Research showed that the capacity of making simple estimations begins to develop already at the age of five, but little is known about the early development of this estimation capacity and the strategies that underly it. The current study longitudinally followed the estimation capacity and strategies of 332 children from first to second grade of…

The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international assessments.…

Mathematics-related affect comprises an individual's attitudes, beliefs, emotions and motivations towards mathematics. These affective constructs have been widely studied in mathematics education and cognitive psychology and have been shown to be related to cognitive outcomes such as performance on a range of mathematical tasks. However, it is not…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…

Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive of early computational estimation development. The current study longitudinally followed a group of about 350 children at four time points: second (K2, 4-year-olds) and third grades of kindergarten…

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high…

This longitudinal cross-lagged panel study investigated the development of the structure of young children's spontaneous number focusing tendencies and their longitudinal associations with numerical abilities and mathematics achievement over the course of a 3-year period, that is, in the second and third year of kindergarten and in first grade of…

We investigated the effect of two visual aids in representational illustrations on pupils' realistic word problem solving. In part 1 of our study, 288 elementary school pupils received an individual paper-and-pencil task with seven problematic items (P-items) in which realistic considerations need to be made to come to an appropriate reaction.…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…

Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children's preference for additive or multiplicative relations has been shown to contribute to those errors.…

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…

Singaporean children are the best performers on international achievement tests in mathematics (i.e. the TIMSS). Their excellent results could be due at least partly to certain characteristics of the textbooks used there (Oates 2014). Therefore, these materials could be taken as a good benchmark to describe and evaluate aspects of the textbooks of…

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers'…

In contrast to previous studies on Spontaneous Focusing on Quantitative Relations (SFOR), the present study investigated not only the "extent" to which children focus on (multiplicative) quantitative relations, but also the "nature" of children's quantitative focus (i.e., the types of quantitative relations that children focus…

This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…