Mathematics Education

Visual representations can help lower-primary learners understand Math Word Problems, but generating classroom-usable visuals remains difficult. Existing symbolic systems are controllable but limited in coverage, while end-to-end text-to-image systems often fail to satisfy exact mathematical constraints. This paper presents a symbolic visual generation framework for lower-primary MWP generation with broader problem coverage and more scalable asset generation. The framework includes an LLM-based routing layer, three worksheet-oriented generation modules, and two fallback mechanisms for open-world SVG asset acquisition. A human evaluation comparing Math2Visual-X with Stable Diffusion XL, Nano Banana, and GPT Image showed that the proposed method achieved the strongest overall performance. The results indicate that the framework offers a scalable and pedagogically grounded approach for automatic MWP visual generation.

Automated feedback systems that rely on answer correctness will reinforce, rather than address, misconceptions when students reach the correct answer through flawed reasoning. We investigate automatic detection of these hidden misconceptions using 20,964 real student responses from the Eedi mathematics platform. Fine-tuned classifiers detect only 57% of these hidden misconceptions, and standard ML interventions do not improve on this. An open-weight reasoning model detects 84%, but at realistic prevalence, false alarms outnumber genuine detections roughly 8 to 1. We present a graduated assessment rubric that separates answer correctness from method validity, and propose a detect-verify-escalate pipeline that routes uncertain cases to diagnostic follow-up questions rather than directly to teachers. Two deployment modes adapt the pipeline: a teacher dashboard where the system filters a review queue, and an autonomous tutor where flags trigger low-cost formative follow-up.

Collaborative Problem Solving (CPS) is a core skill in education, where the process of peer interaction is highly important. However, existing educational dialogue datasets mostly focus on classroom instruction or tutoring (i.e., teacher/tutor-student interaction), yet datasets centering small-group, student-student interaction are limited. This thus leaves research with limited resources for studying how students interact, coordinate, and solve problems together in real educational settings. To address this, we introduce PeerMathDial, the first dataset of peer CPS dialogues collected from authentic middle school math classrooms. It contains 55 dialogues from 27 students, totaling 6,406 turns. To facilitate research on CPS discourse analysis, we further build a corpus-grounded dialogue act taxonomy assisted by LLMs. Using the dataset and the dialogue act taxonomy, we demonstrate the practical applications of PeerMathDial across three use cases. First, we track how dialogues evolve over time and measure the impact of teacher interventions. Second, we align dialogue actions with student surveys to reveal the connection between students' traits (e.g., confidence, leadership) and their actual behaviors. Third, by evaluating LLMs on dialogue act prediction, we glimpse at the potential of LLMs for student simulation in educational applications. Our dataset and source code will be released to the community.

Open-ended mathematics exams are valuable because they assess reasoning, proof construction, algorithmic thinking, and communication of intermediate steps. They are also difficult to grade at scale because instructors must apply partial-credit rubrics consistently while giving feedback that helps students repair misconceptions. This paper evaluates six contemporary large language model (LLM) configurations, Gemini 3.1 Pro Extended, Gemini 3.5 Flash, ChatGPT 5.5 Pro Extended, ChatGPT 5.5 Thinking, Claude Pro Opus 4.7, and Claude Sonnet 4.6, as grading assistants for an undergraduate discrete mathematics examination. The study compares two grading policies. The BASELINE policy uses a stricter rubric-following prompt that emphasizes explicit evidence and complete justification. The LIBERAL policy was added after preliminary grading showed that the baseline condition sometimes applied harsh point deductions and failed to recognize valid partial reasoning. Agreement with human grading is measured at both the question and exam-total levels using mean absolute error, root mean squared error, normalized root mean squared error, Pearson correlation, and exact agreement. The results show that liberal partial-credit prompting reduces average question-level error for every evaluated model family. ChatGPT 5.5 Thinking (LIBERAL) has the lowest average question-level MAE (1.87) and RMSE (2.53), while Gemini 3.1 Pro Extended (LIBERAL) has the lowest total-score MAE (8.00) and RMSE (10.66). However, the strongest total-score Pearson correlation occurs under Gemini 3.1 Pro Extended (BASELINE) at 0.58, showing that point calibration and rank preservation remain distinct goals. We also report practical usability observations.

Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute.

How much have students' ordinary learning processes shifted in response to generative AI, and how does that affect their durable learning outcomes? Self-report surveys show little change, while small-scale behavioral studies report widespread AI use without the scale or duration to measure learning consequences. We address both questions using a ten-year panel of $3.2$ million ALEKS learning interactions for investigating time-on-task, complemented by ALEKS PPL placement-assessment data for examining proctoring and learning outcomes, with a quasi-experimental design exploiting variation in tasks that are more susceptible to AI (text-based word problems) and less susceptible to AI (interactive graph-based problems). Learning time on AI-susceptible problems declines $2.8\%$ per quarter among college students after ChatGPT's release, cumulating to $26.9\%$ over eleven quarters; high-schoolers show $31.3\%$, middle-schoolers $9.0\%$, and Grade 5 students no detectable change. Among college students, the post-ChatGPT divergence vanishes entirely under proctoring, ruling out broad efficiency gains as the likely explanation. Logistic fixed-effects models on randomly assigned proctored retention items yield a $25\%$ cumulative decline in odds of correct response; the same estimator on non-proctored assessment produces a large opposite-signed increase -- inconsistent with any platform, cohort, or curriculum explanation. These results are among the first large-scale behavioral and outcome evidence that generative AI has altered how students study and the knowledge they build -- the population-level indicator of cognitive surrender, with direct implications for educational research, assessment governance, and AI policy.

