meujfe Mersin Üniversitesi Eğitim Fakültesi Dergisi 1306-7850 Mersin University 10.17860/mersinefd.1644006 Mathematics Education Matematik Eğitimi Ortaokul Beşinci Sınıf Öğrencilerinin Ölçümsel ve Yığın Tahmin Becerilerinin Belirlenmesi ve Geliştirilmesine Yönelik Müdahale Çalışması Intervention Study for the Determination and Development of Measurement and Quantity Estimation Skills of Secondary School Fifth Grade Students https://orcid.org/0000-0002-7011-9870 Şahin Handenur Sakarya Üniversitesi https://orcid.org/0000-0001-5119-2813 Ergene Özkan SAKARYA ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ 04 28 2026 22 1 1 21 02 20 2025 02 02 2026 Copyright © 2005, Mersin University Journal of the Faculty of Education 2005 Mersin University Journal of the Faculty of Education

Gündelik yaşamda ve matematik derslerinde tahmin bir beceri olarak tanımlanmaktadır. Bu araştırmada, ortaokul beşinci sınıf öğrencilerinin ölçümsel ve yığın tahmin becerilerinin belirlenmesi ve bu becerilerin geliştirilmesine yönelik müdahale çalışması yapılması amaçlanmıştır. Araştırmanın katılımcılarını kolay ulaşılabilir örnekleme yöntemiyle belirlenmiş 40 ortaokul beşinci sınıf öğrencisi oluşturmaktadır. Nitel araştırma yöntemi ile yürütülen araştırmanın verileri tahmin testleri, etkinliklere verilen öğrenci cevapları ve yarı yapılandırılmış görüşmelerle toplanmıştır. Araştırmanın verileri içerik ve betimsel analiz yöntemleri ile analiz edilmiştir. Araştırma bulguları, müdahale çalışması sonrası öğrencilerin tahmin performanslarında anlamlı bir artış olduğunu ortaya koymuştur. Bununla birlikte araştırmada, öğrencilerin ölçümsel ve yığın tahmin performanslarının müdahale çalışmasının etkisiyle arttığı tespit edilmiştir. Öğrenciler müdahale çalışmasından önce çoğunlukla rastgele ve gözünde canlandırma tahmin etme stratejilerini kullanırken müdahale çalışmasının etkisiyle parçalama, karşılaştırma gibi farklı tahmin etme stratejilerini kullandıkları belirlenmiştir. Ayrıca görüşmelerde, öğrenciler tahmin testlerindeki soru çözümlerinde strateji değişimlerinin sebebinin müdahale çalışması olduğunu ifade etmişlerdir. Bu doğrultuda, tahmin becerilerinin gelişimini desteklemek için öğretim süreçlerine daha fazla tahmin etkinliği entegre edilmesi ve öğrencilere farklı tahmin stratejilerini kullanma fırsatı sunan öğretim ortamlarının oluşturulması önerilmektedir.

Estimation is recognized as a key skill in both everyday life and mathematics lessons. This study aimed to determine the measurement and quantity estimation skills of fifth-grade students and to conduct an intervention study to improve these skills. The participants of the study consisted of 40 fifth-grade secondary school students selected using the easily accessible sampling method. The data for this qualitative research were collected through estimation tests, student responses to activities, and semi-structured interviews. The data were analyzed using content and descriptive analysis methods. The findings revealed a significant improvement in students' estimation performance after the intervention study. Moreover, the study determined that students' measurement and quantity estimation performances increased due to the intervention. Before the intervention, students mostly relied on random guessing and mental imagery strategies, whereas after the intervention, they adopted more structured strategies such as fragmentation and comparison. Additionally, students stated in the interviews that the intervention study played a key role in the changes they made in their estimation strategies between the pre-test and post-test. In this context, it is recommended that more estimation activities be integrated into instructional processes and that teaching materials be developed to allow students to practice different estimation strategies.

