{"id":"https://openalex.org/W1972132018","doi":"https://doi.org/10.2307/749199","title":"Conceptual Knowledge in Introductory Calculus","display_name":"Conceptual Knowledge in Introductory Calculus","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1972132018","doi":"https://doi.org/10.2307/749199","mag":"1972132018"},"language":"en","primary_location":{"id":"doi:10.2307/749199","doi":"https://doi.org/10.2307/749199","is_oa":false,"landing_page_url":"https://doi.org/10.2307/749199","pdf_url":null,"source":{"id":"https://openalex.org/S79038290","display_name":"Journal for Research in Mathematics Education","issn_l":"0021-8251","issn":["0021-8251","1945-2306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-3","ki-jl-1","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315778","host_organization_name":"National Council of Teachers of Mathematics","host_organization_lineage":["https://openalex.org/P4310315778"],"host_organization_lineage_names":["National Council of Teachers of Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal for Research in Mathematics Education","raw_type":"journal-article"},"volume":null,"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/A5021271630","display_name":"Paul James White","orcid":"https://orcid.org/0000-0002-7524-1808","observed_orcids":["https://orcid.org/0000-0002-7524-1808"]},"institutions":[{"id":"https://openalex.org/I86695891","display_name":"Australian Catholic University","ror":"https://ror.org/04cxm4j25","country_code":"AU","type":"education","lineage":["https://openalex.org/I86695891"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Paul White","raw_affiliation_strings":["1 Australian Catholic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Australian Catholic University","institution_ids":["https://openalex.org/I86695891"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057611714","display_name":"Michael C. Mitchelmore","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Michael Mitchelmore","raw_affiliation_strings":["2 #N# #N# #N# Macquarie University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2 #N# #N# #N# Macquarie University","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.6314,"has_fulltext":false,"cited_by_count":178,"citation_normalized_percentile":{"value":0.97115863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"27","issue":"1","first_page":"79","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.611299991607666,"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":0.611299991607666,"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":0.17139999568462372,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.14090000092983246,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conceptual-knowledge","display_name":"conceptual knowledge","score":0.796999990940094},{"id":"https://openalex.org/keywords/introductory-calculus","display_name":"introductory calculus","score":0.9620000123977661},{"id":"https://openalex.org/keywords/rate-of-change","display_name":"rate of change","score":0.9739999771118164},{"id":"https://openalex.org/keywords/word-problems","display_name":"word problems","score":0.8069999814033508},{"id":"https://openalex.org/keywords/concept-based-instruction","display_name":"concept-based instruction","score":0.7020000219345093},{"id":"https://openalex.org/keywords/student-errors","display_name":"student errors","score":0.6330000162124634},{"id":"https://openalex.org/keywords/algebraic-modeling","display_name":"algebraic modeling","score":0.7699999809265137},{"id":"https://openalex.org/keywords/first-year-students","display_name":"first-year students","score":0.7400000095367432}],"concepts":[{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.725064754486084},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.6297010183334351},{"id":"https://openalex.org/C2781329482","wikidata":"https://www.wikidata.org/wiki/Q3823192","display_name":"Conceptual change","level":2,"score":0.5694280862808228},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5293177962303162},{"id":"https://openalex.org/C48164120","wikidata":"https://www.wikidata.org/wiki/Q4491893","display_name":"Concept learning","level":2,"score":0.5066547989845276},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46805232763290405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44575077295303345},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33854126930236816},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14224305748939514},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.14148691296577454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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":3,"locations":[{"id":"doi:10.2307/749199","doi":"https://doi.org/10.2307/749199","is_oa":false,"landing_page_url":"https://doi.org/10.2307/749199","pdf_url":null,"source":{"id":"https://openalex.org/S79038290","display_name":"Journal