{"id":"https://openalex.org/W7123347373","doi":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","title":"Conceptual and procedural knowledge in students\u2019 fraction division thinking: Insights from a hermeneutic phenomenological study","display_name":"Conceptual and procedural knowledge in students\u2019 fraction division thinking: Insights from a hermeneutic phenomenological study","publication_year":2025,"publication_date":"2025-11-17","ids":{"openalex":"https://openalex.org/W7123347373","doi":"https://doi.org/10.22342/jme.v16i4.pp1233-1256"},"language":"en","primary_location":{"id":"doi:10.22342/jme.v16i4.pp1233-1256","doi":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","is_oa":true,"landing_page_url":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","pdf_url":null,"source":{"id":"https://openalex.org/S2764632379","display_name":"Journal on Mathematics Education","issn_l":"2087-8885","issn":["2087-8885","2407-0610"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315074","host_organization_name":"Sriwijaya University","host_organization_lineage":["https://openalex.org/P4310315074"],"host_organization_lineage_names":["Sriwijaya University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal on Mathematics Education","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006265974","display_name":"Rita Novita","orcid":"https://orcid.org/0000-0003-0863-4107","observed_orcids":["https://orcid.org/0000-0003-0863-4107"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rita Novita","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0863-4107","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114029543","display_name":"Mulia Putra","orcid":"https://orcid.org/0000-0003-4877-4825","observed_orcids":["https://orcid.org/0000-0003-4877-4825"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mulia Putra","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4877-4825","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122856307","display_name":"Usman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Usman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109512077","display_name":"Safrina Junita","orcid":"https://orcid.org/0009-0007-6106-0866","observed_orcids":["https://orcid.org/0009-0007-6106-0866"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Safrina Junita","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0007-6106-0866","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":250,"currency":"USD","value_usd":250},"apc_paid":{"value":250,"currency":"USD","value_usd":250},"fwci":6.5223,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.96595193,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"4","first_page":"1233","last_page":"1256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.02590000070631504,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/division-of-fractions","display_name":"fraction division","score":0.8880000114440918},{"id":"https://openalex.org/keywords/conceptual-knowledge","display_name":"conceptual knowledge","score":0.9679999947547913},{"id":"https://openalex.org/keywords/procedural-knowledge","display_name":"procedural knowledge","score":0.9819999933242798},{"id":"https://openalex.org/keywords/fifth-grade-students","display_name":"fifth grade students","score":0.8289999961853027},{"id":"https://openalex.org/keywords/primary-school-mathematics","display_name":"primary school mathematics","score":0.5600000023841858},{"id":"https://openalex.org/keywords/contextualized-problem-solving","display_name":"contextual problem solving","score":0.6549999713897705},{"id":"https://openalex.org/keywords/procedural-fluency","display_name":"procedural fluency","score":0.7789999842643738},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"mathematics education","score":0.6669999957084656}],"concepts":[{"id":"https://openalex.org/C124469403","wikidata":"https://www.wikidata.org/wiki/Q1813993","display_name":"Procedural knowledge","level":3,"score":0.7353000044822693},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5909000039100647},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.5781000256538391},{"id":"https://openalex.org/C48164120","wikidata":"https://www.wikidata.org/wiki/Q4491893","display_name":"Concept learning","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C2779149496","wikidata":"https://www.wikidata.org/wiki/Q442100","display_name":"Procedural justice","level":3,"score":0.4731000065803528},{"id":"https://openalex.org/C90734943","wikidata":"https://www.wikidata.org/wiki/Q17008777","display_name":"Conceptualization","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C14224292","wikidata":"https://www.wikidata.org/wiki/Q13600188","display_name":"Conceptual framework","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.41290000081062317},{"id":"https://openalex.org/C2777413886","wikidata":"https://www.wikidata.org/wiki/Q3276013","display_name":"Fluency","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C84269361","wikidata":"https://www.wikidata.org/wiki/Q179235","display_name":"Phenomenology (philosophy)","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C2776291881","wikidata":"https://www.wikidata.org/wiki/Q6423378","display_name":"Knowledge level","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C511192102","wikidata":"https://www.wikidata.org/wiki/Q5156948","display_name":"Comprehension","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C190248442","wikidata":"https://www.wikidata.org/wiki/Q839486","display_name":"Qualitative research","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C2776950860","wikidata":"https://www.wikidata.org/wiki/Q2914681","display_name":"Originality","level":3,"score":0.31839999556541443},{"id":"https://openalex.org/C14156362","wikidata":"https://www.wikidata.org/wiki/Q3235388","display_name":"Descriptive knowledge","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C164749973","wikidata":"https://www.wikidata.org/wiki/Q18606","display_name":"Procedural memory","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C13606891","wikidata":"https://www.wikidata.org/wiki/Q2623243","display_name":"Conceptual model","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.2874999940395355},{"id":"https://openalex.org/C76188268","wikidata":"https://www.wikidata.org/wiki/Q1783165","display_name":"Context