K12-KGraph：面向教育大语言模型基准测试与训练的课程对齐知识图谱

摘要

大语言模型在K-12教育中的应用日益广泛，但现有基准测试主要检测试题解答能力，而非理解课程知识的结构化组织与视觉呈现方式。我们将这类能力称为"课程认知"，涵盖先决条件链、概念分类、实验-概念关联、教学序列编排及视觉接地等维度。我们构建了K12-KGraph——基于人民教育出版社官方教材（涵盖中小学数学、物理、化学、生物）的课程对齐知识图谱，包含九类节点与十四类关系，覆盖课程结构与视觉接地信息。基于该图谱，我们衍生出K12-Bench基准测试集，包含23640道多选题，涵盖五大任务族：接地(Ground)、先决条件(Prereq)、邻近(Neighbor)、证据(Evidence)与定位(Locate)。同时构建了K12-Train——包含7335个样本的图引导监督微调语料库，其中含2267个纯文本问答对与5068个多模态视觉问答对。在K12-Bench测试中，Gemini-3-Flash仅达57%精确匹配率，Gemma-4-31B-IT为46%，其中Prereq与Neighbor任务难度最高。我们的训练实验表明，领域特化监督可缩小这一差距。在匹配的2300样本预算下，K12-Train-Text在GaokaoBench与EduEval测试中持续优于同等规模的八个主流指令微调语料库子集。对于视觉语言模型，K12-Train-Full在Gaokao-MM、MDK12-medium与K12Vista上取得所有对比训练配置中的最佳综合结果，且使用的样本数少于完整DataFlow与WizardLM基线。该模型同时超越纯文本与纯多模态变体，证明文本与视觉监督具有互补性。我们已开源该图谱、基准测试、训练数据及完整构建流程。

English

Large language models are increasingly used in K-12 education, but existing benchmarks mainly test exam question answering rather than understanding how curriculum knowledge is structured and visually presented. We call this capability curriculum cognition. It covers prerequisite chains, concept taxonomies, experiment-concept links, pedagogical sequencing, and visual grounding. We introduce K12-KGraph, a curriculum-aligned knowledge graph extracted from official People's Education Press textbooks in mathematics, physics, chemistry, and biology across primary, middle, and high school. It contains nine node types and fourteen relation types covering curriculum structure and visual grounding. From this graph, we derive K12-Bench, a 23,640-question multi-select benchmark with five task families: Ground, Prereq, Neighbor, Evidence, and Locate. We also build K12-Train, a graph-guided supervised fine-tuning corpus of 7,335 samples, including 2,267 text-only QA pairs and 5,068 multimodal VQA pairs. On K12-Bench, Gemini-3-Flash achieves only 57 percent exact match and Gemma-4-31B-IT reaches 46 percent, with Prereq and Neighbor being the hardest tasks. Our training experiments show that domain-specific supervision can reduce this gap. Under a matched 2,300-sample budget, K12-Train-Text consistently outperforms equally sized subsets of eight mainstream instruction-tuning corpora on GaokaoBench and EduEval. For vision-language models, K12-Train-Full achieves the best overall results on Gaokao-MM, MDK12-medium, and K12Vista among all compared training configurations, despite using fewer samples than the full DataFlow and WizardLM baselines. It also surpasses both text-only and multimodal-only variants, showing that textual and visual supervision are complementary. We release the graph, benchmark, training data, and complete construction pipeline.