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Effective feedback is essential for refining instructional practices in mathematics education, and researchers often turn to advanced natural language processing (NLP) models to analyze classroom dialogues from multiple perspectives. However, utterance-level discourse analysis encounters two primary challenges: (1) multi-functionality, where a single utterance may serve multiple purposes that a single tag cannot capture, and (2) the exclusion of many utterances from domain-specific discourse move classifications, leading to their omission in feedback. To address these challenges, we proposed a multi-perspective discourse analysis that integrates domain-specific talk moves with dialogue act (using the flattened multi-functional SWBD-MASL schema with 43 tags) and discourse relation (applying Segmented Discourse Representation Theory with 16 relations). Our top-down analysis framework enables a comprehensive understanding of utterances that contain talk moves, as well as utterances that do not contain talk moves. This is applied to two mathematics education datasets: TalkMoves (teaching) and SAGA22 (tutoring). Through distributional unigram analysis, sequential talk move analysis, and multi-view deep dive, we discovered meaningful discourse patterns, and revealed the vital role of utterances without talk moves, demonstrating that these utterances, far from being mere fillers, serve crucial functions in guiding, acknowledging, and structuring classroom discourse. These insights underscore the importance of incorporating discourse relations and dialogue acts into AI-assisted education systems to enhance feedback and create more responsive learning environments. Our framework may prove helpful for providing human educator feedback, but also aiding in the development of AI agents that can effectively emulate the roles of both educators and students. 

A well-known question in planar first-passage percolation concerns the convergence of the empirical distribution of weights as seen along geodesics. We demonstrate this convergence for an explicit model, directed last-passage percolation on\mathbb{Z}^{2}with i.i.d. exponential weights, and provide explicit formulae for the limiting distributions, which depend on the asymptotic direction. For example, for geodesics in the direction of the diagonal, the limiting weight distribution has density(1/4+x/2+x^{2}/8)e^{-x}, and so is a mixture of Gamma(1,1), Gamma(2,1), and Gamma(3,1) distributions with weights1/4,1/2, and1/4respectively. More generally, we study the local environment as seen from vertices along geodesics (including information about the shape of the path and about the weights on and off the path in a local neighborhood). We consider finite geodesics from(0,0)ton\boldsymbol{\rho}for some vector\boldsymbol{\rho}in the first quadrant, in the limit asn\to\infty, as well as semi-infinite geodesics in direction\boldsymbol{\rho}. We show almost sure convergence of the empirical distributions of the environments along these geodesics, as well as convergence of the distributions of the environment around a typical point in these geodesics, to the same limiting distribution, for which we give an explicit description.We make extensive use of a correspondence with TASEP as seen from an isolated second-class particle for which we prove new results concerning ergodicity and convergence to equilibrium. Our analysis relies on geometric arguments involving estimates for last-passage times, available from the integrable probability literature. 

Educational dialogue systems have been used to support students and teachers for decades. Such systems rely on explicit pedagogically motivated dialogue rules. With the ease of integrating large language models (LLMs) into dialogue systems, applications have been arising that directly use model responses without the use of human-written rules, raising concerns about their use in classroom settings. Here, we explore how to constrain LLM outputs to generate appropriate and supportive teacher-like responses. We present results comparing the effectiveness of different constraint variations in a zero-shot prompting setting on a large mathematics classroom corpus. Generated outputs are evaluated with human annotation for Fluency, Relevance, Helpfulness, and Adherence to the provided constraints. Including all constraints in the prompt led to the highest values for Fluency and Helpfulness, and the second highest value for Relevance. The annotation results also demonstrate that the prompts that result in the highest adherence to constraints do not necessarily indicate higher perceived scores for Fluency, Relevance, or Helpfulness. In a direct comparison, all of the non-baseline LLM responses were ranked higher than the actual teacher responses in the corpus over 50% of the time. 

This paper reports the first release of the UMR (Uniform Meaning Representation) data set. UMR is a graph-based meaning representation formalism consisting of a sentence-level graph and a document-level graph. The sentence-level graph represents predicate-argument structures, named entities, word senses, aspectuality of events, as well as person and number information for entities. The document-level graph represents coreferential, temporal, and modal relations that go beyond sentence boundaries. UMR is designed to capture the commonalities and variations across languages and this is done through the use of a common set of abstract concepts, relations, and attributes as well as concrete concepts derived from words from invidual languages. This UMR release includes annotations for six languages (Arapaho, Chinese, English, Kukama, Navajo, Sanapana) that vary greatly in terms of their linguistic properties and resource availability. We also describe on-going efforts to enlarge this data set and extend it to other genres and modalities. We also briefly describe the available infrastructure (UMR annotation guidelines and tools) that others can use to create similar data sets. 

This paper reports the first release of the UMR (Uniform Meaning Representation) data set. UMR is a graph-based meaning representation formalism consisting of a sentence-level graph and a document-level graph. The sentence-level graph represents predicate-argument structures, named entities, word senses, aspectuality of events, as well as person and number information for entities. The document-level graph represents coreferential, temporal, and modal relations that go beyond sentence boundaries. UMR is designed to capture the commonalities and variations across languages and this is done through the use of a common set of abstract concepts, relations, and attributes as well as concrete concepts derived from words from invidual languages. This UMR release includes annotations for six languages (Arapaho, Chinese, English, Kukama, Navajo, Sanapana) that vary greatly in terms of their linguistic properties and resource availability. We also describe on-going efforts to enlarge this data set and extend it to other genres and modalities. We also briefly describe the available infrastructure (UMR annotation guidelines and tools) that others can use to create similar data sets. 

Abstract The Institute for Student‐AI Teaming (iSAT) addresses the foundational question:how to promote deep conceptual learning via rich socio‐collaborative learning experiences for all students?—a question that is ripe for AI‐based facilitation and has the potential to transform classrooms. We advance research in speech, computer vision, human‐agent teaming, computer‐supported collaborative learning, expansive co‐design, and the science of broadening participation to design and study next generation AI technologies (called AI Partners) embedded in student collaborative learning teams in coordination with teachers. Our institute ascribes to theoretical perspectives that aim to create a normative environment of widespread engagement through responsible design of technology, curriculum, and pedagogy in partnership with K–12 educators, racially diverse students, parents, and other community members.