{"id":39974,"date":"2015-06-04T20:59:00","date_gmt":"2015-06-04T17:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"mathinfocontent032015","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles\/mathinfocontent032015\/","title":{"rendered":"Mathematics and Informatics, Number 3\/2015, Volume 58"},"content":{"rendered":"<p><strong><a name=\"top\"><br \/>&nbsp;<\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e<\/strong><\/p>\n<p>231 <a href=\"#art01\">\u0415\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. \u0421\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438&nbsp; \u043c\u043e\u0434\u0435\u043b. \u041a\u043b\u0430\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f. \u0422\u0435\u043a\u0441\u0442\u043e\u0432\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 <br \/>[Elementary Arithmetic Problems. Structure and Mathematical Model. Classification. Word Problems] <\/a>\/ <br \/><i>\u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430<\/i> \/ <i>Margarita Varbanova, Zdravko Lalchev, Irina Voutova<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p>251 <a href=\"#art02\">\u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u0432 \u0434\u043e\u043c\u0430\u0448\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 <br \/>[Using Formative Assesment in Homework] <\/a>\/ <br \/><i>Borislava Kirilova <\/i>\/ <i>Borislava Kirilova<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p>261 <a href=\"#art03\">Comparative Analysis Regarding the Study of Transformations in the Euclidean Plane by Applying Complex Numbers <\/a>\/ <br \/><i>Katerina Anevska, Sava Grozdev, Risto Malcheski<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL TECHNOLOGY \/ \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><a href=\"#art04\">272 \u041f\u0440\u043e\u0435\u043a\u0442\u043d\u043e \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u0437\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u043d\u0435 \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u043d\u0438 \u0443\u043c\u0435\u043d\u0438\u044f, \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0438 \u0447\u0440\u0435\u0437 \u043e\u0441\u044a\u0449\u0435\u0441\u0442\u0432\u044f\u0432\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 \u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 <br \/>[A Project-Based Approach: the Formation of Computing Skills Through Multidisciplinary Interconnections and the Incorporation of Electronic Devices] <\/a>\/ <br \/><i>\u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432, \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, \u041b\u0430\u043c\u0431\u0440\u0438 \u0419\u043e\u0432\u043a\u043e\u0432<\/i> \/ <i>Kosta Garov, Angel Angelov, Lambri Yovkov<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p>279<a href=\"#art05\">\u041f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0438 \u0435\u0440\u0433\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u043f\u0440\u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0443\u043b\u0442\u0438\u043c\u0435\u0434\u0438\u0439\u043d\u0430 \u0441\u0440\u0435\u0434\u0430 \u0437\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u043d\u0430\u0443\u043a\u0438 <br \/>[Pedagogical and Ergonomic Approach in the Development of Multimedia Learning Environment in Computer Science] <\/a>\/ <br \/><i>\u0415\u0432\u0433\u0435\u043d\u0438\u044f \u0413\u043e\u0440\u0430\u043d\u043e\u0432\u0430 <\/i>\/<i> Evgenia Goranova<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL RESEARCH \/ \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>300 <a href=\"#art06\">\u041c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430<br \/>[Motivational Problems in Teaching Mathematics] <\/a>\/ <br \/><i>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430, \u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430 <\/i>\/ <i>Rumjana Mavrova, PenkaRangelova, Zara Danailova-Stojnova<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p>312 <a href=\"#art07\">\u0412\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u0441\u044a\u0433\u043b\u0430\u0441\u0443\u0432\u0430\u043d\u043e\u0441\u0442 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0441\u0440\u0435\u0434\u043d\u0438\u0442\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0430 \u0438 \u0432\u044a\u0432 \u0432\u0438\u0441\u0448\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u0430 <br \/>[Collaboration Within Mathematics Education in Secondary Schools and in Universities] <\/a>\/ <br \/><i>\u041c\u0430\u0440\u0438\u0430\u043d\u0430 \u0414\u0443\u0440\u0447\u0435\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430<\/i> \/<i> Mariana Durcheva, Elena Varbanova<\/i><\/p>\n<p><i><a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>322\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f <br \/>[Contest Problems of the Issue]<\/p>\n<p>&nbsp;<\/p>\n<p>323\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0431\u0440\u043e\u0439 4, 2014 <br \/>[Solutions of the Contest Problems from issue 4, 2014]<\/p>\n<p>&nbsp;<\/p>\n<p>327READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201c JOURNALS \/ <br \/>\u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/p>\n<p>&nbsp;<\/p>\n<p>329 GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u0415\u041b\u0415\u041c\u0415\u041d\u0422\u0410\u0420\u041d\u0418 \u0410\u0420\u0418\u0422\u041c\u0415\u0422\u0418\u0427\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418. \u0421\u0422\u0420\u0423\u041a\u0422\u0423\u0420\u0410 \u0418 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u041c\u041e\u0414\u0415\u041b. \u041a\u041b\u0410\u0421\u0418\u0424\u0418\u041a\u0410\u0426\u0418\u042f. \u0422\u0415\u041a\u0421\u0422\u041e\u0412\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><i><sup>1)<\/sup><\/i><strong>\u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430&nbsp; \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, <\/strong><i><sup>2)<\/sup><\/i><strong>\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, <\/strong><i><sup>2)<\/sup><\/i><strong>\u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430<\/strong><\/p>\n<p><i><sup>1)<\/sup>St. Cyril and St. Methodius University of Veliko Turnovo<\/i><\/p>\n<p><i><sup>2)<\/sup>Sofia University<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u0441\u044a\u0441\u0440\u0435\u0434\u043e\u0442\u043e\u0447\u0435\u043d\u0430 \u0432\u044a\u0440\u0445\u0443 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438\u0442\u0435 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0417\u0430 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u043d\u0438 \u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0446\u0435\u043b\u0438 \u0435 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0430 \u201e\u0434\u0435\u0444\u0438\u043d\u0438\u0446\u0438\u044f\u201c \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0438 \u0435 \u0432\u044a\u0432\u0435\u0434\u0435\u043d\u0430 \u043a\u0430\u0442\u0435\u0433\u043e\u0440\u0438\u044f\u0442\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u0442\u0430 \u043d\u0430 \u201e\u0441\u043f\u0438\u0441\u044a\u043a\u201c \u043e\u0442 12 \u0432\u0438\u0434\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d\u0430 \u043b\u043e\u0433\u0438\u043a\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u043a\u043b\u0430\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f \u043d\u0430 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0432 \u043a\u043e\u044f\u0442\u043e \u0441\u0430 \u043e\u0431\u0445\u0432\u0430\u043d\u0430\u0442\u0438 24 \u043a\u043b\u0430\u0441\u0430. \u0412\u0441\u0435\u043a\u0438 \u043a\u043b\u0430\u0441 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0447\u0440\u0435\u0437 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u0435\u043d \u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u043a\u043e\u0439\u0442\u043e \u0441\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u0438\u0442\u0435 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0432 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u043e. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u043e\u0442\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u0438\u0432\u0438\u0441\u0442\u043a\u0438 \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430 \u043f\u044a\u0440\u0432\u0438 \u0435\u0442\u0430\u043f \u043e\u0442 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043f\u043e \u0442\u0435\u043c\u0430\u0442\u0430 \u201e\u0410\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u201c.