{"id":"https://openalex.org/W2012608463","doi":"https://doi.org/10.1080/10986065.2015.981946","title":"Secondary Students\u2019 Quantification of Ratio and Rate: A Framework for Reasoning about Change in Covarying Quantities","display_name":"Secondary Students\u2019 Quantification of Ratio and Rate: A Framework for Reasoning about Change in Covarying Quantities","publication_year":2015,"publication_date":"2015-01-02","ids":{"openalex":"https://openalex.org/W2012608463","doi":"https://doi.org/10.1080/10986065.2015.981946","mag":"2012608463"},"language":"en","primary_location":{"id":"doi:10.1080/10986065.2015.981946","doi":"https://doi.org/10.1080/10986065.2015.981946","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10986065.2015.981946","pdf_url":null,"source":{"id":"https://openalex.org/S74814605","display_name":"Mathematical Thinking and Learning","issn_l":"1098-6065","issn":["1098-6065","1532-7833"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-2","ki-jl-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Thinking and Learning","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/A5060299286","display_name":"Heather L. Johnson","orcid":"https://orcid.org/0000-0002-8865-2075","observed_orcids":["https://orcid.org/0000-0002-8865-2075"]},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Heather Lynn Johnson","raw_affiliation_strings":["University of Colorado, Denver"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado, Denver","institution_ids":["https://openalex.org/I921990950"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060299286"],"corresponding_institution_ids":["https://openalex.org/I921990950"],"apc_list":null,"apc_paid":null,"fwci":23.3455,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.99250451,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"64","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.7348999977111816,"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":0.7348999977111816,"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":0.17489999532699585,"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"}},{"id":"https://openalex.org/T11875","display_name":"Statistics Education and Methodologies","score":0.02319999970495701,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/covariational-reasoning","display_name":"covariational reasoning","score":0.8870000243186951},{"id":"https://openalex.org/keywords/quantitative-reasoning","display_name":"quantitative reasoning","score":0.7419999837875366},{"id":"https://openalex.org/keywords/secondary-school-students","display_name":"high school students","score":0.6930000185966492},{"id":"https://openalex.org/keywords/proportional-reasoning","display_name":"proportional reasoning","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.49571549892425537},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.4936717450618744}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10986065.2015.981946","doi":"https://doi.org/10.1080/10986065.2015.981946","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10986065.2015.981946","pdf_url":null,"source":{"id":"https://openalex.org/S74814605","display_name":"Mathematical Thinking and Learning","issn_l":"1098-6065","issn":["1098-6065","1532-7833"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-2","ki-jl-2","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Thinking and Learning","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality education","score":0.8278999924659729,"id":"https://metadata.un.org/sdg/4"}],"sustainable_development_goals_aurora":[{"display_name":"Quality education","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W75020212","https://openalex.org/W100018932","https://openalex.org/W107227615","https://openalex.org/W149717767","https://openalex.org/W166014084","https://openalex.org/W184602875","https://openalex.org/W247068855","https://openalex.org/W333076555","https://openalex.org/W656149271","https://openalex.org/W1498027297","https://openalex.org/W1500112243","https://openalex.org/W1521056252","https://openalex.org/W1526703352","https://openalex.org/W1549358040","https://openalex.org/W1556236234","https://openalex.org/W1571527402","https://openalex.org/W1586854670","https://openalex.org/W1968976446","https://openalex.org/W1972451684","https://openalex.org/W1982791773","https://openalex.org/W1995875985","https://openalex.org/W2004685039","https://openalex.org/W2006881691","https://openalex.org/W2009642367","https://openalex.org/W2024439371","https://openalex.org/W2026280650","https://openalex.org/W2027129860","https://openalex.org/W2029028433","https://openalex.org/W2029606604","https://openalex.org/W2042583699","https://openalex.org/W2046654134","https://openalex.org/W2052653488","https://openalex.org/W2081163728","https://openalex.org/W2086040051","https://openalex.org/W2088143288","https://openalex.org/W2153903308","https://openalex.org/W2164565524","https://openalex.org/W2305070471","https://openalex.org/W2354157941","https://openalex.org/W2418619119","https://openalex.org/W2474232830","https://openalex.org/W2477331533","https://openalex.org/W2492098883","https://openalex.org/W2520660681","https://openalex.org/W2554546294","https://openalex.org/W2582819498","https://openalex.org/W2606596494","https://openalex.org/W2900656925","https://openalex.org/W2906151105","https://openalex.org/W2971346777","https://openalex.org/W3217339226","https://openalex.org/W4247163601","https://openalex.org/W4247673340","https://openalex.org/W4256064810","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4390779211","https://openalex.org/W2050921353","https://openalex.org/W2024439371","https://openalex.org/W2506537652","https://openalex.org/W3041782837","https://openalex.org/W2153903308","https://openalex.org/W4205537555","https://openalex.org/W7048872038","https://openalex.org/W75020212","https://openalex.org/W2912092000"],"abstract_inverted_index":{"Contributing":[0],"to":[1,115,130,146],"a":[2,35,123],"growing":[3],"body":[4],"of":[5,26,40,69,79,126,137],"research":[6,139],"addressing":[7],"secondary":[8,23],"students\u2019":[9,24,38,148],"quantitative":[10,81,103,149],"and":[11,28,42,48,63,94,150],"covariational":[12,127,151],"reasoning,":[13],"the":[14,50,70,80,108],"multiple":[15],"case":[16],"study":[17,36,74],"reported":[18],"in":[19,52,72,77,101,110],"this":[20,73,138],"article":[21,31],"investigated":[22],"quantification":[25,39],"ratio":[27,43,93],"rate.":[29,95],"This":[30],"reports":[32],"results":[33],"from":[34,58],"investigating":[37],"rate":[41],"as":[44,120],"relationships":[45],"between":[46],"quantities":[47],"presents":[49],"Change":[51,109],"Covarying":[53,111],"Quantities":[54,112],"Framework,":[55],"which":[56],"builds":[57],"Carlson,":[59],"Jacobs,":[60],"Coe,":[61],"Larsen,":[62],"Hsu\u2019s":[64],"(2002)":[65],"Covariation":[66],"Framework.":[67],"Each":[68],"students":[71,98,118],"was":[75],"consistent":[76],"terms":[78],"operation":[82],"he":[83],"or":[84,88],"she":[85],"used":[86],"(comparison":[87],"coordination)":[89],"when":[90,105],"quantifying":[91,106],"both":[92],"Illustrating":[96],"how":[97],"can":[99],"engage":[100],"different":[102,133],"operations":[104],"rate,":[107],"Framework":[113],"helps":[114],"explain":[116],"why":[117],"classified":[119],"operating":[121],"at":[122],"particular":[124],"level":[125],"reasoning":[128],"appear":[129],"be":[131],"using":[132],"mental":[134],"actions.":[135],"Implications":[136],"include":[140],"recommendations":[141],"for":[142],"designing":[143],"instructional":[144],"tasks":[145],"foster":[147],"reasoning.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}
