{"id":38122,"date":"2012-10-13T02:06:25","date_gmt":"2012-10-12T23:06:25","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"matematika-i-informatika-knizhka-5-godina-lv-2012-2","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/","title":{"rendered":"Mathematics and Informatics, Number 5\/2012, Volume 55"},"content":{"rendered":"

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

\u0414\u0435\u0441\u0435\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430
[Tenth International Linguistics Olympiad] \/
\u0418. \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ I. Derzhanski<\/em> \u2013 p. 391<\/p>\n

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Mathematical Competitions and Students\u2019 Self-Esteem<\/a> \/
G. Dolinar<\/em> \u2013 p. 399<\/p>\n

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\u0410\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0432\u044a\u043d\u0448\u043d\u043e\u0442\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0437\u0430 \u0447\u0435\u0442\u0432\u044a\u0440\u0442\u0438 \u043a\u043b\u0430\u0441 \u0437\u0430 2011 \u0433\u043e\u0434\u0438\u043d\u0430 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f<\/a>
[External Evaluation Analysis of Mathematics at Fourth Grade for Year 2011 in Bulgaria] \/ <\/a>
\u041c. \u0417\u0430\u043c\u0444\u0438\u0440\u043e\u0432 \/ M. Zamfirov<\/em> \u2013 p. 405<\/p>\n

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\u0421\u0438\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u0447\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u201e\u041f\u0440\u043e\u0431\u0443\u0436\u0434\u0430\u0449\u043e \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u201d <\/a>
[Synergetic Model \u201cAwakening Mathematical Teaching\u201d] \/ <\/a>
\u0414. \u0413\u044a\u043b\u044a\u0431\u043e\u0432\u0430 \/ D. Galabova<\/em> \u2013 p. 416<\/p>\n

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\u0415\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u2013 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u201e\u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438\u201d \u0440\u0435\u0448\u0435\u043d\u0438\u044f <\/a>
[One Problem \u2013 Several \u201cElementary\u201d Solutions] \/ <\/a>
\u042e. \u041d\u0438\u043d\u043e\u0432\u0430 \/ J. Ninova, \u0412. \u041c\u0438\u0445\u043e\u0432\u0430 \/ V. Mihova<\/em> \u2013 p. 426<\/p>\n

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\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430 \u0412\u0430\u043d \u041e\u0431\u0435\u043b \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f <\/a>
[Van Aubel\u2019s Theorem and Applications] \/ <\/a>
\u0422. \u0413\u043b\u0443\u0448\u043a\u043e\u0432\u0430 \/ T. Glushkova, \u0411. \u0417\u043b\u0430\u0442\u0430\u043d\u043e\u0432 \/ B. Zlatanov<\/em> \u2013 p. 445<\/p>\n

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\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043b\u0443\u0431 \u201e\u0421\u0438\u0433\u043c\u0430\u201d \u0432 \u0441\u0432\u0435\u0442\u043b\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442 \u0423\u0421\u041f\u0415\u0425 <\/a>
[The Mathematical Club \u201cSigma\u201d in the Light of the Project Success] \/ <\/a>
\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev, \u0418. \u041c\u0430\u0440\u0430\u0448\u0435\u0432\u0430 \/ I. Marasheva, \u0415. \u0414\u0435\u043b\u0438\u043d\u043e\u0432 \/ E. Delinov – <\/em>\u2013 p. 453<\/p>\n

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\u0414\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0438 \u0432 \u043f\u0440\u043e\u0444\u0435\u0441\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u201e\u041f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u043a\u0430\u201d <\/a>
[Dissertations in Professional Direction \u201cPedagogy\u201d] \/ <\/a>
\u041f. \u0410\u0441\u0435\u043d\u043e\u0432\u0430\/ P. Assenova, \u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev<\/em> \u2013 p. 462<\/p>\n

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\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \/ CONTEST PROBLEMS<\/strong> \u2013 p. 470
The column is led by Dr. Svetlozar Doychev and Dr. Veselin Nenkov<\/em><\/p>\n

Solutions of the contest problems from issue 6, 2011 - p. 471<\/p>\n

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In Memoriam<\/strong> - Prof. Ivan Ganchev Donev - p. 473<\/p>\n

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 <\/p>\n

\n

  <\/a>MATHEMATICAL COMPETITIONS AND STUDENTS\u2018 SElf-ESTEEM<\/strong><\/p>\n


Gregor Dolinar
<\/strong>Professor<\/em>
Faculty of Electrical Engineering, University of Ljubljana<\/em><\/p>\n


Abstract.<\/strong> Educational system and mathematical competitions in Slovenia were revised in the recent years. The impact of these changes to students\u2019 self-esteem and to students\u2019 affect towards mathematics is analysed. <\/p>\n

Keywords:<\/em> Educational system reform, mathematical competition<\/p>\n<\/p>\n

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

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 <\/a>\u0410\u041d\u0410\u041b\u0418\u0417 \u041d\u0410 \u0412\u042a\u041d\u0428\u041d\u041e\u0422\u041e \u041e\u0426\u0415\u041d\u042f\u0412\u0410\u041d\u0415 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0417\u0410 \u0427\u0415\u0422\u0412\u042a\u0440\u0422\u0418 \u041a\u041b\u0410\u0421 \u0417\u0410 2011 \u0413. \u0412 \u0411\u042a\u041b\u0413\u0410\u0440\u0418\u042f<\/strong><\/p>\n


Milen Zamfirov
<\/strong>\u041a\u0430\u0442\u0435\u0434\u0440\u0430 \u0421\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u0430 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u043a\u0430<\/em>
\u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442 \u043f\u043e \u043d\u0430\u0447\u0430\u043b\u043d\u0430 \u0438 \u043f\u0440\u0435\u0434\u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u043a\u0430, <\/em>
\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438\u201d<\/em><\/p>\n


\u0420\u0437\u044e\u043c\u0435.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043e\u0442 \u0432\u044a\u043d\u0448\u043d\u043e\u0442\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f\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 \u0432 \u0447\u0435\u0442\u0432\u044a\u0440\u0442\u0438 \u043a\u043b\u0430\u0441, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e \u043f\u0440\u0435\u0437 \u043c\u0435\u0441\u0435\u0446 \u043c\u0430\u0439, 2011 \u0433. \u0441 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u0435\u043b\u043d\u0430 \u0438\u0437\u0432\u0430\u0434\u043a\u0430 (12 000 \u0443\u0447\u0435\u043d\u0438\u0446\u0438). \u0411\u0440\u043e\u044f\u0442 \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u043b\u0438\u0442\u0435 \u0432\u044a\u0432 \u0432\u044a\u043d\u0448\u043d\u043e\u0442\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0447\u0435\u0442\u0432\u044a\u0440\u0442\u043e\u043a\u043b\u0430\u0441\u043d\u0438\u0446\u0438 \u0435 61 408 \u0432 3381 \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u043a\u0438 \u043e\u0442 1886 \u0443\u0447\u0438\u043b\u0438\u0449\u0430, \u0432 262 \u043e\u0431\u0449\u0438\u043d\u0438 \u0432\u044a\u0432 \u0432\u0441\u0438\u0447\u043a\u0438 28 \u0440\u0435\u0433\u0438\u043e\u043d\u0430.
\u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0432\u043a\u043b\u044e\u0447\u0432\u0430:
\u00b7 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u043f\u0441\u0438\u0445\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0442\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043d\u0430 \u0442\u0435\u0441\u0442\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430;
\u00b7 \u043e\u0431\u0449 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u043f\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435;
\u00b7 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f\u0442\u0430 \u0432 \u043f\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0441\u043f\u043e\u0440\u0435\u0434 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u0442\u0435\u0445\u043d\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438.<\/p>\n

Keywords:<\/em> external evaluation 2011, mathematics, general analysis<\/p>\n

EXTERNAL EVALUATION ANALYSIS OF MATHEMATICS AT FOURTH GRADE FOR YEAR 2011 IN BULGARIA<\/strong><\/p>\n


Abstract.<\/strong> This article presents analysis on external evaluation of students\u2019 achievements in mathematics school subject in fourth grade. The evaluation is conducted in May 2011 with a representative number of participants (12 000 students). The number of all participants in fourth grade in mathematics in the external evaluation is 61 408 in 3 381 classes at 1 886 schools in 262 municipalities in all 28 regions of Bulgaria.<\/p>\n