<\/p>\n<p><i>Keywords:<\/i> primary school mathematics, elementary arithmetic problem, structural model, mathematical model, arithmetical equation, arithmetical transformation<\/p>\n<p>&nbsp;<\/p>\n<p><strong>ELEMENTARY ARITHMETIC PROBLEMS. STRUCTURE AND MATHEMATICAL MODEL. CLASSIFICATION. WORD PROBLEMS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>The development is focused on the elementary arithmetic problems in primary school mathematics. For theoretical and practical purposes is suggested \u201ea definition\u201c of an elementary arithmetical problem and category structure of the problem is introduced. Based on \u201ea list\u201c of 12 kinds is developed logic-mathematical classification of elementary arithmetic problems in which included 24 categories. Each category is represented through an examples in which structural and mathematical models of the problems are shown. Mathematical and practical problems are considered as unity. The approach of constructivism in mathematical education in reflected in the development and it s the first stage of a research on \u201eArithmetic Problems in Primary School Mathematics\u201c.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Dr. Margarita Varbanova<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of Veliko Tarnovo<\/p>\n<p>Veliko Tarnovo, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Dr. Zdravko Lalchev<\/strong><\/p>\n<p>Faculty of Preschool and Primary Education<\/p>\n<p>University of Sofia<\/p>\n<p>&nbsp;Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Irina Voutova, Assist. Prof.<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of Sofia<\/p>\n<p>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art02\">&nbsp;<\/a> \u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0424\u041e\u0420\u041c\u0410\u0422\u0418\u0412\u041d\u041e \u041e\u0426\u0415\u041d\u042f\u0412\u0410\u041d\u0415 \u0412 \u0414\u041e\u041c\u0410\u0428\u041d\u0410\u0422\u0410 \u0420\u0410\u0411\u041e\u0422\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Borislava Kirilova<\/strong><\/p>\n<p><i>\u0410\u043c\u0435\u0440\u0438\u043a\u0430\u043d\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u0421\u043e\u0444\u0438\u044f<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0432\u044a\u043f\u0440\u043e\u0441\u0430 \u043a\u0430\u043a \u0434\u0430 \u0441\u0435 \u043f\u043e\u0434\u0431\u0435\u0440\u0430\u0442 \u043f\u0440\u0430\u0432\u0438\u043b\u043d\u043e \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u0434\u043e\u043c\u0430\u0448\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0438 \u0434\u0430\u043b\u0438 \u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0442\u0435 \u043e\u0442 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u043a\u044a\u0449\u0438 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0438 \u0432\u0441\u0435\u043a\u0438 \u0443\u0447\u0435\u0431\u0435\u043d \u0447\u0430\u0441. \u0427\u0430\u0441\u0442 \u043e\u0442 \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442\u0435 \u043a\u044a\u043c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0441\u0430 \u0434\u043e\u0431\u0440\u0435 \u043f\u043e\u0437\u043d\u0430\u0442\u0438 \u043d\u0430 \u0443\u0447\u0438\u0442\u0435\u043b\u0438\u0442\u0435 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f \u0438 \u0441\u0435 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u0442 \u043e\u0442 \u0442\u044f\u0445. \u0412\u044a\u0437\u043c\u043e\u0436\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u0435 \u0438 \u0442. \u043d\u0430\u0440. \u0424\u043e\u0440\u043c\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 (\u0424\u041e) \u2013 \u043e\u0442 \u0430\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u043e\u0442\u043e Formative Assessment, \u0432\u043d\u0435\u0434\u0440\u0435\u043d \u043e\u0442 \u0434\u043e\u043a\u0430\u0437\u0430\u043b\u0430\u0442\u0430 \u0441\u0435 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0446\u0438\u044f International Baccalaureate Organization \u0438 \u043f\u043e\u043b\u0437\u0432\u0430\u0449 \u0441\u0435 \u0441 \u043d\u0430\u0440\u0430\u0441\u0442\u0432\u0430\u0449\u0430 \u043f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u043e\u0441\u0442 \u0443 \u043d\u0430\u0441. \u0412\u044a\u0432 \u0432\u0440\u044a\u0437\u043a\u0430 \u0441 \u043d\u0435\u0433\u043e \u0432 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u0438 \u043d\u044f\u043a\u043e\u0438 \u043d\u043e\u0432\u0438 \u0442\u0435\u0445\u043d\u0438\u043a\u0438 \u0438 \u0438\u0434\u0435\u0438, \u043a\u043e\u0438\u0442\u043e \u043f\u043e\u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0435\u043c \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0442 \u043e\u0441\u043d\u043e\u0432\u043d\u043e \u0438\u0437\u0432\u044a\u043d \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0430\u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435.<\/p>\n<p><i>Keywords: <\/i>formative assessment, summative assessment, homework, IBO, quadratic function, grading, teaching<\/p>\n<p>&nbsp;<\/p>\n<p><strong>USING FORMATIVE ASSESSMENT IN HOMEWORK<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>Th\u0435 present paper is dedicated to the question of how homework tasks should be chosen correctly and whether the student solutions at home should be graded in class. A part of the approaches are well-known to Bulgarian teachers and are applied by them. A possible approach is by the so called Formative Assessment, introduced by the already recognized international educational institution \u2013 the International Baccalaureate Organization, which gains an increasing popularity in Bulgaria. In this connection the paper includes some new techniques and ideas, which are basically used outside the Bulgarian educational system at present.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mrs. Borislava Kirilova<\/strong><\/p>\n<p>Teacher in Mathematics,<\/p>\n<p>American College of Sofia<\/p>\n<p>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art03\">&nbsp;<\/a>COMPARATIVE ANALYSIS REGARDING THE STUDY OF TRANSFORMATIONS IN THE EUCLIDEAN PLANE BY APPLYING COMPLEX NUMBERS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><sup>1)<\/sup>Katerina Anevska, <sup>2)<\/sup>Sava Grozdev,<sup> 3)<\/sup>Risto Malcheski<\/p>\n<p><i><sup>1), 3)<\/sup>FON University<\/i><\/p>\n<p><i><sup>2)<\/sup>Institute of Mathematics and Informatics \u2013 BAS<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>Adopting transformations in the Euclidean plane and their application is compulsory for high school students. The practice shows that even advanced students face difficulties when learning such a material, especially the part which refers to group properties. On the other hand, complex numbers are also studied in high school and they are characterized by an analytical apparatus which helps learning the transformations in the Euclidean plane. This paper presents results from a comparative analysis referring to the accomplishments of the students who study transformations in the Euclidean plane and their application by using complex numbers (see (Malcheski et al., 2015)) and in the classical way (see (Mitrovi\u0107 et al., 1998)).<\/p>\n<p><i>Keywords: <\/i>complex number, transformation, test, assessment<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mrs. Katerina Anevska<\/strong><\/p>\n<p>Faculty for Informatics \u2013 FON University<\/p>\n<p>Skopje, Macedonia<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<\/strong><\/p>\n<p>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p>&nbsp;Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Risto Malcheski, DSc<\/strong><\/p>\n<p>Faculty for Informatics \u2013 FON University<\/p>\n<p>Skopje, Macedonia<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art04\">&nbsp;<\/a> \u041f\u0420\u041e\u0415\u041a\u0422\u041d\u041e \u0411\u0410\u0417\u0418\u0420\u0410\u041d\u0418 \u041f\u041e\u0414\u0425\u041e\u0414\u0418 \u0417\u0410 \u0424\u041e\u0420\u041c\u0418\u0420\u0410\u041d\u0415 \u0418 \u0420\u0410\u0417\u0412\u0418\u0412\u0410\u041d\u0415 \u041d\u0410 \u0418\u0417\u0427\u0418\u0421\u041b\u0418\u0422\u0415\u041b\u041d\u0418 \u0423\u041c\u0415\u041d\u0418\u042f, \u0420\u0415\u0410\u041b\u0418\u0417\u0418\u0420\u0410\u041d\u0418 \u0427\u0420\u0415\u0417 \u041e\u0421\u042a\u0429\u0415\u0421\u0422\u0412\u042f\u0412\u0410\u041d\u0415 \u041d\u0410 \u041c\u0415\u0416\u0414\u0423\u041f\u0420\u0415\u0414\u041c\u0415\u0422\u041d\u0418 \u0412\u0420\u042a\u0417\u041a\u0418 \u0418 \u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u0418 \u0421\u0420\u0415\u0414\u0421\u0422\u0412\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong><sup>1)<\/sup>\u041a\u043e\u0441\u0442\u0430&nbsp; \u0413\u044a\u0440\u043e\u0432, <sup>2)<\/sup>\u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, <sup>3)<\/sup>Lambri Yovkov<\/strong><\/p>\n<p><i><sup>1),3)<\/sup>\u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438&nbsp; \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u041f\u0430\u0438\u0441\u0438\u0439 \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438\u201c<\/i><\/p>\n<p><i><sup>2)<\/sup>\u0421\u041e\u0423 \u201e\u0421\u0430\u0432\u0430 \u0414\u043e\u0431\u0440\u043e\u043f\u043b\u043e\u0434\u043d\u0438\u201c \u2013 \u0428\u0443\u043c\u0435\u043d<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0434\u0430\u0432\u0430\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0438 \u043d\u0430\u0441\u043e\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u043d\u043e \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u043d\u043e \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\u0438 \u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0437\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438. \u041f\u043e\u0441\u043e\u0447\u0432\u0430 \u0441\u0435 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0442\u0430 \u0437\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u043b\u0430\u0447\u043d\u0438 \u0443\u0441\u043b\u0443\u0433\u0438 \u0438 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0438 \u0437\u0430 \u0442\u0430\u0437\u0438 \u0446\u0435\u043b.<\/p>\n<p><i>Keywords:<\/i> project-based learning, cloud service, cloud computing, tablet, mobile<\/p>\n<p>&nbsp;<\/p>\n<p><strong>A PROJECT-BASED APPROACH: THE FORMATION OF COMPUTING SKILLS THROUGH MULTIDISCIPLINARY INTERCONNECTIONS AND THE INCORPORATION OF ELECTRONIC DEVICES<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>The paper proposes a methodology, which provides, examples and guidelines for a project \u2013 based approach in education. It explores the possibilities for using Cloud Computing technology for achieving educative goals. Some popular Cloud platforms are illustrated in this paper.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Dr. Kosta Garov<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>Plovdiv University \u201cPaisii Hilendarski\u201d<\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mr. Angel Angelov<\/strong><\/p>\n<p>Teacher in Informatics and IT<\/p>\n<p>&nbsp;Shumen, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mr. Lambri Yovkov<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>Plovdiv University \u201cPaisii Hilendarski\u201d<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<hr \/>\n<p><strong><a name=\"art05\">&nbsp;<\/a>\u041f\u0415\u0414\u0410\u0413\u041e\u0413\u0418\u0427\u0415\u0421\u041a\u0418 \u0418 \u0415\u0420\u0413\u041e\u041d\u041e\u041c\u0418\u0427\u0415\u041d \u041f\u041e\u0414\u0425\u041e\u0414 \u041f\u0420\u0418 \u0420\u0410\u0417\u0420\u0410\u0411\u041e\u0422\u0412\u0410\u041d\u0415 \u041d\u0410 \u041c\u0423\u041b\u0422\u0418\u041c\u0415\u0414\u0418\u0419\u041d\u0410 \u0421\u0420\u0415\u0414\u0410 \u0417\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u041f\u041e \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0418 \u041d\u0410\u0423\u041a\u0418<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0415\u0432\u0433\u0435\u043d\u0438\u044f \u0413\u043e\u0440\u0430\u043d\u043e\u0432\u0430<\/strong><\/p>\n<p><i>\u0420\u0443\u0441\u0435\u043d\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u0410\u043d\u0433\u0435\u043b \u041a\u044a\u043d\u0447\u0435\u0432\u201c, \u0424\u0438\u043b\u0438\u0430\u043b \u0421\u0438\u043b\u0438\u0441\u0442\u0440\u0430<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0438 \u0435\u0440\u0433\u043e\u043d\u043e\u043c\u0438\u0447\u043d\u0438 \u0441\u044a\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438 \u043f\u0440\u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0443\u043b\u0442\u0438\u043c\u0435\u0434\u0438\u0439\u043d\u0430 \u0441\u0440\u0435\u0434\u0430 \u0437\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u043f\u043e \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u043d\u0430\u0443\u043a\u0438. \u041f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u0441\u044a\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043a\u0430\u0441\u0430\u044f\u0442 