Standardized math assessments require expensive human pilot studies to establish the difficulty of test items. We investigate the predictive value of open-source large language models (LLMs) for evaluating the difficulty of multiple-choice math questions for real-world students. We show that, while LLMs are poor direct judges of problem difficulty, simulation-based approaches with LLMs yield promising results under the right conditions. Under the proposed approach, we simulate a "classroom" of 4th, 8th, or 12th grade students by prompting the LLM to role-play students of varying proficiency levels. We use the outcomes of these simulations to fit Item Response Theory (IRT) models, comparing learned difficulty parameters for items to their real-world difficulties, as determined by item-level statistics furnished by the National Assessment of Educational Progress (NAEP). We observe correlations as high as 0.75, 0.76, and 0.82 for grades 4, 8, and 12, respectively. In our simulations, we experiment with different "classroom sizes," showing tradeoffs between computation size and accuracy. We find that role-plays with named students improves predictions (compared to student ids), and stratifying names across gender and race further improves predictions. Our results show that LLMs with relatively weaker mathematical abilities (Gemma) actually yield better real-world difficulty predictions than mathematically stronger models (Llama and Qwen), further underscoring the suitability of open-source models for the task.

Automated Essay Scoring (AES) plays a crucial role in language assessment. In particular, cross-prompt essay trait scoring provides learners with valuable feedback to improve their writing skills. However, due to the scarcity of prompts, most existing methods overlook critical information, such as content from prompts or essays, resulting in incomplete assessment perspectives. In this paper, we propose a robust AES framework, the Mixture of Ordered Scoring Experts (MOOSE), which integrates information from both prompts and essays. MOOSE employs three specialized experts to evaluate (1) the overall quality of an essay, (2) the relative quality across multiple essays, and (3) the relevance between an essay and its prompt. MOOSE introduces the ordered aggregation of assessment results from these experts along with effective feature learning techniques. Experimental results demonstrate that MOOSE achieves exceptionally stable and state-of-the-art performance in both cross-prompt scoring and multi-trait scoring on the ASAP++ dataset. The source code is released at https://github.com/antslabtw/MOOSE-AES.

Knowing how to use words appropriately has been a key to improving language proficiency. Previous studies typically discuss how students learn receptively to select the correct candidate from a set of confusing words in the fill-in-the-blank task where specific context is given. In this paper, we go one step further, assisting students to learn to use confusing words appropriately in a productive task: sentence translation. We leverage the GiveMe-Example system, which suggests example sentences for each confusing word, to achieve this goal. In this study, students learn to differentiate the confusing words by reading the example sentences, and then choose the appropriate word(s) to complete the sentence translation task. Results show students made substantial progress in terms of sentence structure. In addition, highly proficient students better managed to learn confusing words. In view of the influence of the first language on learners, we further propose an effective approach to improve the quality of the suggested sentences.