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...

This study investigates the effect of the number structure (integer vs. non-integer ratios) and the nature of the quantities (discrete vs. continuous) on the performance of secondary school students and on the strategies they use when solving proportional and non-proportional word problems. 551...

This study builds on two lines of research that so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution...

The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: “Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result.” Since the solution requires minimal technical mathematics, the problem is...

Upper primary school children often routinely apply proportional methods to missing-value problems, also when this is inappropriate. We tested whether this tendency can be broken if children do not need to produce computational answers to word problems. 75 6th graders were asked to classify 9...

Previous research showed that primary school pupils over-use proportional methods especially when solving non-proportional missing-value word problems. The current study examines whether the numbers appearing in these word problems partly explain this phenomenon. In previous studies, the numbers...

A vast amount of research in mathematics education has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides...