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…

In teaching students to write extended definitions it is essential for writing instructors to teach students the concept of criteria. Without such a concept students will never be able to write effective definitions on their own. The criteria they establish for a particular definition allow them to judge which items support their positions on an…

The notion of competence has received sustained and ongoing critical attention. Despite this, many important matters remain unclear. This article argues that much of the confusion can be traced to both proponents and opponents of competence variously sharing highly questionable assumptions about learning that revolve around viewing it as a…