{"id":38762,"date":"2014-04-27T21:59:29","date_gmt":"2014-04-27T18:59:29","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-2-godina-lvi-2014\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"matematika-i-informatika-knizhka-2-godina-lvi-2014","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-2-godina-lvi-2014\/","title":{"rendered":"Mathematics and Informatics, Number 2\/2014, Volume 57"},"content":{"rendered":"

 <\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><\/p>\n

IF YOU WORK WITH YOUNG STUDENTS \/ \u0410\u041a\u041e \u0420\u0410\u0411\u041e\u0422\u0418\u0422\u0415 \u0421 \u041c\u0410\u041b\u041a\u0418\u0422\u0415 \u0423\u0427\u0415\u041d\u0418\u0426\u0418<\/strong>
\u0417\u0430 \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\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 [On the Contemporary Methods in Primary School Mathematics] \/ <\/a>
\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432 \/ Zdravko Lalchev<\/em> \u2013 p. 103<\/p>\n

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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>
\u0414\u0432\u0443\u043c\u0435\u0440\u043d\u0438 \u043c\u0430\u0441\u0438\u0432\u0438: \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0438 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438 [2D Arrays: Search Algorithms and Experiments] \/ <\/a>
\u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov<\/em> – \u0441\u0442\u0440. 107<\/p>\n

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\u0424\u0440\u0430\u043a\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0432 \u0444\u0438\u0437\u0438\u043a\u0435 [Fractal Methods in Physics] \/
\u0412\u0430\u043b\u0435\u0440\u0438\u0439 \u0421\u0435\u043a\u043e\u0432\u0430\u043d\u043e\u0432, \u0415\u043b\u0435\u043d\u0430 \u0421\u0435\u043b\u0435\u0437\u043d\u0435\u0432\u0430, \u0421\u0432\u0435\u0442\u043b\u0430\u043d\u0430 \u0428\u043b\u044f\u0445\u0442\u0438\u043d\u0430 \/ Valerii Sekovanov, Elena Seleznjova, Svetlana Shljahtina <\/em>– \u0441\u0442\u0440. 129<\/p>\n

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\u0425\u043e\u043c\u043e\u0442\u0435\u0442\u0438\u0447\u043d\u0438 \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a [Homothetic Conics in the Plane of a Triangle] \/ <\/a>
\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov <\/em>– \u0441\u0442\u0440. 139<\/p>\n

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\u041d\u044f\u043a\u043e\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0435\u0434\u0438\u043d \u0442\u0438\u043f \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u0442\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430
[Some Methodological Generalizations in the Solution of a Type of Linear Algebra Problems] <\/a>
\u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432 \/ Rosen Nikolaev, Jordan Petkov <\/em>– \u0441\u0442\u0440. 155<\/p>\n

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COMPETITIONS AND OLYMPIADS \/ \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0418 \u0418 \u0421\u042a\u0421\u0422\u0415\u0417\u0410\u041d\u0418\u042f<\/strong>
\u0421\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u0435\u0442\u043e \u201e\u0415\u0432\u0440\u043e\u043f\u0435\u0439\u0441\u043a\u043e \u043a\u0435\u043d\u0433\u0443\u0440\u0443\u201d \u0437\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441\u044a\u0441 \u0437\u0440\u0438\u0442\u0435\u043b\u043d\u0438 \u0443\u0432\u0440\u0435\u0436\u0434\u0430\u043d\u0438\u044f
[The \u2018European Kangaroo\u2019Competition for Students with Visual Impairments] \/ <\/a>
\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0415\u043b\u0438\u0437\u0430 \u041f\u0435\u0442\u0440\u043e\u0432\u0430 \/ Sava Grozdev, Eliza Petrova <\/em>– \u0441\u0442\u0440. 166<\/p>\n

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Analysis of Problem Solving in Informatics for 12-13 Year Old Students in Bulgaria \/ <\/a>
Ivaylo Staribratov, Bistra Taneva<\/em> – \u0441\u0442\u0440. 175<\/p>\n

