{"id":173182,"date":"2025-12-05T15:49:17","date_gmt":"2025-12-05T13:49:17","guid":{"rendered":"https:\/\/azbuki.bg\/?p=173182"},"modified":"2025-12-05T15:49:17","modified_gmt":"2025-12-05T13:49:17","slug":"godishno-sadarzhanie-na-nauchno-spisanie-matematika-i-informatika-godina-lxviii-2025","status":"publish","type":"post","link":"https:\/\/foreignlanguages.azbuki.bg\/en\/matematics\/sadarzhanie-na-sp-matematika-i-informatika-2025-g\/godishno-sadarzhanie-na-nauchno-spisanie-matematika-i-informatika-godina-lxviii-2025\/","title":{"rendered":"\u0413\u043e\u0434\u0438\u0448\u043d\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043d\u0430 \u043d\u0430\u0443\u0447\u043d\u043e \u0441\u043f\u0438\u0441\u0430\u043d\u0438\u0435 &#8222;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&#8220;, \u0433\u043e\u0434\u0438\u043d\u0430 LXVIII, 2025"},"content":{"rendered":"<p style=\"text-align: center;\"><strong>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0418 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>\u041d\u0410\u0423\u0427\u041d\u041e \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>\u0413\u041e\u0414\u0418\u041d\u0410 LXVIII, 2025<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>MATHEMATICS AND INFORMATICS<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>\u00a0BULGARIAN JOURNAL OF EDUCATIONAL RESEARCH AND PRACTICE<\/strong><\/p>\n<p style=\"text-align: center;\">VOLUME 68, 2025<\/p>\n<p>ANNUAL CONTENT 2025 \/ \u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 2025<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 1: 9 \u2013 109<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 2: 125 \u2013 221<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 3: 237 \u2013 348<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 4: 359 \u2013 484<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 5: 359 \u2013 480<\/p>\n<p>\u041a\u043d\u0438\u0436\u043a\u0430 6:<\/p>\n<p><strong>SCIENC<\/strong><strong>\u0415 <\/strong><strong>IN<\/strong> <strong>EDUCATION<\/strong><strong> \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><\/p>\n<p>9 \u2013 17\u00a0 Applying Delaunay Triangulation in Olympiad Problems \/ <em>Dragomir Grozev, Nevena Sybeva<\/em><\/p>\n<p>18 \u2013 34\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A Note on a Generalized Dynamical System occurs in modelling \u2018The Battle of the sexes\u2019: Chaos in Sociobiology \/ <em>Nikolay Kyurkchiev, Anton Iliev, Vesselin Kyurkchiev, Angel Golev,<\/em> <em>Todorka Terzieva, Asen Rahnev<\/em><\/p>\n<p><em>\u00a0<\/em><\/p>\n<p>35 \u2013 50\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apollonian Sphere and Properties of Stereographic Projection around the Lemoine Point \/ <em>Vladislav Natchev<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>125 \u2013 140\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0415\u0434\u043d\u0430 \u043a\u0440\u0430\u0442\u043a\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0437\u0430 \u043b\u0438\u0446\u0435 \u043d\u0430 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0441 \u0434\u0432\u0435 \u0440\u0430\u0432\u043d\u0438 \u0441\u0440\u0435\u0449\u0443\u043f\u043e\u043b\u043e\u0436\u043d\u0438 \u0441\u0442\u0440\u0430\u043d\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u045d [A Short Formula for the Area of a Quadrilateral with Two Equal Opposite Sides and it\u2019s Application] \/ <em>\u0419\u043e\u0440\u0434\u0430\u043d \u0422\u0430\u0431\u043e\u0432, \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432, \u0414\u043e\u0431\u0440\u0438\u043d\u043a\u0430 \u041c\u0438\u043b\u0443\u0448\u0435\u0432\u0430-\u0411\u043e\u0439\u043a\u0438\u043d\u0430 \/ <\/em><em>Yordan Tabov, Stanislav Stefanov, Haim Haimov, Dobrinka Milusheva-Boykina<\/em><\/p>\n<p>237 \u2013 256\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u0432 \u043e\u043b\u0438\u043c\u043f\u0438\u0439\u0441\u043a\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 [Models of Sample Spaces in Olympiad Problems] \/ <em>\u0414\u0440\u0430\u0433\u043e\u043c\u0438\u0440 \u0413\u0440\u043e\u0437\u0435\u0432, \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0425\u0430\u0440\u0438\u0437\u0430\u043d\u043e\u0432 \/ <\/em><em>Dragomir Grozev, Stanislav Harizanov<\/em><\/p>\n<p>365 \u2013 373\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A Generalization