Journal of Educational Innovations

Journal of Educational Innovations

Presenting a conceptual model of factors affecting students' geometric performance, focusing on the subject of quadrilaterals

Document Type : Original Article

Authors
1 Mathematics teacher in Tehran . Ph.D. student in Mathematics Education, Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
2 Associate Professor, Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
Abstract
The purpose of this qualitative research was to analyze the factors influencing students' performance in quadrilaterals, which was done with meta-synthesis method. The statistical population included valid scientific articles related to the subject in the period from 2015 to 2024, which were published in domestic and foreign scientific databases. After examining the title, abstract, and content of the research and using the criterion of critical evaluation skills, 20 sources were selected purposefully and analyzed using the conventional seven-step method in meta-composite research. Also, the reliability of the research was calculated based on the Kappa index of 0.78. According to the research findings, 4 main categories, 14 themes and 101 final codes were identified and extracted. The results indicate that there are many factors that affect the learning of this subject of geometry. The main categories affecting students' performance in the subject of quadrilaterals include challenges and misconceptions of students about quadrilaterals, characteristics and skills of students, teachers and educational resources, which includes factors such as fundamental challenges, basic concepts and mistakes in definitions, characteristics of quadrilaterals and their relationships, drawing and calculating mistakes, effects of language and terms, special quadrilaterals, learning and cognitive characteristics, geometrical skills, teacher's teaching method, teacher's misconceptions, actions that cause misconceptions, teachers' professional competences in the subject of quadrilaterals, textbooks and educational tools. These findings can familiarize teachers and educators with the range of factors affecting students' geometric performance, as well as a set of misconceptions they have in the field of quadrilaterals, and provide researchers with ideas for conducting new research. Audiences can also identify factors emphasized in previous research and research gaps in this area.
Keywords