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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>
\u041c\u043e\u0434\u0435\u043b \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0435\u0434\u0438\u043d \u043a\u043b\u0430\u0441 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0441 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u043d \u0441\u043e\u0444\u0442\u0443\u0435\u0440 [A Model for Construction Problem Solving by Dynamic Software] \/ <\/a>
\u0412\u0430\u043d\u044f \u0411\u0438\u0437\u043e\u0432\u0430-\u041b\u0430\u043b\u0435\u0432\u0430 \/ Vania Bizova-Laleva <\/em>– \u0441\u0442\u0440. 188<\/p>\n

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CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong>
\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 <\/p>\n

\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of the Issue] – \u0441\u0442\u0440. 197<\/p>\n

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\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 3, 2013 [Solutions of the Contest Problems from issue 3, 2013] – \u0441\u0442\u0440. 198<\/p>\n

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READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201d JOURNALS \/ <\/strong>
\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\u201d \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> \u2013 p. 201<\/p>\n

GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> – \u0441\u0442\u0440. 203<\/p>\n

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 <\/a>\u0417\u0410 \u0421\u042a\u0412\u0420\u0415\u041c\u0415\u041d\u041d\u0418\u0422\u0415 \u041c\u0415\u0422\u041e\u0414\u0418 \u0412 \u041d\u0410\u0427\u0410\u041b\u041d\u0410\u0422\u0410 \u0423\u0427\u0418\u041b\u0418\u0429\u041d\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 <\/strong><\/p>\n

\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432 <\/strong>
Sofia University<\/em> <\/p>\n

Abstract<\/strong>. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0441\u0435 \u0430\u043d\u043e\u043d\u0441\u0438\u0440\u0430 \u043d\u0430\u043c\u0435\u0440\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0441\u043f. \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u201c \u0434\u0430 \u043f\u0443\u0431\u043b\u0438\u043a\u0443\u0432\u0430 \u043d\u0430\u0443\u0447\u043d\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u0441 \u0446\u0435\u043b \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435- \u0441\u043a\u0430\u0442\u0430 \u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0430\u0442\u0430 \u043a\u0432\u0430\u043b\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f \u043d\u0430 \u0443\u0447\u0438\u0442\u0435\u043b\u0438\u0442\u0435 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435 \u0438 \u043f\u043e\u0434\u043f\u043e- \u043c\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u0438\u043c \u0432  \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. <\/p>\n

Keywords<\/em>: primary school mathematics, school and nonstandard problem, algorith- mic and heuristic approach, contemporary methods, mathematical and didactical prepa- ration of teachers<\/p>\n

ON THE CONTEMPORARY METHODS IN PRIMARY SCHOOL MATHEMATICS<\/strong><\/p>\n

Abstract<\/strong>. The present note announces the intention of the Mathematics and Informatics Journal to publish research materials aiming at the increase of the mathematical and methodological qualification of Primary school teachers and their support in the mathematical preparation of students. <\/p>\n

* Prof. Dr. Zdravko Lalchev<\/strong>
Faculty of Preschool and Primary School Education
University of Sofia<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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 <\/a>\u0414\u0412\u0423\u041c\u0415\u0420\u041d\u0418 \u041c\u0410\u0421\u0418\u0412\u0418: \u0410\u041b\u0413\u041e\u0420\u0418\u0422\u041c\u0418 \u0417\u0410 \u0422\u042a\u0420\u0421\u0415\u041d\u0415 \u0418 \u0415\u041a\u0421\u041f\u0415\u0420\u0418\u041c\u0415\u041d\u0422\u0418<\/strong><\/p>\n

