Scaling Laws for Educational AI Agents

Mengsong Wu; Hao Hao; Shuzhen Bi; Keqian Li; Wentao Liu; Siyu Song; Hongbo Zhao; Aimin Zhou

cs.AIMar 12, 2026

Scaling Laws for Educational AI Agents

Authors: Mengsong Wu, Hao Hao, Shuzhen Bi, Keqian Li, Wentao Liu, Siyu Song, Hongbo Zhao, Aimin Zhou

Organizations: East China Normal University · Shanghai Innovation Institute

Abstract

While scaling laws for Large Language Models (LLMs) have been extensively studied along dimensions of model parameters, training data, and compute, the scaling behavior of LLM-based educational agents remains unexplored. We propose that educational agent capability scales not merely with the underlying model size, but through structured dimensions that we collectively term the Agent Scaling Law: role definition clarity, skill depth, tool completeness, runtime capability, and educator expertise injection. Central to this framework is AgentProfile, a structured JSON-based specification that serves as the mechanism enabling systematic capability growth of educational agents. We present EduClaw, a profile-driven multi-agent platform that operationalizes this scaling law, demonstrating its effectiveness through the construction and deployment of 330+ educational agent profiles encompassing 1,100+ skill modules across K-12 subjects. Our empirical observations suggest that educational agent performance scales predictably with profile structural richness. We identify two complementary scaling axes -- Tool Scaling and Skill Scaling -- as future directions, arguing that the path to more capable educational AI lies not solely in larger models, but in stronger structured capability systems.

Figures & tables

Figure 1: EduClaw platform main page. The sidebar provides access to the agent repository, agent construction, and skill repository. The platform supports AgentProfile-based automated agent generation and management.

Field	Type	Description
name	String	Concise identifier reflecting the agent’s role
description	String	One-sentence summary of the agent’s purpose
details	Markdown	Structured behavioral spec with four sections (Section 3.2.1 )
agent_template	String	Base runtime template and default configs
skills	List	Skill module references from the repository
tools	List	Tool integrations (solvers, generators, etc.)

Table 1: AgentProfile Schema Fields

Dimension	Focus Points
Divergent Thinking	Path diversity, cross-domain associations
Logical Rigor	Reasoning completeness, counterexample construction
Math Expression	Symbolic normativity, geometry-algebra translation
Inquiry Depth	Problem variation, essential pattern extraction
Metacognition	Strategy evaluation, obstacle diagnosis

Table 2: Example Core Dimensions for Mathematics Tutoring

Panel of Figure 2 — Figure 2: End-to-end pipeline from one-sentence description to running educational agent. Stages 1 and 2 are LLM-powered (dashed arrows); Stage 3 is deterministic construction.

Figure 3: EduClaw agent construction interface. From a one-sentence input, the system generates an AgentProfile, matches skills from the library (shown as tags), and produces a running agent.

Panel of Figure 4 — Figure 4: EduClaw three-tier architecture. AgentProfiles provide declarative specifications that drive agent construction; the management layer orchestrates process lifecycle and request routing; each agent runs as an isolated Open Claw runtime instance.

Figure 5: EduClaw agent repository. Agents are organized by subject and filterable by grade level.

Subject	Primary	Middle	High
Mathematics	45	68	52
Chinese Language	38	42	35
English	32	45	48
Physics	12	28	41
Chemistry	–	18	35
Biology	15	22	38

Table 3: Educational Skill Module Distribution by Subject and Level

Figure 6: An educational agent in action. The agent exhibits structured reasoning (thinking block), recommends relevant skills, and engages in multi-turn pedagogical dialogue.

AI in Education

AI in Education studies how artificial intelligence can support teaching, learning, assessment, and educational decision-making.

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Despite the rapid deployment of LLMs into classrooms, validating educational AI remains uniquely intractable: interventions act on developing learners whose cognitive and social trajectories are irreversibly shaped, while real-world trials are slow, ethically constrained, and institutionally locked. LLM-based educational simulators have emerged as a potential remedy, but many still collapse learning into persona-conditioned role-play and, when optimized only to reproduce existing classrooms, can structurally penalize the institutional novelty that pedagogical reform requires. In this work, we introduce AgentSchool, an LLM-driven multi-agent simulator that models learning as state transition rather than prompted behavior. AgentSchool couples cognitively growable student agents -- equipped with weighted subject knowledge graphs, thinking-workflow pools, and explicit misconceptions -- with adaptive teacher agents that plan, scaffold, and reflect along the Zone of Proximal Development, embedded in a configurable scenery generator that situates instruction within both formal and informal learning fields, and a multi-scale simulator that decouples interaction scale, temporal granularity, and simulation duration. Experiments show that structured student agents produce more differentiated mastery and misconception traces than a baseline simulator, while teacher-agent comparisons show backbone-dependent patterns consistent with ZPD-informed adaptation. Further, AgentSchool generates plausible traces of peripheral participation, clique formation, aggressor-induced cohesion, and opinion-leader emergence consistent with classroom social theories. Beyond its role as an educational research instrument, AgentSchool frames education as a socially meaningful testbed for long-horizon memory, multi-agent coordination, and future institutional reasoning under organizational pressure.

Abstract

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