{"id":"https://openalex.org/W4312901386","doi":"https://doi.org/10.1063/5.0108386","title":"Students\u2019 mathematical representation in solving mathematical problems","display_name":"Students\u2019 mathematical representation in solving mathematical problems","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312901386","doi":"https://doi.org/10.1063/5.0108386"},"language":"en","primary_location":{"id":"doi:10.1063/5.0108386","doi":"https://doi.org/10.1063/5.0108386","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0108386","pdf_url":null,"source":{"id":"https://openalex.org/S2764696622","display_name":"AIP conference proceedings","issn_l":"0094-243X","issn":["0094-243X","1551-7616","1935-0465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIP Conference Proceedings","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065992164","display_name":"Yufid Afkarina Nizar Isyam","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I127859547","display_name":"Yogyakarta State University","ror":"https://ror.org/05fryw881","country_code":"ID","type":"education","lineage":["https://openalex.org/I127859547"]}],"countries":["ID"],"is_corresponding":true,"raw_author_name":"Yufid Afkarina Nizar Isyam","raw_affiliation_strings":["Department of Mathematics Education, Faculty of Mathematics and Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Faculty of Mathematics and Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia","institution_ids":["https://openalex.org/I127859547"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070459468","display_name":"Kana Hidayati","orcid":"https://orcid.org/0000-0002-9226-8500","observed_orcids":["https://orcid.org/0000-0002-9226-8500"]},"institutions":[{"id":"https://openalex.org/I127859547","display_name":"Yogyakarta State University","ror":"https://ror.org/05fryw881","country_code":"ID","type":"education","lineage":["https://openalex.org/I127859547"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Kana Hidayati","raw_affiliation_strings":["Department of Mathematics Education, Faculty of Mathematics and Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Faculty of Mathematics and Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia","institution_ids":["https://openalex.org/I127859547"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065992164"],"corresponding_institution_ids":["https://openalex.org/I127859547"],"apc_list":null,"apc_paid":null,"fwci":5.6789,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.95446738,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2575","issue":null,"first_page":"080026","last_page":"080026"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":1.0,"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":1.0,"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":9.999999747378752e-05,"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":0.0,"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/mathematical-representation","display_name":"mathematical representation","score":0.9909999966621399},{"id":"https://openalex.org/keywords/mathematical-problem-solving","display_name":"mathematical problem solving","score":0.9539999961853027},{"id":"https://openalex.org/keywords/representation-ability","display_name":"representation ability","score":0.6729999780654907},{"id":"https://openalex.org/keywords/mathematics-learning","display_name":"mathematics learning","score":0.8059999942779541}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.8072970509529114},{"id":"https://openalex.org/C66783780","wikidata":"https://www.wikidata.org/wiki/Q1166625","display_name":"Mathematical problem","level":2,"score":0.7436266541481018},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.5928272604942322},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.5828831791877747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5714457035064697},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.525844395160675},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47327136993408203},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3879627287387848},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35732200741767883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3561861515045166},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.2608141601085663},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08399716019630432},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.057343631982803345},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/5.0108386","doi":"https://doi.org/10.1063/5.0108386","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0108386","pdf_url":null,"source":{"id":"https://openalex.org/S2764696622","display_name":"AIP conference proceedings","issn_l":"0094-243X","issn":["0094-243X","1551-7616","1935-0465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIP Conference Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality education","score":0.6164000034332275,"id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2033744902","https://openalex.org/W2145461108","https://openalex.org/W2343372945","https://openalex.org/W2651010679","https://openalex.org/W2892952966","https://openalex.org/W2967280053"],"related_works":["https://openalex.org/W4398763983","https://openalex.org/W4313270988","https://openalex.org/W2946147749","https://openalex.org/W3011622597","https://openalex.org/W3021916364","https://openalex.org/W312337828","https://openalex.org/W292235680","https://openalex.org/W2939034243","https://openalex.org/W2402251054","https://openalex.org/W4391901854"],"abstract_inverted_index":{"Mathematical":[0,24],"representation":[1,25,68,137,151],"is":[2,26],"an":[3],"ability":[4,46],"to":[5,11,15,21,61,74,78,122,133,142,145],"process":[6],"and":[7,38,117,129,147],"reveal":[8],"mathematical":[9,40,59,63,120,127,136,150,160],"ideas/concepts":[10],"discover":[12],"the":[13,29,115],"solution":[14],"a":[16],"problem":[17],"by":[18],"changing":[19],"it":[20,84],"another":[22,79],"form.":[23],"one":[27,76,81],"of":[28,32,58,110,119],"essential":[30],"abilities":[31],"students.":[33],"When":[34],"students":[35,94,157],"build":[36],"ideas":[37],"use":[39],"representation,":[41],"they":[42],"have":[43],"developed":[44],"basic":[45],"indirectly":[47],"that":[48,153],"help":[49,143,156],"them":[50],"in":[51,80,88,100,125],"solving":[52,126],"problems.":[53,64],"There":[54],"are":[55],"various":[56,108],"types":[57,109,118],"representations":[60,121],"solve":[62],"In":[65],"mathematics":[66],"learning,":[67],"should":[69,95],"not":[70],"only":[71],"be":[72,86,96,105,123],"related":[73],"change":[75],"form":[77],"way,":[82],"but":[83],"can":[85,104,155],"done":[87],"two":[89],"ways":[90],"or":[91],"more.":[92],"Therefore,":[93],"provided":[97],"with":[98],"problems":[99,128],"which":[101],"their":[102,159],"solutions":[103],"achieved":[106],"using":[107],"representations.":[111],"This":[112,139],"article":[113,140],"discusses":[114],"definition":[116],"used":[124],"also":[130],"provide":[131],"how":[132],"improve":[134,158],"students\u2019":[135],"ability.":[138],"expected":[141],"teachers":[144,154],"know":[146],"understand":[148],"about":[149],"so":[152],"representation.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-01-05T00:00:00"}