Pavel Azalov <\/strong>
Pennsylvania State University<\/em> <\/p>\n

Abstract<\/strong>. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0432 \u0447\u0438\u0441\u043b\u0435\u043d\u0438 2D \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e \u043d\u0430\u0440\u0435\u0434\u0435\u043d\u0438 \u043c\u0430\u0441\u0438\u0432\u0438, \u0442.\u0435. \u043c\u0430\u0441\u0438\u0432\u0438, \u0447\u0438\u0438\u0442\u043e \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0438 \u0441\u0430 \u043d\u0435\u043d\u0430\u043c\u0430\u043b\u044f\u0432\u0430\u0449\u0438 \u043f\u043e \u0440\u0435\u0434\u043e\u0432\u0435 \u0438 \u043a\u043e\u043b\u043e\u043d- \u043a\u0438. \u041d\u0430\u043a\u0440\u0430\u0442\u043a\u043e \u0441\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0447\u0435\u0442\u0438\u0440\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c\u0430, \u0435\u0434\u0438\u043d\u0438\u044f\u0442 \u043e\u0442 \u043a\u043e\u0438\u0442\u043e \u0435 \u0430\u043b\u0433\u043e\u0440\u0438- \u0442\u044a\u043c\u044a\u0442 \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 Saddleback. \u041e\u043f\u0438\u0441\u0430\u043d \u0435 \u0438 \u0435\u0434\u0438\u043d \u043d\u043e\u0432 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c, \u043d\u0430\u0440\u0435\u0447\u0435\u043d \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0438\u0447\u043d\u0438 \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432\u0438. \u041e\u0441\u043d\u043e\u0432\u043d\u0430\u0442\u0430 \u0438\u0434\u0435\u044f \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c\u0430 \u0435 \u043a\u043e\u043d- \u0441\u0442\u0440\u0443\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0440\u0435\u0434\u0438\u0446\u0430 \u043e\u0442 \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432\u0438 \u0441 \u043d\u0430\u043c\u0430\u043b\u044f\u0432\u0430\u0449\u0438 \u0440\u0430\u0437\u043c\u0435\u0440\u0438 \u043d\u0430 \u0440\u0435\u0434\u043e\u0432\u0435\u0442\u0435 \u0438 \u043a\u043e\u043b\u043e\u043d- \u043a\u0438\u0442\u0435, \u043a\u0430\u0442\u043e \u0432\u0441\u0435\u043a\u0438 \u0441\u043b\u0435\u0434\u0432\u0430\u0449 \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432 \u043d\u0430 \u0440\u0435\u0434\u0438\u0446\u0430\u0442\u0430 \u0441\u0435 \u0441\u044a\u0434\u044a\u0440\u0436\u0430 \u0432 \u043f\u0440\u0435\u0434\u0448\u0435\u0441\u0442\u0432\u0430\u0449\u0438\u044f \u0433\u043e \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432. \u041f\u043e \u0442\u043e\u0437\u0438 \u043d\u0430\u0447\u0438\u043d, \u0430\u043a\u043e \u0442\u044a\u0440\u0441\u0435\u043d\u043e\u0442\u043e \u0447\u0438\u0441\u043b\u043e \u0441\u0435 \u0441\u044a\u0434\u044a\u0440\u0436\u0430 \u0432 \u043f\u044a\u0440\u0432\u043e\u043d\u0430\u0447\u0430\u043b\u043d\u0438\u044f \u043c\u0430\u0441\u0438\u0432, \u0442\u043e \u0447\u0438\u0441\u043b\u043e\u0442\u043e \u0441\u0435 \u0441\u044a\u0434\u044a\u0440\u0436\u0430 \u0438 \u0432\u044a\u0432 \u0432\u0441\u0435\u043a\u0438 \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432 \u043d\u0430 \u0440\u0435\u0434\u0438\u0446\u0430\u0442\u0430, \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u044f\u0442 \u043e\u0442 \u043a\u043e\u0438\u0442\u043e \u0441\u044a- \u0434\u044a\u0440\u0436\u0430 \u0441\u0430\u043c\u043e \u0435\u0434\u0438\u043d \u0435\u043b\u0435\u043c\u0435\u043d\u0442 \u0441\u044a\u0441 \u0441\u0442\u043e\u0439\u043d\u043e\u0441\u0442, \u0440\u0430\u0432\u043d\u0430 \u043d\u0430  \u0442\u044a\u0440\u0441\u0435\u043d\u043e\u0442\u043e \u0447\u0438\u0441\u043b\u043e. \u0412\u0441\u0438\u0447\u043a\u0438\u0442\u0435 \u043f\u0435\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c\u0430 \u0441\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0438 \u0432 \u0441\u0440\u0435\u0434\u0430\u0442\u0430 \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 Microsoft Visual C++. \u0418\u0437\u0432\u044a\u0440- \u0448\u0435\u043d\u0438 \u0441\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438, \u0432 \u043a\u043e\u0438\u0442\u043e \u0441\u0430 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0430\u0442\u0430 \u0437\u0430 \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435\u0442\u043e \u0438\u043c \u0437\u0430 \u0440\u0430\u0437\u043d\u043e- \u043e\u0431\u0440\u0430\u0437\u043d\u0438 \u0441\u0442\u043e\u0439\u043d\u043e\u0441\u0442\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f \u043d\u0430 \u0440\u0435\u0434\u043e\u0432\u0435\u0442\u0435 \u0438 \u043a\u043e\u043b\u043e\u043d\u043a\u0438\u0442\u0435 \u0432 \u043c\u0430\u0441\u0438\u0432\u0438\u0442\u0435. \u0427\u0430\u0441\u0442 \u043e\u0442 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043e\u0442 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0442\u0435 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438 \u0441\u0430 \u0434\u0430\u0434\u0435\u043d\u0438 \u0432 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u0438 \u0438 \u0441\u0430 \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u043d\u0438 \u0441\u044a\u0441 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0438. \u041d\u0430\u0439-\u0434\u043e\u0431\u0440\u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0430 \u043e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\u0442\u0435, \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u0449\u0438 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438\u0442\u0435 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438, \u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u043e\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c\u0430 \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0441 \u043a\u043e\u043d\u0446\u0435\u043d\u0442\u0440\u0438\u0447\u043d\u0438 \u043f\u043e\u0434\u043c\u0430\u0441\u0438\u0432\u0438. <\/p>\n

