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…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

This study examined the development of indirect addition as an alternative for solving multidigit subtractions, by means of two learning environments in traditionally schooled third-graders in Flanders (Belgium). Thirty-five third-graders, who did not demonstrate mastery of indirect addition, participated in an Explicit (n = 20) or Implicit (n =…

This article discusses the characteristics of the indirect addition strategy (IA) in the domain of multi-digit subtraction. In two studies, adults' use of IA on three-digit subtractions with a small, medium, or large difference between the integers was analysed using the choice/no-choice method. Results from both studies indicate that adults…

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…

This study investigated ability-related differences in strategy use and development in the domain of simple arithmetic, in terms of the model of strategic change, using the choice/no-choice method and the chronological-age/ability-level-match design. Twenty-six second-graders with strong mathematical abilities (MA), 25 second-graders with weak MA,…

The activation of real-world knowledge displayed by 91 Japanese fifth graders in solving school mathematics problems was compared to that of 75 previously studied Belgian students. Children in both cultures had a similar tendency to neglect common sense knowledge and realistic considerations as they attempted to solve word problems. (SLD)

Results of a study involving 107 sixth graders, 107 secondary school students, and 99 college education majors support the basic hypothesis of the intuitive model of solving multiplicative problems proposed by E. Fischbein and others (1985) but show that the theory does not account for all the empirical data. (SLD)