Adaptive learning refers to educational technologies that track learners' learning progress and adapt the instructional process based on individual learners' learning performance. It is increasingly recognized as critical for developing an effective learning support tool. Vision language models (VLMs) have seen adoption in mathematics education, and students have been using them as learning aids for personalized instruction. However, it is unknown whether VLMs have the ability to adapt to different learner profiles when providing mathematical instructions. Current VLMs lack a systematic evaluation framework for this adaptivity to different learner profiles in mathematics tutoring tasks. To address this gap, we draw on the learner model from the adaptive learning framework (Shute and Towle, 2018) and propose a learner model-based rubric. Our rubric formalizes adaptivity assessment into three aspects: cognitive aspects, motivational aspects, and complexity. We also evaluate two additional dimensions of VLM responses: correctness (of answers and solutions) and quality (of the response itself). Our experimental results show measurable differences in adaptivity across models and also reveal that current VLMs struggle to consistently produce learner model-based instructional responses, especially when receiving limited learner information.

Large language models can increasingly adapt educational tasks to learners characteristics. In the present study, we examine a multi-agent teacher-in-the-loop system for personalizing middle school math problems. The teacher enters a base problem and desired topic, the LLM generates the problem, and then four AI agents evaluate the problem using criteria that each specializes in (mathematical accuracy, authenticity, readability, and realism). Eight middle school mathematics teachers created 212 problems in ASSISTments using the system and assigned these problems to their students. We find that both teachers and students wanted to modify the fine-grained personalized elements of the real-world context of the problems, signaling issues with authenticity and fit. Although the agents detected many issues with realism as the problems were being written, there were few realism issues noted by teachers and students in the final versions. Issues with readability and mathematical hallucinations were also somewhat rare. Implications for multi-agent systems for personalization that support teacher control are given.

Novice math teachers often encounter students' mistakes that are difficult to diagnose and remediate. Misconceptions are especially challenging because teachers must explain what went wrong and how to solve them. Although many existing large language model (LLM) platforms can assist in generating instructional feedback, these LLMs loosely connect pedagogical knowledge and student mistakes, which might make the guidance less actionable for teachers. To address this gap, we propose MisEdu-RAG, a dual-hypergraph-based retrieval-augmented generation (RAG) framework that organizes pedagogical knowledge as a concept hypergraph and real student mistake cases as an instance hypergraph. Given a query, MisEdu-RAG performs a two-stage retrieval to gather connected evidence from both layers and generates a response grounded in the retrieved cases and pedagogical principles. We evaluate on MisstepMath, a dataset of math mistakes paired with teacher solutions, as a benchmark for misconception-aware retrieval and response generation across topics and error types. Evaluation results on MisstepMath show that, compared with baseline models, MisEdu-RAG improves token-F1 by 10.95% and yields up to 15.3% higher five-dimension response quality, with the largest gains on Diversity and Empowerment. To verify its applicability in practical use, we further conduct a pilot study through a questionnaire survey of 221 teachers and interviews with 6 novices. The findings suggest that MisEdu-RAG provides diagnosis results and concrete teaching moves for high-demand misconception scenarios. Overall, MisEdu-RAG demonstrates strong potential for scalable teacher training and AI-assisted instruction for misconception handling. Our code is available on GitHub: https://github.com/GEMLab-HKU/MisEdu-RAG.

Strategic model selection and reasoning settings are more effective than ensembling for optimizing automated scoring with large language models (LLMs). We examined self-consistency (intra-model majority voting) and reasoning effort for scoring conversation-based assessment items in high school mathematics, evaluating 900 student conversations against human-scored ground truths using frontier and low-cost models from OpenAI and Google. Temperature sampling significantly improved accuracy over deterministic calls, but increasing ensemble size (j = 1 to 7) produced no significant gains. Higher reasoning effort showed a significant positive linear trend with scoring accuracy, though the benefit varied by model family. An efficiency frontier analysis identified Gemini 3.1 Pro Preview at low reasoning as the most accurate but costly configuration; GPT-5.4 Nano and Mini with no reasoning offered the best cost-performance balance.

Past research has defined a general process for the data-driven redesign of educational technologies and has shown that in carefully-selected instances, this process can help make systems more effective. In the current work, we test the generality of the approach by applying it to four units of a middle-school mathematics intelligent tutoring system that were selected not based on suitability for redesign, as in previous work, but on topic. We tested whether the redesigned system was more effective than the original in a classroom study with 123 students. Although the learning gains did not differ between the conditions, students who used the Redesigned Tutor had more productive time-on-task, a larger number of skills practiced, and greater total knowledge mastery. The findings highlight the promise of data-driven redesign even when applied to instructional units not selected as likely to yield improvement, as evidence of the generality and wide applicability of the method.

