的差距中（Vygotsky, 1978; Bloom, 1984; VanLEHN, 2011; Li et al., 2023; Li et al., 2024b; Li et al., 2025; Wong et al., 2026），这需要对学习者当前的理解进行持续诊断（Black and Wiliam, 1998; Li et al., 2026）。简而言之，理想的导师会维护一份关于每个学习者理解和误解的不断完善的记录，并据此采取行动。然而，对于人类教师而言，持续诊断每一位学生既不现实，成本也过高。

Intelligent tutoring systems promise to scale this ideal, but existing deployed tools approximate it badly in three ways. (i) Knowledge-tracing systems. Classic adaptive tutors built on knowledge tracing (Corbett and Anderson, 1994; Anderson et al., 1995; Piech et al., 2015) model knowledge coarsely: every response is reduced to a correct/incorrect bit per skill, discarding the diagnostic content of a free-text answer. (ii) LLM-based tutors. Recent large language model tutors converse fluently and give high-quality feedback (LearnLM Team et al., 2025; Kwon et al., 2024; Macina et al., 2023; Sonkar et al., 2023; Li et al., 2024a; Zhao et al., 2025), but are largely memoryless. CoLearn focuses on connecting answer-level diagnosis to persistent learner-state memory and subsequent adaptive practice. (iii) Opaque adaptation. In both families the adaptation is invisible: the learner cannot inspect what the system believes about them (Bull and Kay, 2007; Bodily and Verbert, 2017).智能辅导系统有望推广这种理想模式，但现有的已部署工具在三个方面表现欠佳。(i) 知识追踪系统。基于知识追踪构建的经典自适应导师（Corbett and Anderson, 1994; Anderson et al., 1995; Piech et al., 2015）对知识的建模较为粗糙：每个反应都被简化为每个技能的正确/错误位，丢弃了自由文本答案中的诊断内容。(ii) 基于大语言模型（LLM）的导师。近期的大语言模型导师能够流畅对话并提供高质量反馈（LearnLM Team et al., 2025; Kwon et al., 2024; Macina et al., 2023; Sonkar et al., 2023; Li et al., 2024a; Zhao et al., 2025），但基本上没有记忆。(iii) 不透明的自适应。在这两类系统中，自适应过程都是不可见的：学习者无法检查系统对他们的评估（Bull and Kay, 2007; Bodily and Verbert, 2017）。CoLearn 专注于将答案层面的诊断与持久的学习者状态记忆及随后的自适应练习联系起来。

Refer to caption — Figure 1: CoLearn demo workflow across learner and administrator views. The learner first configures a practice session, answers an adaptive question, and receives diagnostic feedback with answer-linked annotations and live mastery estimates. The progress and administrator views expose the same personalization evidence through learner progress, blind A/B analytics, and agent convergence diagnostics.图 1：CoLearn 在学习者和管理员视图下的演示工作流。学习者首先配置练习会话，回答自适应问题，并收到带有答案关联标注和实时掌握程度估计的诊断反馈。进度和管理员视图通过学习者进度、盲测 A/B 分析和代理收敛诊断来展示相同的个性化证据。

To close this gap and let more students benefit from personalised tutoring, we present CoLearn, an interactive tutor that operationalises the ideal tutor as a human–AI co-learning loop and, crucially, makes its mastery and misconception estimates visible and its personalisation testable. The learner answers a question; the agent grades it, mines the misconception it reveals, updates a persistent per-topic mastery estimate, and uses that updated belief to generate the next, better-targeted question. The interface renders the agent’s evolving belief in real time, so personalisation is something the user can see rather than take on trust, and a built-in blind A/B test supports blinded comparison of adaptive and random-topic questions. CoLearn is multi-subject (evaluated on Biology and Chemistry curricula), supports both multiple-choice and short-answer style questions, and deploys as a single-node container stack with a provider-selectable LLM backend. We use co-learning in a deliberately modest sense: the learner practises the subject while the system refines its memory of the learner’s mastery and misconceptions. CoLearn surfaces how these estimates change and stabilise during use, while the question strategy stays fixed (§2.3). Our demo video is available at https://youtu.be/I1Lxg4ud3-Y.为了弥合这一差距并让更多学生从个性化辅导中受益，我们提出了 CoLearn，这是一种交互式导师，它将理想导师的操作化为一个人机共学循环，并且至关重要的是，使其实施的掌握程度和误解估计变得可见，个性化效果变得可验证。学习者回答问题；代理对其评分，挖掘其揭示的误解，更新持久的各主题掌握程度估计，并利用更新后的信念来生成下一个更有针对性的问题。界面实时呈现代理不断演变的信念，因此个性化是用户可以看到而非仅凭信任接受的内容，内置的盲测 A/B 测试支持对自适应问题和随机主题问题进行盲法对比。CoLearn 支持多个学科（已在生物学和化学课程中进行评估），支持选择题和简答题，并作为单节点容器堆栈部署，支持可选择提供商的 LLM 后端。我们刻意在适度的意义上使用“共学”一词：学习者练习学科知识，同时系统完善其关于学习者掌握程度和误解的记忆。CoLearn 展示了这些估计在学习过程中的变化和稳定方式，而问题策略保持不变（§2.3）。我们的演示视频可在 https://youtu.be/I1Lxg4ud3-Y 查看。

