As Thurston says? : On using quotations from famous mathematicians to make points about philosophy and education

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11858-020-01154-w.It is commonplace in the educational literature on mathematical practice to argue for a general conclusion from isolated quotations from famous mathematicians. In this paper, we supply a critique of this mode of inference. We review empirical results that show the diversity and instability of mathematicians’ opinions on mathematical practice. Next, we compare mathematicians’ diverse and conflicting testimony on the nature and purpose of proof. We lay especial emphasis on the diverse responses mathematicians give to the challenges that digital technologies present to older conceptions of mathematical practice. We examine the career of one much cited and anthologised paper, WP Thurston’s ‘On Proof and Progress in Mathematics’ (1994). This paper has been multiply anthologised and cited hundreds of times in educational and philosophical argument. We contrast this paper with the views of other, equally distinguished mathematicians whose use of digital technology in mathematics paints a very different picture of mathematical practice. The interesting question is not whether mathematicians disagree—they are human so of course they do. The question is how homogenous is their mathematical practice. If there are deep differences in practice between mathematicians, then it makes little sense to use isolated quotations as indicators of how mathematics is uniformly or usually done. The paper ends with reflections on the usefulness of quotations from research mathematicians for mathematical education.Peer reviewe

Place and Destination Branding: A Review and Conceptual Mapping of the Domain

Although there is increasing interest in place and destination branding, the inter‐disciplinary nature of the field poses challenges for the development of a coherent knowledge base. With a view to informing both research and practice, this article presents a systematic review combining place and destination branding, identifying and defining its core themes, and developing a conceptual map of the inter‐play between them. The following key themes are identified: general, brand identity, image and personality, politics, heritage, communication/media, country‐of‐ origin, and designscape and infrastructure. The article concludes with an agenda for further research including the need for research on specific themes across a wider range of place entities

Human-Machine Collaboration in the Teaching of Proof

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that students have to learn its command language, in addition to mathematics course content and elementary logic

Sudden unexpected death in epilepsy (SUDEP): Development of a safety checklist

AbstractPurposeThe incidence of sudden death appears to be 20 times higher in patients with epilepsy compared with the general population. Epilepsy-related death, particularly sudden unexpected death in epilepsy (SUDEP), is still underestimated by healthcare professionals and this may reflect the mistaken belief that epilepsy is a benign condition. The risk of death associated with epilepsy appeared rarely to have been discussed with patients or their families. It appears the decision to discuss SUDEP and also to peg SUDEP risk is arbitrary and clinical. Unfortunately there is no structured evidenced mechanism at present to represent person centered risk of SUDEP and there is currently no easy manner or template to have this discussion with the family and the patient.MethodsWe conducted a detailed literature review in Medline, Embase and Psychinfo databases to extract the common risk factors as evidenced from literature till date. Research into risk factors has identified a number of risk factors for SUDEP, some of which are potentially modifiable.ResultsBased on the literature review, we believe that the ascertained risk factors could be employed in clinical practice as a checklist to reduce an individual patient's risk of SUDEP. The SUDEP safety checklist may be of practical use in reducing risks in some individuals and is definitely of use in helping communication.ConclusionsAn evidence based checklist identifying the major risk factors can help both clinicians and patients to focus on minimizing certain risk factors and promote safety by focusing on the modifiable factors and guide treatment. It can be a tool to open a person centered discussion with patients and to outline how individual behaviors could impact on risk

German translation, cultural adaptation and testing of the Person‐centred Practice Inventory – Staff (PCPI‐S)

