Processing rational numbers is difficult for many children. The natural number bias is one possible explanation for why children struggle with rational numbers. It refers to the tendency to overgeneralize the properties of natural numbers. In this study, it is argued that in order to be successful in rational number tasks, individuals need to…

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called "natural number bias"). Focusing on rational…

The present study cross-sectionally investigated proportional reasoning abilities in 5- to 9-year-old children (n = 185) before they received instruction in proportional reasoning. This study addressed two important aspects of the development of proportional reasoning that remain unclear in the current literature: (1) the age range in which it…

While previous studies mainly focused on children's additive and multiplicative reasoning abilities, we studied third to sixth graders' "preference" for additive or multiplicative relations. This was investigated by means of schematic problems that were "open" to both types of relations, namely arrow schemes containing three…

We investigated the effect of two visual aids in representational illustrations on pupils' realistic word problem solving. In part 1 of our study, 288 elementary school pupils received an individual paper-and-pencil task with seven problematic items (P-items) in which realistic considerations need to be made to come to an appropriate reaction.…

Graphicacy is an important skill in today's society; however, the interpretation of graphs proofs to be more difficult than it might seem. In this study, we focus on one specific misinterpretation, the area misinterpretation of box plots, which is caused by incorrect heuristic processing of salient features of the box plot. In this study, we tried…

Histograms are widely used, but recent studies have shown that they are not as easy to interpret as it might seem. In this article, we report on three studies on the interpretation of histograms in which we investigated, namely, (1) whether the misinterpretation by university students can be considered to be the result of heuristic reasoning, (2)…

This study investigates the development of proportional and additive methods along primary and secondary school. In particular, it simultaneously investigates the use of additive methods in proportional word problems and the use of proportional methods in additive word problems. We have also studied the role played by integer and non-integer…