{"id":"https://openalex.org/W1550614158","doi":"https://doi.org/10.1109/cie.2002.1186134","title":"Representational versatility and linear algebraic equations","display_name":"Representational versatility and linear algebraic equations","publication_year":2003,"publication_date":"2003-08-27","ids":{"openalex":"https://openalex.org/W1550614158","doi":"https://doi.org/10.1109/cie.2002.1186134","mag":"1550614158"},"language":"en","primary_location":{"id":"doi:10.1109/cie.2002.1186134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cie.2002.1186134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference on Computers in Education, 2002. Proceedings.","raw_type":"proceedings-article"},"type":"article","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/A5109036496","display_name":"Ye Hong","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Ye Yoon Hong","raw_affiliation_strings":["University of Auckland, New Zealand","Auckland University New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Auckland University New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102006785","display_name":"Michael Thomas","orcid":"https://orcid.org/0000-0002-2696-7709"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"M. Thomas","raw_affiliation_strings":["University of Auckland, New Zealand","Auckland University New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Auckland University New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.16635842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"1","issue":null,"first_page":"1002","last_page":"1006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9976999759674072,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9976999759674072,"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/T10072","display_name":"Science Education and Pedagogy","score":0.944599986076355,"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/T10636","display_name":"Innovative Teaching and Learning Methods","score":0.9386000037193298,"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/linear-algebra","display_name":"Linear algebra","score":0.7105141282081604},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6740286946296692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6147373914718628},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.5927315354347229},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5634614825248718},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5325896739959717},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.5045541524887085},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5000295639038086},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4601590633392334},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35300225019454956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3123779892921448},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16756358742713928},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09612247347831726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0590154230594635}],"concepts":[{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.7105141282081604},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6740286946296692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6147373914718628},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.5927315354347229},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5634614825248718},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5325896739959717},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.5045541524887085},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5000295639038086},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4601590633392334},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35300225019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3123779892921448},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16756358742713928},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09612247347831726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0590154230594635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cie.2002.1186134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cie.2002.1186134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference on Computers in Education, 2002. Proceedings.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.699999988079071}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W141887878","https://openalex.org/W349243578","https://openalex.org/W646556946","https://openalex.org/W1974711434","https://openalex.org/W2020606208","https://openalex.org/W2023707110","https://openalex.org/W2075705388","https://openalex.org/W2139356040","https://openalex.org/W2470705670","https://openalex.org/W2993656152","https://openalex.org/W3196015547","https://openalex.org/W4285719527","https://openalex.org/W6605769638","https://openalex.org/W6611848142","https://openalex.org/W6655180476","https://openalex.org/W6720148048","https://openalex.org/W6800364674"],"related_works":["https://openalex.org/W4386576538","https://openalex.org/W2477677129","https://openalex.org/W2088138737","https://openalex.org/W2383813702","https://openalex.org/W2383125250","https://openalex.org/W3008555607","https://openalex.org/W2364540532","https://openalex.org/W2741814932","https://openalex.org/W1971748573","https://openalex.org/W2895486115"],"abstract_inverted_index":{"The":[0,67],"value":[1],"of":[2,12],"encouraging":[3],"students":[4,48,72],"to":[5,36,43,49,63,78],"form":[6],"rich":[7],"links":[8,51],"between":[9,52],"different":[10],"representations":[11],"mathematical":[13],"concepts":[14],"has":[15],"been":[16],"recognised":[17],"for":[18,61],"some":[19],"time.":[20],"However,":[21],"in":[22,29,95],"practice":[23],"this":[24],"is":[25],"often":[26],"not":[27,91],"done":[28],"teaching.":[30],"This":[31],"paper":[32],"describes":[33],"an":[34],"attempt":[35],"use":[37,79],"computer":[38],"algebra":[39,54],"system":[40],"(CAS)":[41],"calculators":[42,76],"assist":[44],"14/15":[45],"year":[46],"old":[47],"build":[50],"the":[53,74,87],"and":[55,58],"graphs,":[56],"tables":[57],"ordered":[59],"pairs":[60],"solutions":[62],"linear":[64],"algebraic":[65],"equations.":[66],"results":[68],"show":[69],"that":[70],"these":[71],"found":[73],"CAS":[75],"difficult":[77],"and,":[80],"although":[81],"they":[82,89],"did":[83,90],"better":[84],"at":[85],"solving":[86],"equations":[88],"improve":[92],"very":[93],"much":[94],"their":[96],"representational":[97],"versatility.":[98]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
