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Yıl 2025, Cilt: 9 Sayı: 20, 219 - 231, 21.07.2025

Zeynep Nur Köse , Murat Çavdar Tuğba Baran Kaya

Öz

Kaynakça

  • Andrews, P., Xenofontos, C., & Sayers, J. (2021). 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
  • 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.
  • Ashcraft, M. H., & Moore, A. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111(2), 246-267
  • Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi [Investigating the middle school students’ estimation ability with respect to fractions]. Master's thesis, Abant İzzet Baysal University, Bolu. Retrieved from
  • Bağdat, A. & Yıldız, B. (2023). Türkiye’de 2012-2022 yılları arasında matematik eğitiminde tahmin konusunda yapılmış çalışmaların incelenmesi [An examination of studies conducted on prediction in mathematics education in Turkey between 2012-2022]. Ulusal Eğitim Dergisi, 3(2), 341-360.
  • 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 (IJRES), 8(2), 243-261. https://doi.org/10.46328/ijres.2897
  • 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.
  • Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016-1031.
  • Boyraz, D. S. & Aygün, M. (2017). Türkiye’de matematikte tahmin konusuyla ilgili yapılmış çalışmalar [Studies on the subject of estimation in mathematics in Turkey]. Milli Eğitim Dergisi, 216, 165-185.
  • 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, 1146458.
  • Bulut, S., Yavuz, F. D., & Yaman, B. (2017). Tahmin becerilerinin 1948’den 2015’e 1-5. sınıflar matematik dersi öğretim programlarındaki yeri [Estimation skill in 1-5th grades mathematics education curricula from 1948 to 2015]. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(1), 19-39.
  • Crites, T. (1992). Skilled and less skilled estimators’ stratejies for estimating discrete quantities. The Elemantary School Journal, 92(5), 601-620.
  • Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 234–265). Erlbaum
  • Ev-Çimen, E., & Bilgiç, E. (2022). Ortaokul matematik ders kitaplarının tahmin becerisi bakımından incelenmesi [Analysis of secondary school mathematics textbooks in terms of estimation skills]. Uluslararası Türk Eğitim Bilimleri Dergisi, 2022(19), 475-500.
  • Gandini, D., Lemaire, P., & Dufau, S. (2008). Older and younger adults’ strategies in approximate quantification. Acta Psychologica, 129(1), 175-189.
  • Gatzke, M. R. (1989). Kindergarten children's estimates of numerosity. University of Illinois at Urbana-Champaign.
  • Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities?. Mathematical Thinking and Learning, 5(4), 259-280.
  • Kayhan Altay, M., Alkaş Ulusoy, Ç., Özer, A., & Umay, A. (2023). Examining kindergarten children’s numerosity estimation skills. Early Childhood Education Journal, 52(3), 503-513.
  • Lang, F. K. (2001). What is a “good guess” anyway? Estimation in early childhood. Teaching Children Mathematics, 7(8), 462–466.
  • Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 13(5), 350–359. https://doi.org/10.2307/749010
  • Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2003). Strategic aspects of numerosity judgment: The effect of task characteristics. Experimental Psychology, 50(1), 63-75.
  • Luwel, K., Lemaire, P., & Verschaffel, L. (2005). Children's strategies in numerosity judgment. Cognitive Development, 20(3), 448-471.
  • Luwel, K., and Verschaffel, L. (2008). Estimation of ‘real’ numerosities in elementary school children. European Journal of Psychology of Education, 23(3), 319–338.
  • Micklo, S. J. (1999), Estimation; Its more than a guess, Childhood Education, 5(3), 142-145.
  • Munakata, M. (2002). Relationships among estimation ability, attitude toward estimation, category width and gender in students of grades 5–11. Columbia University.
  • Newcomb, D. L. (2014). Mathematical estimation and its real-world application in the construction fields (Doctoral dissertation, State University of New York, New York, USA).
  • Reys, B. J. (1986). Estimation and mental computation ıt's “about” time.The Arithmetic Teacher, 34(1), 22-23.
  • Russo, J., MacDonald, A., & Russo, T. (2022). The influence of making predictions on the accuracy of numerosity estimates in elementary-aged children. International Journal of Science and Mathematics Education, 20(3), 531-551. https://doi.org/10.1007/s10763-021-10156-3.
  • Sayers, J., Petersson, R., Rosenqvist, E., & Andrews, P. (2020). Estimation: an inadequately operationalised national curriculum competence. In Proceedings of the British Society for Research into Learning Mathematics, 40(1). BSRLM.
  • Schipper, W. (2009). Handbuch für den mathematikunterricht an grundschulen. Schroedel.
  • Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., ... & Stern, E. (2008). A validation of eye movements as a measure of elementary school children's developing number sense. Cognitive Development, 23(3), 409-422.
  • 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, 13(3), 211–232.
  • Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), The Handbook of Mathematical Cognition (197-212). Psychology Press.
  • Smith, H. D. (1999). Use of the anchoring and adjustment heuristic by children. CurrentPsychology, 18(3), 294-300.
  • Sowder, J., & Wheeler, M. (1989). The development of concepts and strategies used in computational estimation. Journal for Research in Mathematics Education, 20(2), 130–146.
  • Sriraman, B., & Knott, L. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. Interchange, 40(2), 205-223.
  • Tekinkır, D. (2008). İlköğretim 6-8.sınıf öğrencilerinin matematik alanındaki tahmin stratejilerini belirleme ve tahmin becerisi ile matematik başarısı arasındaki ilişki [To determine the estimate strategies in maths field for the primary school studens of 6th-8th grades and the relation between the estimate ability and success for maths]. Master's thesis, Dokuz Eylül University, İzmir.
  • Yıldırım, A. & Şimşek, H. (2021). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (12th ed.). Seçkin Publishing.
  • Wong, T. T., Ho, C. S., & Tang, J. (2016). Consistency of response patterns in different estimation tasks. Journal of Cognition and Development. 17(3), 526–547. https://doi.org/10.1080/15248372.2015.1072091

