Understanding what you are doing: A new angle on CAS?

Powerful Computer Algebra Systems (CAS) are often used only with reluctance in early undergraduate mathematics teaching, partly because of concerns that they may not encourage students to understand what they are doing. In this exploratory study, a version of a CAS that has been designed for secondary school students was used, with a view to considering the value of this sort of student learning support for first year undergraduate students enrolled in degree programs other than mathematics. Workshops were designed to help students understand aspects of elementary symbolic manipulation, through the use of the Algebra mode of an algebraic calculator, the Casio Algebra FX 2.0. The Algebra mode of this calculator allows a user to undertake elementary algebraic manipulation, routinely providing all intermediate results, in contrast to more powerful CAS software, which usually provides simplified results only. The students were volunteers from an introductory level unit, designed to provide a bridge between school and university studies of mathematics and with a focus on algebra and calculus. The two structured workshop sessions focussed respectively on the solution of linear equations and on relationships between factorising and expanding; attention focussed on using the calculators as personal learning devices. Following the workshops, structured interviews were used to systematically record student reactions to the experience. As a result of the study, the paper offers advice on the merits of using algebraic calculators in this sort of way

Graphics calculators in the mathematics curriculum: Integration or differentiation?

Graphics calculators are examples of powerful technologies that we want our students to learn to use well. However if we use them in our courses only for learning, students will not regard them with due importance because they are not integrated into the assessment. On the other hand, if graphics calculators are integrated into both learning and assessment there are risks associated with students becoming calculator dependent, issues of equity arise associated with calculator access and there may be problems with setting an appropriate examination. We discuss this dilemma in the light of our experiences and the reactions of our students over the last two years

Graphics calculator use in examinations: accident or design?

As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be used to help design examinations in which students are permitted to use graphics calculators as well as to interrogate existing examination practice

Symbolic manipulation on a TI-92: New threat or hidden treasures?

The availability of hand held devices that can undertake symbolic manipulation is a recent phenomenon, potentially of great significance for both the algebra and calculus curriculum in the secondary and lower undergraduate years. The significance to date of symbolic manipulation for mathematics is described, and parallels drawn with the significance of arithmetic skills for the primary school. It is suggested that, while symbolic manipulation is central to mathematics, many students develop only a restricted competence with the associated mathematical ideas. The Texas Instruments TI-92 is used to suggest some potential beneficial uses of technology that involves symbolic manipulation

Graphics calculators and assessment

Graphics calculators are powerful tools for learning mathematics and we want our students to learn to use them effectively. The use of these hand held personal computers provides opportunities for learning in interactive and dynamic ways. However, it is not until their use is totally integrated into all aspects of the curriculum that students regard them with due importance. This includes their use in all kinds of assessment tasks such as assignments, tests and examinations as well as in activities and explorations aimed at developing students’ understanding. The incorporation of graphics calculators into assessment tasks requires careful construction of these tasks. In this paper, discuss issues of equity relating to calculator models, levels of calculator use and the purpose and design of appropriate tasks. We also describe a typology we have developed to assist in the design and wording of assessment tasks which encourage appropriate use of graphics calculators, but which do not compromise important course objectives

Research on ion beam diagnostics Final report

Research on ion beam diagnostic

Beyond recurrent costs: an institutional analysis of the unsustainability of donor-supported reforms in agricultural extension

International donors have spent billions of dollars over the past four decades in developing and/or reforming the agricultural extension service delivery arrangements in developing countries. However, many of these reforms, supported through short-term projects, became unsustainable once aid funding had ceased. The unavailability of recurrent funding has predominantly been highlighted in the literature as the key reason for this undesirable outcome, while little has been written about institutional factors. The purpose of this article is to examine the usefulness of taking an institutional perspective in explaining the unsustainability of donor-supported extension reforms and derive lessons for improvement. Using a framework drawn from the school of institutionalism in a Bangladeshi case study, we have found that a reform becomes unsustainable because of poor demands for extension information and advice; missing, weak, incongruent, and perverse institutional frameworks governing the exchange of extension goods (services); and a lack of institutional learning and change during the reform process. Accordingly, we have argued that strategies for sustainable extension reforms should move beyond financial considerations and include such measures as making extension goods (services) more tangible and monetary in nature, commissioning in-depth studies to learn about local institutions, crafting new institutions and/or reforming the weak and perverse institutions prevailing in developing countries. We emphasize the need to address three categories of institutions – regulative, normative, and cultural-cognitive – and call for an alignment among them. We further argue that, in order to be sustainable, a reform should take a systemic approach in institutional capacity building and, for this to be possible, adopt a long-term program approach, as opposed to a short-term project approach

The Rapidly Fading Optical Afterglow of GRB 980519

GRB 980519 had the most rapidly fading of the well-documented GRB afterglows, consistent with t^{-2.05 +/- 0.04} in BVRI as well as in X-rays during the two days in which observations were made. We report VRI observations from the MDM 1.3m and WIYN 3.5m telescopes, and we synthesize an optical spectrum from all of the available photometry. The optical spectrum alone is well fitted by a power law of the form nu^{-1.20 +/- 0.25}, with some of the uncertainty due to the significant Galactic reddening in this direction. The optical and X-ray spectra together are adequately fitted by a single power law nu^{-1.05 +/- 0.10}. This combination of steep temporal decay and flat broad-band spectrum places a severe strain on the simplest afterglow models involving spherical blast waves in a homogeneous medium. Instead, the rapid observed temporal decay is more consistent with models of expansion into a medium of density n(r) proportional to r^{-2}, or with predictions of the evolution of a jet after it slows down and spreads laterally. The jet model would relax the energy requirements on some of the more extreme GRBs, of which GRB 980519 is likely to be an example because of its large gamma-ray fluence and faint host galaxy.Comment: 13 pages, submitted to ApJ Letter