{"id":"https://openalex.org/W4412379561","doi":"https://doi.org/10.25726/m9151-3791-6640-c","title":"\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0430\u0441\u043f\u0435\u043a\u0442\u044b \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u044f \u0443 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u043e\u0432 \u0447\u0435\u0440\u0435\u0437 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0446\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f","display_name":"\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0430\u0441\u043f\u0435\u043a\u0442\u044b \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u044f \u0443 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u043e\u0432 \u0447\u0435\u0440\u0435\u0437 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0446\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f","publication_year":2024,"publication_date":"2024-12-30","ids":{"openalex":"https://openalex.org/W4412379561","doi":"https://doi.org/10.25726/m9151-3791-6640-c"},"language":"ru","primary_location":{"id":"doi:10.25726/m9151-3791-6640-c","doi":"https://doi.org/10.25726/m9151-3791-6640-c","is_oa":true,"landing_page_url":"https://doi.org/10.25726/m9151-3791-6640-c","pdf_url":null,"source":{"id":"https://openalex.org/S5407046019","display_name":"Academic Research Journal","issn_l":"3034-6665","issn":["3034-6665"],"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":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Research Journal","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4412379561"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.25726/m9151-3791-6640-c","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084808024","display_name":"\u0421.\u0421. \u041c\u0443\u0447\u043a\u0430\u0435\u0432\u0430","orcid":"https://orcid.org/0000-0002-2382-6791","observed_orcids":["https://orcid.org/0000-0002-2382-6791"]},"institutions":[{"id":"https://openalex.org/I205923962","display_name":"Kalmyk State University","ror":"https://ror.org/05jfsf459","country_code":"RU","type":"education","lineage":["https://openalex.org/I205923962"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"\u0421.\u0421. \u041c\u0443\u0447\u043a\u0430\u0435\u0432\u0430","raw_affiliation_strings":["\u041a\u0430\u043b\u043c\u044b\u0446\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0438\u043c. \u0411.\u0411. \u0413\u043e\u0440\u043e\u0434\u043e\u0432\u0438\u043a\u043e\u0432\u0430"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u041a\u0430\u043b\u043c\u044b\u0446\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0438\u043c. \u0411.\u0411. \u0413\u043e\u0440\u043e\u0434\u043e\u0432\u0438\u043a\u043e\u0432\u0430","institution_ids":["https://openalex.org/I205923962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5118970490","display_name":"\u0414.\u0410. \u0422\u043e\u043f\u043e\u0440\u043e\u0432\u0430","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I205923962","display_name":"Kalmyk State University","ror":"https://ror.org/05jfsf459","country_code":"RU","type":"education","lineage":["https://openalex.org/I205923962"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"\u0414.\u0410. \u0422\u043e\u043f\u043e\u0440\u043e\u0432\u0430","raw_affiliation_strings":["\u041a\u0430\u043b\u043c\u044b\u0446\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0438\u043c. \u0411.\u0411. \u0413\u043e\u0440\u043e\u0434\u043e\u0432\u0438\u043a\u043e\u0432\u0430"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u041a\u0430\u043b\u043c\u044b\u0446\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0438\u043c. \u0411.\u0411. \u0413\u043e\u0440\u043e\u0434\u043e\u0432\u0438\u043a\u043e\u0432\u0430","institution_ids":["https://openalex.org/I205923962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205923962"],"apc_list":null,"apc_paid":null,"fwci":0.3944,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6073245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2","issue":"1","first_page":"24","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.5547000169754028,"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":0.5547000169754028,"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":0.22669999301433563,"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/T11904","display_name":"Spatial Cognition and Navigation","score":0.057500001043081284,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spatial-thinking","display_name":"spatial thinking","score":0.949999988079071},{"id":"https://openalex.org/keywords/linear-algebra-teaching","display_name":"linear algebra education","score":0.8410000205039978},{"id":"https://openalex.org/keywords/computer-modeling","display_name":"computer modeling","score":0.9179999828338623},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"computer