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…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

Using error analysis and individual interviews, the problem-solving actions of first and second graders were analyzed. Shortcomings of children's knowledge and solution strategies were seen to be overcome by instruction. A control group, with usual arithmetic instruction, and an experimental group were established and the hypothesized…

A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students' learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and…

An overview is first given of some main theoretical frameworks underlying current European research in mathematical thinking, learning, and teaching. Together with the information-processing and the (neo)-Piagetian approaches, both well known in the United States, two other research paradigms can be distinguished: the action-oriented approach to…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

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…

Most studies of children's solution processes on simple addition and subtraction word problems have used individual interviews or the analysis of error patterns on paper-and-pencil tests as the primary data-gathering techniques. The present paper reports an investigation in which the contribution of eye-movement data was explored for studying…