The effectiveness of assessment learning objects produced using pair programming

Pair Programming is a technique from the software development method eXtreme Programming (XP) whereby two programmers work closely together to develop a piece of software. A similar approach has been used to develop a set of Assessment Learning Objects (ALO). Three members of academic staff have developed a set of ALOs for a total of three different modules (two with overlapping content). In each case a pair programming approach was taken to the development of the ALO. In addition to demonstrating the efficiency of this approach in terms of staff time spent developing the ALOs, a statistical analysis of the outcomes for students who made use of the ALOs is used to demonstrate the effectiveness of the ALOs produced via this method.

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, ‘asset value of cattle (representing cattle ownership)' and ‘present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics, and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple ‘no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term, sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from. degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, 'asset value of cattle (representing cattle ownership and 'present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring caring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics,and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple 'no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil. (C) 2004 Elsevier Ltd. All rights reserved.

Formulating generalised 'goal games' against nature: An illustration from decision-making under uncertainty in agriculture

The games-against-nature approach to the analysis of uncertainty in decision-making relies on the assumption that the behaviour of a decision-maker can be explained by concepts such as maximin, minimax regret, or a similarly defined criterion. In reality, however, these criteria represent a spectrum and, the actual behaviour of a decision-maker is most likely to embody a mixture of such idealisations. This paper proposes that in game-theoretic approach to decision-making under uncertainty, a more realistic representation of a decision-maker's behaviour can be achieved by synthesising games-against-nature with goal programming into a single framework. The proposed formulation is illustrated by using a well-known example from the literature on mathematical programming models for agricultural-decision-making. (c) 2005 Elsevier Inc. All rights reserved.