بخشعلی‌زاده، شهرناز، و بروجردیان، ناصر. (1396). شناسایی بدفهمی‌های رایج دانش‌آموزان پایه چهارم ابتدایی در حوزه محتوایی هندسه و اندازه‌گیری و مقایسه عملکرد آنها با میانگین عملکرد در سطح بین المللی. نوآوری‌های آموزشی، 16(4)، 126-101.  https://noavaryedu.oerp.ir/article_79134.html
زارعی، عاطفه. (1397). ارزیابی میزان یادگیری دانش‌آموزان سال هشتم از چهارضلعی‌ها با استفاده از نقشه مفهومی [پایان‌نامه کارشناسی ارشد، دانشگاه آزاد اسلامی مرودشت]. ایرانداک.  https://ganj.irandoc.ac.ir/#/articles/ed2281b5969a7b26d0d0836c2d9967a9
سبزعلی، نوید، و  توانایی، ندا. (1399). بررسی تاثیر آموزش هندسه بر مبنای نظریه ون‌هیلی بر یادگیری دانش‌آموزان. پژوهش در آموزش ریاضی، 1(2)، 11-1.  https://journals.cfu.ac.ir/article_1570.html
شورت، ادموند. (1392). روش‌شناسی مطالعات برنامه درسی (ترجمة محمود مهرمحمدی و همکاران). انتشارات سمت. (اثر اصلی در سال 1991منتشر شده است).
صفرپور‌کلشتری، رضا، رستمی‌مال‌خلیفه، محسن، بهزادی، محمدحسن، و شاهورانی‌سمنانی، احمد. (1402). نقش نظریه ون‌هیلی برای ارتقا مهارت‌های هندسی دانش‌آموزان و بدفهمی‌های هندسه. نشریه پژوهش‌های نوین در ریاضی، 9(4)، 89-102.  https://sanad.iau.ir/fa/Article/798538?FullText=FullText
عالمیان، وحید، سیدی، محمد، و حبیبی، ملوک. (1397). شناسایی بدفهمی‌های دانش‌آموزان پایه هشتم در مهارت‌های هندسی در هندسه و استفاده از نظریه ون‌هیلی برای ارتقاء و بهبود سطح مهارت‌های هندسی دانش‌آموزان. نوآوری‌های آموزشی، 17(3)، 147-123.  https://noavaryedu.oerp.ir/article_82390.html
محمدی، مهدی، صابری، مریم، سلیمی، قاسم، و نوری، نوشین (1397). راهنمای عملی روش فراترکیب در شناسایی شایستگی‌های حرفه‌ای معلمان در تدریس ماهیت علم. مطالعات برنامه درسی ایران، 13(50)، 106-73. https://www.jcsicsa.ir/article_85591.html
ملکی، شیوا، زاهد بابلان، عادل، خالق خواه، علی، و تقوی، حسین. (1402). پیشایندهای تحقق صدای دانش‌آموز: یک مطالعه فراترکیب. مطالعات آموزشی و آموزشگاهی، 12(4)، 267-237.  https://pma.cfu.ac.ir/article_3451.html
Abdullah, A. H., & Shin, B. (2019). A comparative study of quadrilaterals topic content in mathematics textbooks between Malaysia and South Korea. Journal on Mathematics Education, 10(3), 315-340. https://doi.org/10.22342/jme.10.3.7572.315-340
Akar, N., & Işıksal-Bostan, M. (2024). The didactic transposition of quadrilaterals: The case of 5th grade in Turkey. International Journal of Mathematical Education in Science and Technology, 55(3), 628-649. https://doi.org/10.1080/0020739X.2021.2022228
Akkaş, E., & Türnüklü, E. (2015). Middle school mathematics teachers’ pedagogical content knowledge regarding student knowledge about quadrilaterals. İlköğretim Online, 14(2), 744-756. https://doi.org/10.17051/io.2015.1200
Atkins, S., Lewin, S., Smith, H., Engel, M., Fretheim, A., & Volmink, J. (2008). Conducting a meta-ethnography of qualitative literature: Lessons learnt. BMC Medical Research Methodology, 8(21), 1-10. https://doi.org/10.1186/1471-2288-8-21
Critical Appraisal Skills Programme. (2024). CASP qualitative checklist. https://casp-uk.net/casp-checklists/CASP-checklist-qualitative-2024.pdf
Cybulski, F. C., Oliveira, H., & Cyrino, M. C. D. C. T. (2024). Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 20(8), Article em2490. https://doi.org/10.29333/ejmste/14916
de Proença, M. C. (2023). Mathematics teachers’ conceptual knowledge about and for teaching quadrilaterals. Revista Internacional de Pesquisa em Educação Matemática, 13(2), 1-18. https://doi.org/10.37001/ripem.v13i2.3395
Elbehary, S. G. A., Fahem, S. M., & Peni, N. R. N. (2023). Track prospective mathematics teachers' understanding of special quadrilaterals: An exploration of level 3 of geometric thinking. Futurity Education, 3(3), 20-45. https://doi.org/10.57125/FED.2023.09.25.02
Fadillah, I., Kusnandi, K., Juandi, D., & Suparman, S. (2022). The distance between students’ concept image and quadrilateral object definition based on students’ mathematical ability. Al-Jabar: Jurnal Pendidikan Matematika, 13(2), 289-311. https://doi.org/10.24042/ajpm.v13i2.13090
Fujita, T., & Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th PME Conference (Vol. 3, pp. 14-21). PME. http://eprints.soton.ac.uk/id/eprint/41247
Hershkowitz, R., & Vinner, S. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the 4th International Conference for the Psychology of Mathematics Education (pp. 177-184). Lawrence Hall of Science. https://weizmann.elsevierpure.com/en/publications/concept-images-and-common-cognitive-paths-in-the-development-of-s
Korkmaz, E., & Morali, H. S. (2022). A meta-synthesis of studies on the use of augmented reality in mathematics education. International Electronic Journal of Mathematics Education, 17(4), Article em0701. https://doi.org/10.29333/iejme/12269