graphics","score":0.7279999852180481},{"id":"https://openalex.org/keywords/visualization","display_name":"visualization","score":0.4490000009536743},{"id":"https://openalex.org/keywords/interdisciplinary-teaching","display_name":"interdisciplinary teaching","score":0.5759999752044678},{"id":"https://openalex.org/keywords/college-students","display_name":"university students","score":0.7139999866485596},{"id":"https://openalex.org/keywords/student-motivation","display_name":"student motivation","score":0.7269999980926514},{"id":"https://openalex.org/keywords/academic-achievement","display_name":"academic performance","score":0.7960000038146973},{"id":"https://openalex.org/keywords/critical-thinking","display_name":"critical thinking","score":0.6499999761581421},{"id":"https://openalex.org/keywords/mathematics-teaching-methods","display_name":"mathematics teaching methods","score":0.5809999704360962},{"id":"https://openalex.org/keywords/ict-in-education","display_name":"ICT in education","score":0.722000002861023},{"id":"https://openalex.org/keywords/spatial-perception","display_name":"spatial perception","score":0.39100000262260437},{"id":"https://openalex.org/keywords/teaching-methods-comparison","display_name":"teaching methods comparison","score":0.35600000619888306},{"id":"https://openalex.org/keywords/student-self-assessment","display_name":"student self-assessment","score":0.38499999046325684},{"id":"https://openalex.org/keywords/teacher-self-assessment","display_name":"teacher self-assessment","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.2379622757434845}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.25726/m9151-3791-6640-c","doi":"https://doi.org/10.25726/m9151-3791-6640-c","is_oa":true,"landing_page_url":"https://doi.org/10.25726/m9151-3791-6640-c","pdf_url":null,"source":{"id":"https://openalex.org/S5407046019","display_name":"Academic Research Journal","issn_l":"3034-6665","issn":["3034-6665"],"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":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Research Journal","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.25726/m9151-3791-6640-c","doi":"https://doi.org/10.25726/m9151-3791-6640-c","is_oa":true,"landing_page_url":"https://doi.org/10.25726/m9151-3791-6640-c","pdf_url":null,"source":{"id":"https://openalex.org/S5407046019","display_name":"Academic Research Journal","issn_l":"3034-6665","issn":["3034-6665"],"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":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Research Journal","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.975600004196167,"display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W4283583687","https://openalex.org/W4380086331","https://openalex.org/W4406682860"],"related_works":["https://openalex.org/W6888901079","https://openalex.org/W7165269728","https://openalex.org/W6963818294","https://openalex.org/W6945094909","https://openalex.org/W7108475447","https://openalex.org/W7035107715","https://openalex.org/W7166602449","https://openalex.org/W7016512663","https://openalex.org/W7025665915","https://openalex.org/W7095014912"],"abstract_inverted_index":{"\u0412":[0,44,86,98,149],"\u0434\u0430\u043d\u043d\u043e\u0439":[1,67],"\u0441\u0442\u0430\u0442\u044c\u0435":[2],"\u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f":[3],"\u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435":[4,91],"\u043f\u043e\u0434\u0445\u043e\u0434\u044b":[5],"\u043a":[6,169,216],"\u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044e":[7,232],"\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e":[8,161],"\u043c\u044b\u0448\u043b\u0435\u043d\u0438\u044f":[9],"\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u043e\u0432":[10],"\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e\u043c":[11],"\u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0446\u0438\u0438":[12],"\u0437\u0430\u0434\u0430\u0447":[13],"\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439":[14,113,189],"\u0430\u043b\u0433\u0435\u0431\u0440\u044b":[15,114],"\u0438":[16,40,82,92,118,134,141,165,204,221,231,239,265],"\u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u043e\u0433\u043e":[17,58,182],"\u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.":[18],"\u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435":[19],"\u0430\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u043e":[20],"\u0432":[21,74,96,125,211,254],"\u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445":[22],"\u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445":[23],"\u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f":[24],"\u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e-\u043a\u043e\u043c\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445":[25],"\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439,":[26],"\u043a\u043e\u0433\u0434\u0430":[27],"\u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u044b\u0435":[28],"\u043c\u0435\u0442\u043e\u0434\u044b":[29