 Ölçümsel tahmin tahmin etme stratejileri yığın tahmin Estimation strategies measurement estimation quantity estimation Albarracín, L., & Gorgorió, N. (2019). Using Large Number Estimation Problems İn Primary Education Classrooms To İntroduce Mathematical Modelling. International Journal of Innovation in Science and Mathematics Education, 27(2), 45–57. https://doi.org/10.30722/IJISME.27.02.004 Andrews, P., Xenofontos, C., & Sayers, J. (2022). Estimation İn The Primary Mathematics Curricula Of The United Kingdom: Ambivalent Expectations Of An Essential Competence. International Journal of Mathematical Education in Science and Technology, 53(8), 2199–2225. https://doi.org/10.1080/0020739X.2020.1868591 Ardiale, E., & Lemaire, P. (2013). Effects Of Execution Duration on within-İtem Strategy Switching in young and Older Adults. Journal of Cognitive Psychology, 25(4), 464–472. https://doi.org/10.1080/20445911.2013.789854 Artut, P. D., & Aslan, E. (2014). İlköğretim Matematik Dersi Öğretim Programında Yer Alan Tahmin Becerisinin Öğretmen Görüşleri Doğrultusunda Değerlendirilmesi. Çukurova Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 23(1), 239–250. Aytekin, C. & Toluk Uçar, Z. (2014). Ortaokul Öğrencilerinin Kesirlerde Tahmin Becerilerinin İncelenmesi. İlköğretim Online, 13(2), 546–563. Ayyıldız, N. (2014). İlkokul öğrencilerinin sayı doğrusunda tahmin becerilerinin çeşitli değişkenler açısından karşılaştırılması (Tez No. 366565) [Yüksek lisans tezi, Ankara Üniversitesi, Ankara]. Yükseköğretim Kurulu Tez Merkezi. Ayvalı, İ. (2013). Gerçekçi matematik eğitimi yaklaşımıyla yapılan öğretimin hesapsal tahmin başarısına ve strateji kullanımına etkisi (Tez No. 349971) [Yüksek lisans tezi, Marmara Üniversitesi, İstanbul]. Yükseköğretim Kurulu Tez Merkezi. Baroody, A. J.,& Gatzke, M. R. (1991). The Estimation of Set Size by Potentially Gifted Kindergarten-Age Children. Journal for Research in Mathematics Education, 22(1), 59–68. https://doi.org/10.5951/jresematheduc.22.1.0059 Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What Basic Number Processing Measures in Kindergarten Explain Unique Variability in First-Grade Arithmetic Proficiency?. Journal of experimental child psychology, 117, 12–28. Barth,H., Starr, A.,&Sullivan, J. (2009). Children’smappings Of Large Numberwords to Numerosities. Cognitive Development, 24(3), 248–264. https://doi.org/10.1016/j.cogdev.2009.04.001 Boz-yaman, B., & Bulut, S. (2017). Middle School Mathematics Teachers’ Opinions on Estimation. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(1), 48–80. https://doi.org/10.17522/balikesirnef.354985 Bright, G. W. (1985). Estimation as part of learning to measure. In D. Nelson (Ed.), Measurement in school mathematics: 1976 yearbook of the National Council of Teachers of Mathematics (pp. 87–104). The Council. Bright, G. W. (1976). Estimation as Part of Learning to Measure. In D. Nelson & R. E. Reys (Eds.), National Council of Teachers of Mathematics Yearbook (pp. 87–104). Reston, VA: NCTM. Brumm L & Rathgeb-Schnierer E. (2023). The Relationship Between Accuracy in Numerosity Estimation, Math Achievement, And Math İnterest in Primary School Students. Front. Psychol. https://doi.org/10.3389/fpsyg.2023.1146458 Budak, E. B., & Şengül, S. (2021). Senaryolaştırılmış Kavram Karikatürlerinin 5. Ve 6. Sınıf Öğrencilerinin Ölçüsel Tahmin Becerilerine Ve Strateji Tercihlerine Etkisinin İncelenmesi. Asya Studies, 5(17), 49–75. https://doi.org/10.31455/asya.890670 Bulut, A. S., & Şener, Z. T. (2017). İlkokul öğrencilerinin alan ölçme konusundaki tahmin performanslarının belirlenmesi. In International Congress on Politic, Economic and Social Studies 3 (pp. 12–19). Ankara Yıldırım Beyazıt Üniversitesi. Bulut, S., Yavuz, F. D., & Yaman, B. (2017). Tahmin Becerilerinin 1948’den 2015’e 1-5. Sınıflar Matematik Dersi Öğretim Programlarındaki Yeri. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(1), 19–39. Castillo, I., Lévy-Leduc, C., & Matias, C. (2006). Exact Adaptive Estimation of the Shape of A Periodic Function with Unknown Period Corrupted by White Noise. Mathematical methods of statistics, 15(2), 146–175. Creswell, J. W., Hanson, W. E., Clark Plano, V. L., & Morales, A. (2007). Qualitative research designs: Selection and implementation. The counseling psychologist, 35(2), 236–264. Crites, T. (1992). Skilled and Less Skilled Estimators’ Strategies for Estimating Discrete Quantities. The Elementary School Journal, 92(5), 601–619. https://doi.org/10.1086/461709 Çilingir, D. & Türnüklü, E. B. (2009). Estimation Ability and Strategies of the 6-8 the Grades Elementary School Students. Elementary Education Online, 8(3), 637–650. Desli,D., & Giakoumi, M. (2017). Children’s Length Estimation Performance and Strategies in Standard and Non-Standard Units Of Measurement. International Journal for Research in Mathematics Education, 7(3), 61–84. http://sbem.iuri0094.hospedagemdesites.ws/revista/index.php/ripem/ Er, Z. (2022). 7. sınıf öğrencilerinin ölçüsel tahmin becerilerinin geliştirilmesinde Fermi problemlerine dayalı öğretim uygulanması: Eylem araştırması (Tez No. 728500) [Doktora tezi, Ankara Üniversitesi, Ankara]. Yükseköğretim Kurulu Tez Merkezi. Forrester, M. A., & Pike, C. D. (1998). Learning to Estimate in the Mathematics Classroom:A Conversation-Analytic Approach. Journal for Research in Mathematics Education, 29(3), 334–356. https://doi.org/10.2307/749793 Forrester, Michael A.(1990). Exploring estimation in young children. Educational Psychology, 4(10). Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian Students’ Measurement Estimation Performance İnvolving Linear and Area Attributes of Real-World Objects. ZDM, 43(5), 709–722. https://doi.org/ 10.1007/s11858-011-0338-1 Hanson, S.A., & Hogan P.T., (2000). Computational Estimation Skill of College Students. Journal for Research in Mathematics Education, 31(4), 483. Hildreth, D. J. (1983). The Use of Strategies in Estimating Measurements. The Arithmetic Teacher, 30(5), 50–54. Hogan, Thomas P. & Brezinski, Kristen L. (2003). Quantitative Estimation: One, two, or three abilities?. Mathematical Thinking and Learning, 5(4), 259–280. Huang, H. M. E. (2014). Investigating Children's Ability to Solve Measurement Estimation Problems. North American Chapter of the International Group for the Psychology of Mathematics Education. Jones, M. G., & Taylor, A. R. (2009). Developing A Sense Of Scale: Looking Backward. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 46(4), 460–475. Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students' Accuracy of Measurement Estimation: Context, Units, and Logical Thinking. School Science and Mathematics, 112(3), 171–178. https://doi.org/10.1111/j.1949-8594.2011.00130.x Joram, E. (2003). Benchmarks as Tools for Developing Measurement Sense. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 57–67). Reston, VA: National Council of Teachers of Mathematics. Joram, E., Gabriele, A. J., Bertheau, M., Gelman, R. & Subrahmanyam, K. (2005). Children's Use of the Refrence Point Strategy for Measurement Estimation. Journal for Research in Mathematics Education, 36 (1), 4–23. Kılıç, Ç., & Olkun, S. (2013). İlköğretim Öğrencilerinin Gerçek Yaşam Durumlarındaki Ölçüsel Tahmin Performansları Ve Kullandıkları Stratejiler. İlköğretim Online, 12(1), 295–307. Kösece, P., & Doğanay, A. (2021). Gerçekçi Matematik Eğitimi Yoluyla Tahmin Becerisinin Geliştirilmesine Yönelik Bir Eylem Araştırması. Turkish Studies-Educational Sciences, 16(2). http://dx.doi.org/10.47423/TurkishStudies.49135 Kramer, P., Bressan, P., & Grassi, M. (2018). The SNARC Effect is Associated with Worse Mathematical İntelligence and Poorer Time Estimation. Royal Society Open Science, 5(8), 172362–172362. https://doi.org/10.1098/rsos.172362 Lang, F. K. (1999). What is A “Good Guess” Anyway? Teaching Quantity and Measurement Estimation. Young Children, 54(4), 78–81. Levin, J.A. (1981). Estimation Techniques for Arithmetic: Everyday Math and Mathematics Instruction. Education al Studies in Mathematics 12, 421–434. https://doi.org/10.1007/BF00308140 Levine, D. R. (1982). Strategy Use and Estimation Ability of College Students. Journal for Research in Mathematics Education, 13(5), 350–359. doi:10.5951/jresematheduc.13.5. Lipovec, A., & Ferme, J. (2017). The Use of the Reference Point Strategy for Measurement Estimation. Equity and diversity in elementary mathematics education, 311–318. Merriam, S. B. (2013). Nitel araştırma desen ve uygulama için bir rehber (3. bs.). (S.Turan, Çev.). Nobel Akademik Yayıncılık. Micklo, S. J. (1999). Estimation; Its