{"id":"https://openalex.org/W2026499792","doi":"https://doi.org/10.1080/1049482920020304","title":"Mathematical Induction in a Visual Context","display_name":"Mathematical Induction in a Visual Context","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2026499792","doi":"https://doi.org/10.1080/1049482920020304","mag":"2026499792"},"language":"en","primary_location":{"id":"doi:10.1080/1049482920020304","doi":"https://doi.org/10.1080/1049482920020304","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1049482920020304","pdf_url":null,"source":{"id":"https://openalex.org/S90466346","display_name":"Interactive Learning Environments","issn_l":"1049-4820","issn":["1049-4820","1744-5191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","erih-plus","jufo-1","ki-jl-1","norway-1","poland-140","russia-white-list-1","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":"Interactive Learning Environments","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/A5019532482","display_name":"Albert A. Cuoco","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210152198","display_name":"Education Development Center","ror":"https://ror.org/04wnwd012","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210152198"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Albert A. Cuoco","raw_affiliation_strings":["Woburn High School and Education Development Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Woburn High School and Education Development Center","institution_ids":["https://openalex.org/I4210152198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016506070","display_name":"E. Paul Goldenberg","orcid":"https://orcid.org/0000-0002-2077-1430","observed_orcids":["https://orcid.org/0000-0002-2077-1430"]},"institutions":[{"id":"https://openalex.org/I4210152198","display_name":"Education Development Center","ror":"https://ror.org/04wnwd012","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210152198"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Paul Goldenberg","raw_affiliation_strings":["Education Development Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Education Development Center","institution_ids":["https://openalex.org/I4210152198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210152198"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.33659088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"2","issue":"3","first_page":"181","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.8970000147819519,"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":0.8970000147819519,"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/T12170","display_name":"History and Theory of Mathematics","score":0.035999998450279236,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.03220000118017197,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematical-induction","display_name":"mathematical induction","score":1.0},{"id":"https://openalex.org/keywords/visual-proof","display_name":"visual proof","score":0.7549999952316284},{"id":"https://openalex.org/keywords/algebra-and-geometry-integration","display_name":"geometry and algebra integration","score":0.6269999742507935},{"id":"https://openalex.org/keywords/proof-visualization","display_name":"proof visualization","score":0.609000027179718},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"mathematics education","score":0.35199999809265137}],"concepts":[{"id":"https://openalex.org/C2437467","wikidata":"https://www.wikidata.org/wiki/Q378701","display_name":"Perfection","level":2,"score":0.8187091946601868},{"id":"https://openalex.org/C2779829227","wikidata":"https://www.wikidata.org/wiki/Q7936872","display_name":"Vitality","level":2,"score":0.7727504372596741},{"id":"https://openalex.org/C2777526511","wikidata":"https://www.wikidata.org/wiki/Q691543","display_name":"Pace","level":2,"score":0.7165059447288513},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6858925223350525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4295230805873871},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4233143925666809},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.3956637978553772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.356514036655426},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.30114060640335083},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.17271938920021057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1407392919063568},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.11308008432388306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1025354266166687},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/1049482920020304","doi":"https://doi.org/10.1080/1049482920020304","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1049482920020304","pdf_url":null,"source":{"id":"https://openalex.org/S90466346","display_name":"Interactive Learning Environments","issn_l":"1049-4820","issn":["1049-4820","1744-5191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","erih-plus","jufo-1","ki-jl-1","norway-1","poland-140","russia-white-list-1","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":"Interactive Learning Environments","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W196648522","https://openalex.org/W1491003784","https://openalex.org/W2022706962","https://openalex.org/W2088260149","https://openalex.org/W2124818066","https://openalex.org/W2131745871","https://openalex.org/W4232015415","https://openalex.org/W4246097047"],"related_works":["https://openalex.org/W2489100041","https://openalex.org/W7026326597","https://openalex.org/W4232970652","https://openalex.org/W7056842888","https://openalex.org/W4382066047","https://openalex.org/W7131777294","https://openalex.org/W1996718330","https://openalex.org/W2503604434","https://openalex.org/W1495752285","https://openalex.org/W4312832153"],"abstract_inverted_index":{"As":[0],"long":[1],"as":[2],"algebra":[3],"and":[4,14,31],"geometry":[5],"proceeded":[6],"along":[7],"separate":[8],"paths,":[9],"their":[10,15],"advance":[11],"was":[12],"slow":[13],"applications":[16],"limited.":[17],"But":[18],"when":[19],"these":[20],"sciences":[21],"joined":[22],"company,":[23],"they":[24],"drew":[25],"from":[26],"each":[27],"other":[28],"fresh":[29],"vitality":[30],"thenceforward":[32],"marched":[33],"on":[34],"at":[35],"a":[36],"rapid":[37],"pace":[38],"toward":[39],"perfection.":[40],"Joseph":[41],"Louis":[42],"Lagrange":[43]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