,132],"\u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0438\u044f":[30,263],"\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438":[31,264],"\u0442\u0440\u0435\u0431\u0443\u044e\u0442":[32],"\u043c\u043e\u0434\u0435\u0440\u043d\u0438\u0437\u0430\u0446\u0438\u0438":[33],"\u0441":[34,115,185,199,242],"\u0446\u0435\u043b\u044c\u044e":[35],"\u043f\u043e\u0432\u044b\u0448\u0435\u043d\u0438\u044f":[36],"\u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0438":[37],"\u0443\u0441\u0432\u043e\u0435\u043d\u0438\u044f":[38,145],"\u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0430":[39,147],"\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f":[41,53],"\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e":[42],"\u043c\u044b\u0448\u043b\u0435\u043d\u0438\u044f.":[43],"\u0440\u0430\u0437\u0434\u0435\u043b\u0435":[45,87,150],"\u00ab\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u00bb":[46],"\u043e\u0431\u043e\u0441\u043d\u043e\u0432\u044b\u0432\u0430\u0435\u0442\u0441\u044f":[47],"\u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c":[48],"\u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f":[49,251],"\u043c\u0435\u0436\u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0440\u043d\u043e\u0433\u043e":[50],"\u043f\u043e\u0434\u0445\u043e\u0434\u0430":[51],"\u0434\u043b\u044f":[52],"\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445":[54],"\u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0439,":[55],"\u043f\u043e\u0434\u0447\u0435\u0440\u043a\u0438\u0432\u0430\u0435\u0442\u0441\u044f":[56],"\u0440\u043e\u043b\u044c":[57],"\u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f":[59,183],"\u043a\u0430\u043a":[60,138,236],"\u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u0430":[61,101],"\u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438":[62],"\u0441\u043b\u043e\u0436\u043d\u044b\u0445":[63],"\u0430\u0431\u0441\u0442\u0440\u0430\u043a\u0442\u043d\u044b\u0445":[64],"\u043f\u043e\u043d\u044f\u0442\u0438\u0439.":[65],"\u0410\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c":[66],"\u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439":[68],"\u0437\u0430\u0434\u0430\u0447\u0438":[69,112],"\u043e\u0431\u0443\u0441\u043b\u043e\u0432\u043b\u0435\u043d\u0430":[70],"\u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u044e\u0449\u0435\u0439":[71],"\u0440\u043e\u043b\u044c\u044e":[72],"\u0418\u041a\u0422":[73],"\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u043c":[75],"\u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435,":[76],"\u0447\u0442\u043e":[77,155,218,257],"\u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442":[78],"\u043e\u0431\u044a\u0435\u0434\u0438\u043d\u044f\u0442\u044c":[79],"\u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435":[80],"\u0437\u043d\u0430\u043d\u0438\u044f":[81],"\u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435":[83],"\u043d\u0430\u0432\u044b\u043a\u0438":[84],"\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u043e\u0432.":[85],"\u00ab\u041c\u0435\u0442\u043e\u0434\u044b\u00bb":[88],"\u043e\u043f\u0438\u0441\u0430\u043d\u044b":[89],"\u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435":[90],"\u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435":[93],"\u043f\u043e\u0434\u0445\u043e\u0434\u044b,":[94],"\u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0435":[95],"\u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0438.":[97],"\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435":[99],"\u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e":[100],"\u0430\u043d\u0430\u043b\u0438\u0437\u0430":[102,135],"\u043f\u0440\u0438\u043c\u0435\u043d\u044f\u043b\u0430\u0441\u044c":[103],"\u0441\u0440\u0430\u0432\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e-\u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u0430\u044f":[104],"\u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430,":[105],"\u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0430\u044f":[106],"\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0443":[107],"\u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e":[108],"\u0443\u0447\u0435\u0431\u043d\u043e\u0433\u043e":[109,146],"\u043c\u043e\u0434\u0443\u043b\u044f,":[110],"\u043e\u0431\u044a\u0435\u0434\u0438\u043d\u044f\u044e\u0449\u0435\u0433\u043e":[111],"\u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u043e\u0439":[116],"\u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0439":[117],"\u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0435\u0439.":[119],"\u041f\u0440\u0438\u0432\u043e\u0434\u044f\u0442\u0441\u044f":[120],"\u043f\u0440\u0438\u043c\u0435\u0440\u044b":[121],"\u0443\u0447\u0435\u0431\u043d\u044b\u0445":[122,128],"\u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u043e\u0432,":[123],"\u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043c\u044b\u0445":[124],"\u043a\u043b\u0430\u0441\u0441\u0430\u0