Novosibirsk State Pedagogical University Bulletin, 2018, No.4, pp.158-171
UDC: 
37.0 + 371 + 578

General thinking activities in the algebra classroom

Kasura A. V. 1 (Krasnoyarsk, Russian Federation), Aksigitov A. R. 1 (Krasnoyarsk, Russian Federation), Gerashenko V. V. 1 (Krasnoyarsk, Russian Federation), Musin R. M. 1 (Krasnoyarsk, Russian Federation), Dakhin A. N. 2 (Novosibirsk, Russian Federation)
1 Siberian State University of Science and Technology
2 Novosibirsk State Pedagogical University, Novosibirsk, Russian Federation
Abstract: 

Introduction. The article explores the use of general thinking activities for the formation of generic cultural competence - a cultural mediator of contemporary Russian schoolchildren - by means of algebra as a discipline with a wide range of basic types of educational activities. The purpose of the article is to reveal the scientific and pedagogical functions of general thinking activities which contribute to the process of developing generic cultural competence, and to summarize the experience of using such activities in the algebra classroom aimed at modernization of mathematical education.
Materials and Methods. The authors employed the following research methods: a comparative analysis of theories of teaching mathematics using basic types of learning activities, and creating a cognitive scheme of general thinking activities suitable for teaching algebra.
Results. The basic theories of teaching mathematics, found in publications for the last 3 years, are analyzed. As a result, the following basic functional components of general thinking activities were identified 1) the subject of objective scientific research; 2) an explanatory principle; 3) the subject of management; 4) interdisciplinary value.
Conclusions. On the basis of the obtained results, the authors conclude that for completeness of the pedagogical picture of general thinking it is sufficient to single out its 4 basic functional components. School algebra, which possesses "strong" formal means, provides the operational component to general competence and mathematical culture of students and contributes to the interdisciplinary transfer of the student's thinking experience to another learning situation.

Keywords: 

General thinking activity; General thinking competence; Mathematical culture; Modernization of education; Mediator of culture; Functions of general thinking activity; Theory of teaching mathematics; Basic types of educational activities

References: 

1. Dakhin A. N. Mathematics as a way of entering to the culture thinking activities. Mathematics in School, 2017, no. 7, pp. 41–45. (In Russian) URL: https://elibrary.ru/item.asp?id=30604876

2. Malaniceva T. A.  About the Practice of Application of the General Formulas in the Teaching of Mathematics. Mathematics in School, 2016, no. 3, pp. 43–45. (In Russian) URL: https://elibrary.ru/item.asp?id=27324840

3. Andrienko E. V. The value of education in different countries: tradition and innovation as factors of development. Journal of Pedagogical Innovations, 2018, no. 1 (49), pp. 17–22. (In Russian) URL: https://elibrary.ru/item.asp?id=32695132

4. Verbitsky A. A. New facets of the eternal problem of education in the context and outside it. Higher education today, 2017, no. 8, pp. 6–13. (In Russian) URL: https://elibrary.ru/item.asp?id=29816918

5. Khinchin A. Ya. On the educational effect of lessons in mathematics. Mathematics in School, 2015, no. 7, pp. 37–56. (In Russian) URL: https://elibrary.ru/item.asp?id=24172265

6. Pavlova O. A. Historization as a Means of Moral Upbringing in the Teaching of Mathematics. Mathematics in School, 2016, no. 3, pp. 26–31. (In Russian) URL: https://elibrary.ru/item.asp?id=27324836

7. Klepikov V. N. Formation of the mathematical picture of the world in modern school education. Pedagogy, 2017, no. 3, pp. 49–56. (In Russian) URL: https://elibrary.ru/item.asp?id=28916196

8. Smirnov V. A., Smirnova I. M.  How to make a study of the theorems of geometry is more effective? Mathematics in School, 2017, no. 3, pp. 34–39. (In Russian) URL: https://elibrary.ru/item.asp?id=29063727

9. Minnegalieva H. B. Creating Interactive Models Using WolframProgrammingCloud. Mathematics in School, 2015, no. 7, pp. 32–36. (In Russian) URL: https://elibrary.ru/item.asp?id=24172264

10. Tabinova O. A., Kaysina O. V.  Using of Technology of Positional Training in the Study of the Topic "Polyhedra. Mathematics in School, 2016, no. 3, pp. 46–49. (In Russian) URL: https://elibrary.ru/item.asp?id=27324841

