Daily Papers

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

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.

Domain experts across engineering, healthcare, and education follow strict standards for producing quality content such as technical manuals, medication instructions, and children's reading materials. However, current works in controllable text generation have yet to explore using these standards as references for control. Towards this end, we introduce Standardize, a retrieval-style in-context learning-based framework to guide large language models to align with expert-defined standards. Focusing on English language standards in the education domain as a use case, we consider the Common European Framework of Reference for Languages (CEFR) and Common Core Standards (CCS) for the task of open-ended content generation. Our findings show that models can gain 40% to 100% increase in precise accuracy for Llama2 and GPT-4, respectively, demonstrating that the use of knowledge artifacts extracted from standards and integrating them in the generation process can effectively guide models to produce better standard-aligned content.

Providing computer science (CS) offerings in the K-12 education system is often limited by the lack of experienced teachers, especially in small or rural underserved school districts. By helping teachers in underserved areas develop CS curriculum and helping them become certified to teach CS courses, more young people in underserved areas are aware of IT-career opportunities, and prepared for CS education at the university level, which ultimately helps tackle the IT workforce deficit in the United States. This paper discusses a successful implementation of a Google CS4HS grant to a rural underserved area, as well as lessons learned through the implementation of the program. Key elements in the implementation included a face-to-face hands-on workshop, followed by a seven week graduate-level online summer course for the teachers to learn and develop curriculum that covers the CS concepts they will be teaching. The teachers were supported with an online community of practice for the year as they implemented the curriculum.

Curriculum design is a fundamental component of education. For example, when we learn mathematics at school, we build upon our knowledge of addition to learn multiplication. These and other concepts must be mastered before our first algebra lesson, which also reinforces our addition and multiplication skills. Designing a curriculum for teaching either a human or a machine shares the underlying goal of maximizing knowledge transfer from earlier to later tasks, while also minimizing forgetting of learned tasks. Prior research on curriculum design for image classification focuses on the ordering of training examples during a single offline task. Here, we investigate the effect of the order in which multiple distinct tasks are learned in a sequence. We focus on the online class-incremental continual learning setting, where algorithms or humans must learn image classes one at a time during a single pass through a dataset. We find that curriculum consistently influences learning outcomes for humans and for multiple continual machine learning algorithms across several benchmark datasets. We introduce a novel-object recognition dataset for human curriculum learning experiments and observe that curricula that are effective for humans are highly correlated with those that are effective for machines. As an initial step towards automated curriculum design for online class-incremental learning, we propose a novel algorithm, dubbed Curriculum Designer (CD), that designs and ranks curricula based on inter-class feature similarities. We find significant overlap between curricula that are empirically highly effective and those that are highly ranked by our CD. Our study establishes a framework for further research on teaching humans and machines to learn continuously using optimized curricula.

Large Language Models (LLMs) have demonstrated remarkable capabilities in understanding and generating human-like content. This has revolutionized various sectors such as healthcare, software development, and education. In education, LLMs offer potential for personalized and interactive learning experiences, especially in regions with limited teaching resources. However, adapting these models effectively to curriculum-specific content, such as the National Council of Educational Research and Training (NCERT) syllabus in India, presents unique challenges in terms of accuracy, alignment, and pedagogical relevance. In this paper, we present the framework "PustakAI"Pustak means `book' in many Indian languages. for the design and evaluation of a novel question-answering dataset "NCERT-QA" aligned with the NCERT curriculum for English and Science subjects of grades 6 to 8. We classify the curated QA pairs as Factoid, Inferential, and Others (evaluative and reasoning). We evaluate the dataset with various prompting techniques, such as meta-prompt, few-shot, and CoT-style prompting, using diverse evaluation metrics to understand which approach aligns more efficiently with the structure and demands of the curriculum. Along with the usability of the dataset, we analyze the strengths and limitations of current open-source LLMs (Gemma3:1b, Llama3.2:3b, and Nemotron-mini:4b) and high-end LLMs (Llama-4-Scout-17B and Deepseek-r1-70B) as AI-based learning tools in formal education systems.

Can Large Language Models understand how students learn? As LLMs are deployed for adaptive testing and personalized tutoring, this question becomes urgent -- yet we cannot answer it with existing resources. Current educational datasets provide only question identifiers and binary correctness labels, rendering them opaque to LLMs that reason in natural language. We address this gap with FoundationalASSIST, the first English educational dataset providing the complete information needed for research on LLMs in education: full question text, actual student responses (not just right/wrong), records of which wrong answers students chose, and alignment to Common Core K-12 standards. These 1.7 million interactions from 5,000 students enable research directions that were previously impossible to pursue, from fine-tuning student models to analyzing misconception patterns. To demonstrate the dataset's utility, we evaluate four frontier models (GPT-OSS-120B, Llama-3.3-70B, Qwen3-Next-80B variants) on two complementary task families: Knowledge Tracing, testing whether LLMs can predict student performance on questions, and the exact answer a student will give; and Pedagogical Grounding, testing whether LLMs understand the properties that make assessment items effective. Our evaluation reveals significant gaps in current LLM capabilities. Every model barely achieves a trivial baseline on knowledge tracing. All models fall below random chance on item discrimination, indicating that LLMs do not understand what makes one problem more diagnostic than another. Models do show competence at judging relative difficulty (up to 68.6%), but this partial success only highlights the gaps elsewhere. These results establish that substantial advances are needed before LLMs can reliably support personalized learning at scale. We release FoundationalASSIST to support progress on these foundational challenges.