Keywords<\/em>: search in 2D arrays, 2D partially ordered arrays, Saddleback algorithm, empirical analysis<\/p>\n

2D ARRAYS: SEARCH ALGORITHMS  AND EXPERIMENTS<\/strong><\/p>\n

Abstract<\/strong>. The paper presents search algorithms applied to 2D partially ordered numeric arrays, i.e. the elements of the arrays are nonincreasing in both row and column. Four existing algorithms are discussed in the text. One of them is the Saddleback algorithm. A new search algorithm through concentric subarrays is offered by the author. The main idea of this algorithm consists of the construction of a series of subarrays with a decreasing number of their rows and columns. Each next subarray is fully contained in the previous subarray. This means that if the searched number is in the initial array, it belongs to all next subarrays. The last subarray of this series will consist of one single element which equals the searched number. All presented five algorithmsare implemented in the programming environment of Microsoft Visual C++. Additional experiments were conducted to find out the respective execution time for each of these five algorithms by selecting a variety of values for the number of rows and columns. Some of the obtained results are presented in tables, included in the text of the paper, and are also accompanied by the corresponding charts. The best values for the execution time are established for the search algorithm through concentric subarrays.<\/p>\n

* Dr. Pavel Azalov, Assoc. Prof.<\/strong>
Pennsylvania State University
Hazleton campus
U.S.A.<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u0425\u041e\u041c\u041e\u0422\u0415\u0422\u0418\u0427\u041d\u0418 \u041a\u041e\u041d\u0418\u0427\u041d\u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f \u0412 \u0420\u0410\u0412\u041d\u0418\u041d\u0410\u0422\u0410 \u041d\u0410 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a <\/strong><\/p>\n

