Kalit so‘zlar
funksiya xossalari
grafik tahlil
GeoGebra
matematik dasturiy ta’minot
matematika ta’limi
Iqtibos keltirish tartibi
Annotatsiya
Ushbu tadqiqot funksiyalar tushunchasi, ularning asosiy xossalari va zamonaviy matematik dasturiy ta’minot yordamida grafik tahlil usullarini o‘rganadi. Tadqiqot an’anaviy analitik yondashuvlarni interaktiv raqamli vizualizatsiya bilan integratsiya qilishga, funksional bog‘lanishlarni yaxshiroq tushunishga qaratilgan. GeoGebra grafiklarni tuzish va tahlil qilish, parametrlar o‘zgarishini o‘rganish hamda soha, qiymatlar to‘plami, nollar, ekstremumlar, monotonlik va simmetriya kabi muhim xususiyatlarni ko‘rib chiqish uchun foydalanildi. Metodika algebraik ifodalar, sonli jadvallar, grafik tasvirlar va analitik tekshirishni birlashtirdi. Natijalar eksperimental va nazorat guruhlari o‘rtasida pre-test va post-test ko‘rsatkichlarini taqqoslash orqali baholandi. Eksperimental guruhning o‘rtacha natijasi 55 balldan 82 ballgacha oshdi, nazorat guruhida esa 54 balldan 60 ballgacha oshdi. Bu topilmalar interaktiv grafik muhitlar o‘quvchilarga funksiyalarning ramziy va vizual tasvirlarini bog‘lashda yordam berishini ko‘rsatadi. Tadqiqot modern matematik dasturiy ta’minot an’anaviy o‘qitish usullarini to‘ldirishi, dinamik vizualizatsiya ta’minlashi, matematik izlanishni yengillashtirishi va funksiyalar hamda ularning grafik xossalarini chuqurroq konseptual tushunishga ko‘maklashishi mumkin degan xulosaga keladi.
Adabiyotlar ro‘yxati
1. Birgin, O., & Uzun Yazıcı, K. (2026). Effects of GeoGebra-supported instruction on eighth-grade students’ cognitive, affective, and social engagement and mathematics anxiety. International Journal of Educational Research, 137, 103051. https://doi.org/10.1016/j.ijer.2026.103051
2. Mosese, N., & Ogbonnaya, U. I. (2021). GeoGebra and students’ learning achievement in trigonometric functions graphs representations and interpretations. Cypriot Journal of Educational Sciences, 16(2), 827–846. https://doi.org/10.18844/cjes.v16i2.5685
3. Oktaviana, D., Sarassanti, Y., & Elshad, E. Y. (2026). Effectiveness of GeoGebra-assisted collaborative learning on understanding mathematical functions and graphs. International Journal of Science and Mathematics Education, 2(1). https://doi.org/10.62951/ijsme.v2i1.257
4. Pihlap, S. (2026). The impact of the GeoGebra dynamic program on the learning of functions in lower secondary school. LUMAT-B: International Journal on Math, Science and Technology Education, 11(1).
5. Zhang, Y., Wang, P., Jia, W., Zhang, A., & Chen, G. (2025). Dynamic visualization by GeoGebra for mathematics learning: A meta-analysis of 20 years of research. Journal of Research on Technology in Education, 57(2), 437–458. https://doi.org/10.1080/15391523.2023.2250886
6. Soots, K. L., & Shafer, K. G. (2018). Engaging students with linear functions and GeoGebra: An action research study. North American GeoGebra Journal, 7(1).
7. Wassie, Y. A., & Zergaw, G. A. (2018). Capabilities and contributions of the dynamic math software, GeoGebra—A review. North American GeoGebra Journal, 7(1).
8. Olsson, J., & Granberg, C. (2019). Dynamic software, task solving with or without guidelines, and learning outcomes. Technology, Knowledge and Learning, 24, 419–436. https://doi.org/10.1007/s10758-018-9352-5
9. Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48–62. https://doi.org/10.1016/j.jmathb.2014.11.001
10. Papp-Varga, Z. (2008). GeoGebra in mathematics teaching. Teaching Mathematics and Computer Science, 6, 101–110. https://doi.org/10.5485/TMCS.2008.R010
11. Hohenwarter, M., & Jones, K. (2007). Teachers’ professional development with GeoGebra: Integrating dynamic mathematics software in mathematics teaching. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 91–96.
12. Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and calculus with free dynamic mathematics software GeoGebra. Proceedings of the 11th International Congress on Mathematical Education, 1–9.
13. Diković, L. (2009). Applications GeoGebra into teaching some topics of mathematics at the college level. Computer Science and Information Systems, 6(2), 191–203. https://doi.org/10.2298/CSIS0902191D
14. Baltacı, S., Yıldız, A., & Kösa, T. (2015). The potential of GeoGebra dynamic mathematics software in teaching analytic geometry: The opinion of pre-service mathematics teachers. Turkish Journal of Computer and Mathematics Education, 6(3), 483–505.
15. Hohenwarter, M., & Preiner, J. (2007). Dynamic mathematics with GeoGebra. The Journal of Online Mathematics and Its Applications, 7.
Ushbu asar Creative Commons Attribution 4.0 Xalqaro Litsenziyasi asosida litsenziyalangan.
Mualliflik huquqi (c) 2026 Olimova, S.Z. (Author)