Differentiation of Creative Mathematical Problems for Primary School Students
 
More details
Hide details
1
Vyatka State University, Russia
2
Kazan (Volga region) Federal University, RUSSIA
CORRESPONDING AUTHOR
Vyacheslav V. Utemov   

Professor of the Department of Education at Vyatka State University (610000, Kirov, 36 Moscovskaya Street, Russia. Tel. +79229899489,
Online publish date: 2017-06-28
Publish date: 2017-06-28
 
EURASIA J. Math., Sci Tech. Ed 2017;13(8):4351–4362
KEYWORDS
ABSTRACT
The purpose of the study is to reveal a method that will help arrange creative mathematical problems for the development of creative competences of the basic school students. The main method here is modeling of creative mathematical problems taking into account the complexity levels of the tasks in accordance with the systemic scale and the requirements for the formulation of creative tasks in basic school. The article presents author's approaches to the differentiation of creative mathematical tasks for basic school students in accordance with the systemic scale, which were formed by adaptation of creative problem solutions classified in terms of their degree of difficulty and the quality of the obtained results, considered in the theory of inventive problems solving. The author proposes a system of requirements for the creative mathematical problem such as the contradiction in the condition of the problem, the sufficiency of the condition, the rectitude of the question, the independence of facts, the completeness of information, and scientific consistency. The system of requirements allows to preserve the didactic value of the proposed mathematical problem. As a result of experimental research and experiential teaching using creative mathematical tasks, the proposed differentiation and the system of requirements for the condition were successfully tested. That contributes greatly to the development of creative competencies of students in the basic school and their ability to solve creative math problems. Practical use of creative mathematical problems makes it possible to increase schoolchildren’s interest to study mathematics and show interdisciplinary connections with various disciplines, e.g., informatics, chemistry, biology.
 
REFERENCES (43)
1.
Altshuller, G. S. (2004). Creativity as an exact science. Petrozavodsk: Scandinavia.
 
2.
Arnold, V. I. (2002). What is mathematics? Moscow: MTsNMO.
 
3.
Balk, G. D. (1969). On the application of heuristic techniques in the school teaching of mathematics. Mathematics in school, 5, 21-28.
 
4.
Bolden, D. S., Harries, A. V., & Newton, D. P. (2010). Pre-service primary teachers’ conceptions of creativity in mathematics. Educational Studies in Mathematics, 73(2), 143-157.
 
5.
Cheng, C., & Ou, Y. (2017). An Investigation of Basic Design Capacity Performance in Different Background Students. EURASIA Journal of Mathematics, Science and Technology Education, 13(5), 1177-1187.
 
6.
Clement, J. J. (2008). Creative model construction in scientists and students: The role of imagery, analogy, and mental simulation. Dordercht: Springer. Clough, M.P. (2006). Learners' responses to the demands of conceptual change: considerations for the effective nature of science instruction. Science Education, 15, 463-494.
 
7.
Courant, R., & Robbins, G. (1967). What is mathematics? Moscow: Education.
 
8.
Craig, T. S. (2016). The role of expository writing in mathematical problem solving. African Journal of Research in Mathematics, Science and Technology Education, 20(1), 57-66.
 
9.
Danilov, M. A. (1960). The learning process in the Soviet school. M: Publishing house Uchpedgiz.
 
10.
Devecioglu-Kaymakci, Y. (2016). Embedding Analogical Reasoning into 5E Learning Model: A Study of the Solar System. EURASIA Journal of Mathematics, Science and Technology Education, 12(4), 881-911.
 
11.
Episheva, O. B., & Krupich V. I. (1990). To teach schoolchildren to study mathematics: Forming the methods of learning activity. Moscow: Education.
 
12.
Gilford, J. (1967). Measurement of creativity. Exploration in creativity. N.Y. 34-47.
 
13.
Gnedenko, B. V. (1979). On mathematical creativity. Mathematics in school, 6, 16-22.
 
14.
Gorev, P. M., & Utemov, V. V. (2010). Heuristic methods of thinking and activating creativity. Kirov: Publishing house VyatGGU.
 
15.
Gorev, P. M., & Utemov, V. V. (2011). Sovionok’s school: on the way to the creative thinking of creativity. Kirov: Publishing house VyatGGU.
 