2 Overview of CoLearn2 CoLearn 概述

CoLearn is organised as two views of one loop (Figure 1). The learner’s view (§2.1) is where practice happens: the learner answers a question, receives feedback, and watches the agent’s current mastery estimates fill in and update in real time. The evidence view (§2.4) is where personalisation can be inspected through a progress dashboard and a blind A/B comparison of personalised and non-personalised questions. Between the two sits the engine of the loop: a persistent learner-state memory that stores mastery estimates and mined misconception summaries (§2.2), and an adaptive question generator that acts on this memory (§2.3). Figure 2 sketches the full loop.CoLearn 被组织为同一循环的两个视图（图 1）。学习者视图（§2.1）是练习发生的地方：学习者回答问题，接收反馈，并实时观察代理当前的掌握程度估计值的填充与更新。证据视图（§2.4）是可以通过进度仪表板和个性化问题与非个性化问题的盲测 A/B 对比来检查个性化效果的地方。两者之间是该循环的引擎：存储掌握程度估计和挖掘出的误解摘要的持久学习者状态记忆（§2.2），以及基于此记忆运行的自适应问题生成器（§2.3）。图 2 勾勒了完整的循环。

2.1 Learner Interface2.1 学习者界面

A session begins with a short setup: the learner picks a subject, the topics to work on, and a mode (§3 explains the modes; the default is the adaptive system).会话以简短的设置开始：学习者选择学科、要练习的主题和模式（§3 解释了这些模式；默认为自适应系统）。

CoLearn then drives a streamed loop. It selects or generates the next item and streams its reasoning stages (“generating your question…”) so the agent’s work is visible. The learner answers (free text for short-answer items, or an option for multiple-choice), and the answer is graded with streamed stages (“marking your answer…”). The feedback card shows a plain-language verdict, a “watch out” line surfacing the most salient misconception as friendly guidance, and, for free-text answers, the learner’s own words re-rendered with span-level highlights linked to a mark-scheme breakdown.随后，CoLearn 驱动一个流式循环。它选择或生成下一个项目，并流式传输其推理阶段（“正在生成您的问题……”），以便代理的工作可见。学习者回答（简答题使用自由文本，选择题使用选项），答案通过流式阶段进行评分（“正在标记您的答案……”）。反馈卡显示普通语言的结论，一行“注意”提示作为友好指导突出显示最显著的误解，对于自由文本答案，学习者的原话会重新呈现，并附带与评分方案细则链接的跨度级高亮显示。

After each answer, the targeted topic’s mastery bar animates from its previous value to its new one, and a “why this question” chip names what the item was chosen to probe, making the personalisation explicit rather than implicit.每次回答后，目标主题的掌握程度条会从之前的值动画过渡到新值，并且一个“为什么选择此问题”的标签会说明选择该项目是为了探测什么，从而使个性化过程变得显性而非隐性。

2.2 Persistent Learner-State Memory2.2 持久学习者状态记忆

To personalise tutoring across sessions, CoLearn maintains a persistent learner-state memory containing topic-level mastery, recurring misconception, and the mastery trajectory. Its contents are stored in per-(learner, subject) records rather than per-session logs, allowing the agent to accumulate evidence over time and visualise how its belief evolves across sessions.为了在会话间实现个性化辅导，CoLearn 维护了一个持久的学习者状态记忆，其中包含主题级掌握程度、反复出现的误解和掌握轨迹。其内容存储在每个（学习者，学科）记录中，而不是每个会话的日志中，从而允许代理随时间积累证据，并可视化其信念如何在会话间演变。

Formally, we model the interaction as a sequence of rounds: at round $t$ the agent poses a question $q_{t}$ , the learner responds with $r_{t}$ , and the agent returns feedback $f_{t}$ . Each answered round drives an update $A_{t}\!\rightarrow\!A_{t+1}$ of the agent’s belief about the learner, while the learner’s true knowledge state $H_{t}$ remains latent. Concretely, $A_{t}$ holds a mastery estimate $p=P(\text{known})$ per topic, a de-duplicated list of mined misconceptions, and the mastery trajectory. CoLearn measures and visualises $A_{t}$ ; a rising mastery estimate is therefore evidence that the agent’s belief has changed, not proof that the learner has mastered the skill (see the Limitations section).形式上，我们将交互建模为一系列回合：在第 t 回合，代理提出问题 qt，学习者以 rt 响应，代理返回反馈 ft。每个已回答的回合都会驱动代理关于学习者的信念 At→At+1 的更新，而学习者的真实知识状态 Ht 保持潜伏。具体而言，At 持有每个主题的掌握程度估计 p=P(known)、一个已挖掘误解的去重列表以及掌握轨迹。CoLearn 测量并可视化 At；因此，掌握程度估计的上升是代理信念发生改变的证据，而非学习者已掌握该技能的证明（见限制部分）。

Soft-Evidence Knowledge Tracing.软证据知识追踪。

Mastery is updated with a soft-evidence variant of Bayesian Knowledge Tracing (Corbett and Anderson, 1994); extensions to standard BKT typically individualise its parameters or enrich its inputs (Yudelson et al., 2013; Piech et al., 2015; Abdelrahman et al., 2023; Ghosh et al., 2020). Standard BKT consumes a binary correct/incorrect observation. Instead, our LLM grader acts as a continuous observation function: from an answer it emits graded evidence $o=\textit{mastery\_evidence}\in[0,1]$ together with a confidence $w=\textit{evidence\_strength}\in[0,1]$ , and we feed these in without binarising at $0.5$ . Given prior $p$ and BKT parameters $(p_{\text{slip}},p_{\text{guess}},p_{\text{transit}})$ , we form the Bayesian posteriors for a correct and an incorrect observation,掌握程度通过贝叶斯知识追踪（Corbett and Anderson, 1994）的软证据变体进行更新；对标准 BKT 的扩展通常是个性化其参数或丰富其输入（Yudelson et al., 2013; Piech et al., 2015; Abdelrahman et al., 2023; Ghosh et al., 2020）。标准 BKT 使用二元的正确/错误观测值。相反，我们的 LLM 评分器充当连续观测函数：从答案中，它发出评分证据 o=mastery_evidence∈[0,1] 以及置信度 w=evidence_strength∈[0,1]，我们将这些输入直接馈入，而不进行 0.5 的二值化。给定先验 p 和 BKT 参数 (pslip, pguess, ptransit)，我们形成正确和错误观测的贝叶斯后验，

