Early mathematical skills are highly predictive of later mathematical achievement. Importantly, children have large individual differences in these mathematical skills developing before school entry, that not only tend to persist but often widen as children progress through school. Therefore, it is crucial to identify the factors that lead to the emergence of these individual differences in early mathematical skills. Previous research has shown that varying numerical ordering skills explain individual differences in later mathematical skills. However, the development of numerical ordering skills has remained poorly understood. Next to differences in early numerical skills, some of the variation in mathematical skills can also be explained by children’s tendencies to spontaneously focus on mathematical aspects in everyday situations. Some children more frequently recognize and use mathematical aspects in various situations without any adult-guidance, which may lead to increased practice in their mathematical skills. It is possible, that some children also focus on the aspect of numerical order spontaneously more than others, giving them an advantage in learning numerical ordering skills. Therefore, this dissertation aims to provide novel insights into (a) the development of numerical ordering skills (i.e., the skills to order sets of items based on their numerical value) within mathematical development before school entry, and (b) the associations between Spontaneous Focusing On Numerical Order (SFONO) and early mathematical skills, especially numerical ordering skills. In the current dissertation, numerical ordering skills refer to skills required to order sets of items according to their exact number (in numerical order). The specific goals of the four studies of this dissertation were to identify to what extent children exhibit a spontaneous tendency to recognize and use numerical order in non-mathematical situations, and to assess how this tendency, alongside early numerical skills, is related to individual differences in numerical ordering skills.

Study I presented a longitudinal study following 36 children between the ages of 3 and 12 years, with detailed assessments of focusing on numerical order (FONO) and early numerical skills conducted between the ages of 3 to 6 years, and a final follow-up at the age of 12 assessing their mathematical achievement. The results revealed that there were substantial individual and developmental differences in children’s FONO. Furthermore, focusing on numerical order was predictive of mathematical achievement at the age of 12 years, even when other early numerical predictors such as subitizing-based enumeration and spontaneous focusing on numerosity (SFON) were controlled. Focusing on numerical order in this study was measured with a task that required applying numerical ordering skills in a novel play-based situation. Thus, the results showed that the children who noticed the numerical order aspect and had better numerical ordering skills in this novel situation, also had better mathematical skills later in their development. Importantly, the results suggested the importance of numerical ordering skills for later mathematical achievement, and indicated that children may exhibit individual differences in their spontaneous recognition and use of numerical order.

Study II continued the work of Study I, by explicitly measuring individual differences in children’s spontaneous recognition and use of numerical order in 150 three- to four-year-old children. The study used three SFONO tasks that were developed based on findings from Study I in addition to earlier investigations of spontaneous mathematical focusing tendencies, and is the first to specifically report on the relations between SFONO and early numerical skills. The cross-sectional data revealed that children had substantial individual differences in their tendency to spontaneously focus on numerical order, that were related to their early numerical skills. These individual differences in SFONO tendency explained unique variance in children’s numerical ordering skills. In other words, those children who tended to recognize and use numerical order more frequently than others in situations that were not explicitly mathematical, had better numerical ordering skills. These results are the first to suggest that SFONO tendency may be a relevant factor contributing to individual differences in numerical ordering skills.

After Study II, it was still not known whether the individual differences observed in SFONO tendency were due to individual differences in the requisite skills needed to spontaneously focus on numerical order in the SFONO tasks or varying task demands. Therefore, Study III investigated individual differences in SFONO tendency in 51 five- to six-year-old children from Belgium, aiming to address the previous gaps. The results showed individual differences in SFONO tendency across four SFONO tasks with similar task demands. Moreover, these individual differences could not be fully accounted for by the requisite skills involved in the SFONO tasks—namely, the ability to order sets numerically, recognize cardinal values, or recite the number sequence. This study was therefore successful to demonstrate a partial dissociation between SFONO tendency and these underlying skills, suggesting that SFONO represents a distinct construct.

Study IV was a longitudinal study of the participants from Study II, examining the development of numerical ordering skills over a one-year time period between the ages of 3 and 5 years. During the follow-up, children completed measures of numerical ordering skills, cardinality recognition, and number sequence production at three time points. The results indicated that children developed at varying rates in their numerical ordering skills during the follow-up. While some children developed steeply from having very little knowledge on numerical ordering to fully mastering the skill, some children showed very low numerical ordering skills across the follow-up. Furthermore, the findings showed not only that numerical ordering skills started to develop only some time after learning to recognize the smallest cardinal values and learning to recite the number sequence, but also that the development may include a conceptual shift where children integrate their existing knowledge about cardinal values and the number sequence.

Overall, the current dissertation sheds light on the role of numerical ordering skills and SFONO tendency in early mathematical development. The findings suggest that the development of numerical ordering skills is a complex process, that may require the integration of pre-existing numerical knowledge, which is important for later mathematical development. Furthermore, those children who are more likely to notice and use numerical order in situations that are not explicitly mathematical seem to be ahead in their numerical ordering skills. It may be, that these children gain more self-initiated practice with numerical ordering skills in different situations due to increased SFONO tendency. By examining numerical ordering skills and SFONO tendency in preschool-aged children, the dissertation contributes to a more detailed understanding of early mathematical development. These findings may help inform the design of assessment tools aimed at identifying individual differences in early numerical skills, which could be valuable for supporting mathematics learning before the start of formal schooling.