arXiv subjects

Peter Kaiser

Publications and source records attributed to Peter Kaiser.

4 recordsLinked to original sources

arXiv2026

From Prompting to Epistemic Proactivity: Temporal Trajectories of Student-AI Interaction in Mathematics Learning

GenAI is increasingly used by students as learning companions, yet little is known about how they use these tools in open-ended learning settings, where the goal is not to complete a specific task but to improve understanding and making progress. This study examined Grade-9 students' dialogue with a general-purpose LLM during mathematics practice, in which students prepared a curriculum-aligned skill for a later assessment. We investigated whether students' interactions revealed forms of epistemically proactive AI use: trajectories in which they strategically use and regulate AI to advance their understanding, and whether these trajectories predicted immediate AI-free performance on the same skill. A total of 112 students worked with a web-based LLM tutor on a mathematical-modeling task; 97 completed both AI-free pre- and post-tests. Student turns were coded for self-regulated learning functions, help-seeking content, and mathematical-modeling activity; three dimensions hypothesized to capture epistemically proactive AI use in this task. Descriptively, students' interactions showed little explicit regulation and mostly involved procedural or conceptual questions. Static summaries of AI use, including whole-session prompt functions, request types, modeling stages, and behavioral diversity, did not predict post-test performance after controlling for prior knowledge. In contrast, temporal indicators were informative: students performed better when their interactions shifted from early to late phases toward a more epistemically proactive balance of conceptual or procedural help-seeking and mathematical work, rather than verification, answer-seeking, or validation. These findings suggest that productive AI-supported learning is better understood as a domain-specific trajectory of epistemic proactivity. We discuss implications for AI tutor design and classroom orchestration.

cs.CY↗

arXiv2026

Regulating the AI Tutor: Intentions, Help-Seeking, and Self-Regulated Learning in Adolescent GenAI Use

Generative AI (GenAI) tools are now common learning companions for adolescents, yet how they regulate their use during authentic learning tasks remains poorly understood. Self-regulated learning (SRL) and high-level help-seeking (HS) are commonly proposed as safeguards against passive or shortcut-oriented use, but most empirical studies focus on aggregate learning outcomes rather than these moment-to-moment processes during AI-supported learning. This work-in-progress examines open-ended conversational data from 98 Grade-9 students across three German Gymnasium schools, who used a web-based Mistral-Large tutor to prepare a curriculum-aligned mathematics skill before an exam. Alongside chat logs (1,616 turns; 808 student turns), we collected pre-post domain knowledge, pre-chat learning needs, and self-reported cognitive load. We propose a turn-level codebook combining theory-driven SRL and HS constructs with two LLM-specific inductive codes (agency over the AI; epistemic vigilance), and report preliminary AI-coded results. Although students overwhelmingly selected scaffolded support before the chat, their interactions were dominated by instrumental requests with almost no explicit monitoring or evaluation. Post-test performance was significantly lower than pre-test, and higher extraneous cognitive load predicted lower post-test scores after controlling for prior knowledge. We discuss how these patterns can support hybrid human-AI analysis of interaction patterns and inform scaffolds for more agentic and epistemically proactive GenAI use.

cs.CY↗

arXiv2024

Crossing Numbers of Billiard Curves in the Multidimensional Box via Translation Surfaces

The billiard table is modeled as an $n$-dimensional box $[0,a_1]\times [0,a_2]\times \ldots \times [0,a_n] \subset \mathbb{R}^n$, with each side having real-valued lengths $a_i$ that are pairwise commensurable. A ball is launched from the origin in direction $d=(1,1,\ldots,1)$. The ball is reflected if it hits the boundary of the billiard table. It comes to a halt when reaching a corner. We show that the number of intersections of the billiard curve at any given point on the table is either $0$ or a power of $2$. To prove this, we use algebraic and number theoretic tools to establish a bijection between the number of intersections of the billiard curve and the number of satisfying assignments of a specific constraint satisfaction problem.

math.CO↗

arXiv2022

Complexity of Cut-and-Project Sets of Polytopal Type in Special Homogeneous Lie Groups

The aim of this paper is to determine the asymptotic growth rate of the complexity function of cut-and-project sets in the non-abelian case. In the case of model sets of polytopal type in homogeneous two-step nilpotent Lie groups we can establish that the complexity function asymptotically behaves like $r^{homdim(G) dim(H)}$. Further we generalize the concept of acceptance domains to locally compact second countable groups.

math.GR↗