Kozakli Ulger, T., & Tapan Broutin, M. S. (2017). Pre-service mathematics teachers' understanding of quadrilaterals and the internal relationships between quadrilaterals: The case of parallelograms. European Journal of Educational Research, 6(3), 331-345. https://doi.org/10.12973/eu-jer.6.3.331
Leiss, D., Plath, J., & Schwippert, K. (2019). Language and mathematics: Key factors influencing the comprehension process in reality-based tasks. Mathematical Thinking and Learning, 21(2), 131-153. https://doi.org/10.1080/10986065.2019.1570835
Mulia, M. W., Usodo, B., & Kusmayadı, T. A. (2019). Quadrilateral learning based on brain potencies of 7th grade in Karanganyar regency, Indonesia. International Journal of Educational Research Review, 4(4), 652-659. https://doi.org/10.24331/ijere.628478
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Boston College, TIMSS & PIRLS International Study Center. https://timssandpirls.bc.edu/timss2019/international-results/
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/
Noblit, G. W., & Hare, R. D. (1988). Meta-ethnography: Synthesizing qualitative studies. SAGE Publications.
Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 41-48). PME. https://www.researchgate.net/profile/George-Philippou-2/publication/266339265_STUDENTS%27_MOTIVATION_AND_ACHIEVEMENT_AND_TEACHERS%27_PRACTICES_IN_THE_CLASSROOM/links/542f9a1d0cf277d58e91f978/STUDENTS-MOTIVATION-AND-ACHIEVEMENT-AND-TEACHERS-PRACTICES-IN-THE-CLASSROOM.pdf#page=46
Özdemir, A., & Çekirdekci, S. (2022). Geometric habits of mind: The meaning of quadrilaterals for elementary school student teachers. International Journal of Educational Studies in Mathematics, 9(1), 49-66. https://doi.org/10.17278/ijesim.1033078
Ozkan, M., & Bal, A. P. (2017). Analysis of the misconceptions of 7th grade students on polygons and specific quadrilaterals. Eurasian Journal of Educational Research, 16(67), 161-182. https://doi.org/10.14689/ejer.2017.67.10
Pagiling, S. L., & Nur'aini, K. D. (2022). Specialized content knowledge of lower secondary school teachers on quadrilaterals. Pythagoras, 17(1), 333-345. https://doi.org/10.21831/pythagoras.v17i1.42446
Sahidin, L., Fuad, Y., & Budiarto, M. T. (2019). Teachers' content knowledge in generalizing mind maps of quadrilaterals. Journal of Physics: Conference Series, 1157(4), 1-7. https://doi.org/10.1088/1742-6596/1157/4/042091
Sahin, Ö., & Basgül, M. (2020). Pre-service primary school teachers' pedagogical content knowledge on quadrilaterals. Acta Didactica Napocensia, 13(2), 284-305. https://doi.org/10.24193/adn.13.2.19
Sandelowski, M., & Barroso, J. (2006). Handbook for synthesizing qualitative research. Springer.
Seah, R., & Horne, M. (2020). The construction and validation of a geometric reasoning test item to support the development of learning progression. Mathematics Education Research Journal, 32(4), 607-628. https://doi.org/10.1007/s13394-019-00273-2
Strogilos, V., King-Sears, M. E., Tragoulia, E., Voulagka, A., & Stefanidis, A. (2023). A meta-synthesis of co-teaching students with and without disabilities. Educational Research Review, 38, Article 100504. https://doi.org/10.1016/j.edurev.2022.100504
Susanto, D. (2020). Problematic of definition and terminology affecting primary teachers’ mathematical knowledge for teaching geometry. Journal of Physics: Conference Series, 1567, Article 022096. https://doi.org/10.1088/1742-6596/1567/2/022096
Syamsuddin, A. (2019). Investigating students’ geometric thinking in looking for the linkages of quadrilaterals (a case study on students in the formal operation stage). International Journal of Environmental and Science Education, 14(7), 435-444. http://www.ijese.net/makale/2134.html
Walsh, D., & Downe, S. (2005). Meta-synthesis method for qualitative research: A literature review. Journal of Advanced Nursing, 50(2), 204-211. https://doi.org/10.1111/j.1365-2648.2005.03380.x
Youkap, P. T., Ngansop, J. N., Tieudjo, D., & Pedemonte, B. (2020). The introduction of proof at the secondary school in Cameroon: A first approach through the study of quadrilaterals and triangles in the textbook. International Electronic Journal of Mathematics Education, 15(3), Article em0599. https://hdl.handle.net/11584/388166

Articles in Press, Accepted Manuscript
Available Online from 05 August 2025

  • Receive Date 14 December 2024
  • Revise Date 04 May 2025
  • Accept Date 05 August 2025