Large language models (LLMs) solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. To understand this gap, we synthesize cognitive science research into a taxonomy of 28 cognitive elements spanning reasoning invariants, meta-cognitive controls, representations for organizing reasoning and knowledge, and transformation operations. We introduce a fine-grained evaluation framework and apply it to 192K traces from 18 models across text, vision, and audio, alongside 1,346 human think-aloud traces on a new, domain-agnostic dataset for human-model comparison. We find that models are able to deploy cognitive elements seen in human reasoning but differ in how they use them. Leveraging these patterns, we develop test-time reasoning guidance that automatically scaffolds successful reasoning topologies, improving the accuracy of the strongest models by 9.7 percentage points on ill-structured problems. Meta-analysis of 1.6K LLM reasoning papers reveals the research community concentrates on easily quantifiable elements but rarely targets self-awareness, whose use differs between human and model reasoning. By establishing a shared vocabulary between cognitive science and LLM research, our framework enables diagnosis of reasoning failures and principled development of models that reason through robust cognitive mechanisms rather than spurious shortcuts, while providing tools to test theories of human cognition at scale.
Mastering educational concepts requires understanding both their prerequisites (e.g., recursion before merge sort) and sub-concepts (e.g., merge sort as part of sorting algorithms). Capturing these dependencies is critical for identifying students' knowledge gaps and enabling targeted intervention for personalized learning, especially in large-scale courses where instructors cannot feasibly diagnose individual misunderstanding. While knowledge graphs offer a natural representation for capturing these conceptual relationships at scale, existing approaches are either surface-level or disregard the rich pedagogical signals embedded in instructional materials. We propose InstructKG, a framework for automatically constructing instructor-aligned knowledge graphs that capture a course's intended learning progression. Given a course's lecture materials, InstructKG extracts significant concepts as nodes and infers learning dependencies as directed edges (e.g., "part-of" or "depends-on" relationships). The framework synergizes the rich temporal and semantic signals unique to educational materials (e.g., "recursion" is taught before "mergesort") with the generalizability of large language models. Through experiments on diverse lecture materials, human evaluation, and a prerequisite-learning benchmark, we demonstrate that InstructKG captures rich, instructor-aligned learning progressions.