Journals / Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi / 2026 / Cilt: 26 Sayı: 2

An Investigation of Eighth-Grade Students’ Numerosity Estimation Skills and Strategies

Sekizinci Sınıf Öğrencilerinin Çokluğa Dayalı Tahmin Beceri ve Stratejilerinin İncelenmesi

Kübra Aksakal(T.C. Milli Eğitim Bakanlığı)0000-0001-9410-8511
Mesture Kayhan Altay(HACETTEPE ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ, MATEMATİK VE FEN BİLİMLERİ EĞİTİMİ BÖLÜMÜ, MATEMATİK EĞİTİMİ ANABİLİM DALI)0000-0002-1917-2430
Pages
1257–1280
Publication Date
2026-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Overall, the results suggest that providing a reference quantity supports students in producing more accurate estimations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this study is to examine eighth-grade students’ numerosity estimation skills and to explore how the strategies they use vary by question type and gender.
📊
Key Findings & Data:The sample consisted of 102 eighth-grade students from a public school.
💡
Conclusion & Impact:Overall, the results suggest that providing a reference quantity supports students in producing more accurate estimations.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Çokluğa dayalı tahmin · Tahmin stratejileri · Referans alarak karşılaştırma

Abstract

The aim of this study is to examine eighth-grade students’ numerosity estimation skills and to explore how the strategies they use vary by question type and gender. The research employed a process consistent with correlational survey and causal-comparative designs. The sample consisted of 102 eighth-grade students from a public school. Data were collected through the “Numerosity Estimation Test,” developed by the researchers, which includes three types of items: no-reference, multiple-choice reference, and reference-based estimation. The Mann–Whitney U test was used to determine whether students’ scores differed significantly by gender, while Spearman correlation analysis examined relationships among scores across question types. Student response sheets were also analyzed in depth based on strategies identified in the literature. The findings showed that most students demonstrated a moderate level of numerosity estimation skill. Students performed best on reference-based estimation items. They tended to use the “unit iteration” strategy for reference-based questions, “eyeball” for no-reference items, and “reference/benchmark comparison” for multiple-choice reference items. Overall, the results suggest that providing a reference quantity supports students in producing more accurate estimations.

Özet

Bu araştırmanın amacı, sekizinci sınıf öğrencilerinin çokluğa dayalı tahmin becerisini incelemektir. Ayrıca öğrencilerin bu beceriye ilişkin soruları cevaplarken kullandığı tahmin stratejilerinin soru türüne ve cinsiyete göre değişiminin incelenmesi de amaçlanmaktadır. Araştırmada ilişkisel tarama ve nedensel karşılaştırma türüne uygun bir araştırma süreci ve veri analizi gerçekleştirilmiştir. Çalışmanın örneklemi, bir devlet okulunda öğrenim gören 102 sekizinci sınıf öğrencisidir. Veri toplama aracı olarak araştırmacılar tarafından geliştirilen “Çokluğa Dayalı Tahmin Testi” kullanılmıştır. Bu testte “referans sunulmayan”, “seçenekli referans” ve “referanslı tahmin” olmak üzere üç soru türü bulunmaktadır. Verilerin analizinde, çokluğa dayalı tahmin testinden alınan puanların cinsiyete göre anlamlı düzeyde farklı olup olmadığını belirlemek için Mann-Whitney U testi kullanılmıştır. Soru türüne göre alınan puanlar arasındaki ilişkiyi incelemek amacıyla Spearman korelasyon testinden yararlanılmıştır. Ayrıca öğrenci cevap kâğıtları alan yazınında belirlenen stratejilerden yararlanılarak derinlemesine incelenmiştir. Verilerden elde edilen bulgulara göre öğrencilerin büyük bir kısmının çokluğa dayalı tahmin becerisinin orta düzeyde olduğu görülmüştür. Öğrencilerin referanslı tahmin soru türünde daha iyi performans gösterdikleri bulunmuştur. Referanslı tahmin türündeki sorularda “birim yineleme” stratejisi kullanılırken referans sunulmayan tahmin soru türünde “göz kararı”, seçenekli referans soru türünde ise “referans alarak karşılaştırma” stratejisi kullanılmıştır. Tahmin sürecinde referans büyüklüğün sunulması durumunda öğrencilerin daha iyi bir performans gösterdikleri gözlemlenmiştir.

