Science for Education Today, 2019, vol. 9, no. 3, pp. 121–137
UDC: 
378.147

The development of students’ analytical and synthetic activities in studying mathematical analysis

Shmigirilova I. B. 1 (Petropavlovsk, Republic of Kazakhstan), Chugunova A. A. 1 (Petropavlovsk, Republic of Kazakhstan), Pustovalova N. I. 1 (Petropavlovsk, Republic of Kazakhstan)
1 M. Kozybaev North Kazakhstan State University
Abstract: 

Introduction. The article addresses the problem of developing undergraduate students’ analytical and synthetic activities. The purpose of the article is to identify the characteristics for the development of students’ analytical and synthetic activities in the process of studying Mathematical analysis.
Materials and Methods. Characteristic features of developing students’ analytical and synthetic activities are considered in the unity of systemic, activity-based, cultural, anthropological and environmental approaches. The main research methods are analysis of scientific literature, analysis of university practice and personal teaching experience, experimental methods, and methods of statistical processing of empirical data.
Results. The factors contributing to the development of students’ analytical and synthetic activities within the improvement of educational process are established. The study reveals the features of teaching Mathematical analysis focused on improving the development of analytical and synthetic activities. The authors have designed the model of solving a mathematical problems within the framework of analytical and synthetic activities.
Conclusions. The recommendations provided in the article can be used to increase the effectiveness of teaching a range of scientific disciplines to undergraduate and high school students.

Keywords: 

Analytical and synthetic activities; Mental operations; Teaching mathematical analysis; System of problems; Problem solving; University studies; Initial teacher education (training).

URL WoS/RSCI: https://www.webofscience.com/wos/rsci/full-record/RSCI:38538211

Prominence Percentile SciVal: 93.371 Linear Algebra | Mathematics Education | Computer Algebra System

https://www.scopus.com/record/display.uri?eid=2-s2.0-85071445469&origin=...

The development of students' analytical and synthetic activities in studying mathematical analysis

