Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

The OECD Program for International Student Assessment (PISA) and the OECD Teaching and Learning International Survey (TALIS) constitute two of the largest ongoing international student and teacher surveys presently underway. Data generated from these surveys offer researchers and policy-makers opportunities to identify particular educational…

This paper considers the model of school effectiveness (SE) currently dominant in research, policy and practice in England (although the concerns it raises are international). It shows, principally through consideration of initial and propagated error, that SE results cannot be relied upon. By considering the residual difference between the…

This paper reviews methods which have been used to identify and validate learning hierarchies. Specifically, three methods which reflect the notion of a relatively inviolate sequence are discussed and compared. Two of the psychometric methods compare pairs of skills, the ordering-theoretic method (Bart and Krus) and the test of inclusion (White…