**EURASIA Journal of Mathematics, Science and Technology Education**
Volume 13, Issue 6 (June 2017), pp. 1799-1815

DOI: 10.12973/eurasia.2017.00698a

Downloaded 466 times.

**Research Article**

*Published online on May 01, 2017*

How to reference this article?

**Developing Creativity of Schoolchildren through the Course “Developmental Mathematics”**

Pavel M. Gorev, Alfiya R. Masalimova, Farida Sh. Mukhametzyanova & Elena V. Makarova

The relevance of the present study is due to the importance of developing creativity which can be achieved through a variety of school subjects including mathematics. In the article the potential of extended (supplementary) mathematical education (in primary and secondary schools) is highlighted. The main objective of this study is to examine and evaluate the contents, practices and methods that are currently employed in extended education. The main empirical method of this study is modeling of the modular system of lessons (the course) that offers a variety of assignments including non-standard tasks, puzzles and problems; tasks and topics from academic Olympiads and other mathematical competitions; creative tasks, practical assignments and experiments with mathematical materials ("empirical" mathematics); team and individual competitions and organization of home readings on a specific subject. The article describes the author's methodology. The main feature of the developed course is the inclusion of various organizational forms and diverse materials aimed at sustaining schoolchildren’s interest towards mathematics, enabling them to deal with advanced level mathematical problems and developing their curiosity and creativity. The course "Developmental Mathematics" that is presented in this article has been empirically tested since 2008.

Keywords: extended mathematical education; continuous creativity development; organization of extended mathematical education; primary and secondary schoolchildren.

