Educational knowledge graph (EKG) is a critical component of intelligent tutoring systems that is structured around cognitive principles and provides support for interactive teaching. Most existing EKGs usually rely on simplistic relations, bind with single subjects, and lack integration with explicit learning objectives. In this paper, we introduce CogNet-KG, a novel and cognitively-structured large-scale knowledge graph for STEM learning. CogNet-KG models nearly 500 core concepts across five subjects with various cognitively-grounded relations corresponding to specific learning objectives, thereby encoding a rich cognitive schema for guiding more effective teaching. Based on this structure, we then construct a high-quality tutoring dialogue dataset CogDialogue-QA by leveraging adaptive instructional strategies. Additionally, we train CogTutor-LM, a specialized tutorial LLM that internalizes this structured pedagogical reasoning. Overall evaluation demonstrates that CogTutor-LM generates responses with significantly greater instructional coherence and more appropriate pedagogical guidance compared to baselines, validating the effectiveness of our graph-driven approach to fostering knowledge integration and stimulating students’ thinking. The datasets are publicly available at https://github.com/KCAIED/CogNet-KG.

Cross-prompt trait scoring task aims to learn generalizable scoring capabilities from source- prompt data, enabling automatic scoring across multiple dimensions on unseen essays. Existing research on cross-prompt trait essay scoring primarily focuses on improving model generalization by obtaining prompt-invariant representations. In this paper, we approach the research problem from a different perspective on invariance learning and propose a scoring-invariant learning objective. This objective encourages the model to focus on intrinsic information within the essay that reflects its quality during training, thereby learning generic scoring features. To further enhance the model’s ability to score across multiple dimensions, we introduce a trait feature extraction network based on routing gates into the scoring architecture and propose a trait consistency scoring objective to encourage the model to balance the diversity of trait-specific features with scoring consistency across traits when learning trait-specific essay features. Extensive experiments demonstrate the effectiveness of our approach, showing advantages in multi-trait scoring performance and achieving significant improvements with low-resource prompts.