445":[126],"\u0432\u044b\u0441\u0448\u0438\u0445":[127],"\u0437\u0430\u0432\u0435\u0434\u0435\u043d\u0438\u0439,":[129],"\u0430":[130],"\u0442\u0430\u043a\u0436\u0435":[131],"\u0441\u0431\u043e\u0440\u0430":[133],"\u0434\u0430\u043d\u043d\u044b\u0445,":[136],"\u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u0435":[137],"\u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435,":[139],"\u0442\u0430\u043a":[140],"\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435":[142],"\u043e\u0446\u0435\u043d\u0438\u0432\u0430\u043d\u0438\u0435":[143],"\u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432":[144],"\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430\u043c\u0438.":[148],"\u00ab\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b\u00bb":[151],"\u0441\u043e\u043e\u0431\u0449\u0430\u0435\u0442\u0441\u044f":[152],"\u043e":[153],"\u0442\u043e\u043c,":[154],"\u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435":[156],"\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0430\u043d\u043d\u044b\u0445":[157],"\u043c\u0435\u0442\u043e\u0434\u0438\u043a":[158,262],"\u0441\u043f\u043e\u0441\u043e\u0431\u0441\u0442\u0432\u0443\u0435\u0442":[159,225],"\u0443\u043b\u0443\u0447\u0448\u0435\u043d\u0438\u044e":[160],"\u0432\u043e\u0441\u043f\u0440\u0438\u044f\u0442\u0438\u044f,":[162],"\u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438":[163],"\u0437\u043d\u0430\u043d\u0438\u0439":[164],"\u043f\u043e\u0432\u044b\u0448\u0435\u043d\u0438\u044e":[166],"\u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u0438":[167],"\u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f":[168],"\u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044e":[170],"\u043f\u0440\u0435\u0434\u043c\u0435\u0442\u0430.":[171],"\u0421\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439":[172],"\u0430\u043d\u0430\u043b\u0438\u0437":[173],"\u0434\u0430\u043d\u043d\u044b\u0445":[174],"\u043f\u043e\u043a\u0430\u0437\u0430\u043b":[175],"\u0443\u043b\u0443\u0447\u0448\u0435\u043d\u0438\u0435":[176],"\u0430\u043a\u0430\u0434\u0435\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439":[177],"\u0443\u0441\u043f\u0435\u0432\u0430\u0435\u043c\u043e\u0441\u0442\u0438":[178],"\u043f\u0440\u0438":[179],"\u0443\u0441\u043b\u043e\u0432\u0438\u0438":[180],"\u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f":[181],"\u043d\u0430\u0440\u044f\u0434\u0443":[184],"\u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u044b\u043c\u0438":[186],"\u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438":[187],"\u043f\u043e":[188],"\u0430\u043b\u0433\u0435\u0431\u0440\u0435.":[190],"\u0420\u0430\u0437\u0434\u0435\u043b":[191],"\u00ab\u041e\u0431\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0435\u00bb":[192],"\u043f\u043e\u0441\u0432\u044f\u0449\u0435\u043d":[193],"\u0430\u043d\u0430\u043b\u0438\u0437\u0443":[194],"\u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0445":[195],"\u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432,":[196],"\u0438\u0445":[197],"\u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u0438":[198],"\u0442\u043e\u0447\u043a\u0438":[200],"\u0437\u0440\u0435\u043d\u0438\u044f":[201],"\u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e\u0439":[202],"\u0434\u0438\u0430\u0433\u043d\u043e\u0441\u0442\u0438\u043a\u0438":[203],"\u043e\u0431\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u044e":[205],"\u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445":[206,222],"\u0430\u0441\u043f\u0435\u043a\u0442\u043e\u0432":[207],"\u0432\u043d\u0435\u0434\u0440\u0435\u043d\u0438\u044f":[208],"\u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e":[209],"\u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u0430":[210],"\u0443\u0447\u0435\u0431\u043d\u044b\u0439":[212],"\u043f\u0440\u043e\u0446\u0435\u0441\u0441.":[213],"\u0410\u0432\u0442\u043e\u0440\u044b":[214],"\u043f\u0440\u0438\u0445\u043e\u0434\u044f\u0442":[215],"\u0432\u044b\u0432\u043e\u0434\u0443,":[217],"\u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0446\u0438\u044f":[219],"\u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445":[220],"\u043c\u0435\u0442\u043e\u0434\u043e\u0432":[223],"\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f":[224],"\u043d\u0435":[226],"\u0442\u043e\u043b\u044c\u043a\u043e":[227],"\u0443\u0433\u043b\u0443\u0431\u043b\u0435\u043d\u0438\u044e":[228],"\u0437\u043d\u0430\u043d\u0438\u0439,":[229],"\u043d\u043e":[230],"\u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0445":[233],"\u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0446\u0438\u0439,":[234],"\u0442\u0430\u043a\u0438\u0445":[235],"\u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435":[237],"\u043c\u044b\u0448\u043b\u0435\u043d\u0438\u0435":[238],"\u0443\u043c\u0435\u043d\u0438\u0435":[240],"\u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c":[241],"\u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