🔖

Cite This Article

Aksakal, K., Altay, M. K. (2026). An Investigation of Eighth-Grade Students’ Numerosity Estimation Skills and Strategies. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, Cilt: 26 Sayı: 2, 1257–1280. https://doi.org/10.17240/aibuefd.2026..-1834235

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (63)

  1. Adams, L., Onslow, B., Edmunds, G., Chapple, N., & Waters, J. (2005). Children’s development of range based estimation skills: Far more than guess work. In Proceedings of the Third International Conference on Education, Honolulu, HA.
  2. Andrews, P., Xenofontos, C., & Sayers, J. (2022). Estimation in 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.
  3. Anobile, G., Castaldi, E., Turi, M., Tinelli, F., & Burr, D. C. (2016). Numerosity but not texture-density discrimination correlates with math ability in children. Developmental psychology, 52(8), 1206. https://doi.org/10.1037/dev0000155.
  4. Anobile, G., Castaldi, E., Moscoso, P. A. M., Burr, D. C., & Arrighi, R. (2020). “Groupitizing”: a strategy for numerosity estimation. Scientific Reports, 10(1), 13436. https://doi.org/10.1038/s41598-020-68111-1.
  5. Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi [Yayımlanmamış yüksek lisans tezi, Abant İzzet Baysal Üniversitesi Eğitim Bilimleri Enstitüsü].
  6. Baran Kaya, T., & Çelik Demirci, S. (2022). Examination of the Estimation Skills and Strategies of Pre-Service Elementary Mathematics Teachers. International Journal of Research in Education and Science. https://doi.org/10.46328/ijres.2897.
  7. 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.
  8. Berry, R. Q. (1998). Computational estimation skills of eighth-grade students [Master’s thesis, Christopher Newport University]. Graduate Faculty, USA.
  9. Booth, J., & Siegler, R. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189–201. https://doi.org/10.1037/ 0012-1649.41.6.189.
  10. 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.
  11. Briggs, G., Lovett, A., Bridewell, W., & Bello, P. F. (2023). Attentional strategies and the transition from subitizing to estimation in numerosity perception. Cognitive Science, 47(9), Article e13337. https://doi.org/10.1111/cogs.13337.
  12. Brumm, L., & Rathgeb-Schnierer, E. (2023). The relationship between accuracy in numerosity estimation, math achievement, and math interest in primary school students. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1146458.
  13. Bulut, M. (2019). 8. sınıf öğrencilerinin işlemsel ve ölçümsel tahmin becerilerinin incelenmesi [Yüksek lisans tezi, Erciyes Üniversitesi]. https://tez.yok.gov.tr/UlusalTezMerkezi/tezDetay.jsp?id=YFVyFg2H_owEaDv0FoKmEQ&no=YqnqhsohjN1LpPptL1vHrw.
  14. Bulut, S., Yavuz, F. D., & Boz 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.
  15. Büyüköztürk, S., Kılıç Çakmak, E., Akgün, O. E., Karadeniz, S., & Demirel, F. (2017). Bilimsel araştırma yöntemleri (23. Baskı). Pegem Akademi.
  16. Caponi, C., Maldonado Moscoso, P. A., Castaldi, E., Arrighi, R., & Grasso, P. A. (2023). EEG signature of grouping strategies in numerosity perception. Frontiers in Neuroscience, 17, 1190317. https://doi.org/10.3389/fnins.2023.1190317.
  17. Carpenter, T. P., Copurn, T. G., Reys, R. E., & Wilson, J. W. (Eds.). (1976). Using research in teaching: Notes from National Assessment: estimation. The Arithmetic Teacher, 23(4), 296-302. https://doi.org/10.5951/AT.23.4.0296.
  18. Crites, T. (1992). Skilled and less skilled estimators’ strategies for estimating discrete quantities. The Elementary School Journal, 92, 601–619. https://doi.org/10.1086/461709.
  19. Çilingir, D., & Türnüklü, E. (2009). İlköğretim 6-8. Sınıf öğrencilerinin matematiksel tahmin becerileri ve tahmin stratejileri. İlköğretim Online, 8(3), 637-650.
  20. Desli, D., & Lioliou, A. (2020). Relationship between Computational Estimation and Problem Solving. International Electronic Journal of Mathematics Education, 15(3), Article No: em0602. https://doi.org/10.29333/iejme/8435.