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043f\u0441\u0445\u0438\u043e\u043b\u043e\u0433\u043e-\u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u0442\u0435\u043e\u0440\u0438\u0438 \u0437\u0430 \u0443\u0447\u0435\u043d\u0435 \u2013 \u0431\u0438\u0445\u0435\u0432\u0438\u043e\u0440\u0438\u0437\u044a\u043c, \u043a\u043e\u0433\u043d\u0438\u0442\u0438\u0432\u0438\u0437\u044a\u043c, \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u0438\u0432\u0438\u0437\u044a\u043c, \u0438 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0435\u0442\u0430\u043f\u0438 \u043d\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u0430\u043a\u0442 \u2013 \u0441\u044a\u0437\u0435\u0440\u0446\u0430\u043d\u0438\u0435, \u043c\u0438\u0441\u043b\u0435\u043d\u0435, \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430. \u041a\u0430\u0442\u043e \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u0435\u043d \u043f\u0440\u043e\u0434\u0443\u043a\u0442, \u043c\u0443\u043b\u0442\u0438\u043c\u0435\u0434\u0438\u0439\u043d\u0430\u0442\u0430 \u0441\u0440\u0435\u0434\u0430 \u043e\u0441\u0438\u0433\u0443\u0440\u044f\u0432\u0430 \u043f\u043e\u0441\u0442\u0438\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0435\u043d\u0438\u0442\u0435 \u0435\u0440\u0433\u043e\u043d\u043e\u043c\u0438\u0447\u043d\u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438 \u0437\u0430 \u0447\u043e\u0432\u0435\u043a\u043e-\u043c\u0430\u0448\u0438\u043d\u0435\u043d \u0438\u043d\u0442\u0435\u0440\u0444\u0435\u0439\u0441, \u043e\u0431\u043e\u0441\u043e\u0431\u0435\u043d\u0438 \u043a\u0430\u0442\u043e \u043e\u0431\u0449\u0430 \u0438 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0430 \u043f\u043e\u043b\u0437\u0432\u0430\u0435\u043c\u043e\u0441\u0442.<\/p>\n<p><i>Keywords: <\/i>multimedia learning environment, behaviorism, cognitivism, constructivism, cognitive act, human computer interface, usability<\/p>\n<p>&nbsp;<\/p>\n<p><strong>PEDAGOGICAL AND ERGONOMIC APPROACH IN THE DEVELOPMENT OF MULTIMEDIA LEARNING ENVIRONMENT IN COMPUTER SCIENCE<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>The article presents pedagogical and ergonomic considerations at developing multimedia learning environment for students in computer sciences. Pedagogical considerations concern the application of psycho-pedagogical theories of learning \u2013 behaviorism, cognitivism, constructivism and traditional stages of cognitive act \u2013 contemplation, thinking, practice. As a software product the multimedia environment provides the achievement of the established ergonomic standards for Human Computer Interface, specified as general usability and pedagogical usability.<\/p>\n<p><strong>Dr. Evgenia Goranova, Assist. Prof.<\/strong><\/p>\n<p>University of Russe<\/p>\n<p>Silistra Branch<\/p>\n<p>Silistra, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art06\">&nbsp;<\/a>\u041c\u041e\u0422\u0418\u0412\u0410\u0426\u0418\u041e\u041d\u041d\u0418\u0422\u0415 \u0417\u0410\u0414\u0410\u0427\u0418 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong><sup>1)<\/sup>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, <sup>1)<\/sup>\u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430, <sup>2)<\/sup>\u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430<\/strong><\/p>\n<p><strong><i><sup>1)<\/sup><\/i><\/strong><i>University of Plovdiv \u201cPaisii Hilendarski\u201d<\/i><\/p>\n<p><strong><i><sup>2)<\/sup><\/i><\/strong><i>\u0420\u0435\u0433\u0438\u043e\u043d\u0430\u043b\u0435\u043d \u0438\u043d\u0441\u043f\u0435\u043a\u0442\u043e\u0440\u0430\u0442 \u043f\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u0441\u043f\u043e\u0434\u0435\u043b\u0435\u043d \u043e\u043f\u0438\u0442 \u0437\u0430 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0410\u043a\u0446\u0435\u043d\u0442\u044a\u0442 \u0435 \u043f\u043e\u0441\u0442\u0430\u0432\u0435\u043d \u043d\u0430 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u0434\u043e\u043f\u0440\u0438\u043d\u0430\u0441\u044f\u0449\u0438 \u0437\u0430 \u043f\u0440\u043e\u043c\u044f\u043d\u0430 \u043d\u0430 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043a\u044a\u043c \u043f\u0440\u0435\u0434\u043c\u0435\u0442\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.