16.
Gorev, P. M., & Utemov, V. V. (2012). Sovionok’s Magic Dreams. Kirov: Publishing house VyatGGU.
 
17.
Gorev, P. M., & Utemov, V. V. (2013). Expedition to the world of creativity. Kirov: "O-kratkoe" Publishing House.
 
18.
Gorev, P. M., & Utemov, V. V. (2014). Creative walks under the stars. Kirov: Publishing house MTsITO.
 
19.
Gorev, P. M., & Utemov, V. V. (2014). Lessons of developing mathematics. 5-6 grades: The problems of mathematical circle Kirov: Publishing house MTsITO.
 
20.
Gorev, P. M., & Utemov, V. V. (2015). Sovionok’s fascinating journey. Kirov: Publishing house MTsITO.
 
21.
Gorev, P. M., & Utemov, V. V. (2016). Sovionok’s significant events. Kirov: Publishing house MTsITO.
 
22.
Guildford, J. (1969). The three sides of intelligence: The Psychology of Thinking. M: Progress.
 
23.
Gusev, V. A. (2003). Psychological and pedagogical foundations of teaching mathematics. Moscow: Verbum-M.
 
24.
Heim, R. (2006). Hegel and his time. Lectures on the initial origin, development, essence and dignity of Hegel’s philosophy. St. Petersburg: Publishing house Science, 391.
 
25.
Holyoak, K. J., & Thagard, P. (1995). Mental leaps: Analogy in creative thought. Cambridge, MA, Lawrence Erlbaum: The MIT Press. In Dilber, R., & Düzgün, B. (2008). Effectiveness of analogy on students' success and elimination of misconceptions. Latin American Journal of Physics Education, 2(3), 174-183.
 
26.
Kedrov, B. M. (1969). The psychological mechanism of scientific discoveries. Questions of psychology, 3, 45-54.
 
27.
Khinchin, A. Y. (1989). On the educational effect of lessons in mathematics/Increase the effectiveness of teaching mathematics at school/Comp. GD Glaser. Moscow: Education, 240, 18-37.
 
28.
Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal 9, 5-24 .doi:10.1007/BF03217299.
 
29.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For The Learning of Mathematics, 26(1), 20-23.
 
30.
Ministry of Education and Science of the Russian Federation (2010). The federal state educational standard of general education: The federal law of Russian Federation of 17 December 2010 No. 1897-FZ.
 
31.
Nohda, N. (1988). Problem solving using "open endend problems" in mathematics teaching. – In: H. Burkhardt; S. Groves; A. Schoenfeld; K. Stacey (Eds.): Problem solving-A World View, 225-234, Nottingham: Shell Center.
 
32.
Pehkonen, E. (1997). The state-of-art in mathematical creativity, Zentralblatt für Didaktik der Mathematik, 29, 63-67. doi:10.1007/s11858-997-0001-z.
 
33.
Poincare, A. (1983). About the science. Moscow: Science.
 
34.
Poya, D. (1991). How to solve the problem. Lvov: Quantor.
 
35.
Problems of learning and cognitive development at school age. Psychological Science and Education, 4, 5-17.
 
36.
Rosli, R., Capraro, M. M., Goldsby, D., Gonzalez, E. G., Onwuegbuzie, A. J., & Capraro, R. M. (2015). Middle-grade preservice teachers' mathematical problem solving and problem posing. In Mathematical Problem Posing, 333-354.
 
37.
Savic, M., Karakok, G., Tang G., Turkey, H., & Naccarato, E. (2017). Formative Assessment of Creativity in Undergraduate Mathematics: Using a Creativity-in-Progress Rubric (CPR) on Proving. Springer International Publishing, 23-46. doi:10.1007/978-3-319-38840-3_3.
 
38.
Shvartsburd, S. I. (1964). On the development of interests, inclinations and abilities of students to mathematics. Mathematics at school, 6, 32-37.
 
39.
Sidorchuk, T. A. (1998). System of creative tasks as a means of creativity formation at the initial stage of personality formation. PhD Thesis. Moscow: Moscow State Industrial University.
 
40.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing, Zentralblatt für Didaktik der Mathematik, 29, 75-80. doi:10.1007/s11858-997-0003-x.
 
41.
Sriraman, B. (2009). The characteristics of mathematical creativity. The International Journal on Mathematics Education [ZDM], 41, 13-27. doi:10.1007/s11858-008-0114-z
 
42.
The Concept of the Development of Mathematical Education in the Russian Federation, Rossiyskaya Gazeta. Retrieved on Dec. 27, 2013 from http://www.rg.ru/2013/12/27/ma....
 
43.
Wang, H. C., Chang, C. Y., & Li, T. Y. (2008). Assessing creative problem-solving with automated text grading. Computers & Education, 51(4), 1450-1466.
 
eISSN:1305-8223
ISSN:1305-8215