11. Pérez-Jorge D., Barragán-Medero F., Gutiérrez-Barroso J.,  Castro-León F. A Synchronous Tool for Innovation and Improvement of University Communication, Counseling and Tutoring: The WhatsApp Experience. Eurasia Journal of Mathematics, Science and Technology Education, 2018, vol. 14 (7), pp. 2737–2743. DOI: https://doi.org/10.29333/ejmste/90588

12. Zhang Sh.,  Li F.,  Zhao L.,  Xie L.,  Zhao H. The Developmental Changes of Number Processing and Calculation Abilities in Chinese Primary School Students. Eurasia Journal of Mathematics, Science and Technology Education, 2018, vol. 14 (7), pp. 2745–2756. DOI: https://doi.org/10.29333/ejmste/90590

13. Dvoryaninov S. V. Mathematics and physics, or approximate calculations. Mathematics in School, 2017, no. 1, pp. 44–49. (In Russian) URL: https://elibrary.ru/item.asp?id=28394471

14. Purba S. W. D., Hwang W.-Y. Investigation of Learning Behaviors and Achievement of Simple Pendulum for Vocational High School Students with Ubiquitous-Physics App. Eurasia Journal of Mathematics, Science and Technology Education, 2018, vol. 14 (7), pp. 2877–2893. DOI: https://doi.org/10.29333/ejmste/90985

15. Troitskaya S. D. Exam SAT I Mathematics. Mathematics in School, 2017, no. 7, pp. 46–55. (In Russian) URL: https://elibrary.ru/item.asp?id=30604877

16. Zhafyarov A. Zh. Studying the topic "Logarithmic and exponential functions and their applications" on the basis of competence approach. Journal of Pedagogical Innovations, 2018, no. 1 (49), pp. 99–109. (In Russian) URL: https://elibrary.ru/item.asp?id=32695142

17. Zhafyarov A. Zh. Models of the study of the topic: "Quadratic function and its applications" on the competence basis. Siberian Pedagogical Journal, 2014, no. 3, pp. 27–33. (In Russian) URL: https://elibrary.ru/item.asp?id=21707994

18. Zhafyarov A. Zh. Models of formation and increase of competence in the process of studying the topic: "Linear function and its applications". Siberian Pedagogical Journal, 2013, no. 1, pp. 153–159. (In Russian) URL: https://elibrary.ru/item.asp?id=20805880

19. Krachkovskiy S. M. Variability of approaches to extreme values problems. Mathematics in School, 2018, no. 1, pp. 19–32. (In Russian) URL: https://elibrary.ru/item.asp?id=32517574

20. Zelenskiy A. S., Panfilov I. I., Panfilova E. A.  Tasks with a parameter on EGE-2017. Mathematics in School, 2018, no. 1, pp. 8–18. (In Russian) URL: https://elibrary.ru/item.asp?id=32517573

21. Zinchenko V. P. Activity. Knowledge. Spirituality. Higher Education in Russia, 2003, no. 5, pp. 81–91. (In Russian) URL: https://elibrary.ru/item.asp?id=9571390

22. Prediger S., Zindel C. School Academic Language Demands for Understanding Functional Relationships: A Design Research Project on the Role of Language in Reading and Learning. Eurasia Journal of Mathematics, Science and Technology Education, 2017, vol. 13 (7b), pp. 4157–4188. DOI: https://doi.org/10.12973/eurasia.2017.00804a

23. Rezat Se., Rezat Sa. Subject-Specific Genres and Genre Awareness in Integrated Mathematics and Language Teaching. Eurasia Journal of Mathematics, Science and Technology Education, 2017, vol. 13 (7b), pp. 4189–4210. DOI: https://doi.org/10.12973/eurasia.2017.00805a

24. Duran M., Dokme I. The effect of the inquiry-based learning approach on student’s critical thinking skills. Eurasia Journal of Mathematics, Science and Technology Education, 2016, vol. 12 (12), pp. 2887–2908. DOI: https://doi.org/10.12973/eurasia.2016.02311a

25. Budak A. The impact of a standards-based mathematics curriculum on students’ mathematics achievement: The case of Investigations in Number, Data, and Space. Eurasia Journal of Mathematics, Science and Technology Education, 2015, vol. 11 (6), pp. 1249–1264. DOI: https://doi.org/10.12973/eurasia.2015.1377a

Date of the publication 31.08.2018