Personalizing Mathematical Game-based Learning for Children: A Preliminary Study

We introduce GamEDAI, a hierarchical multi-agent framework that transforms instructor-provided questions into fully playable, pedagogically grounded educational games validated through formal mechanic contracts. Built on phase-based LangGraph sub-graphs, deterministic Quality Gates, and structured Pydantic schemas, GamEDAI supports two template families encompassing 15 interaction mechanics across spatial reasoning, procedural execution, and higher-order Bloom's Taxonomy objectives. Evaluated on 200 questions spanning five subject domains, the system achieves a 90% validation pass rate, 98.3% schema compliance, and 73% token reduction over ReAct agents (${\sim}$73,500 $\rightarrow$ ${\sim}$19,900 tokens/game) at $0.46 per game. Within this model configuration, these results suggest that phase-bounded architectural structure correlates more strongly with alignment quality than prompting strategy alone. Our demonstration lets attendees generate Bloom's-aligned games from natural language in under 60 seconds, inspect Quality Gate outputs at each pipeline phase, and browse a curated library of 50 games spanning all 15 mechanic types.

Teachers face increasing demands on their time, particularly in adapting mathematics curricula to meet individual student needs while maintaining cognitive rigor. This study evaluates whether AI tools can accurately classify the cognitive demand of mathematical tasks, which is important for creating or adapting tasks that support student learning. We tested eleven AI tools: six general-purpose (ChatGPT, Claude, DeepSeek, Gemini, Grok, Perplexity) and five education-specific (Brisk, Coteach AI, Khanmigo, Magic School, School$.$AI), on their ability to categorize mathematics tasks across four levels of cognitive demand using a research-based framework. The goal was to approximate the performance teachers will achieve with straightforward prompts. On average, AI tools accurately classified cognitive demand in only 63% of cases. Education-specific tools were not more accurate than general-purpose tools, and no tool exceeded 83% accuracy. All tools struggled with tasks at the extremes of cognitive demand (Memorization and Doing Mathematics), exhibiting a systematic bias toward middle-category levels (Procedures with/without Connections). The tools often gave plausible-sounding explanations likely to be persuasive to novice teachers. Error analysis of AI tools' misclassification of the broad level of cognitive demand (high vs. low) revealed that tools consistently overweighted surface textual features over underlying cognitive processes. Further, AI tools showed weaknesses in reasoning about factors that make tasks higher vs. lower cognitive demand. Errors stemmed not from ignoring relevant dimensions, but from incorrectly reasoning about multiple task aspects. These findings carry implications for AI integration into teacher planning workflows and highlight the need for improved prompt engineering and tool development for educational applications.

This paper introduces a new paradigm for AI game programming, leveraging large language models (LLMs) to extend and operationalize Claude Shannon's taxonomy of game-playing machines. Central to this paradigm is Nemobot, an interactive agentic engineering environment that enables users to create, customize, and deploy LLM-powered game agents while actively engaging with AI-driven strategies. The LLM-based chatbot, integrated within Nemobot, demonstrates its capabilities across four distinct classes of games. For dictionary-based games, it compresses state-action mappings into efficient, generalized models for rapid adaptability. In rigorously solvable games, it employs mathematical reasoning to compute optimal strategies and generates human-readable explanations for its decisions. For heuristic-based games, it synthesizes strategies by combining insights from classical minimax algorithms (see, e.g., shannon1950chess) with crowd-sourced data. Finally, in learning-based games, it utilizes reinforcement learning with human feedback and self-critique to iteratively refine strategies through trial-and-error and imitation learning. Nemobot amplifies this framework by offering a programmable environment where users can experiment with tool-augmented generation and fine-tuning of strategic game agents. From strategic games to role-playing games, Nemobot demonstrates how AI agents can achieve a form of self-programming by integrating crowdsourced learning and human creativity to iteratively refine their own logic. This represents a step toward the long-term goal of self-programming AI.