	$\displaystyle p^{+}$	$\displaystyle=\frac{p\,(1-p_{\text{slip}})}{p\,(1-p_{\text{slip}})+(1-p)\,p_{\text{guess}}},$
	$\displaystyle p^{-}$	$\displaystyle=\frac{p\,p_{\text{slip}}}{p\,p_{\text{slip}}+(1-p)\,(1-p_{\text{guess}})},$

blend them by $o$ , and shrink toward the prior by the confidence $w$ , giving the confidence-shrunk posterior $p_{\text{cond}}=p+w\,(o\,p^{+}+(1-o)\,p^{-}-p)$ . We then apply a competence-gated learning transition:通过 o 将它们混合，并根据置信度 w 向先验收缩，得到置信度收缩后的后验 pcond=p+w(o p+ + (1-o) p- - p)。然后我们应用能力门控的学习转换：

p_{\text{next}}\;=\;p_{\text{cond}}\;+\;o\,(1-p_{\text{cond}})\,p_{\text{transit}}.

(1)

Gating the learning term by $o$ ensures a clearly wrong answer cannot raise the mastery estimate; since standard BKT applies the transition after every attempt, the update is a variant of BKT rather than a strict reduction (recovering standard BKT when $o{=}1$ , $w{=}1$ ). The scheme is pure, unit-tested arithmetic with shared default parameters.通过 o 对学习项进行门控确保了明显的错误答案无法提高掌握程度估计；由于标准 BKT 在每次尝试后都应用转换，因此该更新是 BKT 的变体，而不是严格的简化（当 o=1, w=1 时恢复为标准 BKT）。该方案是纯粹的、经过单元测试的算术，具有共享的默认参数。

Misconception Memory.误解记忆。

For seed items, candidate misconceptions are derived once from curriculum-aligned mark-scheme negative phrasing (e.g. “do not accept…”) and attached to the item, so the diagnostic targets come from the assessment material itself rather than a separately maintained catalogue. For short-answer questions, the grader returns short misconception summaries with verbatim supporting quotes. It distinguishes a positive label (the learner stated something wrong) from an absence label (an omission or a too-vague answer), and reuses a candidate’s canonical wording when one matches, so labels stay consistent across sessions; the summaries accumulate (de-duplicated) in memory. For multiple-choice items, each distractor is tagged with the specific misconception it embodies, so choosing a distractor is itself the diagnostic label, graded deterministically with no LLM call (Gierl et al., 2017; Wang et al., 2021).对于种子项目，候选误解从课程对齐的评分方案负面措辞（例如“不接受……”）中一次性导出并附加到项目中，因此诊断目标来自评估材料本身，而不是单独维护的目录。对于简答题，评分器返回带有逐字支持引用的简短误解摘要。它区分了肯定标签（学习者陈述了错误内容）和缺失标签（遗漏或过于模糊的答案），并在匹配时重用候选者的规范措辞，因此标签在会话间保持一致；摘要在记忆中积累（去重）。对于选择题，每个干扰项都标记有其体现的具体误解，因此选择干扰项本身就是诊断标签，通过确定性方式评分，无需调用 LLM（Gierl et al., 2017; Wang et al., 2021）。

2.3 Adaptive Question Generation2.3 自适应问题生成

Weakness-Targeted Generation. To act on this memory, CoLearn generates the next item to target their specific weaknesses (Kurdi et al., 2020). It ranks the learner’s in-scope topics, targets the weakest, and selects up to two of its stored misconceptions to probe, optionally asking the LLM to link related misconceptions above a threshold. It then generates either a short-answer item or a multiple-choice item whose distractors are each bound to a known misconception. Generated items carry metadata (the targeted topic and misconceptions) that drives the visible “why this question” chip. When the learner has no in-scope history yet, curated seed items give a sensible cold start.弱点针对性生成。为了基于此记忆采取行动，CoLearn 生成下一个项目以针对其特定弱点（Kurdi et al., 2020）。它对学习者范围内的主题进行排名，锁定最弱的主题，并选择最多两个存储的误解进行探测，可选择要求 LLM 链接超过阈值的相关误解。然后，它生成简答题或选择题，后者的干扰项各自绑定到一个已知的误解。生成的问题带有元数据（目标主题和误解），这些元数据驱动可见的“为什么选择此问题”标签。当学习者尚无范围内历史记录时，精选的种子项目可提供合理的冷启动。

