Exploring Changes in Early Number Sense Strategies from Preschool to First Grade: A Longitudinal Multi-Case Study

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.