AI Agent for Education: von Neumann Multi-Agent System Framework

The development of large language models has ushered in new paradigms for education. This paper centers on the multi-Agent system in education and proposes the von Neumann multi-Agent system framework. It breaks down each AI Agent into four modules: control unit, logic unit, storage unit, and input-output devices, defining four types of operations: task deconstruction, self-reflection, memory processing, and tool invocation. Furthermore, it introduces related technologies such as Chain-of-Thought, Reson+Act, and Multi-Agent Debate associated with these four types of operations. The paper also discusses the ability enhancement cycle of a multi-Agent system for education, including the outer circulation for human learners to promote knowledge construction and the inner circulation for LLM-based-Agents to enhance swarm intelligence. Through collaboration and reflection, the multi-Agent system can better facilitate human learners' learning and enhance their teaching abilities in this process.

GAOKAO-Eval: Does high scores truly reflect strong capabilities in LLMs?

Large Language Models (LLMs) are commonly evaluated using human-crafted benchmarks, under the premise that higher scores implicitly reflect stronger human-like performance. However, there is growing concern that LLMs may ``game" these benchmarks due to data leakage, achieving high scores while struggling with tasks simple for humans. To substantively address the problem, we create GAOKAO-Eval, a comprehensive benchmark based on China's National College Entrance Examination (Gaokao), and conduct ``closed-book" evaluations for representative models released prior to Gaokao. Contrary to prevailing consensus, even after addressing data leakage and comprehensiveness, GAOKAO-Eval reveals that high scores still fail to truly reflect human-aligned capabilities. To better understand this mismatch, We introduce the Rasch model from cognitive psychology to analyze LLM scoring patterns and identify two key discrepancies: 1) anomalous consistent performance across various question difficulties, and 2) high variance in performance on questions of similar difficulty. In addition, We identified inconsistent grading of LLM-generated answers among teachers and recurring mistake patterns. we find that the phenomenons are well-grounded in the motivations behind OpenAI o1, and o1's reasoning-as-difficulties can mitigate the mismatch. These results show that GAOKAO-Eval can reveal limitations in LLM capabilities not captured by current benchmarks and highlight the need for more LLM-aligned difficulty analysis.

Boosting Large Language Models with Socratic Method for Conversational Mathematics Teaching

With the introduction of large language models (LLMs), automatic math reasoning has seen tremendous success. However, current methods primarily focus on providing solutions or using techniques like Chain-of-Thought to enhance problem-solving accuracy. In this paper, we focus on improving the capability of mathematics teaching via a Socratic teaching-based LLM (\texttt{SocraticLLM}), which guides learners toward profound thinking with clarity and self-discovery via conversation. We collect and release a high-quality mathematical teaching dataset, named \texttt{SocraticMATH}, which provides Socratic-style conversations of problems with extra knowledge. Also, we propose a knowledge-enhanced LLM as a strong baseline to generate reliable responses with review, guidance/heuristic, rectification, and summarization. Experimental results show the great advantages of \texttt{SocraticLLM} by comparing it with several strong generative models. The codes and datasets are available on \url{https://github.com/ECNU-ICALK/SocraticMath}.

Mathematical Language Models: A Survey

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.