Strategy Layer. Beyond adapting its belief about the learner, CoLearn is designed to adapt its strategy that targets each individual learner’s diagnosis based on the previous outcome: the question generator consults a natural-language guideline appended to its prompt (e.g. “when targeting a stored misconception, prefer MCQ with one distractor per misconception”), so revising this text immediately changes how the next item is written, with no code change or redeployment. This is the hook for the agent-side half of co-learning, stated plainly: today the guideline is a fixed text consulted on every generation; automatic revision from accumulated outcomes is planned but not yet implemented (see the Limitations section). The co-learning the live system demonstrates is therefore memory-side: the learner receives targeted practice while the agent updates its stored estimates from accumulated evidence.策略层。除了调整其关于学习者的信念外，CoLearn 还旨在根据之前的结果调整针对每个个体学习者的诊断策略：问题生成器查阅附加在其提示词后的自然语言指南（例如“当针对存储的误解时，偏向于每个误解对应一个干扰项的选择题”），因此修改此文本会立即改变下一个项目的编写方式，无需修改代码或重新部署。这是共学中代理侧的钩子，简单明了：目前指南是在每次生成时查阅的固定文本；从积累的结果中进行自动修订已规划但尚未实现（见限制部分）。因此，实时系统展示的共学是记忆侧的：学习者获得针对性练习，而代理从积累的证据中更新其存储的估计值。

2.4 Evidence View2.4 证据视图

To make the agent’s adaptation transparent, CoLearn provides a progress dashboard with a branch-graph timeline, concept-mastery radar, and mastery-over-time trajectory, allowing users to inspect how the mastery estimates and misconception summaries change across sessions. CoLearn also includes a blind A/B interface to evaluate personalisation capability, presenting personalised and non-personalised questions in randomised, unlabelled positions and asking users which is more relevant. Results are aggregated into an analytics dashboard reporting the preference rate, a $95\%$ confidence interval, and a two-sided sign test against the $0.5$ chance rate.为了使代理的自适应过程透明，CoLearn 提供了一个带有分支图时间轴、概念掌握雷达和掌握时间轨迹的进度仪表板，允许用户检查掌握程度估计和误解摘要如何在会话间变化。CoLearn 还包括一个盲测 A/B 界面来评估个性化能力，在随机、未标记的位置呈现个性化和非个性化问题，并询问用户哪个更相关。结果汇总到分析仪表板中，报告偏好率、95% 置信区间以及针对 0.5 机会率的双侧符号检验。

2.5 System Architecture2.5 系统架构

CoLearn is a container-deployed web application. The frontend is a Vite + React + TypeScript single-page app. The backend is FastAPI with an async MongoDB store, JWT/bcrypt authentication, and SSE streaming for live generation and grading. The LLM backend is provider-selectable (AWS Bedrock with Claude Sonnet 4.5 as the live default; an OpenAI-compatible path is also supported). The whole stack starts with one command via Docker Compose (MongoDB, backend, a one-shot idempotent seeder, and an Nginx proxy serving the SPA and proxying the API). The backend ships with a test suite covering BKT, grading, generation, streaming, RBAC, and the A/B analytics.CoLearn 是一个容器部署的 Web 应用程序。前端是 Vite + React + TypeScript 单页应用。后端是 FastAPI，带有异步 MongoDB 存储、JWT/bcrypt 身份验证以及用于实时生成和评分的 SSE 流。LLM 后端可由提供商选择（默认使用 AWS Bedrock 上的 Claude Sonnet 4.5；也支持 OpenAI 兼容路径）。整个堆栈通过 Docker Compose（MongoDB、后端、一次性幂等种子生成器以及代理 SPA 和 API 的 Nginx 代理）通过一个命令启动。后端附带一套测试套件，涵盖 BKT、评分、生成、流式传输、RBAC 和 A/B 分析。

3 Evaluation3 评估

We evaluate CoLearn along three dimensions: perceived relevance of personalised versus non-personalised questions (§3.2), learner-state estimation accuracy and convergence under persona simulation (§3.3), and deployment responsiveness and cost (§3.4). §3.1 first defines the session conditions and metrics shared across these studies.我们从三个维度评估 CoLearn：个性化问题与非个性化问题的感知相关性（§3.2）、角色模拟下的学习者状态估计准确性和收敛性（§3.3），以及部署响应性和成本（§3.4）。§3.1 首先定义了这些研究中共享的会话条件和指标。

3.1 Conditions and Metrics3.1 条件和指标

CoLearn supports three session conditions that isolate personalisation as the variable of interest:CoLearn 支持三种会话条件，将个性化作为感兴趣的变量进行隔离：

•

Adaptive: the full system. Items are generated to target the learner’s weakest topics, and memory is updated after every answer.自适应：完整系统。项目生成旨在针对学习者最弱的主题，并且每次回答后都会更新记忆。
•

Random-topic: the non-personalised control. Items are drawn from topics chosen at random within the learner’s selected scope (mastery-blind), but memory is still updated. This isolates the effect of targeting specifically, holding adaptivity constant.随机主题：非个性化对照组。项目从学习者所选范围内随机选择的主题中抽取（掌握程度盲测），但记忆仍会更新。这隔离了针对性的影响，保持自适应性不变。
•

Frozen: a memory-convergence control. Fixed items are served in order, and memory is read but not written, giving a flat agent-state baseline.冻结：记忆收敛对照组。固定项目按顺序提供，读取但不写入记忆，提供平坦的代理状态基准。

3.2 Does Personalisation Produce More Relevant Questions?3.2 个性化是否能产生更相关的问题？

Using the built-in A/B tool, each comparison presents a personalised (Adaptive) question and a non-personalised (Random-topic) question in two blinded slots; slot order is randomised and provenance is hidden server-side. The rater answers the question “which question feels more relevant to this learner right now?”. Picks are stored with their (hidden) provenance for later analysis; A/B items are not written back into the learner-state memory.使用内置的 A/B 工具，每次比较在两个盲测槽位中呈现一个个性化（自适应）问题和一个非个性化（随机主题）问题；槽位顺序随机，来源在服务器端隐藏。评分者回答“哪个问题此时此刻对该学习者感觉更相关？”。选择及其（隐藏的）来源被存储以供后续分析；A/B 项目不会写回学习者状态记忆。

