Mathematical knowledge for teaching (MKT) measures have been widely adopted by researchers. Critics have debated the value of such measures and questioned the type of knowledge that these access. This article reports on a study where the challenges in measuring teachers' knowledge were illuminated through investigating relationships between the…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…