intelligent tutoring system builders

Abstract: Small reasoning models (SRMs) have shown strong performance on complex reasoning tasks by generating extended chain-of-thought trajectories, but they often fail to recover once their reasoning enters an erroneous path. Existing test-time fusion methods rely on local fusion signals to determine when to trigger fusion, which can be misled by transient uncertainty fluctuations and may reinforce unstable reasoning trajectories. We propose ThinkFuse, a training-free test-time fusion framework that selectively intervenes in unreliable reasoning segments. ThinkFuse compares segment-level uncertainty shifts with trajectory-level uncertainty trends to identify unstable reasoning points and fuse auxiliary reasoning paths into the primary model's trajectory. Extensive experiments demonstrate that ThinkFuse outperforms baselines on mathematical and knowledge-intensive reasoning benchmarks, with consistent gains across model-family combinations, and remains robust with a smaller primary model. Our analysis shows that ThinkFuse requires fewer fusion triggers and generates fewer tokens, highlighting the efficiency of selective triggering. Our code is available at https://github.com/js-lee-AI/ThinkFuse.

Abstract: Worked examples are a powerful form of instruction, but learners must infer how the demonstrated steps were produced. A naive simulation of this self-explanation process can generate thousands of numerical explanations that reproduce one observed change without capturing its underlying procedure. We propose structure-mapping-guided self-explanation as a computational account of the cognitive biases that reduce search effort and make this inference tractable. The model represents mathematical expressions as typed relational structures and uses structure mapping to identify corresponding source and target regions. For each changed target value, the corresponding source region serves as an anchor: it guides abductive search toward structurally relevant values and operations before broader alternatives, yielding ordered, executable candidate procedures with inspectable source evidence. Across 70 mathematical transformations containing 120 changed numeric components, the model recovered every intended procedure. It returned the intended procedure before any other computation producing the same target value in 104 subproblems (86.7%), compared with a median of 32 (26.7%) across 100 unguided runs that tested candidate calculations in random order. Our proposed model also tested 93.8% fewer combinations of values and operations than unguided search before reaching the intended procedures. These results provide an efficient, interpretable account of how relational structure can guide procedural learning and a testable hypothesis about human self-explanation from worked examples.

Abstract: Teaching abstract theoretical computer science (TCS) concepts such as algorithm analysis and complexity theory is challenging because students must handle formal proofs and asymptotic reasoning that conventional resources rarely explain in an adaptive, on-demand way. We present AlgoRAG, a specialized Retrieval-Augmented Generation (RAG) system that couples a large language model (LLM) with a curated, domain-specific knowledge base to address these challenges. The knowledge base integrates authoritative textbooks, 847 lecture slides, 312 practice problems with solutions, 156 worked proof templates, and 89 complexity worksheets. AlgoRAG incorporates domain-specific optimizations including mathematical entity recognition, notation-aware retrieval, and pedagogical re-ranking. We evaluate AlgoRAG on 179 curated exam-style questions spanning asymptotic analysis, recurrence relations, dynamic programming, graph algorithms, NP-completeness, sorting, and divide-and-conquer. The system achieves a 100% success rate with a mean response time of 38.0 seconds. While BLEU-4 scores are zero -- a known limitation of n-gram matching on mathematical proofs where equivalent reasoning may use entirely different notation -- AlgoRAG attains ROUGE-1 F1 of 0.0963, ROUGE-L F1 of 0.0683, and a pedagogical quality score of 0.7620, indicating that responses are well-structured and didactically sound even when surface wording diverges from reference answers. Performance is especially strong on NP-completeness (ROUGE-1 F1 = 0.1285, pedagogical quality = 0.7643) and graph algorithms (ROUGE-1 F1 = 0.1023, pedagogical quality = 0.8086). These results support the conclusion that RAG is an effective architecture for personalized theoretical-CS instruction, providing correct, context-rich explanations even for highly abstract topics.