effect","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C207685749","wikidata":"https://www.wikidata.org/wiki/Q2088941","display_name":"Domain knowledge","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C36964233","wikidata":"https://www.wikidata.org/wiki/Q7920942","display_name":"Verbal reasoning","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C186528591","wikidata":"https://www.wikidata.org/wiki/Q619544","display_name":"Body of knowledge","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C88610354","wikidata":"https://www.wikidata.org/wiki/Q1813494","display_name":"Teaching method","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C2781329482","wikidata":"https://www.wikidata.org/wiki/Q3823192","display_name":"Conceptual change","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.2540999948978424},{"id":"https://openalex.org/C2778568292","wikidata":"https://www.wikidata.org/wiki/Q7727275","display_name":"The Conceptual Framework","level":3,"score":0.251800000667572},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.22342/jme.v16i4.pp1233-1256","doi":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","is_oa":true,"landing_page_url":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","pdf_url":null,"source":{"id":"https://openalex.org/S2764632379","display_name":"Journal on Mathematics Education","issn_l":"2087-8885","issn":["2087-8885","2407-0610"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315074","host_organization_name":"Sriwijaya University","host_organization_lineage":["https://openalex.org/P4310315074"],"host_organization_lineage_names":["Sriwijaya University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal on Mathematics Education","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.22342/jme.v16i4.pp1233-1256","doi":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","is_oa":true,"landing_page_url":"https://doi.org/10.22342/jme.v16i4.pp1233-1256","pdf_url":null,"source":{"id":"https://openalex.org/S2764632379","display_name":"Journal on Mathematics Education","issn_l":"2087-8885","issn":["2087-8885","2407-0610"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315074","host_organization_name":"Sriwijaya University","host_organization_lineage":["https://openalex.org/P4310315074"],"host_organization_lineage_names":["Sriwijaya University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal on Mathematics Education","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.975600004196167,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2919855327","https://openalex.org/W2743747173","https://openalex.org/W2888555875","https://openalex.org/W2175680843","https://openalex.org/W4402726007","https://openalex.org/W3046721689","https://openalex.org/W4407291174","https://openalex.org/W3122687180","https://openalex.org/W2912097299","https://openalex.org/W4376602075"],"abstract_inverted_index":{"While":[0],"both":[1,161,192],"conceptual":[2,44,76,100,116,162,172,178,217,235,273],"and":[3,45,54,77,96,108,111,117,138,141,163,174,236,275,281],"procedural":[4,46,78,94,106,118,164,169,181,198,237,276],"knowledge":[5,47,79,199,218,238],"are":[6],"central":[7],"to":[8,51,71,202,259],"mathematical":[9],"competence,":[10],"their":[11],"interaction":[12],"in":[13,20,65,102,120,191,222,278],"students\u2019":[14,49],"reasoning":[15,221],"remains":[16],"insufficiently":[17],"understood,":[18],"particularly":[19],"the":[21,55,73,90,97,103,186,245,253,265],"context":[22],"of":[23,43,61,75,92,99,105,160,185,247],"fraction":[24,279],"division\u2014a":[25],"domain":[26],"widely":[27],"recognized":[28],"as":[29],"conceptually":[30],"demanding.":[31],"This":[32],"study":[33,257],"addresses":[34],"this":[35,62,256],"gap":[36],"by":[37,148,263],"qualitatively":[38],"examining":[39],"how":[40],"different":[41],"configurations":[42],"shape":[48],"approaches":[50,269],"fraction-division":[52],"tasks":[53],"challenges":[56],"they":[57],"experience.":[58],"The":[59,150],"originality":[60],"work":[63],"lies":[64],"applying":[66],"a":[67],"hermeneutic":[68],"phenomenological":[69],"lens":[70],"investigate":[72],"interplay":[74],"beyond":[80],"numerical":[81],"performance":[82],"measures,":[83],"identifying":[84],"three":[85,131,153],"student":[86],"profiles":[87],"that":[88,234,250,270],"reveal":[89],"fragility":[91],"rote-driven":[93],"mastery":[95],"limitations":[98],"understanding":[101,274],"absence":[104],"fluency,":[107],"offering":[109],"theoretical":[110],"pedagogical":[112],"insights":[113],"for":[114,267],"integrating":[115],"domains":[119],"mathematics":[121,260],"instruction.":[122],"Data":[123],"were":[124,200],"collected":[125],"from":[126],"74":[127],"fifth-grade":[128],"students":[129,156,166,175,214],"across":[130],"Indonesian":[132],"elementary":[133],"schools":[134],"through":[135],"written":[136],"assessments":[137],"follow-up":[139],"interviews":[140],"analyzed":[142],"using":[143],"qualitative":[144],"content":[145],"analysis":[146,151],"supported":[147],"NVivo.":[149],"produced":[152],"distinct":[154],"profiles:":[155],"with":[157,167,176,195,215,228],"low":[158,171,180],"levels":[159],"knowledge;":[165,173],"high":[168,177],"but":[170,179,207,225],"knowledge.":[182],"Notably,":[183],"none":[184],"participants":[187],"demonstrated":[188],"strong":[189],"proficiency":[190],"domains.":[193],"Students":[194],"relatively":[196],"advanced":[197],"able":[201],"carry":[203],"out":[204],"symbolic":[205],"calculations":[206],"had":[208],"difficulty":[209],"solving":[210],"contextualized":[211],"problems.":[212],"Conversely,":[213],"stronger":[216],"exhibited":[219],"flexible":[220],"real-world":[223],"contexts":[224],"lacked":[226],"fluency":[227,277],"algorithms.":[229],"These":[230],"patterns":[231],"provide":[232],"evidence":[233],"may":[239],"develop":[240],"along":[241],"independent":[242],"trajectories,":[243],"underscoring":[244],"importance":[246],"instructional":[248],"designs":[249],"deliberately":[251],"integrate":[252],"two.":[254],"Finally,":[255],"contributes":[258],"education":[261],"research":[262],"highlighting":[264],"need":[266],"teaching":[268],"intentionally":[271],"bridge":[272],"division":[280],"beyond.":[282]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-01-14T00:00:00"}