Research article | Open Access
Curricular Studies & Perspectives 2026, Vol. 2(2) 93-110
Exploring Changes in Early Number Sense Strategies from Preschool to First Grade: A Longitudinal Multi-Case Study
pp. 93 - 110
Publish Date: October 30, 2026 | Single/Total View: 0/0 | Single/Total Download: 0/0
Abstract
This exploratory longitudinal multi-case study examines individual changes in number sense performance and strategy use across the transition from preschool to first-grade. The participants were seven students who had been assessed using the Number Sense Skills Scale (NSSS) during preschool and were reassessed with the same instrument approximately one year later, at the end of first grade. The study examined both response accuracy and the strategies underlying students’ responses, with particular attention to number sense-based reasoning, rule-procedure-based approaches, and non-number sense responses. Quantitative analyses included descriptive statistics and the Wilcoxon signed-rank test, while students’ responses and explanations were analyzed qualitatively according to response accuracy and strategy type. The median NSSS score increased from 12 (IQR = 3) at the preschool assessment to 14 (IQR = 6) at the first-grade assessment; however, the median individual difference score was -1, and the Wilcoxon signed-rank test indicated no statistically significant difference between scores at the two assessment occasions (Z = -0.170, p = .813; r = .064). Item-level analysis revealed heterogeneous patterns of strategy continuity and change across students. Some students maintained number-sense-based strategies, whereas others shifted between number-sense-based and rule-procedure-based approaches. Importantly, changes in response accuracy did not always correspond to changes in strategy type, highlighting the value of examining how children reason rather than relying on correctness alone. These findings should be interpreted cautiously because the assessment modalities differed across occasions: preschool items were read aloud by the researcher, whereas first-grade students independently read and responded to the items. Therefore, the observed changes cannot be attributed to literacy acquisition, formal mathematics instruction, or Philosophy for Children (P4C) participation alone. The findings provide exploratory, hypothesis-generating evidence that number sense development across the preschool to first-grade transition may involve heterogeneous individual trajectories and that assessment conditions should be considered when interpreting longitudinal changes in young children’s mathematical reasoning.
Keywords: Number sense, longitudinal study, early childhood, Mathematics education
APA 7th edition
TUTKUN, N., & Sengul, S. (2026). Exploring Changes in Early Number Sense Strategies from Preschool to First Grade: A Longitudinal Multi-Case Study. Curricular Studies & Perspectives, 2(2), 93-110.
Harvard
TUTKUN, N. and Sengul, S. (2026). Exploring Changes in Early Number Sense Strategies from Preschool to First Grade: A Longitudinal Multi-Case Study. Curricular Studies & Perspectives, 2(2), pp. 93-110.
Chicago 16th edition
TUTKUN, NURAN and Sare Sengul (2026). "Exploring Changes in Early Number Sense Strategies from Preschool to First Grade: A Longitudinal Multi-Case Study". Curricular Studies & Perspectives 2 (2):93-110.
Akyol, H. (2013). Programa uygun Türkçe öğretim yöntemleri. (6th ed.). Pegem Akademi.
Başaran, M. (2013). Okuduğunu anlamanın bir göstergesi olarak akıcı okuma, Kuram ve Uygulamada Eğitim Bilimleri Dergisi, 13 (4), 2277-2290.
Beliakoff, A., Jordan, N., Klein, A., Devlin, B., & Huang, C.W. (2025). Stability of early number sense competencies for predicting mathematics difficulties. Learning and Individual Differences, 118, 102633. https://doi.org/10.1016/j.lindif.2025.102633
Can, D. (2017). İlkokul dördüncü sınıf öğrencilerinin sayı duyularının bağlam temelli ve bağlam temelli olmayan problem durumlarında incelenmesi. [Examination of fourth grade elementary school students’ number sense in context-based and noncontext-based problems] [Doctoral dissertation, Hacettepe University]
Clements, D. H., Dong, Y., Day-Hess, C. A., & Sarama, J. (2024). Longitudinal investigation of early mathematical achievement and classroom strategic diversity: A replication and extension study. Learning and Individual Differences, 114, 102516. https://doi.org/10.1016/j.lindif.2024.102516
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Cohen, L., Manion, L., & Morrison, K. (2009). Research methods in education (6th ed.). Routledge.
