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'…

Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

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.…

This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…

Interactive whiteboard offers a high-potential innovative tool in mathematical educational environments, in which teachers' modeling processes and students' exploring activities can easily be executed. Nevertheless, these affordances are not self-evident. There is a gap between the potential claims of the tool and its actual use in the classrooms.…

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…

Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…

This research analyzed how fractions are taught in the fourth grade of elementary school in Flanders. Analysis centered on the presence of five features of instruction recommended by research on teaching and learning fractions (i.e., multiple solution pathways, linking representations, estimation and justification of the solution, collaboration,…

Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task…

The article deals with the way in which authority was established and interpreted by teachers and students in two Flemish sixth-grade mathematics classrooms. Problem-solving lessons during a seven-month observation period were analysed regarding three aspects of teacher-student interactions that explicitly or implicitly reflect who bears…

In mathematics education, a vast amount of research has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too.…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

This contribution reports about a seven-month long video-based study in two regular Flemish sixth-grade mathematics classrooms. The focus is on teachers' approaches towards problem solving. In our analysis we distinguished between a paradigmatic-oriented (focus on the mathematical structure) and a narrative-oriented (focus on the contextual…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…