[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82596-en":3,"doc-seo-82596-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82596,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","LLMs As Teaching Assistants for Mathematics Exam Grading Reliability and Practical Usability","Open-ended mathematics exams evaluate reasoning, proof construction, and communication but are hard to grade consistently at scale because instructors must apply partial-credit rubrics while providing feedback that targets misconceptions. This study tests six large language model configurations as grading assistants on an undergraduate discrete mathematics examination, comparing BASELINE and LIBERAL rubric-following policies. Metrics include error, correlation, and exact agreement at question and exam-total levels, alongside usability observations. Liberal prompting lowers question-level error across models, while calibration effects differ at total-score ranking goals.","LLMs as Teaching Assistants for Mathematics Exam Grading: Reliability, and Practical Usability  \nAastha Sapkota and M. G. Sarwar Murshed  \nComputer Science Department  \nUniversity of Wisconsin - Green Bay, Green Bay, WI, USA  \narXiv :2607 .0 1247v 1 [ cs .CY] 1 Jun 2026  \nAbstract—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 rubricfollowing 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: ChatGPT completed the grading workflow in one attempt, Claude required continuation because of usage limits, and Gemini required dataset splitting after filehandling failures on the full dataset. These findings support a cautious deployment model in which LLMs act as auditable teaching assistants rather than autonomous graders.  \nIndex Terms—Large language models, automated grading, mathematics education, short-answer grading, rubric-based assessment, feedback quality, human-in-the-loop AI, partial credit.  \nI. INTRODUCTION  \nAssessment in mathematics and computer science education is not merely a mechanism for assigning scores. It is a central part of instruction: grading communicates what counts as valid reasoning, reveals misconceptions, and determines whether students receive timely opportunities to improve. Open-ended mathematics questions are especially important because they require students to show intermediate reasoning, construct proofs, interpret definitions, and apply algorithms. These same properties make grading difficult. A correct final answer may conceal invalid reasoning; a wrong final answer may deserve  \nsubstantial partial credit; and semantically equivalent solutions may use different notation, organization, or explanatory style. Large classes amplify these challenges. Human graders must apply rubrics repeatedly across heterogeneous responses while managing fatigue, time pressure, and borderline cases.  \nInstructors often attempt to increase reliability through detailed rubrics, teaching-assistant calibration, and discussion of representative examples. Even with these safeguards, score variance and delayed feedback remain common in open-ended assessment.  \nAutomated short-answer grading systems promise efficiency, but many earlier systems depend on surface similarity, hand-engineered features, or narrow answer templates. Recent LLMs can interpret natural language and mathematical explanations more flexibly, motivating their use","cbCaijdKlFyxV1Pe","https://ap.wps.com/l/cbCaijdKlFyxV1Pe","pdf",319349,1,12,"English","en",105,"# Introduction\n## Research Questions","[{\"question\":\"What problem does the study address in grading open-ended mathematics exams?\",\"answer\":\"Open-ended exams require consistent partial-credit rubric application and misconception-focused feedback, which is difficult to scale and can produce score variance and delayed guidance. The study targets grading reliability and pedagogical usefulness of LLM assistance.\"},{\"question\":\"Which LLM grading configurations and policies are compared?\",\"answer\":\"The evaluation covers six 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, Claude Sonnet 4.6). It compares a BASELINE stricter rubric-following prompt with a LIBERAL policy added to reduce harsh deductions and better recognize valid partial reasoning.\"},{\"question\":\"How do the results evaluate grading reliability and usefulness?\",\"answer\":\"Agreement is measured at question and total-exam levels using mean absolute error, RMSE, normalized RMSE, Pearson correlation, and exact agreement. Usability observations compare how models complete the workflow, including continuation due to limits and dataset handling failures, motivating a cautious, auditable assistant deployment model.\"}]",1784181708,30,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"llms-as-teaching-assistants-for-mathematics-exam-grading-reliability-and-practical-usability","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/llms-as-teaching-assistants-for-mathematics-exam-grading-reliability-and-practical-usability/82596/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the study address in grading open-ended mathematics exams?","Question",{"text":75,"@type":76},"Open-ended exams require consistent partial-credit rubric application and misconception-focused feedback, which is difficult to scale and can produce score variance and delayed guidance. The study targets grading reliability and pedagogical usefulness of LLM assistance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which LLM grading configurations and policies are compared?",{"text":80,"@type":76},"The evaluation covers six 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, Claude Sonnet 4.6). It compares a BASELINE stricter rubric-following prompt with a LIBERAL policy added to reduce harsh deductions and better recognize valid partial reasoning.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the results evaluate grading reliability and usefulness?",{"text":84,"@type":76},"Agreement is measured at question and total-exam levels using mean absolute error, RMSE, normalized RMSE, Pearson correlation, and exact agreement. Usability observations compare how models complete the workflow, including continuation due to limits and dataset handling failures, motivating a cautious, auditable assistant deployment model.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":28,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]