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Eunjoo Lee

Publications and source records attributed to Eunjoo Lee.

4 recordsLinked to original sources

EduClaw-Bench: A Long-Horizon Benchmark for Pedagogical LLM Agents with Simulated Learners

Large language models (LLMs) power educational applications from tutoring to essay scoring, but each is a point solution to a single task, and only recently have these point solutions been integrated into agents operating over a learning management system (LMS). Yet tutoring is long-horizon, since a learner improves over days and weeks rather than in a single turn, and no benchmark evaluates an agent tutor across a sustained relationship. We introduce EduClaw-Bench, a benchmark that places an agent tutor in a continuous 30-day relationship with a simulated learner grounded in knowledge tracing (KT), whose knowledge-concept mastery, from a KT model trained on real-student data, drives its answers and is probed for learning gain across 55 scenarios. Each agent is scored on three primary axes (learning gain, responsiveness, and helpfulness) and two curriculum-design axes (Gagné and Rosenshine), with helpfulness and the curriculum axes judged by a cross-family panel of three LLM judges. Evaluating 10 agent adapters over three base-model tiers yields two findings that single-tier, single-session evaluation cannot reach. First, tutoring quality belongs to the base model and the agent harness together rather than either alone. Second, almost no combination sustains good tutoring over the full horizon. A calibration check ($\text{ECE}=0.049$) and a live-classroom field study confirm that the simulated learner and its measurements track reality. Our work is a step toward trustworthy AI tutors for future education.

cs.CY

LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring

Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute.

cs.CL

New characterizations of the helicoid in a cylinder

This paper characterizes a compact piece of the helicoid $H_C$ in a solid cylinder $C \subset \mathbb{R}^3$ from the following two perspectives. First, under reasonable conditions, $H_C$ has the smallest area among all immersed surfaces $Σ$ with $\partial Σ\subset d_1 \cup d_2 \cup S$, where $d_1$ and $d_2$ are the diameters of the top and bottom disks of $C$ and $S$ is the side surface of $C$. Second, other than $H_C$, there exists no minimal surface whose boundary consists of $d_1$, $d_2$, and a pair of \textcolor{black}{rotationally symmetric} curves $γ_1$, $γ_2$ on $S$ along which it meets $S$ orthogonally. We draw the same conclusion when the boundary curves on $S$ are a pair of helices of a certain height.

math.DG

Generalizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean space

Our goal is to generalize the Choe-Hoppe helicoid and Clifford cones in Euclidean space. By sweeping out $L$ indpendent Clifford cones in ${\mathbb{R}}^{2N+2}$ via the multi-screw motion, we construct minimal submanifolds in ${\mathbb{R}}^{L(2N+2)+1}$. Also, we sweep out the $L$-rays Clifford cone (introduced in Section 2.3) in ${\mathbb{R}}^{L(2N+2)}$ to construct minimal submanifolds in ${\mathbb{R}}^{L(2N+2)+1}$. Our minimal submanifolds unify various interesting examples: Choe-Hoppe's helicoid of codimension one, cone over Lawson's ruled minimal surfaces in ${\mathbb{S}}^{3}$, Barbosa-Dajczer-Jorge's ruled submanifolds, and Harvey-Lawson's volume-minimizing twisted normal cone over the Clifford torus.

math.DG