Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Evidence-based planning and costing palliative care services for children : novel multi-method epidemiological and economic exemplar

Background: Children’s palliative care is a relatively new clinical specialty. Its nature is multi-dimensional and its delivery necessarily multi-professional. Numerous diverse public and not-for-profit organisations typically provide services and support. Because services are not centrally coordinated, they are provided in a manner that is inconsistent and incoherent. Since the first children’s hospice opened in 1982, the epidemiology of life-limiting conditions has changed with more children living longer, and many requiring transfer to adult services. Very little is known about the number of children living within any given geographical locality, costs of care, or experiences of children with ongoing palliative care needs and their families. We integrated evidence, and undertook and used novel methodological epidemiological work to develop the first evidence-based and costed commissioning exemplar. Methods: Multi-method epidemiological and economic exemplar from a health and not-for-profit organisation perspective, to estimate numbers of children under 19 years with life-limiting conditions, cost current services, determine child/parent care preferences, and cost choice of end-of-life care at home. Results: The exemplar locality (North Wales) had important gaps in service provision and the clinical network. The estimated annual total cost of current children’s palliative care was about £5.5 million; average annual care cost per child was £22,771 using 2007 prevalence estimates and £2,437- £11,045 using new 2012/13 population-based prevalence estimates. Using population-based prevalence, we estimate 2271 children with a life-limiting condition in the general exemplar population and around 501 children per year with ongoing palliative care needs in contact with hospital services. Around 24 children with a wide range of life-limiting conditions require end-of-life care per year. Choice of end-of-life care at home was requested, which is not currently universally available. We estimated a minimum (based on 1 week of end-of-life care) additional cost of £336,000 per year to provide end-of-life support at home. Were end-of-life care to span 4 weeks, the total annual additional costs increases to £536,500 (2010/11 prices). Conclusions: Findings make a significant contribution to population-based needs assessment and commissioning methodology in children’s palliative care. Further work is needed to determine with greater precision which children in the total population require access to services and when. Half of children who died 2002-7 did not have conditions that met the globally used children's palliative care condition categories, which need revision in light of findings

A review of topographic controls on moraine distribution

Ice-marginal moraines are often used to reconstruct the dimensions of former ice masses, which are then used as proxies for palaeoclimate. This approach relies on the assumption that the distribution of moraines in the modern landscape is an accurate reflection of former ice margin positions during climatically controlled periods of ice margin stability. However, the validity of this assumption is open to question, as a number of additional, nonclimatic factors are known to influence moraine distribution. This review considers the role played by topography in this process, with specific focus on moraine formation, preservation, and ease of identification (topoclimatic controls are not considered). Published literature indicates that the importance of topography in regulating moraine distribution varies spatially, temporally, and as a function of the ice mass type responsible for moraine deposition. In particular, in the case of ice sheets and ice caps ( > 1000km 2 ), one potentially important topographic control on where in a landscape moraines are deposited is erosional feedback, whereby subglacial erosion causes ice masses to become less extensive over successive glacial cycles. For the marine-terminating outlets of such ice masses, fjord geometry also exerts a strong control on where moraines are deposited, promoting their deposition in proximity to valley narrowings, bends, bifurcations, where basins are shallow, and/or in the vicinity of topographic bumps. Moraines formed at the margins of ice sheets and ice caps are likely to be large and readily identifiable in the modern landscape. In the case of icefields and valley glaciers (10-1000km 2 ), erosional feedback may well play some role in regulating where moraines are deposited, but other factors, including variations in accumulation area topography and the propensity for moraines to form at topographic pinning points, are also likely to be important. This is particularly relevant where land-terminating glaciers extend into piedmont zones (unconfined plains, adjacent to mountain ranges) where large and readily identifiable moraines can be deposited. In the case of cirque glaciers ( < 10km 2 ), erosional feedback is less important, but factors such as topographic controls on the accumulation of redistributed snow and ice and the availability of surface debris, regulate glacier dimensions and thereby determine where moraines are deposited. In such cases, moraines are likely to be small and particularly susceptible to post-depositional modification, sometimes making them difficult to identify in the modern landscape. Based on this review, we suggest that, despite often being difficult to identify, quantify, and mitigate, topographic controls on moraine distribution should be explicitly considered when reconstructing the dimensions of palaeoglaciers and that moraines should be judiciously chosen before being used as indirect proxies for palaeoclimate (i.e., palaeoclimatic inferences should only be drawn from moraines when topographic controls on moraine distribution are considered insignificant). © 2014 Elsevier B.V

Genomic reconstruction of the SARS-CoV-2 epidemic in England.

The evolution of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus leads to new variants that warrant timely epidemiological characterization. Here we use the dense genomic surveillance data generated by the COVID-19 Genomics UK Consortium to reconstruct the dynamics of 71 different lineages in each of 315 English local authorities between September 2020 and June 2021. This analysis reveals a series of subepidemics that peaked in early autumn 2020, followed by a jump in transmissibility of the B.1.1.7/Alpha lineage. The Alpha variant grew when other lineages declined during the second national lockdown and regionally tiered restrictions between November and December 2020. A third more stringent national lockdown suppressed the Alpha variant and eliminated nearly all other lineages in early 2021. Yet a series of variants (most of which contained the spike E484K mutation) defied these trends and persisted at moderately increasing proportions. However, by accounting for sustained introductions, we found that the transmissibility of these variants is unlikely to have exceeded the transmissibility of the Alpha variant. Finally, B.1.617.2/Delta was repeatedly introduced in England and grew rapidly in early summer 2021, constituting approximately 98% of sampled SARS-CoV-2 genomes on 26 June 2021

Calculus demonstrations using Matlab

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton’s method, differentiation and integration. Two of the programs are animated. The programs and the graphical user interface have been specifically designed to help the student understand the processes behind these important introductory concepts. Each program has a series of demonstrations that show unusual, difficult or important cases

Use of fat-suppressed T2-weighted sagittal images after infusion of excess saline into the subarachnoid space as a new diagnostic modality for cerebrospinal fluid hypovolemia: technical note Response

The diagnosis of CSF hypovolemia remains controversial. The primary diagnostic factor relies on confirmation of leakage of the CSF based on reduced spinal fluid pressure. Determining the specific leakage site is the most important issue for effective treatment but remains a difficult task. Although CT myelography, radioisotope cisternography, and MRI are commonly performed in the diagnosis of CSF hypovolemia, these techniques can rarely identify the precise leakage site. Therefore, an epidural blood patch is performed in the lumbar spine in many cases. This study reports a new diagnostic modality that can help to confirm the leakage site. Fat-suppressed T2-weighted sagittal images were compared before and after the infusion of 20 ml of saline into the subarachnoid space of the lumbar region to detect the specific leakage site with high probability. Three patients were successfully treated by the epidural blood patch based on data obtained with the new diagnostic modality. Two patients were treated in the cervical region and 1 in the lumbar region. The use of fat-suppressed T2-weighted sagittal images after saline infusion could be a relevant diagnostic modality compared with images obtained by CT myelography, radioisotope cisternography, and ordinary MRI to achieve accurate diagnosis and effective treatment of patients with CSF hypovolemia