**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33019

##### Holistic Approach to Teaching Mathematics in Secondary School as a Means of Improving Students’ Comprehension of Study Material

**Authors:**
Natalia Podkhodova,
Olga Sheremeteva,
Mariia Soldaeva

**Abstract:**

Creating favourable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. This paper describes a holistic approach to teaching mathematics designed to address the primary challenges of such teaching; specifically, the challenge of students’ comprehension. Essentially, this approach consists of (1) establishing links between the attributes of the notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience—value-based emotions, contextual, procedural and communicative—during the educational process; (3) linking together different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modelling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and techniques influence understanding of material used in teaching mathematics was the primary goal. The study included an experiment in which 256 secondary school students took part: 142 in the study group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics — “Derivative” and “Trigonometric functions”—was evaluated. Control group participants were taught using traditional methods. Students in the study group were taught using the holistic method: under teacher’s guidance, they carried out assignments designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as assignments that required the ability to operate with all modes of presentation. Identification, accounting for and transformation of subjective experience were associated with methods of stimulating the emotional value component of the studied mathematical content (discussions of lesson titles, assignments aimed to create study dominants, performing theme-related physical exercise ...) The use of techniques that forms inter-subject notions based on linkages between, perceptual real and mathematical conceptual spaces proved to be of special interest to the students. Results of the experiment were analysed by presenting students in each of the groups with a final test in each of the studied topics. The test included assignments that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion x2 was used to reveal statistics significance of results (pass-fail the modelling test). Significant difference of results was revealed (p < 0.001), which allowed to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. The total number of completed assignments of each student was analysed as well, with average results calculated for each group. Statistical significance of result differences against the quantitative criterion (number of completed assignments) was determined using Student’s t-test, which showed that students in the study group completed significantly more assignments than those in the control group (p = 0.0001). Authors thus come to the conclusion that suggested increase in the level of comprehension of study material took place as a result of applying implemented methods and techniques.

**Keywords:**
Comprehension of mathematical content,
holistic approach to teaching mathematics in secondary school,
subjective experience,
technology of the formation of inter-subject notions.

**References:**

[1] M. I. Rozhkov, L. V. Baiborodova, O. S. Grebenyuk and T. B. Grebenyuk Pedagogika v 2 t. Tom 1. Obshchie osnovy pedagogiki. Teoriya obucheniya: uchebnik i praktikum dlya vuzov. M.: Izdatel'stvo Yurait, 2020. https://studme.org/368817/pedagogika/tselostnyy_podhod_pedagogicheskim_yavleniyam

[2] Filosofiya obrazovaniya dlya veka / Sbornik statei. - M.: Izd. Firma «Logos», 1992.

[3] M. I. D'yachenko and L. A. Kandybovich, Psikhologicheskii slovar'-spravochnik. Izd-vo AST, Kharvest. 2001.

[4] G. Frege, Logika i logicheskaya semantika: Sbornik trudov. M.: Aspekt Press, 2000.

[5] V. P. Zinchenko, Psihologicheskaja pedagogika. Materialy k kursu lekcij. Chast' 1. Zhivoe znanie. Samara: Samarskij Dom pechati, 1998.

[6] A. A. Brudnyj, Psihologicheskaja germenevtika. M.: Labirint, 1998

[7] G. Wiggins and J. McTighe. Alexandria, VA: Association for Supervision and Curriculum Development, 2005.

[8] I. V. Sapegina, Organizatsiya protsessa obucheniya matematike v 5-6 klassakh, orientirovannogo na ponimanie. dissertatsiya, kandidat pedagogicheskikh nauk RGPU im. A.I.Gertsena, 2002.

[9] M. E. Bershadskii, Ponimanie kak pedagogicheskaya kategoriya: (Monografiya), M.: Kaf. obrazovat. tekhnologii AGKiPRO,

[10] V. V. Znakov, Ponimanie v poznanii i obshhenii. Samara: SamGPU, 1998.

[11] M. Wertgejmer, Produktivnoe myshlenie. M.: Progress, 1987.

[12] S. Abramovich, A. Z. Grinshpan and D. L. Milligan, Teaching Mathematics through Concept Motivation and Action Learning. Hindawi Education Research International Volume, 2019.

[13] S. Asiedu-Addo and A. K. Arhin, “Connecting Mathematics To Real Life Problems: A Teaching Quality That Improves Students’ Mathematics Interest (Translation Journals style),” World Academy of Science, Engineering and Technology IOSR Journal of Research & Method in Education (IOSR-JRME), Volume 8, Issue 4 Ver. II, Jul. – Aug. 2018, pp 65-71.

