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'…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

We investigated the effect of emphasising the realistic modelling complexity in text or in the accompanying picture on the solution of P-items, in relation to pupils' grade. 290 pupils from the 5th and 6th grade of various elementary schools in Flanders (Belgium) made a paper-and-pencil task with 7 word problems that are problematic from a…

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.…

In this study we investigated the effect of the request to reword the text of problematic word problems on the occurrence of realistic answers. We proposed the activity of rewording word problems to fifth grade pupils either working individually or in dyads. We found that the rewording the problems while working individually had no effect, while…

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,…

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 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…

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying…

In this study, we investigated the fluency with which first graders of different mathematical achievement levels applied multiple, school-taught strategies for finding arithmetic sums over 10. We characterized children's strategies with the 4 parameters of Lemaire and Siegler's (1995) model of strategy change (strategy repertoire, distribution,…

Previous research has shown that many secondary school students improperly apply linear models when solving non-linear problems involving lengths, area and volume of similar plane figures and solids. This phenomenon is called the "illusion of linearity". This paper presents a teaching experiment in which we developed and tested a learning…

Investigates the arithmetic and algebra word problem-solving skills and strategies of future primary and secondary school teachers. Describes the evolution of these skills and strategies from the beginning to the end of teacher education. Indicates that, in the education of preservice primary and secondary school teachers, there is need for an…

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…

A major challenge for education and educational research is to build on our present understanding of learning for designing environments for education that are conducive to fostering in students self-regulatory and cooperative learning skills, transferable knowledge, and a disposition toward competent thinking and problem solving. Taking into…