{"id":38292,"date":"2013-06-17T20:59:00","date_gmt":"2013-06-17T17:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfo03-2013\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"mathinfo03-2013","status":"publish","type":"post","link":"https:\/\/science.azbuki.bg\/en\/matematics\/matharticles\/mathinfo03-2013\/","title":{"rendered":"Mathematics and Informatics, Number 3\/2013, Volume 56"},"content":{"rendered":"<p><strong>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS<\/strong><\/p>\n<p>70th anniversary - Academician Kenderov<br \/>Yu. Revalski - 208<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art01\">\u0421\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0443\u0434\u0443\u0449\u0435\u0433\u043e \u0443\u0447\u0438\u0442\u0435\u043b\u044f<\/a> <a href=\"#art02\">\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f <\/a><br \/><a href=\"#art01\" data-mce-name=\"art03\">[Tools For Methodical Competence Formation Of Future Mathematics Teachers in A Heuristic<\/a> <a href=\"\" data-mce-name=\"art04\">Teaching System] \/<\/a><br \/> \u0415. \u0421\u043a\u0430\u0444\u0430 \/ O. Skafa &#8211; 211<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art02\" data-mce-name=\"art03\">\u041f\u043b\u0430\u0432\u0435\u043d \u043f\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u044a\u043c \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \u0432 \u0443\u0432\u043e\u0434\u043d\u0438\u0442\u0435 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u043f\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435<\/a><br \/><a href=\"#art02\" data-mce-name=\"art03\">[Smooth Transition From Problems To projects In Introductory Programming Courses] \/<\/a><br \/> \u041f. \u0410\u0437\u044a\u043b\u043e\u0432 \/ P. Azalov &#8211; 224<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art04\">\u041e\u0431\u043b\u0430\u0447\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e<\/a><br \/><a href=\"#art04\">[Cloud Technologies And Some Possibilities For Application In Education] \/<\/a><br \/>\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev, \u0418. \u041c\u0430\u0440\u0448\u0435\u0432\u0430 \/ I. Marasheva, \u0415. \u0414\u0435\u043b\u0438\u043d\u043e\u0432 \/ E. Delinov &#8211; 239<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art05\">\u041f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0437\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u0435\u0431 2.0 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <\/a><br \/><a href=\"#art05\">[Practical Examples Of Technological Tools For Implementation Of Web 2.0 Education In Mathematics] \/<\/a><br \/>\u0424. \u041f\u0435\u0442\u0440\u043e\u0432 \/ F. Petrov, \u0414. \u0414\u0443\u0440\u0435\u0432\u0430-\u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430 \/ D. Dureva-Tuparova &#8211; 258<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art06\">\u0423\u0447\u0435\u0431\u043d\u0430 \u0434\u0435\u0439\u043d\u043e\u0441\u0442 \u201e\u0420\u0430\u0437\u0431\u0438\u0440\u0430\u043d\u0435\u201c \u043f\u0440\u0438 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0435\u043c\u0430\u0442\u0430 \u201e\u0415\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0438\u201d \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 7 \u043a\u043b\u0430\u0441<\/a><br \/><a href=\"#art06\"> [TheLearning Activity \u201cComprehension\u201d In Studying \u201cElectronic Tables\u201d<\/a><br \/><a href=\"#art06\"> In Information Technology Education In 7th Grade] \/<\/a><br \/>\u041a. \u0413\u044a\u0440\u043e\u0432 \/ K. Garov, \u0415. \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430 \/ E. Todorova &#8211; 267<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art07\">\u0421\u044a\u0441\u0442\u0435\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0437\u0430 \u0433\u0440\u0443\u043f\u0430 \u0415 <\/a><br \/><a href=\"#art07\">[Informatics Tasks For Competitions In Group E] \/ <\/a><br \/>\u0418. \u0421\u0442\u0430\u0440\u0438\u0431\u0440\u0430\u0442\u043e\u0432 \/ I. Staribratov, \u0426. \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432\u0430 \/ T. Dimitrova &#8211; 278<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 [CONTEST PROBLEMS]<\/strong><br \/><em>\u0420\u0443\u0431\u0440\u0438\u043a\u0430\u0442\u0430 \u0441\u0435 \u0432\u043e\u0434\u0438 \u043e\u0442 \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \u0438 \u0434-\u0440 \u0416\u0438\u0432\u043a\u043e \u0416\u0435\u043b\u0435\u0432<\/em><\/p>\n<p>\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f &#8211; 287<br \/>\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, 2012 &#8211; 288<br \/>\u0412 \u043d\u043e\u0432\u0438\u0442\u0435 \u0431\u0440\u043e\u0435\u0432\u0435 \u043d\u0430 \u0441\u043f\u0438\u0441\u0430\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c \u0447\u0435\u0442\u0435\u0442\u0435 \/<br \/> In The Latest Issues of \u201eAz Buki\u201d Journals &#8211; 291<\/p>\n<p><strong>\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS<\/strong> &#8211; 293<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u0421\u0420\u0415\u0414\u0421\u0422\u0412\u0410 \u0424\u041e\u0420\u041c\u0418\u0420\u041e\u0412\u0410\u041d\u0418\u042f \u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u041e\u0419<\/strong> <strong>\u041a\u041e\u041c\u041f\u0415\u0422\u0415\u041d\u0422\u041d\u041e\u0421\u0422\u0418 \u0411\u0423\u0414\u0423\u0429\u0415\u0413\u041e \u0423\u0427\u0418\u0422\u0415\u041b\u042f<\/strong> <strong>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0418 \u0412&nbsp; \u0421\u0418\u0421\u0422\u0415\u041c\u0415 \u0415\u0412\u0420\u0418\u0421\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0413\u041e<\/strong> <strong>\u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f<\/strong><\/p>\n<p><strong>\u0415\u043b\u0435\u043d\u0430 \u0421\u043a\u0430\u0444\u0430<\/strong><\/p>\n<p><strong>Abstract<\/strong>. \u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f \u043d\u0430\u0443\u0447\u043d\u043e \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0432\u043d\u0435\u0434\u0440\u0435\u043d\u0438\u0435 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0441\u0440\u0435\u0434\u0441\u0442\u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u043e\u0432-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u043e\u0432 \u043f\u0440\u0438 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0443\u0434\u0443\u0449\u0435\u0433\u043e \u0443\u0447\u0438\u0442\u0435\u043b\u044f. \u041e\u0441\u043d\u043e\u0432\u043d\u043e\u0439 \u0430\u043a\u0446\u0435\u043d\u0442 \u0441\u0442\u0430\u0442\u044c\u0438 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0443 \u044d\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043f\u0435\u0447\u0430\u0442\u043d\u044b\u0445 \u0438 \u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u044b\u0445 \u0441\u0440\u0435\u0434\u0441\u0442\u0432, \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u0445 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447.<\/p>\n<p><em>Keywords<\/em>: heuristic teaching of mathematics, heuristic and didactic constructions, professionally oriented heuristic activity<\/p>\n<p>&nbsp;<\/p>\n<p><strong>TOOLS FOR METHODICAL COMPETENCE FORMATION<\/strong><br \/><strong>OF FUTURE MATHEMATICS TEACHERS IN<\/strong><br \/><strong>A HEURISTIC TEACHING SYSTEM<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Scientifi cally reasonable introduction of modern educational tools for methodical competence formation of future Mathematics teachers is proposed. The main accent of the article is the development of a heuristic oriented teaching system directed to methodical tasks solving.<\/p>\n<p><strong>Olena Skafa<\/strong><br \/>\u0003Professor, Ph. D, D. Sc.<br \/>Department of Mathematics<br \/>National University Donetsk, Ukraine<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art02\">&nbsp;<\/a>\u041f\u041b\u0410\u0412\u0415\u041d \u041f\u0420\u0415\u0425\u041e\u0414 \u041e\u0422 \u0417\u0410\u0414\u0410\u0427\u0418 \u041a\u042a\u041c \u041f\u0420\u041e\u0415\u041a\u0422\u0418<\/strong> <strong>\u0412 \u0423\u0412\u041e\u0414\u041d\u0418\u0422\u0415 \u041a\u0423\u0420\u0421\u041e\u0412\u0415 \u041f\u041e \u041f\u0420\u041e\u0413\u0420\u0410\u041c\u0418\u0420\u0410\u041d\u0415<\/strong><\/p>\n<p><strong>Pavel Azalov<\/strong><\/p>\n<p><strong>Abstract.