[14] R. Skemp, The Psichology of learning mathematics. Expanded American Edition. Hillsdale, New Jersey, 1987.

[15] V. M. Turkina, “Vzaimosvjaz' ideal'noj i real'noj form znanija v obuchenii (na primere obuchenija matematike) (Translation Journals style),” World Academy of Science, Engineering and Technology Nepreryvnoe obrazovanie: XXI vek, vypusk 3 (23), 2018.

[16] N. S. Podkhodova and O. V. Sheremet'eva, “Logiko-psikhologicheskii podkhod k formirovaniyu matematicheskikh ponyatii v shkole. (Periodical style),” World Academy of Science, Engineering and Technology Vestnik Pomorskogo universiteta. Seriya: Fiziologicheskie i psikhologo-pedagogicheskie nauki. 2006, № 1, pp. 117-125.

[17] O. V. Sheremeteva and V. M. Turkina, “Problems of Mathematical Education of Primary School Teachers: Identifying Relationships between Concepts (Published Conference Proceedings style),” World Academy of Science, Engineering and Technology Society, Integration, Education. Proceedings of the International Scientific Conference,2021, Volume I, pp. 560-570.

[18] N. S. Podkhodova and O. A. Ivanova, “Problemy formirovaniya mezhpredmetnykh ponyatii pri izuchenii matematiki. (Translation Journals style),” World Academy of Science, Engineering and Technology Pis'ma v Emissiya. Offlain. (TheEmissia. OfflainLetters): elektronnyi nauchnyi zhurnal. 2013.

[19] I. S. Yakimanskaya, Lichnostno-orientirovannoe obuchenie v sovremennoi shkole. M.: Sentyabr', 2000.

[20] D. P. Resnick and L. B. Resnick, “Standards, Curriculum, and Performance: A Historical and Comparative Perspective (Periodical style)”, Educational Researcher, 1985, volume 14, issue 4, pp. 5-20.

[21] I.S. Yakimanskaya, Fundamentals of Personally Oriented Education. M.: Binom, 2013.

[22] O.V. Sheremet'eva, “Preobrazovanie sub"ektnogo opyta studentov kak metodicheskaya zadacha podgotovki budushchikh uchitelei nachal'nykh klassov. (Periodical style),” World Academy of Science, Engineering and Technology Izvestiya Rossiiskogo gosudarstvennogo pedagogicheskogo universiteta im. A.I. Gertsena, 2008, № 66, pp. 329-337.

[23] T. Varghese, “Teaching mathematics with a holistic approach. (Translation Journals style),” World Academy of Science, Engineering and Technology International Journal of Inclusive Education 2009, 13(1), pp. 13-22.

[24] A. K. Osnitskii, Struktura, soderzhanie i funktsii regulyatornogo opyta cheloveka. M.: 2001.

[25] D. A. Sousa, How the brain learns mathematics (2nd ed.). Corwin Press, 2015.

[26] M. V. Soldaeva, “Realizatsiya tselostnogo podkhoda k obucheniyu matematike kak uslovie dostizheniya ponimaniya. (Periodical style),” World Academy of Science, Engineering and Technology Izvestiya RGPU im. A. I. Gertsena. Seriya Psikhologo-pedagogicheskie nauki, 2013, № 161, pp. 202-206.

[27] N. S. Podkhodova, “Metametodicheskaya model' kul'turotvorcheskoi shkoly kak sredstvo realizatsii integratsiipri izuchenii matematiki (Translation Journals style),” World Academy of Science, Engineering and Technology Pis'ma v Emissiya.Offlain. (TheEmissOfflineLetters): elektronnyi nauchnyi zhurnal, ART 1416, Mai 2010.

[28] “Metodika obucheniya matematike: Kurs lektsii: uchebnoe posobie (Book style with paper title and editor),” N.S. Podkhodovoi and V. I. Snegurovoi, Ed. M.: Izdatel'stvo Yurait, 2019.

[29] B. L. Leaver, Obuchenie vsego klassa. M.: Novaja shkola, 1995.

[30] PISA for Development Assessment and Analytical Framework: Reading, Mathematics and Science, Preliminary Version, OECD Publishing, Paris. 2017. https://www.oecd.org/pisa/pisa-for-development/PISA-D-Assessment-and-Analytical-Framework-Ebook.pdf