In recent years, natural language processing (NLP) has become integral to educational data mining, particularly in the analysis of student-generated language products. For research and assessment purposes, so-called embedding models are typically employed to generate numeric representations of text that capture its semantic content for use in subsequent quantitative analyses. Y et when it comes to science-related language, symbolic expressions such as equations and formulas introduce challenges that current embedding models struggle to address. Existing research studies and practical applications often either overlook these challenges or remove symbolic expressions altogether, potentially leading to biased research findings and diminished performance of practical applications. This study therefore explores how contemporary embedding models differ in their capability to process and interpret science-related symbolic expressions. To this end, various embedding models are evaluated using physics-specific symbolic expressions drawn from authentic student responses, with performance assessed via two approaches: 1) similarity-based analyses and 2) integration into a machine learning pipeline. Our findings reveal significant differences in model performance, with OpenAI's GPT-text-embedding-3-large outperforming all other examined models, though its advantage over other models was moderate rather than decisive. Overall, this study underscores the importance for educational data mining researchers and practitioners of carefully selecting NLP embedding models when working with science-related language products that include symbolic expressions. The code and (partial) data are available at https: //doi.org/10.17605/OSF.IO/6XQVG.

While cognitive diagnosis (CD) effectively assesses students' knowledge mastery from structured test data, applying it to real-world teacher-student dialogues presents two fundamental challenges. Traditional CD models lack a suitable framework for handling dynamic, unstructured dialogues, and it's difficult to accurately extract diagnostic semantics from lengthy dialogues. To overcome these hurdles, we propose DiaCDM, an innovative model. We've adapted the initiation-response-evaluation (IRE) framework from educational theory to design a diagnostic framework tailored for dialogue. We also developed a unique graph-based encoding method that integrates teacher questions with relevant knowledge components to capture key information more precisely. To our knowledge, this is the first exploration of cognitive diagnosis in a dialogue setting. Experiments on three real-world dialogue datasets confirm that DiaCDM not only significantly improves diagnostic accuracy but also enhances the results' interpretability, providing teachers with a powerful tool for assessing students' cognitive states. The code is available at https://github.com/Mind-Lab-ECNU/DiaCDM/tree/main.

As personalized learning gains increasing attention in mathematics education, there is a growing demand for intelligent systems that can assess complex student responses and provide individualized feedback in real time. In this study, we present a personalized auto-grading and feedback system for constructive geometry tasks, developed using large language models (LLMs) and deployed on the Algeomath platform, a Korean online tool designed for interactive geometric constructions. The proposed system evaluates student-submitted geometric constructions by analyzing their procedural accuracy and conceptual understanding. It employs a prompt-based grading mechanism using GPT-4, where student answers and model solutions are compared through a few-shot learning approach. Feedback is generated based on teacher-authored examples built from anticipated student responses, and it dynamically adapts to the student's problem-solving history, allowing up to four iterative attempts per question. The system was piloted with 79 middle-school students, where LLM-generated grades and feedback were benchmarked against teacher judgments. Grading closely aligned with teachers, and feedback helped many students revise errors and complete multi-step geometry tasks. While short-term corrections were frequent, longer-term transfer effects were less clear. Overall, the study highlights the potential of LLMs to support scalable, teacher-aligned formative assessment in mathematics, while pointing to improvements needed in terminology handling and feedback design.

Automated scoring plays a crucial role in education by reducing the reliance on human raters, offering scalable and immediate evaluation of student work. While large language models (LLMs) have shown strong potential in this task, their use as end-to-end raters faces challenges such as low accuracy, prompt sensitivity, limited interpretability, and rubric misalignment. These issues hinder the implementation of LLM-based automated scoring in assessment practice. To address the limitations, we propose AutoSCORE, a multi-agent LLM framework enhancing automated scoring via rubric-aligned Structured COmponent REcognition. With two agents, AutoSCORE first extracts rubric-relevant components from student responses and encodes them into a structured representation (i.e., Scoring Rubric Component Extraction Agent), which is then used to assign final scores (i.e., Scoring Agent). This design ensures that model reasoning follows a human-like grading process, enhancing interpretability and robustness. We evaluate AutoSCORE on four benchmark datasets from the ASAP benchmark, using both proprietary and open-source LLMs (GPT-4o, LLaMA-3.1-8B, and LLaMA-3.1-70B). Across diverse tasks and rubrics, AutoSCORE consistently improves scoring accuracy, human-machine agreement (QWK, correlations), and error metrics (MAE, RMSE) compared to single-agent baselines, with particularly strong benefits on complex, multi-dimensional rubrics, and especially large relative gains on smaller LLMs. These results demonstrate that structured component recognition combined with multi-agent design offers a scalable, reliable, and interpretable solution for automated scoring.

Learning Progressions (LPs) can help adjust instruction to individual learners needs if the LPs reflect diverse ways of thinking about a construct being measured, and if the LP-aligned assessments meaningfully measure this diversity. The process of doing science is inherently multi-modal with scientists utilizing drawings, writing and other modalities to explain phenomena. Thus, fostering deep science understanding requires supporting students in using multiple modalities when explaining phenomena. We build on a validated NGSS-aligned multi-modal LP reflecting diverse ways of modeling and explaining electrostatic phenomena and associated assessments. We focus on students modeling, an essential practice for building a deep science understanding. Supporting culturally and linguistically diverse students in building modeling skills provides them with an alternative mode of communicating their understanding, essential for equitable science assessment. Machine learning (ML) has been used to score open-ended modeling tasks (e.g., drawings), and short text-based constructed scientific explanations, both of which are time-consuming to score. We use ML to evaluate LP-aligned scientific models and the accompanying short text-based explanations reflecting multi-modal understanding of electrical interactions in high school Physical Science. We show how LP guides the design of personalized ML-driven feedback grounded in the diversity of student thinking on both assessment modes.

Educators evaluate student knowledge using knowledge component (KC) models that map assessment questions to KCs. Still, designing KC models for large question banks remains an insurmountable challenge for instructors who need to analyze each question by hand. The growing use of Generative AI in education is expected only to aggravate this chronic deficiency of expert-designed KC models, as course engineers designing KCs struggle to keep up with the pace at which questions are generated. In this work, we propose KCluster, a novel KC discovery algorithm based on identifying clusters of congruent questions according to a new similarity metric induced by a large language model (LLM). We demonstrate in three datasets that an LLM can create an effective metric of question similarity, which a clustering algorithm can use to create KC models from questions with minimal human effort. Combining the strengths of LLM and clustering, KCluster generates descriptive KC labels and discovers KC models that predict student performance better than the best expert-designed models available. In anticipation of future work, we illustrate how KCluster can reveal insights into difficult KCs and suggest improvements to instruction.

Item (question) difficulties play a crucial role in educational assessments, enabling accurate and efficient assessment of student abilities and personalization to maximize learning outcomes. Traditionally, estimating item difficulties can be costly, requiring real students to respond to items, followed by fitting an item response theory (IRT) model to get difficulty estimates. This approach cannot be applied to the cold-start setting for previously unseen items either. In this work, we present SMART (Simulated Students Aligned with IRT), a novel method for aligning simulated students with instructed ability, which can then be used in simulations to predict the difficulty of open-ended items. We achieve this alignment using direct preference optimization (DPO), where we form preference pairs based on how likely responses are under a ground-truth IRT model. We perform a simulation by generating thousands of responses, evaluating them with a large language model (LLM)-based scoring model, and fit the resulting data to an IRT model to obtain item difficulty estimates. Through extensive experiments on two real-world student response datasets, we show that SMART outperforms other item difficulty prediction methods by leveraging its improved ability alignment.

Exploratory learning environments (ELEs), such as simulation-based platforms and open-ended science curricula, promote hands-on exploration and problem-solving but make it difficult for teachers to gain timely insights into students' conceptual understanding. This paper presents LearnLens, a generative AI (GenAI)-enhanced teacher-facing dashboard designed to support problem-based instruction in middle school science. LearnLens processes students' open-ended responses from digital assessments to provide various insights, including sample responses, word clouds, bar charts, and AI-generated summaries. These features elucidate students' thinking, enabling teachers to adjust their instruction based on emerging patterns of understanding. The dashboard was informed by teacher input during professional development sessions and implemented within a middle school Earth science curriculum. We report insights from teacher interviews that highlight the dashboard's usability and potential to guide teachers' instruction in the classroom.

Automated grading systems can efficiently score short-answer responses, yet they often fail to indicate when a grading decision is uncertain or potentially contentious. We introduce semantic entropy, a measure of variability across multiple GPT-4-generated explanations for the same student response, as a proxy for human grader disagreement. By clustering rationales via entailment-based similarity and computing entropy over these clusters, we quantify the diversity of justifications without relying on final output scores. We address three research questions: (1) Does semantic entropy align with human grader disagreement? (2) Does it generalize across academic subjects? (3) Is it sensitive to structural task features such as source dependency? Experiments on the ASAP-SAS dataset show that semantic entropy correlates with rater disagreement, varies meaningfully across subjects, and increases in tasks requiring interpretive reasoning. Our findings position semantic entropy as an interpretable uncertainty signal that supports more transparent and trustworthy AI-assisted grading workflows.

The marking problem consists in assessing typed student answers for correctness with respect to a ground truth solution. This is a challenging problem that we seek to tackle using a combination of a computer algebra system, an SMT solver and a term rewriting system. A Large Language Model is used to interpret and remove errors from student responses and rewrite these in a machine readable format. Once formalized and language-aligned, the next step then consists in applying automated reasoning techniques for assessing student solution correctness. We consider two methods of automated theorem proving: off-the-shelf SMT solving and term rewriting systems tailored for physics problems involving trigonometric expressions. The development of the term rewrite system and establishing termination and confluence properties was not trivial, and we describe it in some detail in the paper. We evaluate our system on a rich pool of over 1500 real-world student exam responses from the 2023 Australian Physics Olympiad.