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Abramova, O. M. Inversion of School Mathematical Problems as the Basis for Using Contemporary Education Technologies in Teaching Mathematics

Published in journal "Pedagogy and education", 2014-3 in rubric "Developing pedagogical technologies", pages 30-41.

Resume: The article contains a systematic description of some structures of mathematical problems that have proved to be efficient in teaching mathematics such as neighborhood of inversed problems which are meant to improve schoolers’ understanding of a relationship between values given in a problem. Abramova offers her own approach to teaching mathematics based on using inversion of mathematical problems in the process of solving them. According to Abramova, this will allow to enrich teaching methods and to carry out a goal-oriented development of thinking flexibility as an important intellectual quality. Abramova has performed theoretical and methodological analysis of all existing definitions of the term ‘inversed problem’. She underlines prospects and possibilities of using inversed problems in teaching mathematics at school. According to Abramova, this would make their mathematical education complete. The researcher also defines the semantic difference between ‘inversed problem’ and ‘inverse problem’. She describes their material expression in the form of model structures and gives examples of a direct, inverse and inversed problems as well as recommendations on their construction. Abramova also describes the inversion procedure for mathematical problems, defines the main stages of this procedure, gives recommendations regarding each stage and develop an algorithm for an independent inversion of a mathematical problem by a schooler.

Keywords: mathematical problems, inversion of problems, inverse problems, modern (contemporary) teaching technologies, inversion procedure, flexible thinking, algorithmic instructions, problem structure, teaching method, schoolers.

DOI: 10.7256/2306-434X.2014.3.14016

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Bibliography:
Abramova O.M. Odin iz sposobov obrashcheniya zadach kak sredstvo razvitiya gibkosti myshleniya shkol'nikov // Nachal'naya shkola plyus Do i Posle. 2012. ¹1. S.79-83.
Abramova O.M. Vozmozhnosti ispol'zovaniya pryamykh i obratnykh zadach v razvitii gibkosti myshleniya uchashchikhsya na urokakh matematiki // V mire nauchnykh otkrytiy. 2011. ¹ 9.1. S.183-194.
Artyukhina M.S. Interaktivnye tekhnologii v kontekste sovremennoy gumanitarno-orientirovannoy sistemy obrazovaniya // V mire nauchnykh otkrytiy. 2014. ¹ 3(51). S.38-48.
Artyukhina M.S., Artyukhin O.I., Kleshnina I.I. Apparatnaya sostavlyayushchaya interaktivnykh tekhnologiy obrazovatel'nogo naznacheniya // Vestnik Kazanskogo tekhnologicheskogo universiteta. 2014. T. 17. ¹ 8. S.308-314.
Gol'dman A.M., Zvavich L.I. Uchebnye serii na urokakh matematiki // Matematika v shkole, 1990. ¹5. S.19-22.
Gradshteyn I.S. Pryamaya i obratnaya teoremy. – L.: Gosudarstvennoe izd-vo tekhniko-teoreticheskoy literatury, 1950. 80 s.
Draznin I.E. Obrashchenie usloviy planimetricheskikh zadach // Matematika v shkole, 2001. ¹8. S.52–55.
Zaykin M.I., Abramova O.M. Obrashcheniem matematicheskikh zadach // Shkol'nye tekhnologii. 2013. ¹1. S.106-113.
Zaykin M.I., Egulemova N.N., Abramova O.M. Serii, variatsii i okrestnosti matematicheskikh zadach: Monografiya / Pod obshchey red. M.I. Zaykina, Arzamasskiy filial NNGU. – Arzamas: Arzamasskiy filial NNGU, 2014. 149 s.
Kanin E.S. Razvitie temy zadachi // Matematika v shkole, 1991. ¹3. S.8–12.
Tsukar' A.Ya. Metod vzaimno obratnykh zadach v obuchenii matematike. – Novosibirsk: Nauka, 1989. 40 s.
Erdniev P.M. Metodika uprazhneniy po matematike. – M.: Prosveshchenie, 1970. 319 s.

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