Examining the Numerosity Estimation Strategies and Skills Used by Middle School Students

Yıl 2025, Cilt: 9 Sayı: 20, 219 - 231, 21.07.2025

Zeynep Nur Köse , Murat Çavdar Tuğba Baran Kaya

Öz

This study examines the strategies used by middle school students in numerosity estimation and the level of closeness of their estimations to the actual value. A special case study method was used, and 71 students from fifth to eighth grades in a middle school in the Central Black Sea Region participated in the study. The data were analysed using descriptive and content analysis methods. During the analysis of the data, MAXQDA, a software program designed for computer-aided qualitative and mixed exchange data, text and multimedia analysis, was utilized. The findings were presented in the form of MAXQDA maps and quotations from the participants' answers were included. It was concluded that the students mostly made random estimations; that is, they did not use any strategies. Accordingly, it was revealed that they could not estimate close to the actual value, that is, their numerosity estimation skills were low. The most used strategy, other than random estimation, was benchmark comparison, and this strategy provided estimates closer to the actual value. It was also observed that the strategies changed depending on the situation to be estimated.

Anahtar Kelimeler

Numerosity estimation estimation strategies estimation skills middle school students

Etik Beyan

This research was carried out with the permission of Kırıkkale University Publication Ethics Board with the session numbered 22.02.2024-246-751 dated 18.03.2024

