Dissecting Physics Reasoning in Small Language Models: A Multi-Dimensional Analysis from an Educational Perspective

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.

Harnessing Structured Knowledge: A Concept Map-Based Approach for High-Quality Multiple Choice Question Generation with Effective Distractors

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.