{"id":"https://openalex.org/W7148701628","doi":"https://doi.org/10.5815/ijmecs.2026.02.06","title":"Introducing High School Students to the Mystery of Lobachevsky Geometry","display_name":"Introducing High School Students to the Mystery of Lobachevsky Geometry","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7148701628","doi":"https://doi.org/10.5815/ijmecs.2026.02.06"},"language":"en","primary_location":{"id":"doi:10.5815/ijmecs.2026.02.06","doi":"https://doi.org/10.5815/ijmecs.2026.02.06","is_oa":true,"landing_page_url":"https://doi.org/10.5815/ijmecs.2026.02.06","pdf_url":"https://www.mecs-press.org/ijmecs/ijmecs-v18-n2/IJMECS-V18-N2-6.pdf","source":{"id":"https://openalex.org/S2500184344","display_name":"International Journal of Modern Education and Computer Science","issn_l":"2075-0161","issn":["2075-0161","2075-017X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Education and Computer Science","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.mecs-press.org/ijmecs/ijmecs-v18-n2/IJMECS-V18-N2-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002497952","display_name":"Abdullah Kurudirek","orcid":"https://orcid.org/0000-0002-7179-7999","observed_orcids":["https://orcid.org/0000-0002-7179-7999"]},"institutions":[{"id":"https://openalex.org/I4405254665","display_name":"Al-Naji University","ror":"https://ror.org/023mv6842","country_code":"IQ","type":"education","lineage":["https://openalex.org/I4405254665"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Abdullah Kurudirek","raw_affiliation_strings":["College of Education, Al-Naji University, Baghdad, Iraq"],"raw_orcid":"https://orcid.org/0000-0002-7179-7999","affiliations":[{"raw_affiliation_string":"College of Education, Al-Naji University, Baghdad, Iraq","institution_ids":["https://openalex.org/I4405254665"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002497952"],"corresponding_institution_ids":["https://openalex.org/I4405254665"],"apc_list":null,"apc_paid":null,"fwci":1.9662,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77081122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"18","issue":"2","first_page":"100","last_page":"120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.7378000020980835,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.7378000020980835,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.19840000569820404,"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":0.031599998474121094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lobachevsky-geometry","display_name":"Lobachevsky geometry","score":0.9750000238418579},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.9959999918937683},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"non-Euclidean geometry","score":0.9990000128746033},{"id":"https://openalex.org/keywords/klein-model","display_name":"Klein model","score":0.6890000104904175},{"id":"https://openalex.org/keywords/poincare-disk-model","display_name":"Poincar\u00e9 disk model","score":0.9990000128746033},{"id":"https://openalex.org/keywords/critical-thinking-skills","display_name":"critical thinking skills","score":0.7139999866485596}],"concepts":[{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.8276000022888184},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.6098999977111816},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.6053000092506409},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6014000177383423},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.5726000070571899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5620999932289124},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.5019999742507935},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C32990609","wikidata":"https://www.wikidata.org/wiki/Q306542","display_name":"Transformation geometry","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C180110497","wikidata":"https://www.wikidata.org/wiki/Q5474574","display_name":"Foundations of geometry","level":4,"score":0.3449999988079071},{"id":"https://openalex.org/C77730005","wikidata":"https://www.wikidata.org/wiki/Q326905","display_name":"Spherical geometry","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C46175816","wikidata":"https://www.wikidata.org/wiki/Q134787","display_name":"Analytic geometry","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C105653879","wikidata":"https://www.wikidata.org/wiki/Q7100712","display_name":"Ordered geometry","level":5,"score":0.296099990606308},{"id":"https://openalex.org/C190248442","wikidata":"https://www.wikidata.org/wiki/Q839486","display_name":"Qualitative research","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C2992902817","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics curriculum","level":4,"score":0.272599995136261}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5815/ijmecs.2026.02.06","doi":"https://doi.org/10.5815/ijmecs.2026.02.06","is_oa":true,"landing_page_url":"https://doi.org/10.5815/ijmecs.2026.02.06","pdf_url":"https://www.mecs-press.org/ijmecs/ijmecs-v18-n2/IJMECS-V18-N2-6.pdf","source":{"id":"https://openalex.org/S2500184344","display_name":"International