<\/p>\n<p><i>Keywords: <\/i>motivation, interest, motivational problems<\/p>\n<p>&nbsp;<\/p>\n<p><strong>MOTIVATIONAL PROBLEMS IN TEACHING MATHEMATICS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>In the current article an attempt for increasing the students\u2018 motivation in the Mathematics education is presented. It is emphasized on the motivation problems contributing to a positive change in the students\u201a attitude towards Mathematics as a subject.<\/p>\n<p>&nbsp;<\/p>\n<p><strong><sup>1) <\/sup>Dr. Rumjana Mavrova, Assoc. Prof.<\/strong><\/p>\n<p><strong><sup>2) <\/sup>Dr. Penka Rangelova, Assoc. Prof.<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of Plovdiv<\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<p>E-mail: <sup>1) <\/sup><a href=\"mailto:rummav@abv.bg\">rummav@abv.bg<\/a> <sup>2) <\/sup><a href=\"mailto:rangelova_penka@abv.bg\">rangelova_penka@abv.bg<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mrs. Zara Danailova-Stojnova<\/strong><\/p>\n<p>Senior expert of mathematics<\/p>\n<p>Regional Inspectorate of Education<\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art07\">&nbsp;<\/a>\u0412\u042a\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0418 \u0417\u0410 \u0421\u042a\u0413\u041b\u0410\u0421\u0423\u0412\u0410\u041d\u041e\u0421\u0422 \u041d\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0412 \u0421\u0420\u0415\u0414\u041d\u0418\u0422\u0415 \u0423\u0427\u0418\u041b\u0418\u0429\u0410 \u0418 \u0412\u042a\u0412 \u0412\u0418\u0421\u0428\u0418 \u0423\u0427\u0418\u041b\u0418\u0429\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041c\u0430\u0440\u0438\u0430\u043d\u0430 \u0414\u0443\u0440\u0447\u0435\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430<\/strong><\/p>\n<p><i>Technical university \u2013 Sofia<\/i><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u0442\u0430\u0446\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u043d\u043e \u0440\u0430\u0432\u043d\u0438\u0449\u0435\u0442\u043e \u043d\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430\u0442\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043d\u0430 \u0437\u0430\u0432\u044a\u0440\u0448\u0438\u043b\u0438\u0442\u0435 \u0441\u0440\u0435\u0434\u043d\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u0430, \u043a\u043e\u0438\u0442\u043e \u043f\u043e\u0441\u0442\u044a\u043f\u0432\u0430\u0442 \u0432\u044a\u0432 \u0432\u0438\u0441\u0448\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u0430 \u0441\u044a\u0441 \u0438\u043b\u0438 \u0431\u0435\u0437 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u0435\u043d \u0438\u0437\u043f\u0438\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0430 \u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0442\u0430 \u043e\u0442 \u0441\u044a\u0442\u0440\u0443\u0434\u043d\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043c\u0435\u0436\u0434\u0443 \u0442\u0435\u0437\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u0430 \u0441 \u0446\u0435\u043b \u043f\u043e-\u0434\u043e\u0431\u0440\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043d\u0430 \u0431\u044a\u0434\u0435\u0449\u0438\u0442\u0435 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u0441\u044a\u0432\u043c\u0435\u0441\u0442\u043d\u0438 \u0434\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438 \u0443\u0447\u0435\u0431\u043d\u0438 \u0442\u0435\u043c\u0438, \u043f\u043e\u0434\u043a\u0440\u0435\u043f\u0435\u043d\u0438 \u0441 \u0433\u0440\u0430\u0444\u0438\u0447\u043d\u0438 \u0438\u043b\u044e\u0441\u0442\u0440\u0430\u0446\u0438\u0438 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. \u0418\u043c\u043f\u043b\u0438\u0446\u0438\u0442\u043d\u043e \u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u0441\u044a\u0447\u0435\u0442\u0430\u043d\u043e \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u0438 \u0438 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e-\u043f\u043e\u0434\u043f\u043e\u043c\u043e\u0433\u043d\u0430\u0442\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u043d\u043e \u043a\u0430\u0442\u043e \u0442\u0440\u0438\u0435\u0434\u0438\u043d\u0441\u0442\u0432\u043e \u201e\u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u2013 \u0443\u0447\u0435\u043d\u0435 \u2013 \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 (\u043e\u0431\u0440\u0430\u0442\u043d\u0430 \u0432\u0440\u044a\u0437\u043a\u0430)\u201c.