From Crossref via Jisc Publications RouterHistory: epub 2020-05-26, issued 2020-05-26Brendan McCormack - ORCID 0000-0001-8525-8905 https://orcid.org/0000-0001-8525-8905Aim The aim of this study was to translate and culturally adapt the PCPI‐S into German and to eventually test its psychometric properties in long‐term care settings.Background Person‐centred practice has been widely adopted internationally as a best‐practice model in nursing and health care. To ensure a sustainable implementation of this practice and to successively promote it, person‐centred practice should be evaluated on a regular basis. The Person‐centred Practice Inventory—Staff (PCPI‐S), which is based on McCormack & McCance's Person‐centred Practice Framework, is a new instrument for this purpose by assessing perceptions of person‐centredness among healthcare staff.Design A two‐phase research design was used involving the translation and cultural adaption of the PCPI‐S from English to German (PCPI‐S‐G; Phase 1) and a quantitative cross‐sectional survey (Phase 2).Methods Construct validity was evaluated using confirmatory factor analysis (CFA), and internal consistency was calculated using Cronbach's α .Results Phase 1 was conducted using an internationally recommended checklist for translations and cultural adaptations. In Phase 2, the PCPI‐S‐G was tested in 15 residential care homes in Austria with a sample of 255 staff members. The CFA showed good construct validity and supported the theoretical framework. The internal consistency for the three constructs of the PCPI‐S was excellent, revealing Cronbach's α ‐scores from 0.902–0.941.Funder: Office of the Provincial Government of Lower Austria7pubpub

Controlled generation and steering of spatial gap solitons

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and reveal the key features of gap solitons which distinguish them from conventional counterparts, including a dynamical transformation of gap solitons due to nonlinear inter-band coupling. We also predict theoretically and confirm experimentally the effect of anomalous steering of gap solitons in optically-induced photonic lattices.Comment: 4 pages, 5 figure

Discrete interband mutual focusing in nonlinear photonic lattices

We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.Comment: 8 pages, 6 figures. To download the associated .avi movie, go to http://www.rsphysse.anu.edu.au/~crr124/mut_focus

Searching for help online: An analysis of peer-to-peer posts on a male-only infertility forum.

Men’s experiences of infertility help seeking are under-researched and thus less widely understood than women’s experiences, with men’s needs for support often missing from reproductive research knowledge. This article presents a thematic analysis of peer-to-peer posts within the context of a UK men-only online infertility forum. The key themes demonstrate that men value male support from those with experience, and that masculinity influences help-seeking requests and men’s accounts more broadly. We highlight the value of such online communities in offering support to men in need while recognising the importance of further research across other online settings in order to inform practice around supporting men in the reproductive realm

Co-Operative Biofilm Interactions between Aspergillus fumigatus and Pseudomonas aeruginosa through Secreted Galactosaminogalactan Exopolysaccharide

The mold Aspergillus fumigatus and bacterium Pseudomonas aeruginosa form biofilms in the airways of individuals with cystic fibrosis. Biofilm formation by A. fumigatus depends on the self-produced cationic exopolysaccharide galactosaminogalactan (GAG), while P. aeruginosa biofilms can contain the cationic exopolysaccharide Pel. GAG and Pel are rendered cationic by deacetylation mediated by either the secreted deacetylase Agd3 (A. fumigatus) or the periplasmic deacetylase PelA (P. aeruginosa). Given the similarities between these polymers, the potential for biofilm interactions between these organisms were investigated. P. aeruginosa were observed to adhere to A. fumigatus hyphae in a GAG-dependent manner and to GAG-coated coverslips of A. fumigatus biofilms. In biofilm adherence assays, incubation of P. aeruginosa with A. fumigatus culture supernatants containing de-N-acetylated GAG augmented the formation of adherent P. aeruginosa biofilms, increasing protection against killing by the antibiotic colistin. Fluorescence microscopy demonstrated incorporation of GAG within P. aeruginosa biofilms, suggesting that GAG can serve as an alternate biofilm exopolysaccharide for this bacterium. In contrast, Pel-containing bacterial culture supernatants only augmented the formation of adherent A. fumigatus biofilms when antifungal inhibitory molecules were removed. This study demonstrates biofilm interaction via exopolysaccharides as a potential mechanism of co-operation between these organisms in chronic lung disease