Journal of Modern Education and Computer Science","issn_l":"2075-0161","issn":["2075-0161","2075-017X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Education and Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5815/ijmecs.2026.02.06","doi":"https://doi.org/10.5815/ijmecs.2026.02.06","is_oa":true,"landing_page_url":"https://doi.org/10.5815/ijmecs.2026.02.06","pdf_url":"https://www.mecs-press.org/ijmecs/ijmecs-v18-n2/IJMECS-V18-N2-6.pdf","source":{"id":"https://openalex.org/S2500184344","display_name":"International Journal of Modern Education and Computer Science","issn_l":"2075-0161","issn":["2075-0161","2075-017X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Education and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.975600004196167,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7148701628.pdf","grobid_xml":"https://content.openalex.org/works/W7148701628.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1582313966","https://openalex.org/W1619767803","https://openalex.org/W2038928148","https://openalex.org/W2097424227","https://openalex.org/W2101838075","https://openalex.org/W2134095478","https://openalex.org/W2161895011","https://openalex.org/W2293422520","https://openalex.org/W2709117498","https://openalex.org/W2765600495","https://openalex.org/W3012809068","https://openalex.org/W3037970510","https://openalex.org/W3047611873","https://openalex.org/W3095767005","https://openalex.org/W3175612249","https://openalex.org/W4207016192","https://openalex.org/W4211143709","https://openalex.org/W4291017882","https://openalex.org/W4293575658","https://openalex.org/W4307701964","https://openalex.org/W4321639160","https://openalex.org/W4323024853","https://openalex.org/W4323024948","https://openalex.org/W4385431614","https://openalex.org/W4387818530","https://openalex.org/W4390352021","https://openalex.org/W4392923099","https://openalex.org/W4393105042","https://openalex.org/W4393190953","https://openalex.org/W4400010387","https://openalex.org/W4400217255","https://openalex.org/W4401946966","https://openalex.org/W4409688424","https://openalex.org/W6887755097","https://openalex.org/W6911947463","https://openalex.org/W6968389175"],"related_works":["https://openalex.org/W6893004410","https://openalex.org/W7135613092","https://openalex.org/W3047611873","https://openalex.org/W7203864680","https://openalex.org/W6911947463","https://openalex.org/W4385431614","https://openalex.org/W7135550520","https://openalex.org/W7119286463","https://openalex.org/W3177280036","https://openalex.org/W3215621592"],"abstract_inverted_index":{"This":[0,87,170],"article":[1,171],"primarily":[2],"aims":[3],"to":[4,9,162,190],"introduce":[5],"high":[6],"school":[7],"students":[8,106,146],"the":[10,17,52,108,114,120,125,153,181,185,192],"mystery":[11],"of":[12,16,19,41,194],"Lobachevsky":[13,22,42,132],"geometry,":[14,23,28],"one":[15],"cornerstones":[18],"non-Euclidean":[20,67],"geometries.":[21,68],"often":[24],"known":[25],"as":[26,51],"hyperbolic":[27],"differs":[29],"from":[30,105,124],"Euclidean":[31,85],"geometry":[32,43,70,133,142,195],"in":[33,46,150,159,180],"several":[34],"basic":[35],"ways.":[36],"The":[37,100,128],"concepts":[38],"and":[39,54,64,76,97,113,165,175,183],"figures":[40],"can":[44],"appear":[45],"different":[47],"plane":[48],"models,":[49],"such":[50],"Klein":[53],"Poincar\u00e9":[55],"disk":[56],"models.":[57],"It":[58],"further":[59,117],"examines":[60],"students'":[61,74,160],"general":[62],"attitudes":[63],"behaviors":[65],"toward":[66],"Lobachevsky's":[69],"has":[71],"helped":[72],"expand":[73],"horizons":[75],"enriched":[77],"their":[78],"critical":[79],"thinking":[80],"skills":[81],"by":[82,91,119],"challenging":[83],"traditional":[84],"paradigms.":[86],"study":[88,115],"is":[89],"supported":[90,118],"a":[92],"mixed-method":[93],"approach":[94],"utilizing":[95],"quantitative":[96],"qualitative":[98],"data.":[99],"mock":[101],"exam":[102],"results":[103],"obtained":[104],"during":[107],"educational":[109],"process":[110],"were":[111,134],"compared,":[112],"was":[116],"positive":[121],"feedback":[122],"received":[123],"participating":[126],"students.":[127],"intriguing":[129],"lessons":[130],"on":[131],"conducted":[135],"over":[136],"4":[137],"weeks,":[138],"with":[139],"weekly":[140],"2-hour":[141],"classes":[143],"involving":[144],"12th-grade":[145],"at":[147],"Stirling":[148],"Schools":[149],"Erbil.":[151],"Throughout":[152],"study,":[154],"we":[155],"observed":[156],"significant":[157],"improvements":[158],"ability":[161],"adopt,":[163],"understand,":[164],"apply":[166],"advanced":[167],"geometric":[168],"concepts.":[169],"also":[172],"discusses":[173],"findings":[174],"implications":[176],"that":[177],"address":[178],"gaps":[179],"literature":[182],"considers":[184],"potential":[186],"for":[187],"curriculum":[188],"updates":[189],"enhance":[191],"future":[193],"education.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-04-04T00:00:00"}
