{"id":"https://openalex.org/W1968614902","doi":"https://doi.org/10.1007/s10649-013-9492-4","title":"Discernment of invariants in dynamic geometry environments","display_name":"Discernment of invariants in dynamic geometry environments","publication_year":2013,"publication_date":"2013-06-24","ids":{"openalex":"https://openalex.org/W1968614902","doi":"https://doi.org/10.1007/s10649-013-9492-4","mag":"1968614902"},"language":"en","primary_location":{"id":"doi:10.1007/s10649-013-9492-4","doi":"https://doi.org/10.1007/s10649-013-9492-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10649-013-9492-4","pdf_url":null,"source":{"id":"https://openalex.org/S119483640","display_name":"Educational Studies in Mathematics","issn_l":"0013-1954","issn":["0013-1954","1573-0816"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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":"Educational Studies in Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11568/830490","any_repository_has_fulltext":true},"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/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Allen Leung","raw_affiliation_strings":["Hong Kong Baptist University, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hong Kong Baptist University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049835674","display_name":"Anna Baccaglini\u2010Frank","orcid":"https://orcid.org/0000-0002-8116-5370","observed_orcids":["https://orcid.org/0000-0002-8116-5370"]},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Anna Baccaglini-Frank","raw_affiliation_strings":["Universit\u00e0 di Modena e Reggio Emilia, Modena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Modena e Reggio Emilia, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101593544","display_name":"Maria Alessandra Mariotti","orcid":"https://orcid.org/0000-0002-5697-7449","observed_orcids":["https://orcid.org/0000-0002-5697-7449"]},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Alessandra Mariotti","raw_affiliation_strings":["Universit\u00e0 degli Studi di Siena, Siena, Italy","Universita\u2019 degli Studi di Siena, Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Universita\u2019 degli Studi di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000237211"],"corresponding_institution_ids":["https://openalex.org/I141568987"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":16.1277,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.98594029,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"84","issue":"3","first_page":"439","last_page":"460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9672999978065491,"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":0.9672999978065491,"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":0.009999999776482582,"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"}},{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.008799999952316284,"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/dynamic-geometry-environments","display_name":"dynamic geometry environments","score":0.8399999737739563},{"id":"https://openalex.org/keywords/invariants","display_name":"invariants","score":0.8410000205039978},{"id":"https://openalex.org/keywords/variation-theory","display_name":"variation theory","score":0.6909999847412109},{"id":"https://openalex.org/keywords/simultaneity","display_name":"simultaneity","score":0.7900000214576721},{"id":"https://openalex.org/keywords/sensorimotor-perception","display_name":"sensorimotor perception","score":0.9829999804496765},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.8090000152587891}],"concepts":[{"id":"https://openalex.org/C2780211513","wikidata":"https://www.wikidata.org/wiki/Q1132167","display_name":"Discernment","level":2,"score":0.9735753536224365},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6350988745689392},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6054115891456604},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5226535797119141},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5202190279960632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4978477954864502},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.4650868773460388},{"id":"https://openalex.org/C26760741","wikidata":"https://www.wikidata.org/wiki/Q160402","display_name":"Perception","level":2,"score":0.4297521114349365},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3665594160556793},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3602406680583954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3336857557296753},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31548136472702026},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2809738516807556},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10649-013-9492-4","doi":"https://doi.org/10.1007/s10649-013-9492-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10649-013-9492-4","pdf_url":null,"source":{"id":"https://openalex.org/S119483640","display_name":"Educational Studies in Mathematics","issn_l":"0013-1954","issn":["0013-1954","1573-0816"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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":"Educational Studies in Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkbu.edu.hk:hkbu_staff_publication-3275","doi":null,"is_oa":false,"landing_page_url":"https://repository.hkbu.edu.hk/hkbu_staff_publication/2261","pdf_url":null,"source":{"id":"https://openalex.org/S4377196872","display_name":"HKBU Institutional Repository (Hong Kong Baptist University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I141568987","host_organization_name":"Hong Kong Baptist University","host_organization_lineage":["https://openalex.org/I141568987"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"HKBU Staff Publication","raw_type":"text"},{"id":"pmh:oai:arpi.unipi.it:11568/830490","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11568/830490","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/788201","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/788201","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/46644","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/46644","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arpi.unipi.it:11568/830490","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11568/830490","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Quality education","id":"https://metadata.un.org/sdg/4","score":0.6164000034332275}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W17148407","https://openalex.org/W47452736","https://openalex.org/W72631365","https://openalex.org/W87727849","https://openalex.org/W192304492","https://openalex.org/W324630069","https://openalex.org/W622392493","https://openalex.org/W1500839707","https://openalex.org/W1546442734","https://openalex.org/W1551895856","https://openalex.org/W1576700219","https://openalex.org/W1598440682","https://openalex.org/W1598980025","https://openalex.org/W1982406337","https://openalex.org/W2052346120","https://openalex.org/W2061124530","https://openalex.org/W2066948210","https://openalex.org/W2133194741","https://openalex.org/W2163093128","https://openalex.org/W2181601072","https://openalex.org/W2246941817","https://openalex.org/W2284479145","https://openalex.org/W2315637430","https://openalex.org/W2608989150"],"related_works":["https://openalex.org/W2466132752","https://openalex.org/W2625852956","https://openalex.org/W2052346120","https://openalex.org/W4226059972","https://openalex.org/W4286632448","https://openalex.org/W2246941817","https://openalex.org/W72631365","https://openalex.org/W7029979360","https://openalex.org/W7099019561","https://openalex.org/W7097816345"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}