Small Language Models (SLMs) offer computational efficiency and accessibility, making them promising for educational applications. However, their capacity for complex reasoning, particularly in domains such as physics, remains underexplored. This study investigates the high school physics reasoning capabilities of state-of-the-art SLMs (under 4 billion parameters), including instruct versions of Llama 3.2, Phi 4 Mini, Gemma 3, and Qwen series. We developed a comprehensive physics dataset from the OpenStax High School Physics textbook, annotated according to Bloom's Taxonomy, with LaTeX and plaintext mathematical notations. A novel cultural contextualization approach was applied to a subset, creating culturally adapted problems for Asian, African, and South American/Australian contexts while preserving core physics principles. Using an LLM-as-a-judge framework with Google's Gemini 2.5 Flash, we evaluated answer and reasoning chain correctness, along with calculation accuracy. The results reveal significant differences between the SLMs. Qwen 3 1.7B achieved high `answer accuracy' (85%), but `fully correct reasoning' was substantially low (38%). The format of the mathematical notation had a negligible impact on performance. SLMs exhibited varied performance across the physics topics and showed a decline in reasoning quality with increasing cognitive and knowledge complexity. In particular, the consistency of reasoning was largely maintained in diverse cultural contexts, especially by better performing models. These findings indicate that, while SLMs can often find correct answers, their underlying reasoning is frequently flawed, suggesting an overreliance on pattern recognition. For SLMs to become reliable educational tools in physics, future development must prioritize enhancing genuine understanding and the generation of sound, verifiable reasoning chains over mere answer accuracy.
Generating high-quality MCQs, especially those targeting diverse cognitive levels and incorporating common misconceptions into distractor design, is time-consuming and expertise-intensive, making manual creation impractical at scale. Current automated approaches typically generate questions at lower cognitive levels and fail to incorporate domain-specific misconceptions. This paper presents a hierarchical concept map-based framework that provides structured knowledge to guide LLMs in generating MCQs with distractors. We chose high-school physics as our test domain and began by developing a hierarchical concept map covering major Physics topics and their interconnections with an efficient database design. Next, through an automated pipeline, topic-relevant sections of these concept maps are retrieved to serve as a structured context for the LLM to generate questions and distractors that specifically target common misconceptions. Lastly, an automated validation is completed to ensure that the generated MCQs meet the requirements provided. We evaluate our framework against two baseline approaches: a base LLM and a RAG-based generation. We conducted expert evaluations and student assessments of the generated MCQs. Expert evaluation shows that our method significantly outperforms the baseline approaches, achieving a success rate of 75.20% in meeting all quality criteria compared to approximately 37% for both baseline methods. Student assessment data reveal that our concept map-driven approach achieved a significantly lower guess success rate of 28.05% compared to 37.10% for the baselines, indicating a more effective assessment of conceptual understanding. The results demonstrate that our concept map-based approach enables robust assessment across cognitive levels and instant identification of conceptual gaps, facilitating faster feedback loops and targeted interventions at scale.
Automatically grading the diverse range of question types in high school physics problem is a challenge that requires automated grading techniques from different fields. We report the findings of a Systematic Literature Review of potential physics grading techniques. We propose a multi-modal AI grading framework to address these challenges and examine our framework in light of Australia's AI Ethical Principles.
The application of formulas (e.g., physics formulas) is a fundamental ability of humans when solving numerical reasoning problems. Existing numerical reasoning datasets seldom explicitly indicate the formulas employed in reasoning, as their questions rely on implicit commonsense mathematical knowledge. In contrast, in this paper, we introduce FormulaReasoning, a new dataset specifically designed for formula-based numerical reasoning. Each of the 4,751 questions in our dataset requires numerical calculation with external physics formulas, making it a more challenging benchmark for evaluating large language models (LLMs). We offer normalized fine-grained annotations for the questions, available in English and Chinese, including formula structures, parameter names, symbols, numerical values, and units, derived from extensive manual effort with LLM assistance for guaranteed quality. We also provide a consolidated formula database to serve as an external knowledge base accompanying the dataset. We employ FormulaReasoning to evaluate LLMs with 7B to over 100B parameters, and explore retrieval-augmented generation with the formula database. Our evaluation also covers supervised methods that break down the reasoning process into formula generation, parameter extraction, and numerical calculation, as well as direct preference optimization methods based on derived preference data.
Our work demonstrates that large language model (LLM) pre-trained on texts can not only solve pure math word problems, but also physics word problems, whose solution requires calculation and inference based on prior physical knowledge. We collect and annotate the first physics word problem dataset-PhysQA, which contains over 1000 junior high school physics word problems (covering Kinematics, Mass&Density, Mechanics, Heat, Electricity). Then we use OpenAI' s GPT3.5 to generate the answer of these problems and found that GPT3.5 could automatically solve 49.3% of the problems through zero-shot learning and 73.2% through few-shot learning. This result demonstrates that by using similar problems and their answers as prompt, LLM could solve elementary physics word problems approaching human level performance. In addition to solving problems, GPT3.5 can also summarize the knowledge or topics covered by the problems, provide relevant explanations, and generate new physics word problems based on the input. Our work is the first research to focus on the automatic solving, explanation, and generation of physics word problems across various types and scenarios, and we achieve an acceptable and state-of-the-art accuracy. This underscores the potential of LLMs for further applications in secondary education.
Language modelling provides a step towards intelligent communication systems by harnessing large repositories of written human knowledge to better predict and understand the world. In this paper, we present an analysis of Transformer-based language model performance across a wide range of model scales -- from models with tens of millions of parameters up to a 280 billion parameter model called Gopher. These models are evaluated on 152 diverse tasks, achieving state-of-the-art performance across the majority. Gains from scale are largest in areas such as reading comprehension, fact-checking, and the identification of toxic language, but logical and mathematical reasoning see less benefit. We provide a holistic analysis of the training dataset and model's behaviour, covering the intersection of model scale with bias and toxicity. Finally we discuss the application of language models to AI safety and the mitigation of downstream harms.