Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

A discussion of the history of error analysis in mathematics education research provides an overview of research published in German and Anglo-American publications since the early 1900s. (MP)

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

Presents a selection of solutions of the "Three Hungry Men" problem from grade three to college students with three different strategies used: backward, forward, and forward/backward strategies. Provides error patterns in each strategy. Discusses some implications for teaching of problem solving. (YP)

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)