1\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, <\/strong>
2\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong>
1\u0411\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0430 \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u043d\u0430 \u043d\u0430\u0443\u043a\u0438\u0442\u0435 <\/em>
2\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 – \u041b\u043e\u0432\u0435\u0447<\/em><\/p>\n

Abstract<\/strong>. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043e\u043f\u0438\u0441\u0430\u043d \u0435\u0434\u0438\u043d \u043d\u0430\u0447\u0438\u043d \u0437\u0430 \u043e\u0431\u0435\u0434\u0438\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u043e\u043d\u0438\u0447\u043d\u0438\u0442\u0435 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0434\u0430\u0434\u0435\u043d \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0432 \u043a\u043b\u0430\u0441\u043e\u0432\u0435 \u043e\u0442 \u0445\u043e\u043c\u043e\u0442\u0435\u0442\u0438\u0447\u043d\u0438 \u043a\u0440\u0438\u0432\u0438. \u0422\u0435\u0437\u0438 \u043a\u043b\u0430\u0441\u043e\u0432\u0435 \u0441\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442 \u043e\u0442 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0442\u0435 \u0437\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f.<\/p>\n

Keywords<\/em>: triangle, homothety, conic, pole, polar<\/p>\n

HOMOTHETIC CONICS IN THE PLANE OF A TRIANGLE<\/strong><\/p>\n

Abstract<\/strong>. The present paper considers a method for the classification of the conics in the plane of a triangle into classes of homothetic curves. The classes are determined by the circumscribed conics of the triangle. <\/p>\n

*  Prof. Sava Grozdev,<\/strong>
DSc Institute of Mathematics and Informatics \u2013 BAS <\/p>\n

*  Dr. Veselin Nenkov, Assoc. Prof.<\/strong>
Technical College Lovech<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u041d\u042f\u041a\u041e\u0418 \u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u041e\u0411\u041e\u0411\u0429\u0415\u041d\u0418\u042f  \u0417\u0410 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0415\u0414\u0418\u041d \u0422\u0418\u041f \u0417\u0410\u0414\u0410\u0427\u0418  \u041e\u0422 \u041b\u0418\u041d\u0415\u0419\u041d\u0410\u0422\u0410 \u0410\u041b\u0413\u0415\u0411\u0420\u0410 <\/strong><\/p>\n

\u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, <\/strong>
\u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432<\/strong>
University of Economics \u2013 Varna<\/em><\/p>\n

Abstract<\/strong>. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f, \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u0442\u0430 \u043d\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u043e \u043f\u043e\u0434\u0431\u0440\u0430\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, e \u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0430 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0437\u0430 \u043f\u0440\u0435\u0441\u043c\u044f\u0442\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u043d\u0430 \u0441\u0442\u0435\u043f\u0435\u043d \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0430 \u043c\u0430- \u0442\u0440\u0438\u0446\u0430 \u043e\u0442 \u0432\u0442\u043e\u0440\u0438 \u0440\u0435\u0434 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0440\u0435\u043a\u0443\u0440\u0435\u043d\u0442\u043d\u0438 \u0440\u0435\u0434\u0438\u0446\u0438. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0438\u043c\u0430 \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e- \u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440, \u043a\u0430\u0442\u043e \u0430\u043a\u0446\u0435\u043d\u0442\u044a\u0442 \u0435 \u043f\u043e\u0441\u0442\u0430\u0432\u0435\u043d \u0432\u044a\u0440\u0445\u0443 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u043e\u0441\u0442\u0442\u0430 \u043e\u0442 \u0440\u0430\u0437\u0441\u044a\u0436- \u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435 – \u043e\u0442 \u0438\u0434\u0435\u044f\u0442\u0430 \u0437\u0430 \u0441\u044a\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u043d\u0430 \u043f\u043e\u0434\u043e\u0431\u0435\u043d \u0432\u0438\u0434 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435, \u0434\u0430\u0432\u0430\u0449\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u0434\u0438\u0440\u0435\u043a\u0442\u043d\u043e\u0442\u043e \u0438\u043c \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435. <\/p>\n