  21. Duro, M. L., & Dorneles, B. V. (2019). Diferentes habilidades de estimativa: um estudo de comparação entre desempenho em tarefas. Ciência & Educação (Bauru), 25(1), 43–56. https://doi.org/10.1590/1516-731320190010004.
  22. Fabre, L., Melani, P., & Lemaire, P. (2023). How negative emotions affect young and older adults’ numerosity estimation performance. Quarterly Journal of Experimental Psychology, 76(5), 1098-1110. https://doi.org/10.1177/17470218221107766.
  23. Fraenkel, J. R. & Wallen, N. E. (2009). How to Design Evaluate Research in Education. New York: McGrawHill Companies, 7th edition.
  24. Gandini, D., Lemaire, P., Anton, J. L., & Nazarian, B. (2008a). Neural correlates of approximate quantification strategies in young and older adults: An fMRI study. Brain Research, 1246, 144-157. https://doi.org/10.1016/j.brainres.2008.09.096.
  25. Gandini, D., Lemaire, P., & Dufau, S. (2008b). Older and younger adults’ strategies in approximate quantification. Acta psychologica, 129(1), 175-189. https://doi.org/10.1016/j.actpsy.2008.05.009.
  26. George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference (4th ed.). Allyn & Bacon.
  27. Güven, Y., & Göncü, H. B. (2021). Tahmin Becerilerinin Geliştirilmesinin Çocukların Akıl Yürütme Becerileri ve Sezgisel Matematik Yeteneklerine Etkisi. Akdeniz Üniversitesi Eğitim Fakültesi Dergisi, 4(1), 1-19.
  28. Hanson, S.A. & Hogan P.T. (2000). Computational Estimation Skill of College Students. Journal for Research in Mathematics Education, 31 (4), 483-499. https://doi.org/10.2307/749654.
  29. Kayhan Altay, M., Alkaş Ulusoy, Ç., Özer, A., & Umay, A. (2024). Examining kindergarten children’s numerosity estimation skills. Early Childhood Education Journal, 52(3), 503-513. https://doi.org/10.1007/s10643-023-01449-z
  30. Kim, O. K., & Kasmer, L. (2007). Using “prediction” to promote mathematical reasoning. Mathematics Teaching in the Middle School, 12, 294–299. https://doi.org/10.5951/MTMS.12.6.0294.
  31. Köse, Z. N., Çavdar, M., & Baran Kaya, T. (2025). Examining the Numerosity Estimation Strategies and Skills Used by Middle School Students. International E-Journal of Educational Studies, 9(20), 219-231. https://izlik.org/JA23AC76XC.
  32. Lemaire, P., & Lecacheur, M. (2007). Aging and numerosity estimation. The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 62(6), P305–P312. https://doi.org/10.1093/geronb/62.6.P305.
  33. Leutzinger, L. P., Rathmell, E. C., & Urbatsch, T. D. (1986). Developing estimation skills in the primary grades. In H. L. Schoen & M. J. Zweng (Eds.), Estimation and mental computation (pp. 82‑92). Reston, VA: National Council of Teachers of Mathematics.
  34. Levine, D. J., (1982). Strategy use, and estimation ability of college students. Journal for Research in Mathematics Education, 13(5), 350–359. DOI: https://doi.org/10.595/jresema theduc.13.5.0350.
  35. Luwel, K., & Verschaffel, L. (2008). Estimation of ‘real’numerosities in elementary school children. European journal of psychology of education, 23(3), 319-338. https://doi.org/10.1007/BF03173002.
  36. Markovits, Z., & Hershkowitz, R. (1993). Visual estimation of discrete quantities. Zentralblatt für Didaktik der Mathematik, 25(4), 137–140.
  37. Mayer, R. E. (Ed.). (2005). The Cambridge handbook of multimedia learning. Cambridge University Press.
  38. Mejias, S., & Schiltz, C. (2013). Estimation abilities of large numerosities in Kindergartners. Frontiers in Psychology, 4, 518. https://doi.org/10.3389/fpsyg.2013.00518
  39. Micklo, S. J. (1999). Estimation; its more than a guess. Childhood Education, 5(3), 142- 145. https://doi.org/10.1080/00094056.1999.10522001
  40. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  41. Millî Eğitim Bakanlığı. (2024). Türkiye Yüzyılı Maarif Modeli Ortaokul Matematik Dersi Öğretim Programı (5‑8. Sınıflar). https://tymm.meb.gov.tr/upload/program/2024programmat5678Onayli.pdf.
  42. Mitchell, J. H., Hawkins, E. F., Stancavage, F. B., & Dossey, J. A. (1999). Estimation skills, mathematics-in-context, and advanced skills in mathematics: Results from three studies of the National Assessment of Educational Progress 1996 mathematics assessment. U.S. Government Printing Office.