- Akkaya, R. (2016) Research on the Development of Middle School Mathematics Pre-service Teachers’ Perceptions Regarding the Use of Technology in Teaching Mathematics.
*EURASIA Journal of Mathematics, Science and Technology Education*, 12(4). doi: 10.12973/eurasia.2016.1257a. - Antonijević, R. (2016) Cognitive Activities in Solving Mathematical Tasks: The role of a Cognitive Obstacle.
*EURASIA Journal of Mathematics, Science and Technology Education*, 12(9). doi: 10.12973/eurasia.2016.1306a. - Arnold, V. I. (2002).
*What is mathematics?*Moscow: MTsNMO. - Bahar, A. & Maker, C. J. (2015) Cognitive Backgrounds of Problem Solving: A Comparison of Open-ended vs. Closed Mathematics Problems.
*EURASIA Journal of Mathematics, Science and Technology Education*, 11(6). doi: 10.12973/eurasia.2015.1410a. - Balk, G. D. (1969). About application of heuristic methods in school teaching mathematics.
*Mathematics at school*, 5, 21–28. - Balk, M. B. (1956).
*Organization and content of out-of-class classes in mathematics*. Moscow: GUPI MT RSFSR. - Barr, S. (1987)
*Placers puzzles*. Moscow: Mir. - Bruner, J. (1977).
*Psychology of cognition. Outside the direct information*. Moscow: Progress. - Courant, R. & Robbins G. (1967).
*What is mathematics?*Moscow: Education. - Episheva, O. B. & Krupich, V. I. (1990).
*To teach school students to study mathematics: formation of methods of educational activity*. Moscow: Education. - Farkov A. V. (2008).
*Out-of-class work on mathematics. 5–11 grades*. Moscow: Ayres-press. - Gabdrakhmanova, R.G., Khuziakhmetov, A.N. & Yesnazarova, U.A. (2015). The Formation of Values of Education in the Mathematics Teachers of the Future in the Process of Adaptation into University Study.
*IEJME-Mathematics Education, 10(3),*147-155. - Galkin, E. V. (1996)
*Custom math problems: the logical nature of the problem*. Moscow: Education. - Gardner, M. (1999)
*A Math Puzzles and entertainment*. Moscow: Mir. - Genkin, S. A. & Itenberg, I. V. & Fomin D. V. (1994).
*Leningrad mathematical sections*. Kirov: ASA. - Gin, A. & Barkan, M. (2014).
*Open tasks as an instrument for creative thinking development.*Moscow: National education. - Gnedenko, B. V. (1979). About mathematical creativity.
*Mathematics at School*, 6, 16-22. - Gorbachev, N. V. (2004)
*Collection Olympiad problems in mathematics*. Moscow: MTsNMO. - Gorev, P. M. & Utemov, V. V. (2011).
*Formula of creativity: solve open problems.*Kirov: Publishing house VyaTGGU. - Gorev, P. M. & Utemov, V. V. (2012).
*Flight to the creativity horizons*. Kirov: Publishing house of "O-short”. - Gorev, P. M. & Utemov, V. V. (2012).
*Magic dreams of the Owlet*. Kirov: Publishing house VyaTGGU. - Gorev, P. M. & Utemov, V. V. (2013).
*Expedition to the world of creativity*. Kirov: Publishing house "O-kratkoe. - Gorev, P. M. & Utemov, V. V. (2013).
*Travel to the Country of creativity*. Kirov: Publishing house VyaTGGU. - Gorev, P. M. & Utemov, V. V. (2014).
*Creative walks under the stars*. Kirov: Publishing house MTsITO. - Gorev, P. M. & Utemov, V. V. (2014).
*Lessons of the Developmental Mathematics. 5–6 grades: Problems of a mathematical section.*Kirov: Publishing house MTsITO. - Gorev, P. M. & Utemov, V. V. (2015).
*Fascinating voyage of the Owlet*. Kirov: Publishing house MTsITO. - Gorev, P. M. & Utemov, V. V. (2015).
*Twenty smart problems of the Owlet*. Kirov: Publishing house MTsITO. - Gorev, P. M. & Utemov, V. V. (2016).
*Significant events of the Owlet*. Kirov: Publishing house MTsITO. - Gorev, P. M. (2012).
*Familiarizing with mathematical creativity: additional mathematical education.*Saarbrucken: Lambert Academic Publishing. - Gusev, V. A. (2003).
*Psychology-pedagogical bases of training mathematics.*Moscow: Verbum-M. - Hardy, J. (1998)
*Logical absurdities, trompe l'oeil*. Moscow: AST-Press. - Karagöz-Akar, G. (2016) Prospective Secondary Mathematics Teachers’ Perspectives and Mathematical Knowledge for Teaching.
*EURASIA Journal of Mathematics, Science and Technology Education*, 12(1), doi: 10.12973/eurasia.2015.1378a. - Kennedy, E. & Smolinsky, L. (2016) Math Circles: A Tool for Promoting Engagement among Middle School Minority Males.
*EURASIA Journal of Mathematics, Science and Technology Education*, 12(4), 717-732. doi: 10.12973/eurasia.2016.1223a. - Khinchin, A. Ya. (1989). About educational effect of lessons of mathematics.
*Increase of efficiency of learning mathematics at school*, 3, 18-37. - Kozlova, E. G. (2006)
*Tales and Tips (tasks for mathematical circle)*. Moscow: MTsNMO. - Kubiatko, M., Usak, M. & Masalimova, A. R. (2016). Czech Lower Secondary School Pupils' Knowledge about Developing Countries.
*Revista de cercetare si interventie sociala, 55*, 215-230. - Leikin, R. & Pitta-Pantazi, D. (2013) Creativity and mathematics education: the state of the art.
*ZDM Mathematics Education*, 45: 159. doi: 10.1007/s11858-012-0459-1. - Masalimova, A. R., Usak, M., Shaidullina, A. R. (2016). Advantages and disadvantages of national and international corporate training techniques in adult education.
*Current science, 111(9)*, 1480-1485. - Mochalov, L. P. (1996)
*Puzzle*. Moscow: Education. - Parfilova, G. G. & Kalimullin, A. M. (2013). Research of Russian Students' Ecological Competency. 3rd world conference on educational technology researches 2013, WCETR 2013.
*Procedia Social and Behavioral Sciences, 131*, 35-39. - Petrakov, I. S. (1987).
*Mathematical section at 8-10 grades*. Moscow: Education. - Pino-Fan, L. R., Assis, A. & Castro W. F. (2015) Towards a Methodology for the Characterization of Teachers’ Didactic-Mathematical Knowledge.
*EURASIA Journal of Mathematics, Science and Technology Education*, 11(6). doi: 10.12973/eurasia.2015.1403a. - Poincare, H. (1983).
*About science.*Moscow: Science. - Polya, D. (1991).
*How to solve a problem*. Lviv: Quantifier. - Sharygin, I. F. (2002)
*Mathematical vinaigrette*. Moscow: Mir. - Sharygin, I. F. & Erganzhiyeva, L. N. (2001).
*Visual geometry. 5–6 grades.*Moscow: Drofa. - Shvartsburd, S. I. (1964). About development of learners’ interests, tendencies and abilities to mathematics.
*Mathematics at school*, 6, 32–37. - Singer F.M., Sheffield, L.J. & Leikin, R. (2017). Advancements in research on creativity and giftedness in mathematics education: introduction to the special issue.
*ZDM Mathematics Education,*49(1): 5. doi:10.1007/s11858-017-0836-x - Spivak, A. V. (2004)
*Mathematical holiday*. Moscow: Quantum. - Sriraman, B., Haavold P. & Lee, K. (2014)
*Creativity in Mathematics Education*. Encyclopedia of Mathematics Education, 109-115. - Sriraman, B., Yaftian, N. & Lee, K. H. (2011)
*Mathematical Creativity and Mathematics Education*. Chapter of The Elements of Creativity and Giftedness in Mathematics, Volume 1 of the series Advances in Creativity and Giftedness, 119-130. - Tabach, M. & Friedlander, A. (2013) School mathematics and creativity at the elementary and middle-grade levels: how are they related?
*ZDM Mathematics Education,*45, 227-234. doi: 10.1007/s11858-012-0471-5. - The concept of development of mathematical education in the Russian Federation. (2013).
*The Russian newspaper*. December 27, 2003, from http://www.rg.ru/2013/12/27/matematika-site-dok.html. - Valeeva, R. A. & Kalimullin, A. M. (2014). Social Orphanhood in Russia: Historical Background, Present and Perspective. Proceedings of 6th World Conference on Educational Sciences.
*Procedia Social and Behavioral Sciences, 191*, 2122-2126. - Valeeva, R.A. & Shakirova, K.B. (2015). Development of the Future Mathematics Teachers’ Constructive Skills.
*IEJME-Mathematics Education, 10(3),*221-229. - Yaschenko, I. V. (2009)
*Invitation Math holiday*. Moscow: MTsNMO. - Zinovkina, M. M. (2008). NFTM-TRIZ
*: creative education of the XXI century. Theory and practice*. Moscow: MGIU. - Singer F.M., Sheffield, L.J. & Leikin, R. (2017). Advancements in research on creativity and giftedness in mathematics education: introduction to the special issue.
*ZDM Mathematics Education, 49(1),*5. doi:10.1007/s11858-017-0836-x