We recruited $18$ raters with a relevant background (e.g., they have studied and passed the curriculum). Each rater completed $12$ comparisons, yielding $M=18\times 12$ judgements. We report the preference rate (fraction of comparisons in which the personalised item was chosen), its 95% confidence interval, and a two-sided sign test against the chance rate of $0.5$ .我们招募了 18 名具有相关背景的评分者（例如，他们学习并通关了课程）。每位评分者完成了 12 次比较，产生 M=18×12 次判断。我们报告偏好率（选择个性化项目的比较比例）、其 95% 置信区间以及针对 0.5 机会率的双侧符号检验。

The personalised item is preferred $0.68$ of the time across Biology raters ( $0.74$ and $0.73$ for mixed- and strong-ability learners) and $0.69$ across Chemistry raters ( $p=0.008$ , sign test over 18 raters). Preference is lower in the strong tier ( $0.73$ Biology, $0.66$ Chemistry) than the mixed tier, consistent with targeting mattering less when there is little weakness to target; we do not test the six-rater tiers individually.个性化项目在生物学评分者中被选择的比例为 0.68（混合和强能力学习者分别为 0.74 和 0.73），在化学评分者中为 0.69（p=0.008，18 名评分者的符号检验）。强能力组的偏好率（生物学 0.73，化学 0.66）低于混合组，这与当弱点较少时针对性作用减弱的预期一致；我们没有单独测试六人评分者层级。

Breakdown	$n$	Pref. rate	95% CI	$p$
Biology (overall)	18	0.68	[0.60, 0.77]	0.008
mixed learners	6	0.74	[0.71, 0.77]
strong learners	6	0.73	[0.59, 0.88]
Chemistry (overall)	18	0.69	[0.60, 0.77]	0.008
mixed learners	6	0.77	[0.61, 0.93]
strong learners	6	0.66	[0.52, 0.80]

Table 1: Blind A/B preference for personalised over non-personalised questions. Pref. rate is the mean per-rater preference, 95% CI is across raters, and $p$ is a two-sided sign test vs.

0.5

. The mixed/strong rows are learner ability tiers (not subjects); weak-tier learners are excluded because, being weak on every skill, they cannot discriminate targeting, so the tier rows sum to fewer than the all row.表 1：对个性化问题优于非个性化问题的盲测 A/B 偏好。偏好率是每位评分者的平均偏好，95% CI 是评分者间的置信区间，p 是针对 0.5 的双侧符号检验。混合/强行是指学习者能力层级（非学科）；弱能力层级学习者被排除在外，因为他们在每个技能上都很弱，无法区分针对性，因此层级行之和少于总行。

Metric	Adaptive	Random	Frozen
Weak-skill hit (warm)	0.72	0.55	0.57
Mixed learners	0.89	0.57	–
Strong learners	0.28	0.08	–
Mastery MAE $\downarrow$	0.12	0.16	0.20

Table 2: User-simulation (hidden ground-truth mastery). Weak-skill hit rows are from an 18-persona warm-start sweep; the Mastery MAE row is from the 6-persona Claude Sonnet 4.5-graded run. Weak-skill hit = fraction of served items on a truly-weak skill (higher = better targeting); Mastery MAE = final agent belief vs. true mastery (lower = better). Adaptive beats the Random-topic / Frozen controls on both. (Weak personas are weak on every skill, so they cannot discriminate targeting and are excluded from the per-tier rows.)表 2：用户模拟（隐藏真实掌握程度）。弱技能命中行来自 18 个角色的预热启动扫描；掌握程度 MAE 行来自 6 个角色的 Claude Sonnet 4.5 评分运行。弱技能命中 = 在真正薄弱的技能上提供的项目比例（越高越好）；掌握程度 MAE = 最终代理信念与真实掌握程度的差异（越低越好）。自适应在两项指标上均优于随机主题/冻结对照组。（弱能力角色在所有技能上都很弱，因此无法区分针对性，被排除在分层行之外。）

3.3 Do Learner-State Estimates Track Ground Truth?3.3 学习者状态估计是否追踪真实情况？

Mastery prediction error and misconception P/R/F1 require ground truth, so we drive the loop with synthetic personas whose per-skill mastery and misconceptions are hidden from the system (Markel et al., 2023; Tack and Piech, 2022): a database-free harness exercises the real grading and BKT services, so answers flow through the live system’s observation function. On a run graded by the live framework model (Claude Sonnet 4.5; 6 personas, 132 rounds; the LLM grade serves as the observation, cf. LLM-as-judge reliability (Zheng et al., 2023)), per-answer mastery_evidence correlates with true mastery at Pearson $r=0.68$ pooled across tiers. This pooled figure is driven mainly by between-tier separation; however, mean evidence rises cleanly by ability tier ( $0.25$ weak / $0.67$ mixed / $0.77$ strong), but the within-tier correlation is much weaker ( $r\approx 0.15$ / $0.48$ / $0.41$ ), and weakest for low-ability personas. The observation function is therefore least reliable for exactly the learners who most need accurate diagnosis (see Limitations). Mined misconceptions match the personas’ assigned ones at F1 $\approx 0.56$ .¹¹ 1 Computed post hoc by token-overlap matching of mined labels against assigned misconceptions over all 132 rounds. This F1 score evaluates the grader’s recovery of persona misconception labels from learner answers. It does not test whether a generated question elicits the misconception named in its generation metadata.掌握程度预测误差和误解的 P/R/F1 需要真实情况，因此我们使用合成角色驱动循环，其各技能掌握程度和误解对系统隐藏（Markel et al., 2023; Tack and Piech, 2022）：一个无数据库的工具利用真实的评分和 BKT 服务，因此答案流经实时系统的观测函数。在由实时框架模型（Claude Sonnet 4.5；6 个角色，132 回合；LLM 评分作为观测值，cf. LLM-as-judge 可靠性 (Zheng et al., 2023)）评分的运行中，每次回答的 mastery_evidence 与真实掌握程度的相关性在各层级汇总后 Pearson r=0.68。该汇总数据主要由层级间的分离驱动；然而，平均证据确实随能力层级清晰上升（0.25 弱 / 0.67 混合 / 0.77 强），但层级内的相关性要弱得多（r≈0.15 / 0.48 / 0.41），且对于低能力角色最弱。因此，对于最需要准确诊断的学习者，观测函数的可靠性最低（见限制）。挖掘出的误解与角色分配的误解匹配度 F1 ≈0.56。

