Thirty-six secondary school students aged 14-16 were interviewed while they chose between a table, a graph or a formula to solve three linear function problems. The justifications for their choices were classified as (1) task-related if they explicitly mentioned the to-be-solved problem, (2) subject-related if students mentioned their own…

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…

This study tested the hypothesis that intuitions about the effect of operations, e.g., "addition makes bigger" and "division makes smaller", are still present in educated adults, even after years of instruction. To establish the intuitive character, we applied a reaction time methodology, grounded in dual process theories of reasoning. Educated…

Subtractions of the type M - S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children's use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 - 9 = .) and addition…

This study aimed at analysing traditionally taught children's acquisition and use of shortcut strategies in the number domain 20-100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions…

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…

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

Investigates the thinking process underlying students' improper linear reasoning and how this process is affected by their mathematical conceptions, beliefs, and habits. Explores the actual process of problem solving from students falling into the linearity trap and the mechanism behind it. Discusses specific mathematical conceptions, habits, and…

Reports on two closely related studies on students' tendency to use linear models in situations in which they are not applicable. Results provide a convincing demonstration of the predominance of the linear model in secondary students' solutions to this kind of mensurational problem. Contains 25 references. (Author/ASK)