Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, "What varieties of use of geometry in the teaching of linear algebra exist?" This question is addressed through an analysis of six…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

In many parts of the world, there is an increased demand for effectiveness and equity in education and for the development of students who see themselves as lifelong learners to meet economic and social challenges. Assessment for learning (AfL) can play a significant role in achieving these three demands. The purpose of AfL is to inform learning,…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

This paper examines perspectives regarding the mathematical skills expected of adults and school graduates, comparing ideas developed as part of two major multinational comparative assessments of skills: the Programme for International Student Assessment and the Programme for International Assessment of Adult Competencies (also known as the OECD…

Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…

While understanding rational numbers forms an essential part of mathematical literacy, research has repeatedly shown that they form a stumbling block in education. A big source of difficulty is the inappropriate application of natural number knowledge. The research literature points at three main aspects where natural number knowledge is…

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore…