Development of complex mathematical competencies in young math-gifted children

Children’s early mathematical development is marked by large individual differences. In the past decades, a large body of research has emerged on children’s typical and atypical mathematical development and the factors (e.g., general cognitive abilities) associated with it. Thus far, little attention has been paid to individuals with high mathematics achievement levels. This doctoral dissertation was set up to learn more about what characterizes young high mathematics achievers. It contributed to the previous work in three important ways: (1) a focus on high mathematics achievers early on in their development, (2) a consideration of their mathematics-specific abilities, and (3) an integrative analysis of different factors and their unique role in high mathematics achievement.

The first study specifically focused on the number processing abilities (i.e., symbolic magnitude comparison and numerical order abilities) of high achievers (Chapter 2). Results indicated that, at least at the age of 8-10, the importance of these abilities for success in mathematics is limited. The results did, however, reveal that a heightened spatial visualization ability might be a particularly important correlate of high mathematics achievement.

The second study addressed the mathematical abilities previously suggested to be characteristics of high mathematics achievers in the seminal work of Krutetskii: mathematical cast of mind, flexibility of mental processes, and striving for elegance. Those abilities were linked to mathematical concepts of more recent literature (Chapter 3). The study also involved a consideration of general cognitive and motivational factors. Differences between high and average achievers were observed for all tasks, except for the attention to number task. The logistic regression further revealed that spatial visualization ability, strategy variety, and need for cognition were linked to a higher likelihood of belonging to the high mathematics achievement group.

The third study investigated high and average achievers in Grade 1 and Grade 3 and retrospectively analyzed their numerical abilities (e.g., numeral recognition), complex mathematical abilities (e.g., proportional reasoning), and general cognitive abilities (e.g., working memory) when they were of preschool age (Chapter 4). Results indicated that in preschool the high achievers already outperformed the average achievers on most of the administered measures. Number order, numeral recognition, and proportional reasoning emerged as significant predictors for high mathematics achievement.

A limitation of the first three studies is that they used a cut-off approach to select the high and average achievers. In the fourth study, we took a different approach by investigating the full ability spectrum and subsequently used a person-centered approach to delineate subgroups with similar developmental patterns in their numerical abilities in preschool (Chapter 5). Four pathways emerged: low, below-average, above-average, and high numerical ability pathways. The contributions of several correlates to pathway membership were examined, with visual-spatial working memory, in particular, emerging as an important predictor. Most of the pathways were also found to differ in their later mathematics achievement, even after controlling for covariates (e.g., general cognitive abilities).