The article includes:
\u00b7 analysis of psychometricla characteristics of the test for mathematics;
\u00b7 general analysis of students\u2019 achievements;
\u00b7 analysis of the differentces in students\u2019 achievements which correspond to their characteristics.<\/p>\n

Milen Zamfirov, (corresponding author) <\/strong>
PhD<\/em>
Department of Special Education, <\/em>
Faculty of Preschool and Primary School Education<\/em>
University of Sofia<\/em><\/p>\n

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

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 <\/a>\u0421\u0418\u041d\u0415\u0420\u0413\u0415\u0422\u0418\u0427\u0415\u041d \u041c\u041e\u0414\u0415\u041b \u201e\u041f\u0420\u041e\u0411\u0423\u0416\u0414\u0410\u0429\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u201d<\/strong><\/p>\n

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\u0414\u0430\u0440\u0438\u043d\u043a\u0430 \u0413\u044a\u043b\u044a\u0431\u043e\u0432\u0430<\/strong><\/p>\n


Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0437\u0430 \u0441\u0438\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u0447\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f \u0438\u0434\u0435\u044f\u0442\u0430 \u0437\u0430 \u201e\u043f\u0440\u043e\u0431\u0443\u0436\u0434\u0430\u0449\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u201d, \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u043e\u0442 \u043f\u0440\u043e\u0444. \u0415\u043b\u0435\u043d\u0430 \u041a\u043d\u044f\u0437\u0435\u0432\u0430 \u0438 \u043f\u0440\u043e\u0444. \u0421.\u041f.\u041a\u0443\u0440\u0434\u044e\u043c\u043e\u0432. \u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u0441\u0435 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u043f\u0440\u043e\u0431\u0443\u0436\u0434\u0430\u0449\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u043e\u0442 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u201e\u041f\u0440\u043e\u0431\u0443\u0436\u0434\u0430\u0449\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u201d. \u041c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435\u0442\u043e \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0430 \u0447\u0440\u0435\u0437 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u0418\u041a\u0422 (\u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u0443\u0440\u043e\u0447\u043d\u0438 \u043f\u0440\u0435\u0437\u0435\u043d\u0442\u0430\u0446\u0438\u0438, \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0435\u043d \u0443\u0447\u0435\u0431\u0435\u043d \u043c\u043e\u0434\u0443\u043b \u0432 \u0441\u0440\u0435\u0434\u0430\u0442\u0430 GeoNext).<\/p>\n

Keywords:<\/em> synergetics, awakening teaching, mathematical education, interactive methods, computer presentation of a lesson, dynamic teaching software GeoNext<\/p>\n

SYNERGETIC MODEL \u201cAWAKENING MATHEMATICAL TEACHING\u201d<\/strong><\/p>\n

Abstract.<\/strong> The paper analyzes the problem of the synergetic approach in mathematical education, and promotes the idea of \u201cawakening teaching\u201d introduced by Professor Helena Knyazeva and Professor S. P. Kurdyumov. A structural model of awakening teaching and the results of the \u201cAwakening mathematical teaching\u201d research are presented. The methodology of research through educational Informational Computer Technologies (computer lesson presentations, online training module in the GeoNext space) and interactive methods are also described.<\/p>\n

Darinka Galabova<\/strong>
Assistant Professor, Doktor <\/em>
St. Cyril and St Methodius University of Veliko Tarnovo<\/em><\/p>\n

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

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  <\/a>\u0415\u0414\u041d\u0410 \u0417\u0410\u0414\u0410\u0427\u0410 \u2013 \u041d\u042f\u041a\u041e\u041b\u041a\u041e \u201e\u0415\u041b\u0415\u041c\u0415\u041d\u0422\u0410\u0420\u041d\u0418\u201c \u0420\u0415\u0428\u0415\u041d\u0418\u042f<\/strong><\/p>\n

\n

Julia Ninova<\/strong>
\u0412\u0435\u0441\u0435\u043b\u043a\u0430 \u041c\u0438\u0445\u043e\u0432\u0430<\/strong><\/p>\n

Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0435\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442-\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0441\u043a\u0438\u044f \u0438\u0437\u043f\u0438\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0421\u0423 \u201e\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438\u201c, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d \u043d\u0430 11 \u044e\u043b\u0438 2011 \u0433. \u0412 \u043d\u0435\u044f \u0441\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u0438 \u043a\u043e\u043c\u0435\u043d\u0442\u0438\u0440\u0430 \u043f\u0443\u0431\u043b\u0438\u043a\u0443\u0432\u0430\u043d\u043e\u0442\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 (http:\/\/www.fmi.uni-sofia.bg\/priem\/ksi2011-2tema2-reshenia.pdf) \u0438 \u0441\u0435 \u0434\u0430\u0432\u0430\u0442 \u0447\u0435\u0442\u0438\u0440\u0438 \u201c\u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438\u201d \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u0432 \u043a\u043e\u0438\u0442\u043e \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0442 \u043f\u043e\u0437\u043d\u0430\u043d\u0438\u044f \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043f\u0440\u0438 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0439 \u043a\u0430\u0442\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u0438\u0440\u0430\u0449 \u043f\u0440\u0435\u0434\u043c\u0435\u0442.<\/p>\n

Keywords:<\/em> function, graphical representation, continuity, derivative, trigonometric equation.<\/p>\n

ONE PROBLEM \u2013 SEVERAL \u201cELEMENTARY\u201d SOLUTIONS<\/strong><\/p>\n

Abstract.<\/strong> The paper considers a mathematical problem from the entrance exam in the Sofia University \u201cSt. Kliment Ohridski\u201d, held on July 11, 2011. It analyzes and comments the published exemplary solution (http:\/\/www.fmi.uni- sofia.bg\/priem\/ksi2011-2tema2-reshenia.pdf) and proposes four \u201celementary\u201d solutions, based on familiar and exercised knowledge in Mathematics as a profiling subject.<\/p>\n

Julia Ninova<\/strong>
Associated professor, PhD <\/em>
FMI, Sofia University<\/em><\/p>\n


Vesselka Mihova
<\/strong>Associated professor, PhD 
<\/em>FMI, Sofia University<\/em><\/p>\n

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

 <\/p>\n

 <\/p>\n

\n

 <\/a>\u0422\u0415\u041e\u0420\u0415\u041c\u0410 \u041d\u0410 \u0412\u0410\u041d \u041e\u0411\u0415\u041b \u0418 \u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u042f<\/strong><\/p>\n


\u0422\u043e\u0434\u043e\u0440\u043a\u0430 \u0413\u043b\u0443\u0448\u043a\u043e\u0432\u0430, \u0411\u043e\u044f\u043d \u0417\u043b\u0430\u0442\u0430\u043d\u043e\u0432<\/strong><\/p>\n


Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0422\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0412\u0430\u043d \u041e\u0431\u0435\u043b \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043e\u0442 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u044f \u043a\u0443\u0440\u0441. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0430 \u0435 \u0438 \u0435\u0434\u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430. <\/p>\n

Keywords:<\/em> Van Aubel\u2019s Theorem, Ceva\u2019s Theorem, Nagel Point, Gergonne point.<\/p>\n

VAN AUBEL\u2019S THEOREM AND APPLICATIONS<\/strong><\/p>\n

Abstract.<\/strong> Applications of Van Aubel\u2019s theorem to solve problems of school geometry course are discussed in the paper. One authors\u2019 task is presented.<\/p>\n

Todorka Glushkova<\/strong>
Ph.D.<\/em>
\u201cHristo Smirnenski \u201d school<\/em><\/p>\n

Boyan Zlatanov<\/strong>
Associate Professor, Ph.D.<\/em>
Plovdiv University \u201cPaisii Hilendarski\u201d<\/em>
Faculty of Mathematics and Informatics<\/em><\/p>\n

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

 <\/p>\n

 <\/p>\n

\n

 <\/a>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u041a\u041b\u0423\u0411 \u201e\u0421\u0418\u0413\u041c\u0410\u201d \u0412 \u0421\u0412\u0415\u0422\u041b\u0418\u041d\u0410\u0422\u0410 \u041d\u0410 \u041f\u0420\u041e\u0415\u041a\u0422 \u0423\u0421\u041f\u0415\u0425<\/strong><\/p>\n

