Math Word Problems (MWPs) play a vital role in assessing the capabilities of Large Language Models (LLMs), yet current research primarily focuses on questions with concise contexts. The impact of longer contexts on mathematical reasoning remains under-explored. This study pioneers the investigation of Context Length Generalizability (CoLeG), which refers to the ability of LLMs to solve MWPs with extended narratives. We introduce Extended Grade-School Math (E-GSM), a collection of MWPs featuring lengthy narratives, and propose two novel metrics to evaluate the efficacy and resilience of LLMs in tackling these problems. Our analysis of existing zero-shot prompting techniques with proprietary LLMs along with open-source LLMs reveals a general deficiency in CoLeG. To alleviate these issues, we propose tailored approaches for different categories of LLMs. For proprietary LLMs, we introduce a new instructional prompt designed to mitigate the impact of long contexts. For open-source LLMs, we develop a novel auxiliary task for fine-tuning to enhance CoLeG. Our comprehensive results demonstrate the effectiveness of our proposed methods, showing improved performance on E-GSM. Additionally, we conduct an in-depth analysis to differentiate the effects of semantic understanding and reasoning efficacy, showing that our methods improves the latter. We also establish the generalizability of our methods across several other MWP benchmarks. Our findings highlight the limitations of current LLMs and offer practical solutions correspondingly, paving the way for further exploration of model generalizability and training methodologies.

Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly less attention. Existing benchmarks often fall short in evaluating LLMs’ abilities on the breadth and depth of undergraduate-level physics, underscoring the need for a comprehensive evaluation. To fill this gap, we introduce UGPhysics, a large-scale and diverse benchmark specifically designed to evaluate **U**nder**G**raduate-level **Physics** (**UGPhysics**) reasoning with LLMs. UGPhysics includes 5,520 undergraduate-level physics problems in both English and Chinese across 13 subjects with seven different answer types and four distinct physics reasoning skills, all rigorously screened for data leakage. Additionally, we develop a Model-Assistant Rule-based Judgment (**MARJ**) pipeline specifically tailored for assessing physics problems, ensuring accurate evaluation. Our evaluation of 31 leading LLMs shows that the highest overall accuracy, 49.8% (achieved by OpenAI-o1-mini), emphasizes the need for models with stronger physics reasoning skills, beyond math abilities. We hope UGPhysics, along with MARJ, will drive future advancements in AI for physics reasoning. Codes and data are available at \href{https://github.com/YangLabHKUST/UGPhysics}{https://github.com/YangLabHKUST/UGPhysics}.

Large language models (LLMs) are considered a crucial technology for advancing intelligent education since they exhibit the potential for an in-depth understanding of teaching scenarios and providing students with personalized guidance. Nonetheless, current LLM-based application in personalized teaching predominantly follows a "Question-Answering" paradigm, where students are passively provided with answers and explanations. In this paper, we propose SocraticLM, which achieves a Socratic "Thought-Provoking" teaching paradigm that fulfills the role of a real classroom teacher in actively engaging students in the thought process required for genuine problem-solving mastery. To build SocraticLM, we first propose a novel "Dean-Teacher-Student" multi-agent pipeline to construct a new dataset, SocraTeach, which contains $35$K meticulously crafted Socratic-style multi-round (equivalent to $208$K single-round) teaching dialogues grounded in fundamental mathematical problems. Our dataset simulates authentic teaching scenarios, interacting with six representative types of simulated students with different cognitive states, and strengthening four crucial teaching abilities. SocraticLM is then fine-tuned on SocraTeach with three strategies balancing its teaching and reasoning abilities. Moreover, we contribute a comprehensive evaluation system encompassing five pedagogical dimensions for assessing the teaching quality of LLMs. Extensive experiments verify that SocraticLM achieves significant improvements in the teaching performance, outperforming GPT4 by more than 12\%. Our dataset and code is available at https://github.com/Ljyustc/SocraticLM.