{"id":"https://openalex.org/W4414973944","doi":"https://doi.org/10.48550/arxiv.2510.05162","title":"Artificial-Intelligence Grading Assistance for Handwritten Components of a Calculus Exam","display_name":"Artificial-Intelligence Grading Assistance for Handwritten Components of a Calculus Exam","publication_year":2025,"publication_date":"2025-10-04","ids":{"openalex":"https://openalex.org/W4414973944","doi":"https://doi.org/10.48550/arxiv.2510.05162"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.05162","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.05162","pdf_url":"https://arxiv.org/pdf/2510.05162","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.05162","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048855408","display_name":"Gerd Kortemeyer","orcid":"https://orcid.org/0000-0001-6643-9428"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kortemeyer, Gerd","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033808081","display_name":"Alexander Caspar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Caspar, Alexander","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5119912892","display_name":"Daria Horica","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Horica, Daria","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048855408"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14414","display_name":"Artificial Intelligence in Education","score":0.6310999989509583,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14414","display_name":"Artificial Intelligence in Education","score":0.6310999989509583,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.6254000067710876,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rubric","display_name":"Rubric","score":0.9575999975204468},{"id":"https://openalex.org/keywords/grading","display_name":"Grading (engineering)","score":0.807699978351593},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4794999957084656},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.39469999074935913},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3698999881744385},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.35929998755455017},{"id":"https://openalex.org/keywords/grading-scale","display_name":"Grading scale","score":0.34779998660087585},{"id":"https://openalex.org/keywords/equating","display_name":"Equating","score":0.3402000069618225}],"concepts":[{"id":"https://openalex.org/C111640148","wikidata":"https://www.wikidata.org/wiki/Q847349","display_name":"Rubric","level":2,"score":0.9575999975204468},{"id":"https://openalex.org/C2777286243","wikidata":"https://www.wikidata.org/wiki/Q5591926","display_name":"Grading (engineering)","level":2,"score":0.807699978351593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5367000102996826},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43720000982284546},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3986999988555908},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.39469999074935913},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C2993012660","wikidata":"https://www.wikidata.org/wiki/Q18185","display_name":"Grading scale","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C106347477","wikidata":"https://www.wikidata.org/wiki/Q5384228","display_name":"Equating","level":3,"score":0.3402000069618225},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.33820000290870667},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C19875794","wikidata":"https://www.wikidata.org/wiki/Q1207340","display_name":"Item response theory","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C2777489069","wikidata":"https://www.wikidata.org/wiki/Q1589822","display_name":"Ceiling (cloud)","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2782000005245209},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C2781035248","wikidata":"https://www.wikidata.org/wiki/Q186150","display_name":"Fallacy","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2615000009536743},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C12174686","wikidata":"https://www.wikidata.org/wiki/Q1058438","display_name":"Risk assessment","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C83849319","wikidata":"https://www.wikidata.org/wiki/Q7295720","display_name":"Rating scale","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.05162","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.05162","pdf_url":"https://arxiv.org/pdf/2510.05162","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.05162","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.05162","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.05162","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.05162","pdf_url":"https://arxiv.org/pdf/2510.05162","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,49],"investigate":[1],"whether":[2],"contemporary":[3],"multimodal":[4],"LLMs":[5],"can":[6],"assist":[7],"with":[8,38,59],"grading":[9],"open-ended":[10,132],"calculus":[11],"at":[12],"scale":[13],"without":[14],"eroding":[15],"validity.":[16],"In":[17],"a":[18,51,56,134,161,183],"large":[19],"first-year":[20],"exam,":[21],"students'":[22],"handwritten":[23],"work":[24,149],"was":[25,85],"graded":[26,120],"by":[27,34,121,127],"GPT-5":[28],"against":[29],"the":[30,69,72,76,99,116,131],"same":[31],"rubric":[32,43,138],"used":[33],"teaching":[35],"assistants":[36],"(TAs),":[37],"fractional":[39],"credit":[40],"permitted;":[41],"TA":[42],"decisions":[44],"served":[45],"as":[46,154],"ground":[47],"truth.":[48],"calibrated":[50,173],"human-in-the-loop":[52],"filter":[53],"that":[54],"combines":[55],"partial-credit":[57],"threshold":[58],"an":[60],"Item":[61],"Response":[62],"Theory":[63],"(2PL)":[64],"risk":[65],"measure":[66],"based":[67],"on":[68,130],"deviation":[70],"between":[71,143],"AI":[73,106,179],"score":[74,78],"and":[75,140,147,158,175],"model-expected":[77],"for":[79,88,93,193],"each":[80],"student-item.":[81],"Unfiltered":[82],"AI-TA":[83],"agreement":[84],"moderate,":[86],"adequate":[87],"low-stakes":[89],"feedback":[90],"but":[91,110],"not":[92],"high-stakes":[94],"use.":[95],"Confidence":[96],"filtering":[97],"made":[98],"workload-quality":[100],"trade-off":[101],"explicit:":[102],"under":[103],"stricter":[104],"settings,":[105],"delivered":[107],"human-level":[108],"accuracy,":[109],"also":[111],"left":[112],"roughly":[113],"70%":[114],"of":[115,137,186],"items":[117],"to":[118,180],"be":[119],"humans.":[122],"Psychometric":[123],"patterns":[124],"were":[125],"constrained":[126],"low":[128],"stakes":[129],"portion,":[133],"small":[135],"set":[136],"checkpoints,":[139],"occasional":[141],"misalignment":[142],"designated":[144],"answer":[145],"regions":[146],"where":[148],"appeared.":[150],"Practical":[151],"adjustments":[152],"such":[153],"slightly":[155],"higher":[156],"weight":[157],"protected":[159],"time,":[160],"few":[162],"rubric-visible":[163],"substeps,":[164],"stronger":[165],"spatial":[166],"anchoring":[167],"should":[168],"raise":[169],"ceiling":[170],"performance.":[171],"Overall,":[172],"confidence":[174],"conservative":[176],"routing":[177],"enable":[178],"reliably":[181],"handle":[182],"sizable":[184],"subset":[185],"routine":[187],"cases":[188],"while":[189],"reserving":[190],"expert":[191],"judgment":[192],"ambiguous":[194],"or":[195],"pedagogically":[196],"rich":[197],"responses.":[198]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
