An Examination of the Interaction Between Modelling and Its Relationship with Construction Kits: Lessons from the Past and for the Future

Construction kits have played a significant part in nurturing the growth and development of the minds and manipulation-based skills of children (and adults) in formal and non-formal education settings. These kits have origins rooted in the representation of the built world and now have a diversity of form and function, including technical versions with moving parts. This article examines some of the historically based ideas that lie behind the role that kits may have in terms of physical modelling. The article traces the transformation of kits from simple bricks and blocks into more complicated pieces for space-filling and achieving the transfer of forces and motion. This transformation occurred during the Victorian era when the influence of the ideas of educationalists and, perhaps rather strangely, exponents of early aviation, played major roles in determining the diversity of forms of construction kit and modelled possibilities that are now to be seen in classrooms and homes. The article ends with a review of some of the lessons from the past and present that will need to be considered in relation to concrete modelling in schools for the future. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Impact of the Implementation of Technology Education on In-Service Teacher Education in South Africa (Impact of Technology Education in the RSA)

In this article the impact of technology education, as a new learning area (subject) in the curriculum, on in-service teacher education in South Africa is described in order to ascertain the extent of the impact. The research on which this article is based draws on a variety of experiences and observations in the field at grassroots level (in particular an outreach project in rural communities). The envisaged impact of technology education on South African schools, communities, teacher educators and teachers, the range of in-service teacher education that is required, and the impacts in urban and rural areas are discussed. Finally a number of concluding remarks are made about the extent of the impact of the inclusion of technology education in the new National Curriculum Statement and whether the situation has changed since the implementation of a pilot technology education project in 1998. This revised version was published online in July 2006 with corrections to the Cover Date.     

A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.