Accuracy and convergence. A shrinking update magnitude shows only that the belief has stabilised, not that it is correct, so accuracy against the hidden ground truth is the primary metric: final-belief mastery MAE is lowest under Adaptive ( $0.12$ vs. $0.16$ / $0.20$ ; Table 2), and the per-learner belief error $|\hat{p}-p^{*}|$ falls in step (Figure 3a). As a secondary aggregate signal, mean $|\Delta p|$ shrinks across the six Adaptive persona sessions ( $0.14\rightarrow 0.10$ ) but stays flat or drifts upward under both controls (Figure 3b). Appendix C walks one live adaptive round end-to-end.准确性和收敛性。更新幅度的缩小仅表明信念已稳定，并不代表它是正确的，因此针对隐藏真实情况的准确性是主要指标：最终信念掌握程度 MAE 在自适应模式下最低（0.12 vs. 0.16/0.20；表 2），且每位学习者的信念误差 |p^−p∗| 随之下降（图 3a）。作为次要汇总信号，平均 |Δp| 在六个自适应角色会话中收缩（0.14→0.10），但在两个对照组中保持平坦或向上漂移（图 3b）。附录 C 完整演示了一个实时自适应回合。

3.4 Usability and Efficiency3.4 可用性和效率

To evaluate the learner-facing experience, we asked $16$ human raters to answer a 1–5 Likert questionnaire of 13 items across six dimensions after a session (full instrument in Appendix A). This questionnaire are designed to capture perceived relevance and usefulness. It does not evaluate whether generated questions reliably elicit their intended misconceptions. Figure 4 shows the per-item distribution; the overall mean is $4.0/5$ , no dimension below ${\approx}3.7$ , and $75\%$ ( $12/16$ ) would reuse. The lowest-rated dimension is Responsiveness ( $3.7$ ), consistent with the measured short-answer latency (§3); researchers were the most critical (mean $3.8$ ) and students the most positive ( $4.4$ ).为了评估学习者体验，我们邀请了 16 名人类评分者在会话结束后回答一份 1–5 李克特量表问卷，包含 13 个项目，覆盖六个维度（完整工具见附录 A）。该问卷旨在捕捉感知相关性和有用性。它不评估生成的问题是否可靠地引出了预期的误解。图 4 显示了每个项目的分布情况；总体平均分为 4.0/5，没有任何维度低于 ≈3.7，75% (12/16) 的人愿意再次使用。评分最低的维度是响应性 (3.7)，这与测量的简答题延迟一致（§3）；研究人员最挑剔（平均 3.8），学生最积极（4.4）。

易于导航明确要做什么响应足够快流式等待可接受与我的弱点相关难度适中 “为什么选择此问题”清晰识别了我的错误帮助我改进掌握程度更新建立了信任看到它模拟了我所知道的总体有用愿意再次使用/推荐 0 50 100% 强烈不同意不同意中立同意强烈同意

Figure 4: Per-item response distribution of the 1–5 Likert questionnaire over 16 raters. Blue = agree, grey = neutral, red = disagree. No item drew a strongly-disagree response; the weakest is the streamed-wait item (Q4), echoing the measured latency (§3).图 4：16 名评分者对 1–5 李克特问卷的每项反应分布。蓝色 = 同意，灰色 = 中立，红色 = 不同意。没有项目收到“强烈不同意”的反应；最弱的是流式等待项目 (Q4)，呼应了测量的延迟 (§3)。

Efficiency.效率。

Round type	Next/gen (s)	Answer (s)	Cost ($/rnd)
Short-answer	12.1	20.2	$\approx$ 0.015
Multiple-choice	7.6	0.01	$\approx$ 0.005

Table 3: Efficiency on the live backend (Bedrock Claude Sonnet 4.5). Short-answer

\approx

32 s/round (grade+feedback dominate); MCQ

\approx

7.6 s (deterministic answer). Cost is estimated from token usage.表 3：实时后端（Bedrock Claude Sonnet 4.5）上的效率。简答题 ≈32 秒/回合（评分+反馈占主导）；选择题 ≈7.6 秒（确定性答案）。成本根据 Token 使用量估算。