Keywords: 2\u00d72 matrices, recurrent sequence, characteristic equation, methodology.<\/p>\n

SOME METHODOLOGICAL GENERALIZATIONS IN THE SOLUTION OF A TYPE  OF LINEAR ALGEBRA PROBLEMS<\/strong><\/p>\n

Abstract<\/strong>. In the present article, on the basis of appropriately selected problems, a general formula for calculating a second-order square matrix to an unspecified power is derived using recurrences. The material concerns methodology with a stress on the consistency of the authors\u2019 reasoning \u2013 starting with the initial idea for composing such type of problems and ending with a conclusion, leading to their direct solutions.  <\/p>\n

* Dr. Rosen Nikolaev, Assoc. Prof.<\/strong>
University of Economics – Varna <\/p>\n

* Dr. Jordan Petkov, Assist. Prof.<\/strong>
University of Economics – Varna<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u0421\u042a\u0421\u0422\u0415\u0417\u0410\u041d\u0418\u0415\u0422\u041e \u201e\u0415\u0412\u0420\u041e\u041f\u0415\u0419\u0421\u041a\u041e \u041a\u0415\u041d\u0413\u0423\u0420\u0423\u201c \u0417\u0410 \u0423\u0427\u0415\u041d\u0418\u0426\u0418  \u0421\u042a\u0421 \u0417\u0420\u0418\u0422\u0415\u041b\u041d\u0418 \u0423\u0412\u0420\u0415\u0416\u0414\u0410\u041d\u0418\u042f <\/strong><\/p>\n

1\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, <\/strong>
2\u0415\u043b\u0438\u0437\u0430 \u041f\u0435\u0442\u0440\u043e\u0432\u0430 <\/strong>
1\u0411\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0430 \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u043d\u0430 \u043d\u0430\u0443\u043a\u0438\u0442\u0435 <\/em>
2\u0421\u041e\u0423 \u0437\u0430 \u0434\u0435\u0446\u0430 \u0441 \u043d\u0430\u0440\u0443\u0448\u0435\u043d\u043e \u0437\u0440\u0435\u043d\u0438\u0435 \u201e\u041b\u0443\u0438 \u0411\u0440\u0430\u0439\u043b\u201d<\/em> <\/p>\n

Abstract<\/strong>. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441\u044a\u0441 \u0437\u0440\u0438\u0442\u0435\u043b\u043d\u0438 \u0443\u0432\u0440\u0435\u0436- \u0434\u0430\u043d\u0438\u044f \u0437\u0430 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u0438\u044f \u0432 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u044f. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438 \u043e\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0430 \u0433\u043b\u0435\u0434\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u0432\u044a\u0432 \u0432\u0440\u044a\u0437\u043a\u0430 \u0441 \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u0430\u0442\u0430 \u0430\u0434\u0430\u043f\u0442\u0430\u0446\u0438\u044f \u043d\u0430 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438\u0442\u0435 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. <\/p>\n

Keywords: students with visual impairments, mathematics, competition, problem solving<\/p>\n

THE \u201cEUROPEAN KANGAROO\u201d COMPETITION FOR STUDENTS WITH VISUAL IMPAIRMENTS<\/strong><\/p>\n

Abstract.<\/strong> The paper is dedicated to students with visual impairments for their moti- vation of studying Mathematics by participating in competitions. Basic problems from methodological point of view are considered in connection with a suitable adaptation of corresponding test problems.   <\/p>\n

* Prof. Sava Grozdev, DSc<\/strong>
Institute of Mathematics and Informatics \u2013 BAS<\/p>\n

* Mrs. Eliza Petrova<\/strong>
\u201cLouis Braille\u201d Secondary School<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>ANALYSIS OF PROBLEM SOLVING IN INFORMATICS FOR 12 \u2013 13 YEAR OLD STUDENTS IN BULGARIA <\/strong><\/p>\n