Game-based learning (GBL) is widely adopted in mathematics education. It enhances learners' engagement and critical thinking throughout the mathematics learning process. However, enabling players to learn intrinsically through mathematical games still presents challenges. In particular, effective GBL systems require dozens of high-quality game levels and mechanisms to deliver them to appropriate players in a way that matches their learning abilities. To address this challenge, we propose a framework, guided by adaptive learning theory, that uses artificial intelligence (AI) techniques to build a classifier for player-generated levels. We collect 206 distinct game levels created by both experts and advanced players in Creative Mode, a new tool in a math game-based learning app, and develop a classifier to extract game features and predict valid game levels. The preliminary results show that the Random Forest model is the optimal classifier among the four machine learning classification models (k-nearest neighbors, decision trees, support vector machines, and random forests). This study provides insights into the development of GBL systems, highlighting the potential of integrating AI into the game-level design process to provide more personalized game levels for players.

Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching, technology, and ethics. We offer recommendations on safeguarding our intellectual autonomy, rethinking our practice, broadening curricula, building academically oriented infrastructure, and developing shared ethical principles - with the aim of ensuring that the future of mathematics is shaped by the community itself.

Evaluating the pedagogical quality of AI tutors remains challenging: standard NLG metrics do not determine whether responses identify mistakes, scaffold reasoning, or avoid revealing the answers. For the task of mistake remediation, we derive a hierarchy of pedagogical aspects from human pairwise preferences on MRBench, and synthesize minimally contrastive response pairs that differ along key aspects (e.g., mistake identification and location, targetedness, scaffolding, actionability, clarity, and coherence). We develop and release Bradley-Terry preference models trained on weighted-sum rankings that we automatically create from MRBench, synthetic pairs, and data combinations. Using only synthetic data, our best model reaches 0.69 pairwise accuracy on a human preference test, and combining weighted-sum data with targeted synthetic groups improves accuracy to 0.74, outperforming larger general-purpose reward models while using only a 0.5B-parameter backbone.

It is crucial to explore the impact of different teaching methods on student learning in educational research. However, real-person experiments face significant ethical constraints, and we cannot conduct repeated teaching experiments on the same student. LLM-based generative agents offer a promising avenue for simulating student behavior. Before large-scale experiments, a fundamental question must be addressed: are student agents truly credible, and can they faithfully simulate human learning? In this study, we built a Big Five Personality-based student agent model with a full pipeline of student-teacher interaction, self-study, and examination. To evaluate behavioral fidelity, we collected 13 empirical studies on Big Five traits and learning, and distilled them into 14 criteria. We found that the 71.4% of the student agents' behavior was aligned with human learners.

Large-enrollment university courses face persistent challenges in providing timely and scalable instructional support. While generative AI holds promise, its effective use depends on reliability and pedagogical alignment. We present a human-centered case study of AI-assisted support in a Calculus I course, implemented in close collaboration with the course instructor. We developed a system to answer students' questions on a discussion forum, fine-tuning a lightweight language model on 2,588 historical student-instructor interactions. The model achieved 75.3% accuracy on a benchmark of 150 representative questions annotated by five instructors, and in 36% of cases, its responses were rated equal to or better than instructor answers. Post-deployment student survey (N = 105) indicated that students valued the alignment of the responses with the course materials and their immediate availability, while still relying on the instructor verification for trust. We highlight the importance of hybrid human-AI workflows for safe and effective course support.

Effective mathematics education requires identifying and responding to students' mistakes. For AI to support pedagogical applications, models must perform well across different levels of student proficiency. Our work provides an extensive, year-long snapshot of how 11 vision-language models (VLMs) perform on DrawEduMath, a QA benchmark involving real students' handwritten, hand-drawn responses to math problems. We find that models' weaknesses concentrate on a core component of math education: student error. All evaluated VLMs underperform when describing work from students who require more pedagogical help, and across all QA, they struggle the most on questions related to assessing student error. Thus, while VLMs may be optimized to be math problem solving experts, our results suggest that they require alternative development incentives to adequately support educational use cases.

The capabilities of generative AI in mathematics education are rapidly evolving, posing significant challenges for research to keep pace. Research syntheses remain scarce and risk being outdated by the time of publication. We present a Living Meta-Analysis (LIMA) on the effects of generative AI-based interventions for learning mathematics. We update the literature base every two months and apply a cumulative Bayesian multilevel meta-regression model. This paper reports results from the fifth version, including 34 studies, 7 of which were newly included since the fourth version. Results indicate an increasingly positive effect (g = 0.57, CrI [0.36, 0.79]) and no evidence in favor of a publication bias. Moderator analyses indicate that effects vary by integration mode and intervention duration: Larger effects were observed when generative AI supplemented teacher instruction and in longer interventions. Moderate evidence for stronger effects was observed in studies involving younger learners and more recent technology. For other moderators, evidence is still inconclusive.