Educational innovation, learning technologies and Virtual culture potential’

Learning technologies are regularly associated with innovative teaching but will they contribute to profound innovations in education itself? This paper addresses the question by building upon Merlin Donald's co‐evolutionary theory of mind, cognition and culture. He claimed that the invention of technologies for storing and sharing external symbol systems, such as writing, gave rise to a ‘theoretic culture’ with rich symbolic representations and a resultant need for formal education. More recently, Shaffer and Kaput have claimed that the development of external and shared symbol‐processing technologies is giving rise to an emerging ‘virtual culture’. They argue that mathematics curricula are grounded in theoretic culture and should change to meet the novel demands of ‘virtual culture’ for symbol‐processing and representational fluency. The generic character of their cultural claim is noted in this paper and it is suggested that equivalent pedagogic arguments are applicable across the educational spectrum. Hence, four general characteristics of virtual culture are proposed, against which applications of learning technologies can be evaluated for their innovative potential. Two illustrative uses of learning technologies are evaluated in terms of their ‘virtual culture potential’ and some anticipated questions about this approach are discussed towards the end of the paper

How Ordinary Elimination Became Gaussian Elimination

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.Comment: 56 pages, 21 figures, 1 tabl