<\/strong> \u041a\u0430\u043a \u0434\u0430 \u0438\u0437\u0433\u0440\u0430\u0434\u0438\u043c \u0443\u0432\u043e\u0434\u043d\u0438\u0442\u0435 \u0441\u0438 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u043f\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0442\u0430\u043a\u0430, \u0447\u0435 \u0442\u0435 \u0434\u0430 \u0441\u0430 \u0434\u043e\u0441\u0442\u044a\u043f\u043d\u0438 \u0437\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u0442\u0435 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438, \u0440\u0430\u0437\u0431\u0438\u0440\u0430 \u0441\u0435 \u0431\u0435\u0437 \u0434\u0430 \u0441\u0435 \u043d\u0430\u043b\u0430\u0433\u0430 \u0434\u0430 \u0441\u0435 \u043f\u0440\u0430\u0432\u044f\u0442 \u043a\u043e\u043c\u043f\u0440\u043e\u043c\u0438\u0441\u0438 \u0432 \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435\u0442\u043e \u0438 \u0432 \u0438\u0437\u0438\u0441\u043a\u0432\u0430\u043d\u0438\u044f\u0442\u0430 \u043a\u044a\u043c \u0442\u044f\u0445? \u0422\u043e\u0432\u0430 \u0435 \u0446\u0435\u043d\u0442\u0440\u0430\u043b\u043d\u0438\u044f\u0442 \u0432\u044a\u043f\u0440\u043e\u0441 \u0432 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430, \u043d\u0430 \u043a\u043e\u0439\u0442\u043e \u0441\u0435 \u043f\u0440\u0430\u0432\u0438 \u043e\u043f\u0438\u0442 \u0437\u0430 \u043e\u0442\u0433\u043e\u0432\u043e\u0440 \u0447\u0440\u0435\u0437 \u043f\u043b\u0430\u0432\u0435\u043d \u043f\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u044a\u043c \u043f\u0440\u043e\u0435\u043a\u0442\u0438. \u0418\u0434\u0435\u044f\u0442\u0430 \u043d\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u0441\u0435 \u0441\u044a\u0441\u0442\u043e\u0438 \u0432 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043d\u043e-\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0432 \u043a\u0443\u0440\u0441\u0430 \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 1 \u0438 \u043f\u043b\u0430\u0432\u043d\u043e\u0442\u043e \u043c\u0443 \u043f\u0440\u043e\u0434\u044a\u043b\u0436\u0435\u043d\u0438\u0435 \u0432 \u043f\u0440\u043e\u0435\u043a\u0442\u043d\u043e-\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0432 \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 2. \u041d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u0435 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u0438\u0442\u0435, \u043a\u043e\u0438\u0442\u043e \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438\u0442\u0435 \u0438\u043c\u0430\u0442 \u0432 \u0442\u0435\u0437\u0438 \u043a\u0443\u0440\u0441\u043e\u0432\u0435, \u043a\u0430\u0442\u043e \u0441\u0435 \u043f\u043e\u0441\u043e\u0447\u0432\u0430\u0442 \u0438 \u043f\u0440\u0435\u043f\u043e\u0440\u044a\u043a\u0438 \u0437\u0430 \u043f\u0440\u0435\u043e\u0434\u043e\u043b\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c. \u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u0441\u0435 \u0432\u0441\u044f\u043a\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u043e\u0442 \u0432\u0437\u0430\u0438\u043c\u043d\u043e-\u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0430 \u0441\u0435 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u0440\u0430 \u0432 \u0440\u0435\u0434\u0438\u0446\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438, \u043f\u0440\u0438 \u043a\u043e\u0435\u0442\u043e \u0432\u0441\u044f\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u0434\u0435\u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0440\u0430 \u0434\u043e \u043f\u0440\u0435\u0434\u0448\u0435\u0441\u0442\u0432\u0443\u0432\u0430\u0449\u0438 \u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0441\u044a\u0449\u0430\u0442\u0430 \u0440\u0435\u0434\u0438\u0446\u0430. \u041f\u043e \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u044f \u0441\u044a\u0441 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435, \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0442\u0435 \u0441\u044a\u0449\u043e \u0441\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u0442 \u0438 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442 \u043a\u0430\u0442\u043e \u0440\u0435\u0434\u0438\u0446\u0438 \u043e\u0442 \u043f\u0440\u043e\u0435\u043a\u0442\u0438, \u043f\u0440\u0438 \u043a\u043e\u044f\u0442\u043e \u0447\u0430\u0441\u0442 \u043e\u0442 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u0442\u0438\u0442\u0435 (\u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043b\u0430\u0441\u043e\u0432\u0435) \u043e\u0442 \u0435\u0434\u0438\u043d \u043f\u0440\u043e\u0435\u043a\u0442 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0442 \u043f\u0440\u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u0438 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\u0442\u0430 \u043d\u0430 \u0441\u043b\u0435\u0434\u0432\u0430\u0448\u0438\u0442\u0435 \u0432 \u0440\u0435\u0434\u0438\u0446\u0430\u0442\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438. \u041f\u043b\u0430\u0432\u043d\u0438\u044f\u0442 \u043f\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u044a\u043c \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \u0441\u0435 \u043f\u043e\u0441\u0442\u0438\u0433\u0430 \u0447\u0440\u0435\u0437 \u0434\u0435\u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0442\u0435 \u043e\u0442 \u0432\u0442\u043e\u0440\u0438\u044f\u0442 \u043a\u0443\u0440\u0441 \u043f\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0434\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u043a\u043e\u0438\u0442\u043e \u0441\u043b\u0435\u0434\u0432\u0430 \u0434\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043e\u0449\u0435 \u0432 \u043f\u044a\u0440\u0432\u0438\u044f \u043a\u0443\u0440\u0441.<\/p>\n<p><em>Keywords<\/em>: Computer Science Education, Computer Science I, Computer Science II, Problem-based learning, Project-based Learning, Sequences of problems, Sequences of projects<\/p>\n<p>&nbsp;<\/p>\n<p><strong>SMOOTH TRANSITION FROM PROBLEMS TO PROJECTS <\/strong><strong>IN INTRODUCTORY PROGRAMMING COURSES<\/strong><\/p>\n<p><strong>Abstract.<\/strong> How to build up our courses that are comprehensible to the current students without affecting the established requirements and without allowing compromises relevant to the course content? This is the main question discussed in the paper. The corresponding answer is based on the smooth transition from problems to projects. The idea of this approach consists of the implementation of the problem-based teaching in the Computer Science I course and then continuing with the project-based teaching in the Computer Science II course. The analysis of the possible diffi culties, which could be met by the students attending these courses, and corresponding ways to overcome them are also presented in the text. Every set of interconnected problems is structured as a sequence of problems so that<br \/>each problem could derive from preceding problems of the same sequence. Similarly, projects are organized as a sequence of projects whose components such as functions and classes could be incorporated into the design and development of next projects. The smooth transition from problems to projects can be achieved by decomposing the projects to problems which should have been considered already in Computer Science I.<\/p>\n<p><strong>Pavel Azalov<\/strong><br \/>\u0003Associate Prof. of Computer Science, Ph. D.<br \/>Pennsylvania State University, USA<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art04\">&nbsp;<\/a>\u041e\u0411\u041b\u0410\u0427\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u0418 \u0412\u042a\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0418<\/strong> <strong>\u0417\u0410 \u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u0415 \u0412 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415\u0422\u041e<\/strong><\/p>\n<p><strong>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0418\u0432\u0430\u043d\u043a\u0430 \u041c\u0430\u0440\u0430\u0448\u0435\u0432\u0430, \u0415\u043c\u0438\u043b \u0414\u0435\u043b\u0438\u043d\u043e\u0432<\/strong><\/p>\n<p><strong>Abstract.<\/strong> \u041f\u0440\u0435\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 5-6 \u0433\u043e\u0434\u0438\u043d\u0438 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f \u0443\u0441\u0438\u043b\u0435\u043d\u043e \u0441\u0435 \u0433\u043e\u0432\u043e\u0440\u0438 \u0437\u0430 \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438 \u0438\u0437\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f\u201c, \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u201d, \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438 \u0443\u0441\u043b\u0443\u0433\u0438\u201d \u0438 \u0434\u0440\u0443\u0433\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u201e\u043e\u0431\u043b\u0430\u043a\u201d (cloud) \u043f\u043e\u0434 \u043e\u0431\u0449\u043e \u043d\u0430\u0438\u043c\u0435\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u201d. \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 \u0438\u0437\u044f\u0441\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0433\u043e\u0440\u043d\u0438\u0442\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u043f\u0440\u043e\u0441\u043b\u0435\u0434\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u044a\u0437\u043d\u0438\u043a\u0432\u0430\u043d\u0435\u0442\u043e \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u0438\u043c. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u043f\u0435\u0442\u0442\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043d\u0430 \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438\u0442\u0435 \u0438\u0437\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f\u201d \u0438 \u0443\u0441\u043b\u0443\u0433\u0438\u0442\u0435, \u043a\u043e\u0438\u0442\u043e \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u201d \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0438 \u0432\u0438\u0434\u043e\u0432\u0435\u0442\u0435 \u201e\u043e\u0431\u043b\u0430\u0446\u0438\u201d. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u0440\u0435\u0434\u0438\u043c\u0441\u0442\u0432\u0430 \u043d\u0430 \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u201d, \u0440\u0438\u0441\u043a\u043e\u0432\u0435 \u043f\u0440\u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c \u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u043d\u0438 \u0431\u0435\u043b\u0435\u0436\u043a\u0438. \u041a\u043b\u0430\u0441\u0438\u0444\u0438\u0446\u0438\u0440\u0430\u043d\u0438 \u0441\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0437\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u201e\u043e\u0431\u043b\u0430\u0447\u043d\u0438\u0442\u0435 \u0438\u0437\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f\u201d \u0432 \u0441\u0444\u0435\u0440\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e.<\/p>\n<p><em>Keywords<\/em>: Cloud computing; usage of Cloud technologies in education<\/p>\n<p><strong>CLOUD TECHNOLOGIES AND SOME POSSIBILITIES <\/strong><strong>FOR APPLICATION IN EDUCATION<\/strong><\/p>\n<p><strong>Abstract.<\/strong> During the last 5-6 years there is an active discussion in Bulgaria related to \u201ccloud calculations\u201d, \u201ccloud structures\u201d, \u201ccloud services\u201d and other notions under the common name of \u201ccloud technologies\u201d connected with the \u201ccloud concept\u201d. The goal of the present paper is to clarify some of these notions and to trace their appearance and development. Five characteristics are discussed concerning \u201ccloud calculations\u201d and services which \u201ccloud technologies\u201d propose. The \u201ccloud\u201d types are considered too. What are pointed out are some advantages of the \u201ccloud technologies\u201d, some risks in their use and critical notes. Possible applications of \u201ccloud calculations\u201d to Education domain are classified.<\/p>\n<p><strong>Sava Grozdev<\/strong><br \/>\u0003Professor, Doctor in Mathematics, DSc in Pedagogy<br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p><strong>Ivanka Marasheva,<\/strong><br \/>\u0003Doctor in Pedagogy<br \/>21st Secondary School \u201cHristo Botev\u201d<\/p>\n<p><strong>Emil Delinov<\/p>\n<p><\/strong><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art05\">&nbsp;<\/a>\u041f\u0420\u0410\u041a\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u041f\u0420\u0418\u041c\u0415\u0420 \u041d\u0410 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0427\u041d\u0418<\/strong> <strong>\u0421\u0420\u0415\u0414\u0421\u0422\u0412\u0410 \u0417\u0410 \u0420\u0415\u0410\u041b\u0418\u0417\u0418\u0420\u0410\u041d\u0415<\/strong><br \/><strong>\u041d\u0410 \u0423\u0415\u0411 2.0 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p><strong>\u0424\u0438\u043b\u0438\u043f \u041f\u0435\u0442\u0440\u043e\u0432, \u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0414\u0443\u0440\u0435\u0432\u0430-\u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430<\/strong><\/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 \u0441\u043e\u0444\u0442\u0443\u0435\u0440\u043d\u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0437\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0437\u0430 \u0438\u0437\u043e\u0431\u0440\u0430\u0437\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0438 \u0438 \u0432\u044a\u0432\u0435\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0435\u043a\u0441\u0442 \u0432 \u0443\u0435\u0431 \u0444\u043e\u0440\u043c\u0438. \u041f\u043e\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u0430\u043a\u0446\u0435\u043d\u0442 \u0432\u044a\u0440\u0445\u0443 \u0438\u0437\u0431\u043e\u0440 \u043d\u0430 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430, \u043a\u043e\u0438\u0442\u043e \u043d\u0435 \u0438\u0437\u0438\u0441\u043a\u0432\u0430\u0442 \u0438\u043d\u0441\u0442\u0430\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u043d\u0430 \u0441\u044a\u0440\u0432\u0435\u0440\u043d\u0438\u0442\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u0438. \u0422\u043e\u0432\u0430 \u043f\u043e\u043c\u0430\u0433\u0430 \u043d\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u0446\u0438\u0442\u0435 \u043d\u0430 \u0441\u044a\u0449\u0435\u0441\u0442\u0432\u0443\u0432\u0430\u0449\u0438 \u0441\u0430\u0439\u0442\u043e\u0432\u0435 \u0434\u0430 \u043f\u0440\u0435\u043c\u0438\u043d\u0430\u0442 \u043f\u043e-\u043b\u0435\u0441\u043d\u043e \u043a\u044a\u043c \u0443\u0435\u0431 2.0 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0431\u0435\u0437 \u0434\u0430 \u0438\u043c\u0430 \u043d\u0443\u0436\u0434\u0430 \u043e\u0442 \u043f\u0440\u0435\u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0432\u0435\u0447\u0435 \u0440\u0430\u0431\u043e\u0442\u0435\u0449\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438, \u043a\u043e\u0435\u0442\u043e \u0435 \u0432\u0430\u0436\u0435\u043d \u0444\u0430\u043a\u0442\u043e\u0440 \u0437\u0430 \u0441\u0430\u0439\u0442\u043e\u0432\u0435 \u0441\u044a\u0441 \u0441\u043f\u043e\u0434\u0435\u043b\u0435\u043d \u0445\u043e\u0441\u0442\u0438\u043d\u0433 \u043d\u0430 \u0441\u044a\u0440\u0432\u0435\u0440\u0438 \u0432 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u0438 \u0438\u043b\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438 \u043c\u0440\u0435\u0436\u0438 \u0438 \u043e\u0431\u0438\u0447\u0430\u0439\u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430 \u0430\u0434\u043c\u0438\u043d\u0438\u0441\u0442\u0440\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u0434\u0430 \u0431\u044a\u0434\u0435 \u0438\u0437\u043a\u043b\u044e\u0447\u0438\u0442\u0435\u043b\u043d\u043e \u043a\u043e\u043d\u0441\u0435\u0440\u0432\u0430\u0442\u0438\u0432\u043d\u043e. \u0421\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u043e \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u0435 \u043e\u0442\u0434\u0435\u043b\u0435\u043d\u043e \u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0437\u0430 \u043f\u0440\u0435\u0445\u0432\u044a\u0440\u043b\u044f\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0443\u0435\u0431 \u0441\u0430\u0439\u0442\u0430 \u0438 \u0434\u0440\u0443\u0433\u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u043a\u0430\u043a\u0442\u043e \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0437\u0430 \u0438\u043d\u0434\u0435\u043a\u0441\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0432\u044a\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0435\u043a\u0441\u0442 \u043e\u0442 \u0442\u044a\u0440\u0441\u0435\u0449\u0438 \u043c\u0430\u0448\u0438\u043d\u0438.<\/p>\n<p><em>Keywords<\/em>: web 2.0 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435, latex, mathml, \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430<\/p>\n<p>&nbsp;<\/p>\n<p><strong>PRACTICAL EXAMPLES OF TECHNOLOGICAL TOOLS FOR<\/strong><br \/><strong>IMPLEMENTATION OF WEB 2.0 EDUCATION IN MATHEMATICS<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Software technologies for integration of visualization and editing of mathematical formulas in web forms are presented in the article. The main focus is set on choice of technological resources which do not require installation of specifi c software on the hosting servers. This helps the conversion of existing web sites into web 2.0 educational resources without the need of reconfi guring of the existing systems. Sometimes this is an important factor for shared hosting, school and university networks which are traditionally very conservative to changes. A special attention is given to the copy\/paste capabilities for transferring of mathematical formulas back and forth between the web site and other software products.<\/p>\n<p><strong>Filip Petrov<\/strong><br \/>\u0003Assistant<br \/>Computer Systems Department<br \/>Technical university Sofia<br \/><a href=\"http:\/\/www.cphpvb.net\">http:\/\/www.cphpvb.net<\/a><\/p>\n<p><strong>Daniela Dureva-Tuparova<\/strong><br \/>\u0003Docent, PhD<br \/>Informatics Department<br \/>South-West Universiti \u201cNeofit Rilski\u201d<br \/>Blagoevgrad<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art06\">&nbsp;<\/a>\u0423\u0427\u0415\u0411\u041d\u0410\u0422\u0410 \u0414\u0415\u0419\u041d\u041e\u0421\u0422 \u201e\u0420\u0410\u0417\u0411\u0418\u0420\u0410\u041d\u0415\u201c \u041f\u0420\u0418 \u0418\u0417\u0423\u0427\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0422\u0415\u041c\u0410\u0422\u0410<br \/> \u201e\u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u0418<\/strong> <strong>\u0422\u0410\u0411\u041b\u0418\u0426\u0418\u201d \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e<\/strong> <strong>\u041f\u041e \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u0412 7. \u041a\u041b\u0410\u0421<\/strong> <\/p>\n<p><strong>\u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432, \u0415\u043b\u0435\u043d\u0430 \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0449\u0435 \u0441\u043f\u043e\u0434\u0435\u043b\u0438\u043c \u043e\u043f\u0438\u0442\u0430 \u0441\u0438 \u0437\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u043e\u0442\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043f\u0440\u0438 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0435\u043c\u0430\u0442\u0430 \u201e\u0415\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0438\u201d \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 7. \u043a\u043b\u0430\u0441.<br \/><em><br \/>Keywords<\/em>: learning activity, comprehension, Information Technology, electronic table.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>THE LEARNING ACTIVITY \u201eCOMPREHENSION\u201c IN STUDYING<\/strong> <strong>\u201cELECTRONIC TABLES\u201d IN INFORMATION TECHNOLOGY <\/strong><strong>EDUCATION IN 7-TH GRADE<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper shares the experience of the authors in the realization of comprehension activity in teaching \u201cElectronic Tables\u201d during Information Technology education in the 7-th grade.<\/p>\n<p><strong>Kosta Garov<\/strong><br \/>\u0003Associated professor, PhD<br \/>Faculty of Mathematics and Informatics<br \/>Plovdiv University \u201cPaisii Hilendarski\u201d<\/p>\n<p><strong>Elena Todorova<\/strong><br \/>\u0003Associated<br \/>Faculty of Mathematics and Informatics<br \/>Plovdiv University \u201cPaisii Hilendarski\u201d<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\"><br \/>\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art07\">&nbsp;<\/a>\u0421\u042a\u0421\u0422\u0415\u0417\u0410\u0422\u0415\u041b\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><strong>\u041f\u041e \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410 \u0417\u0410 \u0413\u0420\u0423\u041f\u0410 \u0415<\/strong><\/p>\n<p><strong>Ivaylo Staribratov, Tcvetana Dimitrova<\/strong><\/p>\n<p><strong>Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u043d\u0438 \u043e\u0441\u043e\u0431\u0435\u043d\u043e\u0441\u0442\u0438 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430, \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u043d\u0438 \u0443 \u043d\u0430\u0441 \u043d\u0430 \u043d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0438 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u044f \u0438 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0438 \u0437\u0430 4-5 \u043a\u043b\u0430\u0441 (\u0441\u044a\u0441\u0442\u0435\u0437\u0430\u0442\u0435\u043b\u043d\u0430 \u0433\u0440\u0443\u043f\u0430 \u0415). \u0418\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435\u0442\u043e \u043e\u0431\u0445\u0432\u0430\u0449\u0430 \u043f\u0435\u0440\u0438\u043e\u0434 \u043e\u0442 9 \u0433\u043e\u0434\u0438\u043d\u0438 (2004\u20132012). \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u0442\u0430\u0431- \u043b\u0438\u0446\u0438 \u0438 \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u0438, \u0441 \u043a\u043e\u0438\u0442\u043e \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u043e\u043f\u0438\u0442 \u0437\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435, \u0434\u0430\u0432\u0430\u043d\u0438 \u043d\u0430 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0438\u0442\u0435 \u0447\u0435\u0442\u0438\u0440\u0438 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u044f \u0438 \u0442\u0443\u0440\u043d\u0438\u0440\u0438 \u0441 \u043d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432 \u0433\u043e\u0434\u0438\u043d\u0430\u0442\u0430, \u043a\u0430\u043a\u0442\u043e \u0438 \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0442\u0435, \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0438 \u0432 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435.<\/p>\n<p><em>Keyword<\/em>: Informatics in competitions, classifi cation<\/p>\n<p>&nbsp;<\/p>\n<p><strong>INFORMATICS TASKS FOR COMPETITIONS IN GROUP E<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Characteristic features of Informatics tasks for 4-5th grade Bulgarian national competitions are considered (competitions for Group E). The study comprises a period of 9 years (2004-2012). Tables and diagrams are presented, thus realizing an attempt to investigate the relative diffi culty of the tasks from yearly held four competitions and tournaments with national signifi cance. The algorithms of the solutions are examined too with respect to diffi culty.<\/p>\n<p><strong>Ivaylo Staribratov<\/strong><br \/>\u0003PhD<br \/>HSM \u201eAkad. Kiril Popov\u201c<\/p>\n<p><strong>Tzvetana Dimitrova<\/strong><br \/>\u0003HSM \u201eAkad. Kiril Popov\u201c<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0410\u043a\u0430\u0434\u0435\u043c\u0438\u043a \u041ae\u043d\u0434\u0435\u0440\u043e\u0432 \u043d\u0430 70 \u0433\u043e\u0434\u0438\u043d\u0438 \/\u042e. \u0420\u0435\u0432\u0430\u043b\u0441\u043a\u0438 &#8211; 208 \u0421\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0443\u0434\u0443\u0449\u0435\u0433\u043e \u0443\u0447\u0438\u0442\u0435\u043b\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f [Tools For Methodical Competence Formation Of Future Mathematics Teachers in A Heuristic Teaching System] \/ \u0415. \u0421\u043a\u0430\u0444\u0430 \/ O. Skafa &#8211; 211 \u041f\u043b\u0430\u0432\u0435\u043d \u043f\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u044a\u043c \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \u0432 \u0443\u0432\u043e\u0434\u043d\u0438\u0442\u0435 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u043f\u043e [&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 LVI, 2013 - \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:\/\/press.azbuki.bg\/matematics\/matharticles\/mathinfo03-2013\/\" \/>\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 LVI, 2013 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0410\u043a\u0430\u0434\u0435\u043c\u0438\u043a \u041ae\u043d\u0434\u0435\u0440\u043e\u0432 \u043d\u0430 70 \u0433\u043e\u0434\u0438\u043d\u0438 \/\u042e. \u0420\u0435\u0432\u0430\u043b\u0441\u043a\u0438 &#8211; 208 \u0421\u0440\u0435\u0434\u0441\u0442\u0432\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0443\u0434\u0443\u0449\u0435\u0433\u043e \u0443\u0447\u0438\u0442\u0435\u043b\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f [Tools For Methodical Competence Formation Of Future Mathematics Teachers in A Heuristic Teaching System] \/ \u0415. \u0421\u043a\u0430\u0444\u0430 \/ O. 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