{"id":"https://openalex.org/W2041027364","doi":"https://doi.org/10.1016/j.jmathb.2015.03.003","title":"On students\u2019 understanding of the differential calculus of functions of two variables","display_name":"On students\u2019 understanding of the differential calculus of functions of two variables","publication_year":2015,"publication_date":"2015-04-05","ids":{"openalex":"https://openalex.org/W2041027364","doi":"https://doi.org/10.1016/j.jmathb.2015.03.003","mag":"2041027364"},"language":"en","primary_location":{"id":"doi:10.1016/j.jmathb.2015.03.003","doi":"https://doi.org/10.1016/j.jmathb.2015.03.003","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jmathb.2015.03.003","pdf_url":null,"source":{"id":"https://openalex.org/S161209770","display_name":"The Journal of Mathematical Behavior","issn_l":"0732-3123","issn":["0732-3123","1873-8028"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Mathematical Behavior","raw_type":"journal-article"},"volume":null,"type":"article","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/A5048907159","display_name":"Rafael Mart\u00ednez-Planell","orcid":"https://orcid.org/0000-0001-5512-8405","observed_orcids":["https://orcid.org/0000-0001-5512-8405"]},"institutions":[{"id":"https://openalex.org/I60388903","display_name":"University of Puerto Rico-Mayaguez","ror":"https://ror.org/00wek6x04","country_code":"PR","type":"education","lineage":["https://openalex.org/I200399037","https://openalex.org/I60388903"]}],"countries":["PR"],"is_corresponding":true,"raw_author_name":"Rafael Mart\u00ednez-Planell","raw_affiliation_strings":["University of Puerto Rico at Mayag\u00fcez, Mayag\u00fcez, Puerto Rico","Univ of Puerto Rico at Mayag\u00fcez, Mayag\u00fcez, Puerto Rico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Puerto Rico at Mayag\u00fcez, Mayag\u00fcez, Puerto Rico","institution_ids":["https://openalex.org/I60388903"]},{"raw_affiliation_string":"Univ of Puerto Rico at Mayag\u00fcez, Mayag\u00fcez, Puerto Rico","institution_ids":["https://openalex.org/I60388903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031684109","display_name":"Mar\u00eda Trigueros","orcid":"https://orcid.org/0000-0001-7527-6704","observed_orcids":["https://orcid.org/0000-0001-7527-6704"]},"institutions":[{"id":"https://openalex.org/I187481652","display_name":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico","ror":"https://ror.org/029md1766","country_code":"MX","type":"education","lineage":["https://openalex.org/I187481652"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Maria Trigueros Gaisman","raw_affiliation_strings":["Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, M\u00e9xico D.F., Mexico","Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, M\u00e9xico D.F., Mexico#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, M\u00e9xico D.F., Mexico","institution_ids":["https://openalex.org/I187481652"]},{"raw_affiliation_string":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, M\u00e9xico D.F., Mexico#TAB#","institution_ids":["https://openalex.org/I187481652"]}]},{"author_position":"last","author":{"id":null,"display_name":"Daniel McGee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I168416876","display_name":"Northern Kentucky University","ror":"https://ror.org/01k44g025","country_code":"US","type":"education","lineage":["https://openalex.org/I168416876"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel McGee","raw_affiliation_strings":["Kentucky Center for Mathematics, Highland Heights, KY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kentucky Center for Mathematics, Highland Heights, KY, USA","institution_ids":["https://openalex.org/I168416876"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048907159"],"corresponding_institution_ids":["https://openalex.org/I60388903"],"apc_list":{"value":3170,"currency":"USD","value_usd":3170},"apc_paid":null,"fwci":7.856,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.96549541,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"38","issue":null,"first_page":"57","last_page":"86"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.6636000275611877,"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":0.6636000275611877,"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.09229999780654907,"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/T14079","display_name":"Mathematics Education and Programs","score":0.07079999893903732,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"multivariable calculus","score":0.8190000057220459},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"differential calculus","score":0.675000011920929},{"id":"https://openalex.org/keywords/tangent-planes","display_name":"tangent planes","score":0.9559999704360962},{"id":"https://openalex.org/keywords/directional-derivatives","display_name":"directional derivatives","score":0.9240000247955322},{"id":"https://openalex.org/keywords/differentials","display_name":"differentials","score":0.7630000114440918},{"id":"https://openalex.org/keywords/genetic-decomposition","display_name":"genetic decomposition","score":0.8180000185966492},{"id":"https://openalex.org/keywords/apos-theory","display_name":"APOS theory","score":0.9129999876022339},{"id":"https://openalex.org/keywords/student-understanding","display_name":"student understanding","score":0.9190000295639038},{"id":"https://openalex.org/keywords/mental-constructions","display_name":"mental constructions","score":0.6499999761581421},{"id":"https://openalex.org/keywords/conceptual-understanding","display_name":"conceptual understanding","score":0.4490000009536743}],"concepts":[{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.8189597129821777},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.8076403141021729},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.668036937713623},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6350911259651184},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.5527132153511047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5474260449409485},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5104348063468933},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.4908459782600403},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4729055166244507},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4046567678451538},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26906633377075195},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.19470208883285522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14537063241004944},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.08853223919868469},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07334870100021362},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jmathb.2015.03.003","doi":"https://doi.org/10.1016/j.jmathb.2015.03.003","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jmathb.2015.03.003","pdf_url":null,"source":{"id":"https://openalex.org/S161209770","display_name":"The Journal of Mathematical Behavior","issn_l":"0732-3123","issn":["0732-3123","1873-8028"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Mathematical Behavior","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality education","score":0.6000999808311462,"id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W221060856","https://openalex.org/W575532802","https://openalex.org/W943492097","https://openalex.org/W1541105928","https://openalex.org/W1581642424","https://openalex.org/W1965950906","https://openalex.org/W1971707972","https://openalex.org/W1980429170","https://openalex.org/W1984448126","https://openalex.org/W1991960715","https://openalex.org/W2014947032","https://openalex.org/W2026904544","https://openalex.org/W2064375619","https://openalex.org/W2068677198","https://openalex.org/W2069689981","https://openalex.org/W2071670711","https://openalex.org/W2079128428","https://openalex.org/W2086670154","https://openalex.org/W2110662615","https://openalex.org/W2159771929","https://openalex.org/W2290221749","https://openalex.org/W2598937130","https://openalex.org/W2599002918","https://openalex.org/W3003825801","https://openalex.org/W3046057615","https://openalex.org/W3076407288","https://openalex.org/W4230103882","https://openalex.org/W4385888964","https://openalex.org/W6634690819"],"related_works":["https://openalex.org/W2590240638","https://openalex.org/W2465780229","https://openalex.org/W4381250560","https://openalex.org/W4407557155","https://openalex.org/W3036285305","https://openalex.org/W4293646223","https://openalex.org/W4387222652","https://openalex.org/W2767258427","https://openalex.org/W4413370503","https://openalex.org/W4403186556"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