for Research in Mathematics Education","issn_l":"0021-8251","issn":["0021-8251","1945-2306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-3","ki-jl-1","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315778","host_organization_name":"National Council of Teachers of Mathematics","host_organization_lineage":["https://openalex.org/P4310315778"],"host_organization_lineage_names":["National Council of Teachers of Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal for Research in Mathematics Education","raw_type":"journal-article"},{"id":"doi:10.5951/jresematheduc.27.1.0079","doi":"https://doi.org/10.5951/jresematheduc.27.1.0079","is_oa":false,"landing_page_url":"https://doi.org/10.5951/jresematheduc.27.1.0079","pdf_url":null,"source":{"id":"https://openalex.org/S79038290","display_name":"Journal for Research in Mathematics Education","issn_l":"0021-8251","issn":["0021-8251","1945-2306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-3","ki-jl-1","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315778","host_organization_name":"National Council of Teachers of Mathematics","host_organization_lineage":["https://openalex.org/P4310315778"],"host_organization_lineage_names":["National Council of Teachers of Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal for Research in Mathematics Education","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.517.9100","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.517.9100","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://tpc2.net/IME/1996White.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality education","id":"https://metadata.un.org/sdg/4","score":0.8278999924659729}],"sustainable_development_goals_aurora":[{"display_name":"Quality education","id":"https://metadata.un.org/sdg/4","score":0.5600000023841858}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W37313586","https://openalex.org/W50137115","https://openalex.org/W82428586","https://openalex.org/W124812290","https://openalex.org/W155092010","https://openalex.org/W164758814","https://openalex.org/W259584814","https://openalex.org/W283356536","https://openalex.org/W292652742","https://openalex.org/W1152235306","https://openalex.org/W1577290313","https://openalex.org/W1949020749","https://openalex.org/W1974711434","https://openalex.org/W1988680010","https://openalex.org/W1996714773","https://openalex.org/W2006045181","https://openalex.org/W2022706962","https://openalex.org/W2038100663","https://openalex.org/W2049926613","https://openalex.org/W2072267223","https://openalex.org/W2074811583","https://openalex.org/W2079553224","https://openalex.org/W2085289501","https://openalex.org/W2135327179","https://openalex.org/W2233896616","https://openalex.org/W2507919779"],"related_works":["https://openalex.org/W1982791773","https://openalex.org/W2765596796","https://openalex.org/W2940277046","https://openalex.org/W7095187973","https://openalex.org/W2584973795","https://openalex.org/W2073775303","https://openalex.org/W1940730102","https://openalex.org/W3101803862","https://openalex.org/W7099854865","https://openalex.org/W2895466463"],"abstract_inverted_index":{"Responses":[0],"to":[1,23,100,107],"word":[2],"problems":[3],"involving":[4],"rates":[5,46,66],"of":[6,18,26,31,41,47,67,89,93,120,135],"change":[7,48,68],"were":[8],"collected":[9],"on":[10],"four":[11],"occasions":[12],"during":[13],"and":[14],"after":[15],"24":[16],"hours":[17],"concept-based":[19],"calculus":[20,35],"instruction":[21],"given":[22],"a":[24,78,121],"group":[25],"first-year":[27],"university":[28],"students,":[29],"all":[30,92],"whom":[32],"had":[33,115],"studied":[34],"in":[36,49,60,69,73,91],"secondary":[37],"school.":[38],"The":[39],"number":[40,62],"students":[42,114],"who":[43,63],"could":[44,64],"symbolize":[45,65],"noncomplex":[50],"situations":[51],"increased":[52],"dramatically.":[53],"However,":[54],"there":[55],"was":[56],"almost":[57],"no":[58],"increase":[59],"the":[61,113,125,132],"complex":[70],"items":[71,74],"or":[72],"that":[75,112,128],"required":[76],"modeling":[77],"situation":[79],"using":[80],"algebraic":[81],"variables.":[82],"Detailed":[83],"analysis":[84],"revealed":[85],"three":[86],"main":[87],"categories":[88],"error,":[90],"which":[94],"variables":[95],"are":[96],"treated":[97],"as":[98,105],"symbols":[99],"be":[101,108],"manipulated":[102],"rather":[103,123],"than":[104,124],"quantities":[106],"related.":[109],"We":[110],"surmise":[111],"developed":[116],"an":[117],"\u201cabstract-apart\u201d":[118],"concept":[119,127],"variable":[122],"\u201cabstract-general\u201d":[126],"is":[129],"needed":[130],"for":[131],"successful":[133],"study":[134],"calculus.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":6}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}