Ivaylo Staribratov, <\/strong>
BistraTaneva<\/strong>
High School of Mathematics \u201eAkad. Kiril Popov\u201c<\/em><\/p>\n

Abstract<\/strong>. The present study aims at characterizing the solutions of tasks in Infor- matics from National competitions and Olympiads for Group D students relevant to 6th school grade. The study covers a 10-year-period (2004-2013). An application proposes a classification of these tasks based on their main characteristics. An evaluation of the relative difficulty of the tasks is also included. Keywords: Olympiad, Informatics, task, classification<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u041c\u041e\u0414\u0415\u041b \u0417\u0410 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0415\u0414\u0418\u041d \u041a\u041b\u0410\u0421 \u0417\u0410\u0414\u0410\u0427\u0418 \u0417\u0410 \u041f\u041e\u0421\u0422\u0420\u041e\u0415\u041d\u0418\u0415 \u0421 \u0414\u0418\u041d\u0410\u041c\u0418\u0427\u0415\u041d \u0421\u041e\u0424\u0422\u0423\u0415\u0420 <\/strong><\/p>\n

\u0412\u0430\u043d\u044f \u0411\u0438\u0437\u043e\u0432\u0430-\u041b\u0430\u043b\u0435\u0432\u0430<\/strong>
\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0430 \u0442\u044a\u0440\u0433\u043e\u0432\u0441\u043a\u0430 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u044f<\/em><\/p>\n

Abstract<\/strong>: \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0447\u0438\u0438\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0435 \u0441\u0432\u0435\u0436\u0434\u0430\u0442 \u0434\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0438\u0433\u0443\u0440\u0438. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u0438\u043d\u043e\u0432\u0430\u0442\u0438\u0432\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0438\u0433\u0443\u0440\u0438, \u0437\u0430 \u043a\u043e\u0438\u0442\u043e \u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442 \u043c\u0435\u0436\u0434\u0443 \u0434\u044a\u043b\u0436\u0438\u043d\u0438\u0442\u0435 \u043d\u0430 \u0434\u0432e \u043e\u0442\u0441\u0435\u0447\u043a\u0438 \u043e\u0442 \u0444\u0438\u0433\u0443\u0440\u0430\u0442\u0430 \u0441 \u043e\u0431\u0449 \u043a\u0440\u0430\u0439. \u041c\u043e\u0434\u0435\u043b\u044a\u0442 \u0435 \u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d, \u0447\u0440\u0435\u0437 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e GeoGebra. <\/p>\n

Keywords<\/em>: school mathematics, construction of geometric figures, geometric place of points, dynamic model, GeoGebra<\/p>\n

A MODEL FOR CONSTRUCTION PROBLEM SOLVING BY DYNAMIC SOFTWARE <\/strong><\/p>\n

Abstract<\/strong>. The paper considers practical problems, the solutions of which are reduced to the construction of geometrical figures. An innovative model is presented for the construction of geometrical figures, for which a relation between the lengths of two segments with a common extremity from the figure is known. The model is realized by means of GeoGebra application.<\/p>\n

* Mrs. Vania Bizova-Laleva<\/strong>
National High School of Commerce<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/p>","protected":false},"excerpt":{"rendered":"

 CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 IF YOU WORK WITH YOUNG STUDENTS \/ \u0410\u041a\u041e \u0420\u0410\u0411\u041e\u0422\u0418\u0422\u0415 \u0421 \u041c\u0410\u041b\u041a\u0418\u0422\u0415 \u0423\u0427\u0415\u041d\u0418\u0426\u0418 \u0417\u0430 \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\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 [On the Contemporary Methods in Primary School Mathematics] \/ \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432 \/ Zdravko Lalchev – \u0441\u0442\u0440. 103       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 \u0414\u0432\u0443\u043c\u0435\u0440\u043d\u0438 \u043c\u0430\u0441\u0438\u0432\u0438: \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0437\u0430 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0438 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438 [2D Arrays: Search […]<\/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":"\n"\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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LVII, 2014 - 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