More than A Guess. Childhood Education, 5(3), 142–145 Milli Eğitim Bakanlığı (2024). Ortaokul matematik dersi öğretim programı Türkiye yüzyılı maarif modeli. https://tymm.meb.gov.tr/upload/program/2024programmat5678Onayli.pdf NCTM (2000). Principles and Standards for School Mathematics. Reston, Va: NCTM Publications. O’Daffer P. (1979). A Case and Techniques for Estimation: Estimation Experiences in Elementary School Mathematics-Essential, Not Extra! Arith Teach 26, 46–51 Patton, M. Q. (1997). Utilization-Focused Evaluation. In International handbook of educational evaluation (pp. 223-242). Dordrecht: Springer Netherlands. Pizarro, N.; Gorgorió, N. & Albarracín, L. (2015). Primary teachers' Approach to Measurement Estimation Activities. https://www.researchgate.net/publication/272019867 Reys, B. J. (1986). Teaching Computational Estimation: Concepts and Strategies. In H. L.Schoen ve M. J. Zweng (Eds.), Estimation and mental computation: 1986 yearbook (pp. 31–45). Reston, VA: National Council of Teachers of Mathematics. Roebyanto, G. (2018). Enhancing the calculating estimation skill of the students of grade vi in the primary school. In 1st International Conference on Early Childhood and Primary Education (ECPE 2018) (pp. 47–52). Atlantis Press. Sasanguie,D., Göbel, S.,Moll, K., Smets, K.,&Reynvoet, B. (2013). Approximatenumber Sense, Symbolic Number Processing, or Number–Spacemappings:What Underliesmathematics Achievement? Journal of Experimental Child Psychology, 114(3), 418–431. https://doi.org/10.1016/j.jecp.2012.10.012 Satan, N., & Yetkin, İ. (2022). An analysis of the middle school students’ performance in the measurement estimation. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, 53, 700–724. https://doi.org/10.53444/deubefd.1038366 Sayers, J., Petersson, R., Rosenqvist, E., & Andrews, P. (2020). Estimation: An inadequately operationalised national curriculum competence. In R. Marks (Ed.), Proceedings of the British Society for Research into Learning Mathematics (1st ed., Vol. 40, Article 14). https://bsrlm.org.uk/wp-content/uploads/2020/05/BSRLM-CP-40-1-14.pdf Segovia, I. & Castro, E. (2009). Computational and Measurement Estimation; Curriculum Foundations and Research Carried Out at the University of Granada. Electronic Journal of Research in and Educational Psychology, 17(7), 499–536. Siegel, A. W.; Goldsmith, L. T. & Madson, C. R. (1982), Skill in Estimation Problems of Extent and Numerosity. Journal for Research in Mathematics Education, 0(13), 211–232. Siegler, R. S.& Booth, J. L. (2005). Development of Numerical Estimation A Review. Edited Jamie I.D. Campbell. Handbook of Mathematical Cognition. Smets, K., Sasanguie, D., Szücs, D., & Reynvoet, B. (2015). The Effect of Different Methods to Construct Non-Symbolic Stimuli in Numerosity Estimation and Comparison. Journal of Cognitive Psychology, 27(3), 310–325. https://doi.org/10.1080/20445911.2014.996568 Sowder, J. ( 1992). Estimation and number sense. In D, A, Grouws (Ed.), Handbook of Research on Mathematics teaching and Learning, (ss. 371–389), New York: Macmillan. Taylor, P. M.; Simms, K., Kim, O. & Reys, R. E. (2001). Do Your Students Measure Up? Teaching Children Mathematics, 7(4), 282–287. Tekinkır, D. (2008). İlköğretim 8. sınıf öğrencilerinin matematik alanındaki tahmin stratejilerini belirleme ve tahmin becerisi ile matematik başarısı arasındaki ilişki (Tez No. 215761) [Yüksek lisans tezi, Dokuz Eylül Üniversitesi, İzmir]. Yükseköğretim Kurulu Tez Merkezi. Thompson, A. G. (1979). Estimating and approximating. In Sowder, J. (1992), Estimation and Number Sense. In D.A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp.371–389). New York: Macmillan. Türk Dil Kurumu, (2024). Güncel Türkçe sözlük. 27 Kasım 2024 tarihinde http://www.tdk.gov.tr/ adresinden edinilmiştir. Umay, A. (2003). Matematiksel Muhakeme Yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(24). Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim. (S. Durmuş, Çev.). Nobel Yayıncılık. Van Garderen, D., & Montague, M. (2003). Visual‐Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities. Learning Disabilities Research & Practice, 18(4), 246–254. Yin, R. K. (1994). Discovering The Future of The Case Study. Method in Evaluation Research. Evaluation practice, 15(3), 283–290