Exploring the potential, limitations and use of objective questions in advanced calculus

This paper describes our experiences with authoring and trialling questions in advanced calculus topics, namely ordinary differential equations, Laplace transforms and Fourier series. These topics are generally taught at the end of the first year or during the second year of a mathematics or engineering undergraduate degree. We expect that many of the lessons learned here will apply to other conceptually-advanced mathematical and scientific content. Typically, what is significant for such content is that many skills are needed from previous exposure to calculus and algebra, and that paper-based questions at this level tend to be more abstract, holistic and open-ended, requiring the sort of flexibility in marking generally associated with human markers. For objective, and therefore more constrained questions, we do not know what is feasible and whether or not questions on advanced topics will actually test the skills they are designed to test. For example, a student may carry out e.g. a Laplace transform correctly, but make an elementary algebraic mistake near the end; this would be easily recognised by a human marker, but simply marked wrong by any current CAA system which cannot assess the (generally handwritten) intermediate steps in a student’s solution. Conversely, any question that can be marked by a CAA system is likely to be structured or scaffolded (e.g. by asking for intermediate steps explicitly) so that the original requirement on the student to devise a solution strategy is lost. This paper explores what can be asked effectively: facility with such questions is a necessary (but not sufficient) condition for students to master more advanced topics, so some sort of blended assessment (with human markers) may still be needed for higher-level skills. We describe the process of authoring higher-level objective and report of the experience of running the questions with our second year cohort, including an analysis of the answer files produced. Our evidence suggests that the assessments were useful to students in establishing a solid foundation of skills, mainly by being encouraged, or even forced, to engage with the extensive feedback screens

Cheap Retrieval Bag for Laparoscopic Cholecystectomy

Gallstone disease is one of the most common gastrointestinal conditions that require surgery and currently laparoscopic cholecystectomy (LC) is the standard treatment for symptomatic cholelithiasis. Use of a laparoscopic bag for facilitating extraction/ morcellation of the operative specimen has been shown to minimize infection of wound and abdominal cavity. Various laparoscopic bag substitutes like latex gloves and glove fingers have been used. We described a sterilized plastic surgical drain cover as a reasonable substitute for retrieving the gallbladder after LC

Photo-excitation of a light-harvesting supra-molecular triad: a Time-Dependent DFT study

We present the first time-dependent density-functional theory (TDDFT) calculation on a light harvesting triad carotenoid-diaryl-porphyrin-C60. Besides the numerical challenge that the ab initio study of the electronic structure of such a large system presents, we show that TDDFT is able to provide an accurate description of the excited state properties of the system. In particular we calculate the photo-absorption spectrum of the supra-molecular assembly, and we provide an interpretation of the photo-excitation mechanism in terms of the properties of the component moieties. The spectrum is in good agreement with experimental data, and provides useful insight on the photo-induced charge transfer mechanism which characterizes the system.Comment: Accepted for publication on JPC, March 09th 200

Classical Stern-Gerlach profiles of Mn5 and Mn6 clusters

Mn5 and Mn6 clusters have recently been found to exhibit Stern-Gerlach profiles marked by a central peak that broadens with the increasing field gradient. The profiles neither exhibit a reminiscence of space quantization as observed through a splitting of beams for the case of free atoms, nor a net deflection characteristic of superparamagnetic relaxations observed in other transition metal clusters. It is proposed that this new behavior results from a weak coupling of localized atomic moments. ab initio electronic structure studies are carried out to show that a Mn5cluster has isomers with spin magnetic moments of 3μB, 13μB, and 23μBwhile a Mn6 cluster has isomers with moments of 2μB, 8μB, 16μB, and 26μB, respectively. The isomers can be obtained by sequential turning of the local atomic moments starting from the ferromagnetic state and can be seen in the negative ion photoelectron spectra of the anions. The weak coupling of the atomic moments, however, leads to unconventional spin dynamics that result in classical broadening of the Stern-Gerlach profiles and lower apparent magnetic moments. The theoretical results illustrate how a combination of the negative ion photodetachment spectroscopy and Stern-Gerlach profiles can provide information on the net spin moment, interatomic spin coupling, and spin dynamics

Issues with setting online objective mathematics questions and testing their efficacy