Deployability hinges on cost and latency. A short-answer round uses two LLM calls (grading and feedback) plus generation of the next item; a multiple-choice round is graded and explained deterministically with no LLM call. Table 3 reports mean latency measured on the live single-node deployment (AWS Bedrock, Claude Sonnet 4.5). The grader/feedback pass dominates short-answer latency; multiple-choice rounds are $\approx 4\times$ faster because only the next-item generation calls the LLM. A faster model (e.g. Claude Haiku) is the obvious lever for a booth setting.可部署性取决于成本和延迟。简答题回合使用两次 LLM 调用（评分和反馈）加上下一个项目的生成；选择题回合通过确定性方式评分和解释，无需 LLM 调用。表 3 报告了在实时单节点部署（AWS Bedrock, Claude Sonnet 4.5）上测量的平均延迟。评分/反馈过程主导了简答题延迟；选择题回合快约 4 倍，因为只有下一个项目的生成调用了 LLM。更快的模型（例如 Claude Haiku）是展位设置的显而易见的选择。

4 Conclusion4 结论

CoLearn demonstrates how an LLM tutor can maintain a persistent learner-state memory, use that memory to generate personalised questions, and expose the resulting adaptation through live visualisation and built-in A/B evaluation. Its soft-evidence knowledge-tracing memory converges on the learner across sessions, its generator targets the learner’s weakest topics and misconceptions, and its evidence view makes the personalisation testable by anyone. By connecting learner-state estimation,, question generation, and transparent evidence surfaces in one deployable, container-deployed research prototype, CoLearn provides a platform for the harder question ahead: whether visible, converging personalisation produces durable, transferable learning.CoLearn 展示了 LLM 导师如何维护持久的学习者状态记忆，利用该记忆生成个性化问题，并通过实时可视化和内置 A/B 评估展示由此产生的自适应过程。其软证据知识追踪记忆在会话间收敛于学习者，其生成器针对学习者最弱的主题和误解，其证据视图使任何人都能验证个性化效果。通过将学习者状态估计、问题生成和透明的证据界面连接在一个可部署的容器化研究原型中，CoLearn 为未来的难题提供了一个平台：可见且收敛的个性化是否能产生持久、可迁移的学习。

Acknowledgments致谢

This work was supported in part by the UK Engineering and Physical Sciences Research Council (EPSRC) through a Turing AI Fellowship (grant no. EP/V020579/1, EP/V020579/2) and the Prosperity Partnership scheme (grant no. UKRI566).本工作部分得到了英国工程与物理科学研究理事会 (EPSRC) 通过图灵 AI 奖学金（授权号 EP/V020579/1, EP/V020579/2）和繁荣伙伴关系计划（授权号 UKRI566）的支持。

Limitations限制

The agent’s mastery estimate is its belief $A_{t}$ , not a direct measurement of human knowledge $H_{t}$ ; we therefore do not claim learning gains, and our A/B study measures perceived relevance rather than learning outcomes. BKT parameters are shared priors, not fit per skill, so absolute mastery values are indicative rather than calibrated. The LLM observation function is also least reliable for low-performing learners: within-tier, per-answer evidence correlates with true mastery at only $r\approx 0.15$ for the weak tier, versus $0.48$ / $0.41$ for mixed/strong (the higher pooled $r=0.68$ reflects between-tier separation, not within-tier accuracy). These are precisely the learners who most need accurate diagnosis; improving grading fidelity on weak answers is a priority for future work. Our evaluation does not establish that generated questions elicit their intended misconceptions, nor does it independently assess factual correctness, curriculum fit, answerability, or distractor quality. These properties require expert annotation and learner-response studies. Automatic strategy self-evolution and the co-evolution diagnostics (convergence/transfer estimation) are designed but not yet implemented: during use the strategy guideline is fixed, so only the agent’s memory adapts. Far-transfer learning, the strongest test of genuine competence, is out of scope here and left to future work. Due to differences in experimental setup and evaluation protocols, we do not make direct comparisons with other LLM-based tutoring systems.代理的掌握程度估计是其信念 At，而非对人类知识 Ht 的直接测量；因此我们不主张学习收益，我们的 A/B 研究测量的是感知相关性而非学习成果。BKT 参数是共享先验，而非针对每个技能拟合，因此绝对掌握值仅具指示性而非校准性。LLM 观测函数对于低表现学习者也是最不可靠的：在层级内，每次回答的证据与真实掌握程度的相关性在弱能力层级仅为 r≈0.15，而混合/强能力层级为 0.48/0.41（较高的汇总 r=0.68 反映了层级间的分离，而非层级内的准确性）。这些正是最需要准确诊断的学习者；提高对弱答案的评分保真度是未来工作的优先事项。我们的评估并未证实生成的问题确实引出了预期的误解，也未独立评估事实正确性、课程契合度、可回答性或干扰项质量。这些属性需要专家标注和学习者反应研究。自动策略自我演化和共演化诊断（收敛/迁移估计）已设计但尚未实现：在使用过程中策略指南是固定的，因此只有代理的记忆在自适应。远迁移学习（衡量真正能力的最强测试）在此超出范围，留待未来工作。由于实验设置和评估协议的差异，我们未与其他基于 LLM 的辅导系统进行直接比较。

Ethics Statement伦理声明

CoLearn involves human participants (the A/B and survey raters) and learner data. Accounts are admin-provisioned with no public signup, learner data is stored locally in the single-node deployment, and the system can run fully offline with a deterministic LLM for privacy-sensitive settings. Misconception summaries are surfaced to learners as supportive guidance rather than verbatim labels.CoLearn 涉及人类参与者（A/B 和调查评分者）和学习者数据。账户由管理员配置，无公开注册，学习者数据本地存储在单节点部署中，系统可以在隐私敏感设置下完全离线运行，并使用确定性 LLM。误解摘要作为支持性指导而非逐字标签呈现给学习者。