of the Collinearity of the Stereographic Projection around the Lemoine Point \/ <em>Vladislav Natchev<\/em><\/p>\n<p>374 \u2013 407\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u0437\u0430 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0447\u0438\u0441\u043b\u043e\u0432\u0438\u0442\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 [Competency Models for studying Numerical Sets] \/ <em>\u0414\u0435\u0441\u0438\u0441\u043b\u0430\u0432\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0432\u0430 \u00a0\/ <\/em><em>Desislava Georgieva<\/em><\/p>\n<p>408 \u2013 421\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0423\u0441\u044a\u0432\u044a\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043e\u0442 \u0442\u0440\u0435\u0442\u0438 \u043a\u043b\u0430\u0441 \u0447\u0440\u0435\u0437 \u043f\u0440\u043e\u0435\u043a\u0442\u043d\u043e \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u0430 \u0434\u0435\u0439\u043d\u043e\u0441\u0442 [Improving Students\u2019 Mathematical Competences through Project-based Learning Activities] \/ <em>\u0412\u0435\u0440\u0438\u0446\u0430 \u0410\u0440\u0441\u043e\u0432 \/ Veritsa Arsov<\/em><\/p>\n<p>365 \u2013 380\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Nonparametric Maximum Likelihood Estimation in branching Processes with Random Migration \/ <em>Tsvetomira Zlatkova, Vessela Stoimenova<\/em><\/p>\n<p>381 \u2013 410\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Exploring Pick\u2019s Theorem in the Classroom: A Comparison between Traditional and Digital Methodologies using Picksolver Software \/ <em>Ruben Molano, Mar Avila, Jose Carlos Sancho, Pablo G. Rodriguez, Andres Caro<\/em><\/p>\n<p>411 \u2013 423\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0421\u0435\u043b\u0435\u043a\u0446\u0438\u044f \u043d\u0430 \u043e\u0442\u0431\u043e\u0440\u0430 \u043d\u0430 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f \u0437\u0430 \u0434\u0432\u0430\u0434\u0435\u0441\u0435\u0442 \u0438 \u0434\u0435\u0432\u0435\u0442\u0430\u0442\u0430 \u041c\u043b\u0430\u0434\u0435\u0436\u043a\u0430 \u0411\u0430\u043b\u043a\u0430\u043d\u0441\u043a\u0430 \u041e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Selection of the Bulgarian Team for the Twenty-Ninth Junior Balkan Mathematical Olympiad] \/ <em>\u041c\u0438\u0440\u043e\u0441\u043b\u0430\u0432 \u041c\u0430\u0440\u0438\u043d\u043e\u0432, \u0418\u0432\u0430\u0439\u043b\u043e \u041a\u043e\u0440\u0442\u0435\u0437\u043e\u0432 \/ <\/em><em>Miroslav Marinov, Ivaylo Kortezov<\/em><\/p>\n<p>??? \u2013 ???\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enhancing Student Motivation and Achievement through Digital Mind Mapping \/ <em>Miklos Kovac, Mirjana Brdar, Goran Radojev, Radivoje Stojkovic<\/em><\/p>\n<p>??? \u2013 ???\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Application of Python in Data Forecasting using Sarima Models \/ <em>Vesela Dimitrova<\/em><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL TECHNOLOGIES \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong><\/p>\n<p>51 \u2013 62\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Educational Resources for Studying Midsegment of Triangle and Trapezoid \/ <em>Toni Chehlarova,<\/em> <em>Neda Chehlarova,<\/em> <em>Georgi Gachev<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>63 \u2013 73\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Digital Competency Self-assessment of Computer Science Teachers in Bulgarian Secondary Schools \/ <em>Ivaylo Staribratov, Muharem Mollov<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>74 \u2013 95\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Utilizing Geographical Information System for Mapping Schools Distribution. Case Study: the 4th Lower Secondary in Florina City, Greece \/ <em>Ilias Solakis, Irena Atanasova<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>96 \u2013 109\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Addressing Data Literacy in Information Systems Education \/ <em>Kalinka Kaloyanova<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>141 \u2013 155\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Artificial Intelligence \u2013 Assisted Learning in Moodle \/ <em>Maria Gorgorova, Silvia Gaftandzhieva, Stanka Hadzhikoleva<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>156 \u2013 