The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing…

Although a good rational number understanding is of crucial importance for learners' general maths achievement, many learners have misconceptions about fractions. An often described misconception is that a fraction's numerical magnitude increases when its denominator, numerator, or both increase. The present intervention study investigated how…

Refutational text is one of the many instructional techniques that have been proposed to be used in education as a way to achieve effective learning. The aim of refutational text is to transform misconceptions into conceptions that are in line with current scientific concepts. This is done by explicitly stating a misconception, refuting it, and…

The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation…

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this…

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…

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.…

Already at a very young age, children experience the wide applicability and intrinsic simplicity of linear/proportional relations. In primary and secondary school mathematics education, moreover, extensive attention is paid to this type of relations. In the long run, students develop the misbelief that each relation can be quantified as…