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Appendix A User-study questionnaire附录 A 用户研究问卷

The instrument used in the user study (§3.4). Each statement is rated 1–5 (1 = strongly disagree, 5 = strongly agree); Q13 is the adoption item. Raters span a range of backgrounds (teacher, researcher, student, parent) and complete the items after a session.用户研究中使用的工具（§3.4）。每个陈述按 1–5 分评分（1 = 非常不同意，5 = 非常同意）；Q13 为采纳意向项。评分者背景各异（教师、研究员、学生、家长），并在会话结束后完成这些题目。

Usability.
Q1 The interface was easy to navigate.
Q2 At each step it was clear what I was meant to do.易用性。 Q1 界面易于导航。 Q2 在每一步中，我都很清楚自己该做什么。
Responsiveness.
Q3 The system responded quickly enough to keep me engaged.
Q4 The streamed “thinking” stages made any wait feel acceptable.响应性。 Q3 系统响应足够快，让我能够保持专注。 Q4 流式传输的“思考”阶段让等待变得可以接受。
Question quality.
Q5 The questions were relevant to my weak areas.
Q6 The questions were pitched at an appropriate difficulty.
Q7 The “why this question” note made the targeting understandable.问题质量。 Q5 问题与我的薄弱环节相关。 Q6 问题的难度设置恰当。 Q7 “为什么问这个问题”的注释让我理解了提问的目的。
Feedback usefulness.
Q8 The feedback clearly identified my mistakes/misconceptions.
Q9 The feedback helped me understand how to improve.反馈有用性。 Q8 反馈清楚地指出了我的错误/误解。 Q9 反馈帮助我理解了如何改进。
Transparency (co-learning).
Q10 Seeing the mastery estimate update after each answer built my trust.
Q11 I could see the tutor building a model of what I know.透明度（共同学习）。 Q10 看到掌握程度估计值在每次回答后更新，增强了我的信任感。 Q11 我能看到辅导系统在构建我的知识模型。
Overall.
Q12 Overall, CoLearn was useful for learning.总体评价。 Q12 总的来说，CoLearn 对学习很有帮助。
Adoption.
Q13 I would use CoLearn again / recommend it.采纳意向。 Q13 我会再次使用 CoLearn / 推荐它。

Appendix B Generation & grading prompts附录 B 生成与评分提示词

The boxes below give the system prompts used by the live system, lightly reformatted for the single-column width (code identifiers are shown in {}; the {subject_label} slot is filled with the active subject, e.g. “AQA GCSE Biology”).下方的方框展示了实际系统使用的系统提示词，为适应单栏宽度进行了简单的格式调整（代码标识符显示在 {} 中；{subject_label} 插槽填充为当前学科，例如“AQA GCSE 生物学”）。

A fourth prompt plans whether two misconceptions can be tested together (same mechanism, cause–effect, commonly-confused contrast, etc.) before generation; it is omitted here for space.第四个提示词在生成前规划是否可以将两个误解一起测试（相同的机制、因果关系、常见的混淆对比等）；此处因篇幅原因省略。

Appendix C Worked co-learning trace附录 C 共同学习过程跟踪示例

One real round captured from the live deployment (AWS Bedrock, Claude Sonnet 4.5), GCSE Biology, skill Levels of organisation within an ecosystem.从实际部署（AWS Bedrock, Claude Sonnet 4.5）中捕获的一个真实轮次，学科为 GCSE 生物学，技能为生态系统内的组织层次。

Question. “Water is an abiotic factor. Name one biotic factor which may affect the number of buttercups growing on the field.”
Learner answer. “Water is a biotic factor, and biotic and abiotic factors basically mean the same thing.”
Grader (observation function) $\rightarrow$ mastery_evidence=0.0; mined misconceptions: (i) “incorrectly states water is a biotic factor”; (ii) “incorrectly states biotic and abiotic factors mean the same thing”; (iii) “fails to name any biotic factor”.
Feedback shown. “Not quite yet — let’s work on this together.”
Memory update. mastery $0.56\rightarrow 0.23$ (the competence-gated BKT lowers the estimate because the answer is clearly wrong; the misconceptions are stored on the skill).
Next turn. this skill is now the learner’s weakest, so the adaptive engine re-targets it; on the follow-up item the learner answered correctly and the estimate recovered ( $0.23\rightarrow 0.56$ ).问题。“水是一种非生物因素。请说出一个可能影响田间毛茛生长数量的生物因素。” 学习者回答。“水是一种生物因素，而且生物和非生物因素基本上是一个意思。” 评分员（观察函数） → mastery_evidence=0.0；挖掘出的误解：(i) “错误地陈述水是生物因素”；(ii) “错误地陈述生物和非生物因素意思相同”；(iii) “未能说出任何生物因素”。显示的反馈。“还不太对——让我们一起研究一下。” 记忆更新。mastery 0.56→0.23（受能力门控的 BKT 因为答案明显错误而降低了估计值；误解被存储在该技能下）。下一轮。该技能现在是学习者最薄弱的环节，因此自适应引擎重新针对该技能进行提问；在后续题目中，学习者回答正确，估计值恢复（0.23→0.56）。

This is the loop in miniature: a graded answer becomes structured evidence, the agent’s belief moves, and the next question is chosen from that updated belief.这就是循环的缩影：评分后的答案转化为结构化的证据，智能体的信念发生改变，下一道问题便基于更新后的信念进行选择。

CoLearn: An Agentic Tutor that Learns its Learner in a Human–AI Co-Learning LoopCoLearn：一种在人机共学循环中学习其学习者的代理导师