u043c\u0438":[243],"\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u044f\u043c\u0438.":[244],"\u0422\u0430\u043a\u0438\u043c":[245],"\u043e\u0431\u0440\u0430\u0437\u043e\u043c,":[246],"\u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0435":[247],"\u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435":[248],"\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442":[249],"\u043f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c":[250],"\u043c\u0435\u0436\u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0440\u043d\u044b\u0445":[252],"\u043f\u043e\u0434\u0445\u043e\u0434\u043e\u0432":[253],"\u0432\u044b\u0441\u0448\u0435\u043c":[255],"\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438,":[256],"\u043c\u043e\u0436\u0435\u0442":[258],"\u0441\u043f\u043e\u0441\u043e\u0431\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c":[259],"\u0434\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0435\u043c\u0443":[260],"\u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u044e":[261],"\u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0438.":[266],"This":[267],"article":[268],"discusses":[269],"methodological":[270,362,395,547],"approaches":[271,398,603],"to":[272,314,337,366,380,480,490,520,568,575,588,610],"the":[273,280,297,316,322,331,338,345,367,373,393,401,410,415,460,466,473,476,492,497,521,524,530,543,546,550,557,569,576,586,594,598],"development":[274,298,416,577],"of":[275,282,296,299,307,318,324,340,347,360,370,387,417,432,438,448,459,462,475,496,523,532,534,539,542,545,559,571,578,600,613,616],"students'":[276,463,488],"spatial":[277,341,482],"thinking":[278,584],"through":[279],"integration":[281,558],"linear":[283,423,512],"algebra":[284,424,513],"and":[285,301,321,343,384,396,429,451,456,486,537,561,585,618],"computer":[286,348,427,507,619],"modeling":[287,349,508],"tasks.":[288,514],"The":[289,327,358,389,515,553],"research":[290,596],"is":[291,364,470,518],"relevant":[292],"in":[293,312,372,400,436,502,549,604],"modern":[294],"conditions":[295],"information":[300,591],"communication":[302],"technologies,":[303],"when":[304,505],"traditional":[305,511],"methods":[306,447,564,615],"teaching":[308,563,614],"mathematics":[309,617],"require":[310],"modernization":[311],"order":[313],"increase":[315,487],"efficiency":[317],"material":[319],"assimilation":[320],"formation":[323,339],"critical":[325],"thinking.":[326],"Introduction":[328],"section":[329,391,517],"substantiates":[330],"need":[332],"for":[333,354],"an":[334,418,500],"interdisciplinary":[335,602],"approach":[336],"representations,":[342],"emphasizes":[344],"role":[346,369],"as":[350,409,444,446,582],"a":[351],"visualization":[352],"tool":[353],"complex":[355,548],"abstract":[356],"concepts.":[357],"relevance":[359],"this":[361],"task":[363],"due":[365],"increasing":[368],"ICT":[371],"educational":[374,433,440,551],"process,":[375],"which":[376,607],"makes":[377],"it":[378,469],"possible":[379],"combine":[381],"theoretical":[382,560],"knowledge":[383,485],"practical":[385,540,562],"skills":[386],"students.":[388],"Methods":[390],"describes":[392],"main":[394,411],"experimental":[397],"used":[399,408],"study.":[402],"A":[403],"comparative":[404],"dynamic":[405],"methodology":[406],"was":[407],"analysis":[412,495,522],"tool,":[413],"including":[414,453],"integrated":[419],"learning":[420],"module":[421],"combining":[422],"problems":[425],"with":[426,510,590],"graphics":[428],"visualization.":[430],"Examples":[431],"experiments":[434],"conducted":[435],"classrooms":[437],"higher":[439,605],"institutions":[441],"are":[442],"given,":[443],"well":[445],"data":[449,498],"collection":[450],"analysis,":[452],"both":[454],"quantitative":[455],"qualitative":[457],"assessment":[458],"results":[461,525],"learning.":[464],"In":[465],"\"Results\"":[467],"section,":[468],"reported":[471],"that":[472,556],"application":[474],"developed":[477],"techniques":[478],"helps":[479],"improve":[481],"perception,":[483],"systematize":[484],"motivation":[489],"study":[491],"subject.":[493],"Statistical":[494],"showed":[499],"improvement":[501,612],"academic":[503],"performance":[504],"using":[506],"along":[509],"Discussion":[516],"devoted":[519],"obtained,":[526],"their":[527],"interpretation":[528],"from":[529],"point":[531],"view":[533],"pedagogical":[535],"diagnostics":[536],"discussion":[538],"aspects":[541],"implementation":[544],"process.":[552],"authors":[554],"conclude":[555],"contributes":[565],"not":[566],"only":[567],"deepening":[570],"knowledge,":[572],"but":[573],"also":[574],"key":[579],"competencies":[580],"such":[581],"analytical":[583],"ability":[587],"work":[589],"technology.":[592],"Thus,":[593],"presented":[595],"demonstrates":[597],"prospects":[599],"applying":[601],"education,":[606],"can":[608],"contribute":[609],"further":[611],"science.":[620]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-10-10T00:00:00"}