{"id":"https://openalex.org/W1606587809","doi":"https://doi.org/10.1007/978-0-387-09729-9_50","title":"Using Alnuset to construct the notions of equivalence and equality in algebra","display_name":"Using Alnuset to construct the notions of equivalence and equality in algebra","publication_year":2008,"publication_date":"2008-07-19","ids":{"openalex":"https://openalex.org/W1606587809","doi":"https://doi.org/10.1007/978-0-387-09729-9_50","mag":"1606587809"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-09729-9_50","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-09729-9_50","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-09729-9_50.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP \u2013 The International Federation for Information Processing","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-09729-9_50.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039890633","display_name":"Giampaolo Chiappini","orcid":null},"institutions":[{"id":"https://openalex.org/I4210124735","display_name":"Istituto per le Tecnologie Didattiche","ror":"https://ror.org/02xz4xc25","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210124735","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giampaolo Chiappini","raw_affiliation_strings":["Istituto per le Tecnologie Didattiche, CNR, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Tecnologie Didattiche, CNR, Genova, Italy","institution_ids":["https://openalex.org/I4210124735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023935030","display_name":"Bettina Pedemonte","orcid":"https://orcid.org/0000-0002-7220-5123"},"institutions":[{"id":"https://openalex.org/I4210124735","display_name":"Istituto per le Tecnologie Didattiche","ror":"https://ror.org/02xz4xc25","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210124735","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bettina Pedemonte","raw_affiliation_strings":["Istituto per le Tecnologie Didattiche, CNR, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Tecnologie Didattiche, CNR, Genova, Italy","institution_ids":["https://openalex.org/I4210124735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007425489","display_name":"Elisabetta Robotti","orcid":"https://orcid.org/0000-0002-7866-7388"},"institutions":[{"id":"https://openalex.org/I4210124735","display_name":"Istituto per le Tecnologie Didattiche","ror":"https://ror.org/02xz4xc25","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210124735","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elisabetta Robotti","raw_affiliation_strings":["Istituto per le Tecnologie Didattiche, CNR, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Tecnologie Didattiche, CNR, Genova, Italy","institution_ids":["https://openalex.org/I4210124735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039890633"],"corresponding_institution_ids":["https://openalex.org/I4210124735"],"apc_list":null,"apc_paid":null,"fwci":0.564,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.67725668,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"345","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10636","display_name":"Innovative Teaching and Learning Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10636","display_name":"Innovative Teaching and Learning Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9915000200271606,"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/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.9671000242233276,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7002538442611694},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.648952305316925},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6100594997406006},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5013997554779053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47973576188087463},{"id":"https://openalex.org/keywords/abstract-algebra","display_name":"Abstract algebra","score":0.43510088324546814},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42248648405075073},{"id":"https://openalex.org/keywords/comprehension","display_name":"Comprehension","score":0.4198231101036072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40801575779914856},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.3942298889160156},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3200533390045166},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06435799598693848}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7002538442611694},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.648952305316925},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6100594997406006},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5013997554779053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47973576188087463},{"id":"https://openalex.org/C185701065","wikidata":"https://www.wikidata.org/wiki/Q159943","display_name":"Abstract algebra","level":3,"score":0.43510088324546814},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42248648405075073},{"id":"https://openalex.org/C511192102","wikidata":"https://www.wikidata.org/wiki/Q5156948","display_name":"Comprehension","level":2,"score":0.4198231101036072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40801575779914856},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.3942298889160156},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3200533390045166},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06435799598693848},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-0-387-09729-9_50","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-09729-9_50","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-09729-9_50.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP \u2013 The International Federation for Information Processing","raw_type":"book-chapter"},{"id":"pmh:oai:pumaoai.isti.cnr.it:cnr.itd/cnr.itd.ge/2008-A2-008","is_oa":true,"landing_page_url":"http://puma.isti.cnr.it/dfdownloadnew.php?ident=cnr.itd/cnr.itd.ge/2008-A2-008","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"In: WCC 2008 - IFIP 20th World Computer Congress 2008: Learning to Live in the Knowledge Society (Milano, Italy, 7-10 September 2008). Proceedings, pp. 345 - 348. M. Kendall, B. Samways (eds.). (Computer Science). Springer, 2008.","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1007/978-0-387-09729-9_50","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-09729-9_50","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-0-387-09729-9_50.pdf","source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP \u2013 The International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1606587809.pdf","grobid_xml":"https://content.openalex.org/works/W1606587809.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1911686750"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W2381570729","https://openalex.org/W1976205134","https://openalex.org/W4248336175","https://openalex.org/W3009369890","https://openalex.org/W2031260042","https://openalex.org/W2391445434","https://openalex.org/W4312490297","https://openalex.org/W2062212388"],"abstract_inverted_index":{"We":[0,71],"analyse":[1,72],"the":[2,7,20,25,58,64,73,76,86,119,125],"role":[3],"of":[4,9,24,27,33,69,75,127],"technology":[5,38],"in":[6,19,118],"development":[8],"algebraic":[10,59,120],"crucial":[11],"knowledge":[12,60,117],"and":[13,22,29,47,61,66,105,116,122],"competences,":[14],"such":[15,108],"as":[16],"those":[17],"involved":[18],"comprehension":[21],"use":[23],"notions":[26],"equivalence":[28],"equality.":[30],"The":[31],"hypothesis":[32],"our":[34],"research":[35],"is":[36],"that":[37,97],"can":[39,110],"be":[40,111],"exploited":[41,112],"to":[42,56,62,113,123],"make":[43],"available":[44],"new":[45,53],"operative":[46],"representative":[48],"possibilities":[49],"which":[50],"structure":[51],"a":[52,82],"phenomenological":[54,77],"space":[55,78],"investigate":[57],"improve":[63,124],"teaching":[65,126],"learning":[67],"processes":[68],"algebra.":[70,128],"characteristics":[74,109],"structured":[79],"by":[80,85],"Alnuset,":[81,102],"system":[83],"developed":[84],"authors":[87],"within":[88],"ReMath":[89],"European":[90],"project.":[91],"Through":[92],"examples":[93],"taken":[94],"from":[95],"experimentations":[96],"we":[98,103],"have":[99],"performed":[100],"with":[101],"illustrate":[104],"discuss":[106],"how":[107],"develop":[114],"competences":[115],"domain":[121]},"counts_by_year":[{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
