{"id":"https://openalex.org/W1598440682","doi":"https://doi.org/10.1023/a:1021195015288","title":"Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction","display_name":"Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction","publication_year":2002,"publication_date":"2002-05-01","ids":{"openalex":"https://openalex.org/W1598440682","doi":"https://doi.org/10.1023/a:1021195015288","mag":"1598440682"},"language":"en","primary_location":{"id":"doi:10.1023/a:1021195015288","doi":"https://doi.org/10.1023/a:1021195015288","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1021195015288","pdf_url":null,"source":{"id":"https://openalex.org/S174140584","display_name":"International Journal of Computers for Mathematical Learning","issn_l":"1382-3892","issn":["1382-3892","1573-1766"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computers for Mathematical 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/A5000237211","display_name":"Allen Yuk Lun Leung","orcid":"https://orcid.org/0000-0002-7995-0951","observed_orcids":["https://orcid.org/0000-0002-7995-0951"]},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Allen Leung","raw_affiliation_strings":["Department of Curriculum Studies, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China","Department of Curriculum Studies, The University of Hong Kong, Hong Kong SAR, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Curriculum Studies, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"Department of Curriculum Studies, The University of Hong Kong, Hong Kong SAR, China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077683919","display_name":"Francis Lopez\u2010Real","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Francis Lopez-Real","raw_affiliation_strings":["Department of Curriculum Studies, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China","Department of Curriculum Studies, The University of Hong Kong, Hong Kong SAR, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Curriculum Studies, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"Department of Curriculum Studies, The University of Hong Kong, Hong Kong SAR, China","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":8.1176,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.96437309,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":"2","first_page":"145","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9531000256538391,"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":0.9531000256538391,"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/T12504","display_name":"Mathematics and Applications","score":0.0203000009059906,"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"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.01209999993443489,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/dynamic-geometry-environments","display_name":"dynamic geometry environments","score":0.984000027179718},{"id":"https://openalex.org/keywords/proof-by-contradiction","display_name":"reductio ad absurdum","score":0.9549999833106995},{"id":"https://openalex.org/keywords/cyclic-quadrilaterals","display_name":"cyclic quadrilaterals","score":0.9570000171661377},{"id":"https://openalex.org/keywords/cabri-geometre","display_name":"Cabri-G\u00e9om\u00e8tre","score":0.7860000133514404},{"id":"https://openalex.org/keywords/visualization","display_name":"visualization","score":0.8859999775886536},{"id":"https://openalex.org/keywords/dynamic-templates","display_name":"dynamic templates","score":0.6510000228881836},{"id":"https://openalex.org/keywords/geometry-teaching","display_name":"geometry teaching","score":0.4490000009536743}],"concepts":[{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6470354199409485},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5591461658477783},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5222845077514648},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4989910125732422},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.47994711995124817},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.4641609787940979},{"id":"https://openalex.org/C2777122596","wikidata":"https://www.wikidata.org/wiki/Q1247560","display_name":"Praxis","level":2,"score":0.45897477865219116},{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.44015151262283325},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.4179121255874634},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4149826765060425},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38055458664894104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3622255325317383},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3389507532119751},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24300417304039001},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.21349069476127625},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2092013657093048},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1884940266609192},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1023/a:1021195015288","doi":"https://doi.org/10.1023/a:1021195015288","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1021195015288","pdf_url":null,"source":{"id":"https://openalex.org/S174140584","display_name":"International Journal of Computers for Mathematical Learning","issn_l":"1382-3892","issn":["1382-3892","1573-1766"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computers for Mathematical Learning","raw_type":"journal-article"},{"id":"pmh:oai:hub.hku.hk:10722/48565","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/48565","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8278999924659729,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W17148407","https://openalex.org/W62187108","https://openalex.org/W103161854","https://openalex.org/W233361944","https://openalex.org/W1538143337","https://openalex.org/W1548074571","https://openalex.org/W1982406337","https://openalex.org/W1995875985","https://openalex.org/W2010353619","https://openalex.org/W2043865937","https://openalex.org/W2045752304","https://openalex.org/W2065430068","https://openalex.org/W2072267223","https://openalex.org/W2135943618","https://openalex.org/W2177820238","https://openalex.org/W2270361819","https://openalex.org/W2601433704","https://openalex.org/W2946813334","https://openalex.org/W4238947095","https://openalex.org/W4243742846","https://openalex.org/W7018441295"],"related_works":["https://openalex.org/W1575319075","https://openalex.org/W4318069842","https://openalex.org/W1576049394","https://openalex.org/W2793818477","https://openalex.org/W7033485344","https://openalex.org/W2284324573","https://openalex.org/W2529988568","https://openalex.org/W7099486778","https://openalex.org/W1496528293","https://openalex.org/W2120727441"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}