Devlin, D., Moeller, K., & Sella, F. (2022). The structure of early numeracy: Evidence from multi-factorial models. Trends in Neuroscience and Education, 26, 1-9. https://doi.org/10.1016/j.tine.2022.100171
Erdoğan, S., & Baran, G. (2003). Erken çocukluk döneminde matematik. Eğitim ve Bilim, 28(130), 32–40.
Fuchs, L. S., Fuchs, D., Hosp, M. K., & Jenkins, J. R. (2001). Oral reading fluency as an indicator of reading competence: A theoretical, empirical, and historical analysis. Scientific Studies of Reading, 5(3), 239-256. https://doi.org/10.1207/S1532799XSSR0503_3
Gözüm, A.İ.C., Özberk, E.H., Kaya, Ü.Ü., & Uyanık Aktulun, Ö. (2024). Number sense across the transition from preschool to elementary school: A latent profile analysis. Early Childhood Education Journal, 52(6), 1221-1243. https://doi.org/10.1007/s10643-023-01511-w
Griffin, S. (2004). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19(1), 173-180. https://doi.org/10.1016/j.ecresq.2004.01.012
Hickendorff, M. (2022). Flexibility and adaptivity in arithmetic strategy use: What children know and what they show. Journal of Numerical Cognition, 8(3), 367-381. https://doi.org/10.5964/jnc.7277
Hojnoski, R. L., Polignano, J. C., & Caskie, G. I. (2023). Number sense development during the preschool years: Relations within and between key skill indicators. Early Education and Development, 34(7), 1631-1646. https://doi.org/10.1080/10409289.2022.2120327
Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
Jordan, N. C., Devlin, B. L., & Botello, M. (2022). Core foundations of early mathematics: Refining the number sense framework. Current Opinion in Behavioral Sciences, 46, 101181. https://doi.org/10.1016/j.cobeha.2022.101181
Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39(2), 181-195. https://doi.org/10.1080/02796015.2010.12087772
McIntosh, A., Reys, B.J., & Reys, R.E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8. https://flm-journal.org/Articles/94F594EF72C03412F1760031075F2.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Palabıyık, E. (2022). Okul öncesi ve ilkokul öğrencilerinin sayı hissi becerilerinin incelenmesi. [Examination of pre-school and primary school students’ number sense skills] [Doctoral dissertation, Gazi University].
Pardo, L. S. (2004). What every teacher needs to know about comprehension. The reading teacher, 58(3), 272-280. https://doi.org/10.1598/RT.58.3.5
Siegler, R. S. (2006). Microgenetic analyses of learning. In D. Kuhn & R. S. Siegler (Eds.), Handbook of child psychology: Vol. 2. Cognition, perception, and language (6th ed., pp. 464-510). Wiley.
Snow, C. (2002). Reading for understanding: Toward a research and development program in reading comprehension. RAND Education. https://www.rand.org/pubs/monograph_reports/MR1465.html
Şengül, S., & Gülbağcı, H. (2013). 7. ve 8. sınıf öğrencilerin sayı hissi ile matematik öz yeterlikleri arasındaki ilişkinin incelenmesi. The Journal of Academic Social Science Studies, 6(4), 1049-1060.
Torres-Peña, R. C., Peña-González, D., & Ariza-Echeverri, E. A. (2025). Mathematical thinking in preschool: Strengthening seriation and counting through problem solving. International Journal of Early Childhood, 57(2), 379-401. https://doi.org/10.1007/s13158-024-00402-4
Tutkun, N. (2025). Çocuklar için felsefe uygulamalarının okul öncesi öğrencilerinin sayı hissi becerilerine etkisi. [The effect of philosophy for children practices on number sense skills of preschool students] [Doctoral dissertation, Marmara University].
Yıldırım, A., & Şimşek, H. (2016). Sosyal Bilimlerde nitel araştırma yöntemleri (10th ed.). Seçkin Yayıncılık.
Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). SAGE.