169\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432 \u0438\u0437\u0440\u0430\u0432\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0445\u0438\u043c\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f [Application of Systems of Linear Equations in balancing Chemical Equations] \/ <em>\u0426\u0432\u0435\u0442\u0435\u043b\u0438\u043d\u0430 \u041f\u0435\u0435\u0432\u0430 \/ <\/em><em>Tsvetelina Peeva<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>257 \u2013 283\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statistical Analysis of Academic Achievement and Intrinsic Motivation in Stem Students educated through a Competency-based Approach \/ <em>Muharem Mollov, Dimitar Stoitsov, Gencho Stoitsov<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>284 \u2013 301\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041f\u0440\u0438\u043c\u0435\u0440\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u0437\u043a\u0443\u0441\u0442\u0432\u0435\u043d \u0438\u043d\u0442\u0435\u043b\u0435\u043a\u0442 \u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u043d\u0430 \u0434\u0435\u0439\u043d\u043e\u0441\u0442 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [A Model Approach to the Application of Artificial Intelligence and Project-based Method in Mathematics Education\/ <em>\u0418\u0432\u0435\u043b\u0438\u043d\u0430 \u0412\u0435\u043b\u0447\u0435\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u041a\u0430\u0440\u0442\u0430\u043b\u0435\u0432\u0430 \/ <\/em><em>Ivelina Velcheva, Irina Kartaleva<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>302 \u2013 314\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u044a\u0440\u0445\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0438 \u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438 \u043c\u0440\u0435\u0436\u0438 \u0441\u044a\u0441 \u0421\u0442\u0440\u0443\u043d\u0438\u043c\u0430 \u0438 Geogebra [Combinatorial Problems using Square and Triangular Grids with Strunima and Geogebra] \/ <em>\u041c\u043b\u0430\u0434\u0435\u043d \u0412\u044a\u043b\u043a\u043e\u0432 \/ Mladen Valkov<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>422 \u2013 433\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Educational Resources with Percentages for the Development of the Visual Estimation \/ <em>Toni Chehlarova<\/em><\/p>\n<p>434 \u2013 450\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The Impact of Using GeoGebra on Understanding Quadratic Functions and Equations for Tenth-Grade Students \/ <em>Er\u00ebmir\u00eb R. Aliu, Shp\u00ebtim Rexhepi, Egzona Iseni<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>451 \u2013 474\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Bridging the Gap: a Pedagogical Tool for teaching Mathematical Modeling with Spreadsheets \/ <em>D\u00e1vid Paksi, M\u00e1rk Cs\u00f3ka, Szil\u00e1rd Svitek<\/em><\/p>\n<p>424 \u2013 440\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0418\u043d\u0444\u0440\u0430\u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u043d\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0447\u0430\u0442\u0431\u043e\u0442 \u0441 \u0433\u043e\u043b\u0435\u043c\u0438 \u0435\u0437\u0438\u043a\u043e\u0432\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u0438 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u043d\u043e \u0440\u0430\u0437\u0448\u0438\u0440\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438\u0442\u0435 [Infrastructure for deploying large Language Models in Chatbots with Retrieval AI-Augmented Generation] \/ <em>\u0419\u043e\u0440\u0434\u0430\u043d \u041a\u0440\u0430\u043b\u0435\u0432 <\/em><em>\/ Jordan Kralev<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>441 \u2013 455\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The Pythagorean Tree with Geogebra as a Motivator for the Implementation of augmented Reality in School \/ <em>Koya Chehlarova, Toni Chehlarova<\/em><\/p>\n<p>??? \u2013 ???\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u0432 \u043c\u044a\u0440\u0432\u0438 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u0430\u043b\u0435\u043d \u0435\u0442\u0430\u043f: \u0418\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u043c\u0435\u0436\u0434\u0443\u043f\u0440\u0435\u0434\u043c\u0435\u0442\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, 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