  43. Montague, M., & Van Garderen, D. (2003). A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability. Journal of learning disabilities, 36(5), 437-448. https://doi.org/10. 1177/0022219 4030360050501.
  44. Munakata, M. (2002). Relationships among estimation ability, attitude toward estimation, category width, and gender in students of grades 5–11 [Unpublished doctoral dissertation]. Columbia University.
  45. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA. NCTM
  46. Reys, B. J. (1986). Teaching computational estimation: Concepts and strategies. In H. L. Schoen & M. J. Zweng (Eds.), Estimation and Mental Computation: 1986 Yearbook (ss. 31‑44). Reston, VA: National Council of Teachers of Mathematics.
  47. Reys, R. E. (1984). Mental computation and estimation: Past, present and future. The Elementary School Journal, 84(5), 547-559. https://doi.org/10.1086/461383.
  48. Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. https://doi.org/10.5951/jresematheduc.29.2.0225.
  49. Russo, J., MacDonald, A., & Russo, T. (2021). The Influence of Making Predictions on the Accuracy of Numerosity Estimates in Elementary-Aged Children. International Journal of Science and Mathematics Education, 20, 531- 551. https://doi.org/10.1007/s10763-021-10156-3.
  50. Segovia, I., & Castro, E. (2009). Computational and measurement estimation: curriculum foundations and research carried out at the University of Granada, Mathematics Didactics Department. Electronic Journal of Research in Educational Psychology, 7(1), 499-536. https://doi.org/10.25115/ejrep.v7i17.1359.
  51. Siegel, A. W., Goldsmith, L. T., & Madson, C. R. (1982). Skill in estimation problems of extent and numerosity. Journal for Research in Mathematics Education, 13(3), 211- 232. https://doi.org/10.5951/jresematheduc.13.3.0211.
  52. Siegler, R. S. & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444. https://doi: 10.1111/j.1467-8624.2004.00684.x.
  53. Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197–212). Psychology Press.
  54. Smith, H. D. (1999). Use of the anchoring and adjustment heuristic by children. Current Psychology, 18(3), 294-300. https://doi.org/10.1007/s12144-999-1004-4.
  55. Sowder, J. T. (1989). Estimation and Mathematical Flexibility. In I. Wirszup & S. L. Carver (Eds.), Mathematics and cognition (pp. 123-160). Cambridge University Press.
  56. Sowder, J. T. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 371–389). Macmillan Publishing Co.
  57. Starkey, G. S., & McCandliss, B. D. (2014). The emergence of “groupitizing” in children’s numerical cognition. Journal of experimental child psychology, 126, 120-137. https://doi.org/10.1016/j.jecp.2014.03.006
  58. Sunde, P. B., Petersson, J., Nosrati, M., Rosenqvist, E., & Andrews, P. (2021). Estimation in the Mathematics Curricula of Denmark, Norway and Sweden: Inadequate Conceptualisations of an Essential Competence. Scandinavian Journal of Educational Research, 66(4), 626–641. https://doi.org/10.1080/00313831.2021.1897881.
  59. Thompson, A. G. (1979). Estimating and Approximating. School Science and Mathematics. 79(7), 575-586. https://doi.org/10.1111/j.1949-8594.1979.tb13899.x.
  60. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and Middle School Mathematics: Teaching Developmentally. Pearson Education.
  61. Yaman, H. (2025). Türkiye'deki matematik dersi öğretim programlarında sayı duyusunun yeri: Geçmişten günümüze bir inceleme. A. Umay (Ed.), Sayı Duyusu Doğuştan Gelen Matematik Algımız (ss. 95-127). Nobel Akademik Yayıncılık.
  62. Yang, D. C. (2007), Investigating the Strategies Used by Pre-Service Teachers in Taiwan When Responding to Number Sense Questions. School Science and Mathematics, 107: 293-301. https://doi.org/10.1111/j.1949-8594.2007.tb17790.x.
  63. Zang, Z., Chi, X., Luan, M., Hu, S., Zhou, K., & Liu, J. (2024). Inter-individual, hemispheric and sex variability of brain activations during numerosity processing. Brain Structure and Function, 229(2), 459-475. https://doi.org/10.1007/s00429-023-02747-3.