\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

Abstract.<\/strong> \u041e\u0442 \u043d\u0430\u0447\u0430\u043b\u043e\u0442\u043e \u043d\u0430 \u0432\u0442\u043e\u0440\u0438 \u0441\u0440\u043e\u043a \u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u0430\u0442\u0430 2011\/2012 \u0433\u043e\u0434\u0438\u043d\u0430 \u0441\u0442\u0430\u0440\u0442\u0438\u0440\u0430 \u043f\u0440\u043e\u0435\u043a\u0442 \u0423\u0421\u041f\u0415\u0425, \u043a\u043e\u0439\u0442\u043e \u0440\u0430\u0437\u0432\u0438\u0432\u0430 \u0438\u0437\u0432\u044a\u043d\u043a\u043b\u0430\u0441\u043d\u0438 \u0434\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0430\u0442\u0430. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u0430 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043b\u0443\u0431 \u201e\u0421\u0438\u0433\u043c\u0430\u201d \u043a\u044a\u043c 21 \u0421\u041e\u0423 \u201e\u0425\u0440\u0438\u0441\u0442\u043e \u0411\u043e\u0442\u0435\u0432\u201d, \u0421\u043e\u0444\u0438\u044f \u0432 \u0440\u0430\u043c\u043a\u0438\u0442\u0435 \u043d\u0430 \u0442\u043e\u0437\u0438 \u043f\u0440\u043e\u0435\u043a\u0442. \u0414\u0435\u0439\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u043a\u043b\u0443\u0431\u0430 \u0441\u0435 \u0441\u044a\u0441\u0442\u043e\u0438 \u0432 \u043f\u0440\u043e\u0443\u0447\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430 \u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0420\u0430\u0431\u043e\u0442\u0430\u0442\u0430 \u0435 \u0432 \u0435\u043a\u0438\u043f\u0438 \u0438 \u0432\u043a\u043b\u044e\u0447\u0432\u0430 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u0438 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 \u043d\u043e\u0432\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438. \u041e\u0441\u043d\u043e\u0432\u043d\u0430\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0435 \u0434\u0430 \u0441\u0435 \u0441\u044a\u0437\u0434\u0430\u0434\u0435 \u0442\u0430\u043a\u044a\u0432 \u043c\u0438\u043a\u0440\u043e\u043a\u043b\u0438\u043c\u0430\u0442, \u043a\u043e\u0439\u0442\u043e \u0440\u0430\u0437\u0432\u0438\u0432\u0430 \u043b\u0438\u0447\u043d\u0438\u044f \u0438\u043d\u0442\u0435\u0440\u0435\u0441 \u0438 \u0442\u0430\u043b\u0430\u043d\u0442\u0430, \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0442\u0430 \u0438 \u0436\u0435\u043b\u0430\u043d\u0438\u0435\u0442\u043e \u0437\u0430 \u043f\u0440\u0438\u0434\u043e\u0431\u0438\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u043e\u0432\u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u0438 \u0443\u043c\u0435\u043d\u0438\u044f.<\/p>\n

Keywords:<\/em> project work; team work; new technologies; Dropbox in the school; usage of cloud technology in school<\/p>\n

THE MATHEMATICAL CLUB \u201cSIGMA\u201d I<\/strong>N THE LIGHT OF THE PROJECT SUCCESS<\/strong><\/p>\n


Abstract.<\/strong> Since the beginning of the second term of the 2011\/2012 school year the Ministry of Education, Youth and Science started the Project SUCCESS, which develops extracurricular activities. The present paper registers the work within the project of the Mathematical club \u201cSigma\u201d at the Sofia Secondary School No 21 \u201cHristo Botev\u201d. The activities of the club include both examination of mathematical literature and elaboration of mathematical projects. It is applied a team work. Teaching is based on new technologies. Fundamental aim is to create such a microclimate, which enables the development of personal interest and talent, corresponding activity and presence of willingness to gain new knowledge and skills.<\/p>\n

Sava Grozdev<\/strong>
Professor, Doctor in Mathematics, DSc in Pedagogy<\/em>
Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n


Ivanka Marasheva<\/strong>, 
Doctor in Pedagogy<\/em>
21st Secondary School Hristo Botev<\/em><\/p>\n