<\/p>\n<p><i>Keywords: <\/i>secondary school, university, mathematics education, collaboration, computer-supported mathematics education<\/p>\n<p>&nbsp;<\/p>\n<p><strong>COLLABORATION WITHIN MATHEMATICS EDUCATION IN SECONDARY SCHOOLS AND IN UNIVERSITIES<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract. <\/strong>Students\u2018 preparation in mathematics at secondary school is discussed. It determines pupils\u2019 results in entry exams on mathematics and the difficulties they meet later in the learning of undergraduate mathematics. A reasoned opinion about the necessity of collaborative work of mathematics teachers at secondary schools and universities is expressed. Three suitable topics for joint activities are pointed out. Graphic illustrations and sample tasks are given. A combined use of classic and computer-supported approaches in mathematics education viewed as trinity \u201cteaching-learning-assessment\u201d is mentioned as well.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Mariana Durcheva, Assoc. Prof.<\/strong><\/p>\n<p>Faculty of Applied Mathematics and Informatics<\/p>\n<p>Technical University of Sofia<\/p>\n<p>Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Dr. Elena Varbanova, Assoc.Prof.<\/strong><\/p>\n<p>Faculty of Applied Mathematics and Informatics<\/p>\n<p>Technical University of Sofia<\/p>\n<p>Sofia, Bulgaria<strong>&nbsp;<\/strong><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>","protected":false},"excerpt":{"rendered":"<p>&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e 231 \u0415\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. \u0421\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438&nbsp; \u043c\u043e\u0434\u0435\u043b. \u041a\u043b\u0430\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f. \u0422\u0435\u043a\u0441\u0442\u043e\u0432\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 [Elementary Arithmetic Problems. Structure and Mathematical Model. Classification. Word Problems] \/ \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Margarita Varbanova, Zdravko Lalchev, Irina Voutova &nbsp; 251 \u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u0432 \u0434\u043e\u043c\u0430\u0448\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 [Using [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[2882],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e 231 \u0415\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. \u0421\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438&nbsp; \u043c\u043e\u0434\u0435\u043b. \u041a\u043b\u0430\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f. \u0422\u0435\u043a\u0441\u0442\u043e\u0432\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 [Elementary Arithmetic Problems. Structure and Mathematical Model. Classification. Word Problems] \/ \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Margarita Varbanova, Zdravko Lalchev, Irina Voutova &nbsp; 251 \u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u0432 \u0434\u043e\u043c\u0430\u0448\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 [Using [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2015-06-04T17:59:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-24T14:33:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\"},\"author\":{\"name\":\"\",\"@id\":\"\"},\"headline\":\"&#8222;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&#8220;, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015\",\"datePublished\":\"2015-06-04T17:59:00+00:00\",\"dateModified\":\"2019-06-24T14:33:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\"},\"wordCount\":2025,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"articleSection\":[\"\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043f. \\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\"\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\",\"url\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/mathinfocontent032015\/\",\"name\":\"\\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\", \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015 - 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