Kaynakça

  • Andrews, P., Xenofontos, C., & Sayers, J. (2021). 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
  • 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.
  • Ashcraft, M. H., & Moore, A. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111(2), 246-267
  • Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi [Investigating the middle school students’ estimation ability with respect to fractions]. Master's thesis, Abant İzzet Baysal University, Bolu. Retrieved from
  • Bağdat, A. & Yıldız, B. (2023). Türkiye’de 2012-2022 yılları arasında matematik eğitiminde tahmin konusunda yapılmış çalışmaların incelenmesi [An examination of studies conducted on prediction in mathematics education in Turkey between 2012-2022]. Ulusal Eğitim Dergisi, 3(2), 341-360.
  • 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 (IJRES), 8(2), 243-261. https://doi.org/10.46328/ijres.2897
  • 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.
  • Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016-1031.
  • Boyraz, D. S. & Aygün, M. (2017). Türkiye’de matematikte tahmin konusuyla ilgili yapılmış çalışmalar [Studies on the subject of estimation in mathematics in Turkey]. Milli Eğitim Dergisi, 216, 165-185.
  • 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, 1146458.
  • Bulut, S., Yavuz, F. D., & Yaman, B. (2017). Tahmin becerilerinin 1948’den 2015’e 1-5. sınıflar matematik dersi öğretim programlarındaki yeri [Estimation skill in 1-5th grades mathematics education curricula from 1948 to 2015]. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(1), 19-39.
  • Crites, T. (1992). Skilled and less skilled estimators’ stratejies for estimating discrete quantities. The Elemantary School Journal, 92(5), 601-620.
  • Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 234–265). Erlbaum
  • Ev-Çimen, E., & Bilgiç, E. (2022). Ortaokul matematik ders kitaplarının tahmin becerisi bakımından incelenmesi [Analysis of secondary school mathematics textbooks in terms of estimation skills]. Uluslararası Türk Eğitim Bilimleri Dergisi, 2022(19), 475-500.
  • Gandini, D., Lemaire, P., & Dufau, S. (2008). Older and younger adults’ strategies in approximate quantification. Acta Psychologica, 129(1), 175-189.
  • Gatzke, M. R. (1989). Kindergarten children's estimates of numerosity. University of Illinois at Urbana-Champaign.
  • Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities?. Mathematical Thinking and Learning, 5(4), 259-280.
  • Kayhan Altay, M., Alkaş Ulusoy, Ç., Özer, A., & Umay, A. (2023). Examining kindergarten children’s numerosity estimation skills. Early Childhood Education Journal, 52(3), 503-513.
  • Lang, F. K. (2001). What is a “good guess” anyway? Estimation in early childhood. Teaching Children Mathematics, 7(8), 462–466.
  • Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 13(5), 350–359. https://doi.org/10.2307/749010
  • Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2003). Strategic aspects of numerosity judgment: The effect of task characteristics. Experimental Psychology, 50(1), 63-75.
  • Luwel, K., Lemaire, P., & Verschaffel, L. (2005). Children's strategies in numerosity judgment. Cognitive Development, 20(3), 448-471.
  • Luwel, K., and Verschaffel, L. (2008). Estimation of ‘real’ numerosities in elementary school children. European Journal of Psychology of Education, 23(3), 319–338.
  • Micklo, S. J. (1999), Estimation; Its more than a guess, Childhood Education, 5(3), 142-145.
  • Munakata, M. (2002). Relationships among estimation ability, attitude toward estimation, category width and gender in students of grades 5–11. Columbia University.
  • Newcomb, D. L. (2014). Mathematical estimation and its real-world application in the construction fields (Doctoral dissertation, State University of New York, New York, USA).
  • Reys, B. J. (1986). Estimation and mental computation ıt's “about” time.The Arithmetic Teacher, 34(1), 22-23.
  • Russo, J., MacDonald, A., & Russo, T. (2022). The influence of making predictions on the accuracy of numerosity estimates in elementary-aged children. International Journal of Science and Mathematics Education, 20(3), 531-551. https://doi.org/10.1007/s10763-021-10156-3.
  • Sayers, J., Petersson, R., Rosenqvist, E., & Andrews, P. (2020). Estimation: an inadequately operationalised national curriculum competence. In Proceedings of the British Society for Research into Learning Mathematics, 40(1). BSRLM.
  • Schipper, W. (2009). Handbuch für den mathematikunterricht an grundschulen. Schroedel.
  • Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., ... & Stern, E. (2008). A validation of eye movements as a measure of elementary school children's developing number sense. Cognitive Development, 23(3), 409-422.
  • 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, 13(3), 211–232.
  • Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), The Handbook of Mathematical Cognition (197-212). Psychology Press.
  • Smith, H. D. (1999). Use of the anchoring and adjustment heuristic by children. CurrentPsychology, 18(3), 294-300.
  • Sowder, J., & Wheeler, M. (1989). The development of concepts and strategies used in computational estimation. Journal for Research in Mathematics Education, 20(2), 130–146.
  • Sriraman, B., & Knott, L. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. Interchange, 40(2), 205-223.
  • Tekinkır, D. (2008). İlköğretim 6-8.sınıf öğrencilerinin matematik alanındaki tahmin stratejilerini belirleme ve tahmin becerisi ile matematik başarısı arasındaki ilişki [To determine the estimate strategies in maths field for the primary school studens of 6th-8th grades and the relation between the estimate ability and success for maths]. Master's thesis, Dokuz Eylül University, İzmir.
  • Yıldırım, A. & Şimşek, H. (2021). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (12th ed.). Seçkin Publishing.
  • Wong, T. T., Ho, C. S., & Tang, J. (2016). Consistency of response patterns in different estimation tasks. Journal of Cognition and Development. 17(3), 526–547. https://doi.org/10.1080/15248372.2015.1072091
Toplam 41 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi
Bölüm Research Article
Yazarlar

Zeynep Nur Köse 0000-0001-8755-8266

Murat Çavdar 0000-0003-0707-681X

Tuğba Baran Kaya 0000-0001-9924-4352

Erken Görünüm Tarihi 5 Temmuz 2025
Yayımlanma Tarihi 21 Temmuz 2025
Gönderilme Tarihi 14 Nisan 2025
Kabul Tarihi 13 Haziran 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 9 Sayı: 20

Kaynak Göster

APA 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.
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