Developing Primary School Students’ Understanding of Functional Relationships through Problem Solving
DOI: 10.23951/2782-2575-2026-3-22-33
The article examines the theoretical and methodological foundations for developing primary school students’ understanding of functional relationships between quantities through solving word problems. The study’s relevance stems from the need to foster students’ functional thinking at the early stages of schooling, in response to educational modernization and rising quality standards in mathematics education. The study aims to develop and validate a methodology to foster primary school students’ understanding of functional relationships between quantities using an analogical approach. The research combines theoretical analysis of the scientific and methodological literature with empirical modeling of instructional situations and analysis of teaching practice. The research combines theoretical methods (analysis and synthesis of scientific and methodological literature) and empirical methods (simulation of learning scenarios, analysis of teaching experience). The relationship among price, quantity, and cost serves as the basic model. It is extended by analogy to other groups of quantities, including speed, time, and distance, and productivity, time, and amount of work. These groups are shown to share a common structure and can be described using the same mathematical models of direct and inverse proportions. Theoretical analysis and the synthesis of pedagogical experience suggest that the systematic use of analogy fosters a meaningful understanding of functional relationships, promotes the development of generalized problemsolving strategies, and develops analytical thinking. The findings indicate that the traditional emphasis on the formal application of arithmetic operations is insufficient for developing a deep understanding of relationships among quantities. The study provides methodological recommendations for the training of future primary school teachers, professional development programs, and primary school mathematics instruction.
Ключевые слова: functional relationship, primary education, word problems, analogy method, proportionality
Библиография:
1. Andronov I.K. Arifmetika [Arithmetic]. Moscow, Uchpedgiz Publ., 1962 (in Russian).
2. Moro M.I., et al. (Eds.) Aktual’nyye problemy metodiki obucheniya matematike v nachalnykh klassakh [Current problems of teaching methods of mathematics in primary grades]. Moscow, Pedagogika Publ., 1977 (in Russian).
3. Ashurov M.M. Teoretiko-mnozhestvennyy podkhod k izucheniyu arifmeticheskikh deystviy v nachalnykh klassakh [Set-theoretic approach to the study of arithmetic operations in primary grades]. Mezhdunarodnyy nauchno-issledovatel’skiy tsentr “Endless Light in Science” [International Research Center “Endless Light in Science”]. Almaty, 2024 (in Russian).
4. Ashurov M.M. Tekstovyye zadachi v nachalnykh klassakh i metody ikh resheniya [Text problems in primary grades and methods of their solution]. Baku, 2025 (in Azerbaijani).
5. Schoenfeld A. Mathematical Thinking and Problem Solving. New York: Routledge, 2016.
6. Hiebert J., Grouws D.A. The Effects of Classroom Mathematics Teaching. Handbook of Research on Mathematics Teaching and Learning. In: F.K. Lester Jr. (Ed.). Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age Publishing, 2007. Pp. 371–404.
7. Kyazimov Z.F. Tipovyye zadachi i ikh resheniya: uchebnoye posobiye [Standard problems and their solutions: a study guide]: Baku, 2008 (in Azerbaijani).
8. Programma “Tekstovyye zadachi i metody ikh resheniya v nachalnykh klassakh” dlya fakul’teta “Nachal’noye obrazovaniye” vysshikh pedagogicheskikh vuzov [Program “Text problems and methods of their solution in primary grades” for the faculty of “Primary education” of higher pedagogical universities]. Baku, ASPU Publ., 2022 (in Azerbaijani).
9. Statkevich V.V. O nachal’nom obuchenii resheniyu zadach [On primary teaching of problem solving]. Minsk, 1970 (in Russian).
10. Stoylova S.P. Teoreticheskiye osnovy nachal’nogo kursa matematiki [Theoretical foundations of the primary course of mathematics]. Saratov, 2014 (in Russian).
11. Polya G. How to Solve It. Princeton: Princeton University Press, 2004.
12. Skemp R. The Psychology of Learning Mathematics. London: Routledge, 1987.
13. Vergnaud G. The Theory of Conceptual Fields. Human Development, 1996, vol. 39, pp. 123–150.
14. Carpenter T.P., Fennema E. Cognitively Guided Instruction. Portsmouth: Heinemann, 1999.
15. Dzhabrailov B.S. Aktual’nyye problemy metodiki prepodavaniya matematiki: uchebnoye posobiye dlya magistrantov spetsial’nosti “uchitel’ nachal’nykh klassov” [Current problems of teaching methods of mathematics: a study guide for master’s students of the specialty “primary school teacher”]. Baku, ASPU Publ., 2019. 115 p. (in Azerbaijani).
16. Dzhabrailov B.S. Matematika: uchebnoye posobiye dlya studentov pedagogicheskogo fakul’teta ASPU [Mathematics: a study guide for students of the pedagogical faculty of ASPU]. Baku, 2008 (in Azerbaijani).
17. Pyshkalo A.M., Stoylova L.P., et al. Teoreticheskiye osnovy nachal’nogo kursa matematiki [Theoretical foundations of the primary course of mathematics]. Moscow, Prosveshcheniye Publ., 1974 (in Russian).
18. Feyziyev S.N., Shukyurov R.Yu. Nauchnyye osnovy nachal’nogo kursa matematiki (Uchebnik) [Scientific foundations of the primary course of mathematics (Textbook)]. Baku, 2010 (in Azerbaijani).
19. Gurova L.L. Psikhologicheskiy analiz resheniya zadach [Psychological analysis of problem solving]. Voronezh, Voronezhskiy universitet Publ., 1976 (in Russian).
20. Moro M.I., Pyshkalo A.M. Metodika obucheniya matematike v I–III klassakh [Methods of teaching mathematics in grades I–III]. 2nd ed. Moscow, Prosveshcheniye Publ., 1978 (in Russian).
21. Polya G. How to Solve It. Princeton: Princeton University Press, 1957. (Russ. ed.: Polya G. Kak reshat’ zadachu [How to solve it]. Moscow, 1959. 208 p.).
( 419.82 kB ) 
( 414.12 kB )
Выпуск: 3, 2026
Серия выпуска: Issue 3
Рубрика: PEDAGOGY
Страницы: 22 — 33
Скачиваний: 4