The present study cross-sectionally investigated proportional reasoning abilities in 5- to 9-year-old children (n = 185) before they received instruction in proportional reasoning. This study addressed two important aspects of the development of proportional reasoning that remain unclear in the current literature: (1) the age range in which it…

The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children's understanding of missing-value proportional situations, (b) investigating how children transition…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

This study investigates children's metarepresentational competence (MRC) with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2002) seminal work on MRC in mathematics and sciences as background, it aims to assess the relative importance children attribute to several criteria for representational adequacy…

This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…

To date, a number of studies have demonstrated the existence of mismatches between children's "implicit" and "explicit" knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

The number line estimation task captures central aspects of children's developing number sense, that is, their intuitions for numbers and their interrelations. Previous research used children's answer patterns and verbal reports as evidence of how they solve this task. In the present study we investigated to what extent eye movements recorded…

Describes an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop a disposition toward more realistic mathematical modeling in pupils. The learning and transfer effects of an experimental class of 10- and 11-year-old students that were compared to the results of two control groups support this…

Studied the development of early numeracy in 207 5- to 7-year-old Flemish children compared with 299 Dutch peers. Results suggest that the Early Numeracy Test (J. van Luit and others, 1994) is moderately reliable and has construct validity. Flemish children lagged at the first assessment but caught up by the third in the middle of the first year…

Design and results of an investigation attempting to analyze and improve children's solution processes in elementary addition and subtraction problems are described. As background for the study, a conceptual model was developed based on previous research. One dimension of the model relates to the characteristics of the tasks (numerical versus word…