Emil Delinov<\/strong><\/p>\n

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

 <\/p>\n

\n

 <\/a>\u0414\u0418\u0421\u0415\u0420\u0422\u0410\u0426\u0418\u0418 \u0412 \u041f\u0420\u041e\u0424\u0415\u0421\u0418\u041e\u041d\u0410\u041b\u041d\u041e \u041d\u0410\u041f\u0420\u0410\u0412\u041b\u0415\u041d\u0418\u0415 \u201c\u041f\u0415\u0414\u0410\u0413\u041e\u0413\u0418\u041a\u0410\u201d<\/strong><\/p>\n

\n

\u041f\u0435\u0442\u044f \u0410\u0441\u0435\u043d\u043e\u0432\u0430, \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432<\/strong><\/p>\n


Abstract.<\/strong> \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0437\u0430\u0449\u0438\u0442\u0435\u043d\u0438\u0442\u0435 \u0434\u043e\u043a\u0442\u043e\u0440\u0441\u043a\u0438 \u0434\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0438 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442 \u043d\u0430 \u0432\u0438\u0441\u0448\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 1. \u041f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0430\u0443\u043a\u0438, \u043f\u0440\u043e\u0444\u0435\u0441\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 1.3. \u041f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u043a\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0438\u0438 \u043d\u0430 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438\u0442\u0435 \u0434\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u0438.<\/p>\n

\n

Keywords:<\/em> dissertation, pedagogy, mathematics, informatics, information technology<\/p>\n

DISSERTATIONS IN PROFESSIONAL DIRECTION \u201cPEDAGOGY\u201d<\/strong><\/p>\n

Petya Assenova, Sava Grozdev<\/strong><\/p>\n

\n

Abstract.<\/strong> The information note is dedicated to the defended doctoral dissertations in Higher education domain 1. Pedagogical sciences, professional direction 1.3. Pedagogy of Mathematics, Informatics and Information technologies. Annotations of the corresponding dissertations are proposed. <\/p>\n

\n

Petya Assenova
<\/strong>Associated Professor, PhD in Pedagogy<\/em>
New Bulgarian Unversity<\/em><\/p>\n

Sava Grozdev<\/strong>
Professor, Doctor in Mathematics, DSc in Pedagogy<\/em>
Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n

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

 <\/p>\n

\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

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

 \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0414\u0435\u0441\u0435\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430 [Tenth International Linguistics Olympiad] \/ \u0418. \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ I. Derzhanski – \u0441\u0442\u0440. 391 Mathematical Competitions and Students\u2019 Self-Esteem \/ G. Dolinar – \u0441\u0442\u0440. 399 \u0410\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0432\u044a\u043d\u0448\u043d\u043e\u0442\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0437\u0430 \u0447\u0435\u0442\u0432\u044a\u0440\u0442\u0438 \u043a\u043b\u0430\u0441 \u0437\u0430 2011 \u0433\u043e\u0434\u0438\u043d\u0430 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f[External Evaluation Analysis of Mathematics at Fourth Grade for Year 2011 in […]<\/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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012 - \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:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\""\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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\" \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0414\u0435\u0441\u0435\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430 [Tenth International Linguistics Olympiad] \/ \u0418. \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ I. Derzhanski – \u0441\u0442\u0440. 391 Mathematical Competitions and Students\u2019 Self-Esteem \/ G. Dolinar – \u0441\u0442\u0440. 399 \u0410\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0432\u044a\u043d\u0448\u043d\u043e\u0442\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0437\u0430 \u0447\u0435\u0442\u0432\u044a\u0440\u0442\u0438 \u043a\u043b\u0430\u0441 \u0437\u0430 2011 \u0433\u043e\u0434\u0438\u043d\u0430 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f[External Evaluation Analysis of Mathematics at Fourth Grade for Year 2011 in […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\" \/>\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=\"2012-10-12T23:06:25+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-24T14:33:15+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=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\"},\"author\":{\"name\":\"\",\"@id\":\"\"},\"headline\":\"„\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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012\",\"datePublished\":\"2012-10-12T23:06:25+00:00\",\"dateModified\":\"2019-06-24T14:33:15+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\"},\"wordCount\":1668,\"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:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\",\"url\":\"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lv-2012-2\/\",\"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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LV, 2012 - 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