The Mathletics database now comprises many mathematical topics from GCSE to level 2 undergraduate. The aim of this short paper is to document, explore and provide some solutions to the pedagogic issues we are facing whilst setting online objective questions across this range. Technical issues are described in the companion paper by Ellis, Greenhow and Hatt (2006). That paper refers to “question styles to stress that we author according to the pedagogic and algebraic structure of the content of a question; random parameters are chosen at runtime ... This results in each style having thousands, or even millions, of realisations seen by the users.” With this emphasis, and with new topics being included, new question types beyond the usual multi-choice (MC) etc have been developed to ask appropriate and challenging questions. We feel that their pedagogic structure (and underlying code) is widely applicable to testing beyond the scope of Mathematics. This paper describes three of the new question types: Word Input, Responsive Numerical Input and 4/True/False/Undecidable/Statement/Property. Of generic importance is the fact that each of these question types can include post-processing of submitted answers; sample Javascript coding that checks the validity of the input(s) before marking takes place is described. In common with most of the rest of the question style’s content this could be exported to other CAA systems. Ellis et al (2005) and Gill & Greenhow (2006) describe initial results of a trial of level 1 undergraduate mechanics questions. This academic year we have expanded the range of tests to foundation and level 1 undergraduate algebra and calculus, involving several hundred students. First and foremost we have underlined the value of Random Numerical Input (RNI) question types compared with traditional Numerical Input (NI) types for which answer files resulting from questions with randomised parameters are exceptionally difficult to interpret. Despite our current lack of a consistent and fullymeaningful way of encoding the mal-rules within the question outcome metadata, mal-rule-based question types (MC, RNI etc) have been analysed in terms of difficulty, discrimination and item analysis. In the case of multiplechoice questions any weaknesses are separately identified as skill-based or conceptual

Post Reform Period Trends in Deposits and Credit Deployments of Regional Rural Banks in Karnataka

This study analyse the trends in deposits and credit deployments of Regional Rural Banks (RRBs) in the State of Karnataka during the post reform period (March 1992- March 2008). Basic data for this study were collected from the various issues of Basic Statistical Returns of Scheduled Commercial Banks in India published by Reserve Bank of India. Deposits, advances (outstanding) and credit-deposit ratios were three important parameters used to assess the performance of RRBs. Kendall’s coefficient of concordance (W) was computed to study whether there were any changes in the pattern of the flow of sectoral credit lending by the RRBs over the study period. In the area of deposit mobilisation and credit disbursements, the RRBs had made a notable progress during the post reform period. C-D ratios of RRBs were fluctuating throughout the study period. It was found that RRBs continued to focus on agriculture credit disbursements in the Sate of Karnataka. At the same time, RRBs had favored credit to personal loans in place of rural artisan industries credit and “other small scale industries” credit.Regional Rural Banks,trends, deposits and credit deployments, Karnataka, India

Effect of Graded Levels of Condensed Tannin (CT) from \u3cem\u3eMimosa pudica\u3c/em\u3e on \u3cem\u3ein-Vitro\u3c/em\u3e Methane Production

Livestock in the country are primarily being fed on fibrous feed resulted in high enteric methane (CH4) emission along with low nutrients availability to host animal. Rumen methano genesis is necessary for the host system as this process ensure the removal of fermentative H2 through the reduction of CO2 into CH4. At the same time this process is wasteful because the emission also represents a loss of dietary energy (6-12% of gross energy intake) apart from contributing to global warming. Worldwide livestock contribute around 90-95 Tg methane to the pool with a contribution of 12-13% from the Indian livestock. Various nutritional and other approaches have been attempted with highly variable success rate in the country and elsewhere for the enteric methane amelioration. The cost of the item used for the mitigation purpose, adaptation of ruminal microbes and toxicity to either host animal or inhabiting microbes are few important criteria for an economic, sustainable and effective amelioration approach (Malik et al. 2015). Herbal materials are being used by the peoples since ages; however, their anti-methanogenic effect is recently established. The anti-methanogenic effect of different herbal materials mainly lies in their secondary metabolites which are highly effective even at very low concentration (Bhatta et al., 2014). Keeping these facts in view, a study was carried to ascertain the effect of varying levels of CT on in vitro total gas and methane production

Hydrogen adsorption and magnetic behavior of Fen and Con clusters: Controlling the magnetic moment and anisotropy one atom at a time

Theoretical studies to investigate the effect of H absorption on the magnetic moment of small Fen and Con clusters have been carried out using gradient corrected density-functional approach. Our studies on clusters containing up to four transition metal and 2 H atoms show that the successive addition of H atoms can lead to monotonic or oscillatory change from the free cluster magnetic moment. A detailed analysis of the density of electronic states shows that the variations in the magnetic moment can be related to the location of the lowest unoccupied molecular orbital in the parent cluster. It is shown that the addition of hydrogen can substantially change the magnetic anisotropy. In particular Co3H2is shown to exhibit magnetic anisotropy that is higher than any of the known anisotropies in the molecular nanomagnets

Magnetic moment and anisotropy in FenCom clusters

Electronic structure calculations of FenCom (n+m=5 and 13) are used to examine the effects of alloying on the magnetic moment and magnetic anisotropies. Our density-functional studies show that many mixed clusters have moments comparable to or higher than the pure clusters. The mixed clusters, however, have very low anisotropies and could be ideal as soft magnetic materials. It is shown that shape, composition, and compositional ordering must be considered for optimization of anisotropy energies