Matricial computations: Classroom practice with a computer algebra system

There are three standard methods for computing the inverse of a square matrix. We compare the efficiency of these methods, both in theory and tested in the classroom. This gives an insight to the efficiency of the corresponding methods of solution of a system of linear equations. Then we describe the usage of a computer algebra system to solve some problems whose solution involves matricial computations, in particular an application of the Cayley-Hamilton theorem.     

Production and use of information. Characterization of informetric distributions using effort function and density function: Exponential informetric process

Statistical regularities observed in the production or use of information have been studied for a long time. In this article we define an exponential informetric process to formalize these stochastic process. It is defined by combining an effort function with a density function. Without using the powerful results of Price on the cumulative advantages process this characterization clarifies the principle of least effort. Some links between statistical theory of information and some informetric distributions are enhanced.     

Exploring the phase space of a system of differential equations: different mathematical registers

We describe and analyze a situation involving symbolic representation and graphical visualization of the solution of a system of two linear differential equations, using a computer algebra system. Symbolic solution and graphical representation complement each other. Graphical representation helps to understand the behavior of the symbolic solution. Together with it, the symbolic solution and its analysis are needed to understand the graphical representation and to overcome the limiting constraints of the CAS. The study described in this paper points out the importance of flexibility in building connections between different mathematical registers, together with the fact that the balance between the usage of symbolic representations and of graphical representations can be very different from one student to the other. Research supported by Israel Science Foundation, grant number 1340/05.     

Neural Differences in Bilingual Children's Arithmetic Processing Depending on Language of Instruction

Many children in bilingual regions follow lessons in a language at school (school‐language) that they hardly ever speak at home or in other informal settings. What are the neural effects of this phenomenon? This functional magnetic resonance imaging (fMRI) study investigates the effects of using school‐language on brain activity during a high cognitive task in two groups of French/Dutch bilingual children. Participants were asked to assess the correctness of 3‐operand (e.g., 5 ? 2 = 3) and 4‐operand (e.g., 3 ? 2 = 1 + 4) equations, respectively. Instructions about the task were given either in the children's school‐language or in another language that they only used at home. It was found that although both groups recruited a visuomotor occipitofrontal network in the left hemisphere, the children who performed the task in their school‐language showed less activation than the children who did not, indicating the importance of language of instruction for bilingual children's arithmetic processing.     

Higher Education Funding: A Decade of Changes

The authors, two French specialists on the financing of higher education, reflect on the conclusions they drew in an article, "Rethinking the Financing of Post-Compulsory Education", which they published in this review ten years ago. As they foresaw, higher education funding became increasingly based on mixed sources with students being required to pay a greater share of the costs of their education. But mechanisms to make cost sharing increasingly equitable have been refined. At the same time, the determination of actual costs per institution, per course programme, and even per course has become increasingly accurate, and funding is increasingly taking into account the verdict of performance indicators of various kinds. The funding of research is being increasingly differentiated from funding for teaching/learning. Across the board, higher education institutions have had to do more for less.