For citation:
Shmigirilova I. B., Chugunova A. A., Pustovalova N. I. The development of students’ analytical and synthetic activities in studying mathematical analysis. Science for Education Today, 2019, vol. 9, no. 3, pp. 121–137. DOI: http://dx.doi.org/10.15293/2658-6762.1903.07
References: 
  1. Battilotti G. Symmetry vs. duality in logic: An interpretation of Bi-logic to model cognitive processes beyond inference. International Journal of Cognitive Informatics and Natural Intelligence, 2014, vol. 8, issue 4, pp. 83‒97. DOI: https://doi.org/10.4018/ijcini.2014100105
  2. Dhatsuwan A., Precharattana M. Blockyland: A cellular automata-based game to enhance logical thinking. Simulation and Gaming, 2016, vol. 47, issue 4, pp. 445‒464. DOI: https://doi.org/10.1177/1046878116643468
  3. Kazachek N. A., Epova E. V. Formation of pupils' analytic-synthetic activity while algebra studying in the context of summer professionally-oriented school. Scholarly Notes of Transbaikal State University, 2014, no. 6, pp. 145‒151. (In Russian) URL: https://elibrary.ru/item.asp?id=22675375
  4. Welling H. Four mental operations in creative cognition: The importance of abstraction. Creativity Research Journal, 2007, vol. 19, issue 2-3, pp. 163‒177. DOI: https://doi.org/10.1080/10400410701397214
  5. Ahmad S., Prahmana R. C. I., Kenedi A. K., Helsa Y., Arianil Y., Zainil M. The instruments of higher order thinking skills. Journal of Physics: Conference Series, 2017, vol. 943, pp. 012053. DOI: https://doi.org/10.1088/1742-6596/943/1/012053
  6. 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, issue 12, pp. 2887–2908. DOI: https://doi.org/10.12973/eurasia.2016.02311a
  7. Florea N. M., Hurjui E. Critical thinking in elementary school children. Procedia ‒ Social and Behavioral Sciences, 2015, vol. 180, pp. 565–572. DOI: http://doi.org/10.1016/j.sbspro.2015.02.161
  8. Shadrikov V. D. The system of intellectual operations in ability and intelligence structure. Acmeology, 2014, no. 1, pp. 25‒36. (In Russian) URL: https://elibrary.ru/item.asp?id=21267665
  9. Condor M., Chira M. The importance of mental operations in forming notions. Euromentor Journal – Studies about Education, 2011, no. 1, pp. 134–139. URL: https://www.ceeol.com/search/article-detail?id=272154
  10. Berberyan H. S. Mental operations'' place in the structure of abilities and thinking. Russian Psychological Journal, 2016, vol. 13, no. 1, pp. 19‒28. (In Russian) URL: https://elibrary.ru/item.asp?id=26002158
  11. Aksu G., Koruklu N. Determination the effects of vocational high school students’ logical and criticalthinking skills on mathematics success. Eurasian Journal of Educational Research, 2015, issue 59, pp. 181‒206. DOI: http://doi.org/10.14689/ejer.2015.59.11 URL: http://ejer.com.tr/public/assets/catalogs/en/nkoruklu59.pdf  
  12. Kholodnaya M. A. Psychology of conceptual thinking: from conceptual structures to conceptual abilities. Monograph. Moscow, Kogito-Center Publ., 2012, 288 p. (In Russian) URL: https://elibrary.ru/item.asp?id=20247680
  13. Seyhan H. G. The efficacy of problem-based learning in an instrumental analyse laboratory. Higher Education Studies, 2016, vol. 6, no. 4, pp. 100‒118. DOI: http://dx.doi.org/10.5539/hes.v6n4p100
  14. Dalinger V. A. Mathematics means for students' thinking development. The Scientific Opinion, 2011, no. 9, pp. 43‒50. (In Russian) URL: https://elibrary.ru/item.asp?id=17271258
  15. Ayllón M. F., Góme I. A., Ballesta-Claver J. Mathematical thinking and creativity through mathematical problem posing and solving. Propósitos y Representaciones, 2016, vol. 4, no. 1, pp. 169‒218. DOI: http://dx.doi.org/10.20511/pyr2016.v4n1.89
  16. Temel S. The effects of problem-based learning on prospective teachers’ critical thinking dispositions and perceptions of problem-solving ability. South African Journal of Education, 2014, vol. 34, no. 1, art. 769. DOI: https://dx.doi.org/10.15700/201412120936
  17. Bochkareva L. V. Application of strategic problems for the development of analytic-synthetic competence by students of the technical professions in the process of probability theory and mathematical statistic training. Modern Problems of Science and Education, 2013, no. 2, pp. 275. (In Russian) URL: https://elibrary.ru/item.asp?id=21285629
  18. Tokareva L. I. Learning by students of the techniques of analytical and synthetic activity in solving geometric problems. Mathematical Bulletin of Universities and Universities of the Volga-Vyatka region, 2014, no. 16, pp. 278‒283. (In Russian) URL: https://elibrary.ru/item.asp?id=28101361
  19. Malakhova E. I. Formation of methods and techniques of analytical and synthetic activity as a component of meta-subject content of education. Modern Problems of Science and Education, 2013, no. 1, pp. 212. URL: https://elibrary.ru/item.asp?id=18829145
  20. Testov V. A. Some types of metasubject results when teaching mathematics. Education and Science, 2016, no. 1, pp. 4‒20. (In Russian) URL: https://elibrary.ru/item.asp?id=25430413
  21. Chuprikova N. I. Mental development and learning (to the rationale of the system-structural approach): monograph. Moscow, MPSI Publ., 2003, 320 p. (In Russian) URL: https://elibrary.ru/item.asp?id=19901662
  22. Koldunova I. D. Designing analytic-synthetic learning tasks in the theory of algorithms. Pedagogical Education in Russia, 2015, no. 4, pp. 133‒139. (in Russian) URL: https://elibrary.ru/item.asp?id=23588901
  23. Bezusova T. A., Richter T. V., Sugrobova N.  Y., Chugainova L. V., Shestakova L. G. Types of work in forming analytic and synthetic activity skills in teaching the algebra course. Eurasia Journal of Mathematics, Science and Technology Education, 2017, vol. 13, no. 11, pp. 7257–7267. DOI: https://doi.org/10.12973/ejmste/79443
  24. Ermosh E. N. Development of the cognitive abilities of the students during learning proces. Actual Problems of Modernity: Science and Society, 2017, no. 2, pp. 45–50. (In Russian) URL: https://elibrary.ru/item.asp?id=30304049
  25. Chugunova A. A., Shmigirilova I. B. The analytico-synthetic activity in the context of the competence approach in education. Science Vector of Togliatti State University. Series: Pedagogy, psychology, 2013, no. 4, pp. 217‒220. (In Russian) URL: https://elibrary.ru/item.asp?id=21097976
  26. Kasura A. V., Aksigitov A. R., Gerashenko V. V., Musin R. M., Dakhin A. N. General thinking activities in the algebra classroom. Novosibirsk State Pedagogical University Bulletin, 2018, vol. 8, no. 4, pp. 158–171. (In Russian) DOI: http://dx.doi.org/10.15293/2226-3365.1804.10
  27. Antonova N. L., Merenkov A. V. Flipped Learning in higher education: Problems and contradictions. Integration of Education, 2018, vol. 22, no. 2, pp. 237–247. (In Russian) DOI: http://dx.doi.org/10.15507/1991-9468.091.022.201802.237-247
  28. Bauer-Ramazani C., Graney J. M., Marshall H. W., Sabieh C. Flipped learning in TESOL: definitions, approaches, and implementation. TESOL Journal, 2016, vol. 7, issue 2, pp. 429–437. DOI: https://doi.org/10.1002/tesj.250

 

Date of the publication 30.06.2019