Discrete mathematics topics in the secondary school curriculum

This thesis discusses two topics of discrete mathematics in a manner suitable for presentation at a secondary-school level. The introduction outlines the benefits of including discrete mathematics in the secondary-school curriculum. The two chapters which follow include detailed treatment of the two selected topics: the Traveling Salesman Problem and RSA encryption. The discussion of the Traveling Salesman Problem consists of introduction to the problem through several real-life scenarios, followed by a discussion of various methods for solving the problem. We discuss exact and approximate algorithms together with their computational complexity and practical limitations. The discussion of RSA encryption begins with an introduction to the necessary background in number theory, which includes the Chinese Remainder Theorem, Bezout\u27s Equation, and Fermat\u27s Little Theorem. Following this is a discussion of encryption and decryption techniques, which are illustrated through an example that is accessible to any student with a basic scientific calculator

“Fond and Frivolous Gestures”: A Blocking Workshop on Marlowe’s Tamburlaine

Since 2012, second-year English and Drama undergraduates at the University of Exeter have had the opportunity to take a course called “Theatrical Cultures”. This option introduces students to plays and entertainments that were popular between the 1580s and the 1640s, with a view to opening an understanding of the period that is deeply informed by theatre history. In this essay, we share and reflect on our teaching of Christopher Marlowe’s Tamburlaine, Parts One and Two, which examines the plays as productions by the Lord Admiral’s Men in the Rose playhouse. We start by explaining the learning context for the blocking workshop we use as a practical teaching method. We then share instructions for setting up the workshop and outline our “learning-by-doing” methodology, which involves placing the bodies of our students and the properties necessary to perform a scene within the dimensions of the first Rose stage. The intended learning outcomes of the workshop include a practical understanding of the affordances of the early modern playhouse and the ability to translate this understanding into a critical interpretation of Marlowe’s drama. As students deliver lines, wield swords and crowns, and try to imagine how a chariot navigates the stage space available, they recognise moments of potential bathos and physical comedy in the plays, hinting at those “fond and frivolous gestures” that Marlowe’s publisher, Richard Jones, sought to remove from the 1590 play-text. In the third section of the essay, we evaluate these insights and the workshop’s pedagogical value by sharing reflections by tutors and students who have participated in the blocking workshop

Trophic status of Chlamydomonas reinhardtii influences the impact of iron deficiency on photosynthesis

To investigate the impact of iron deficiency on bioenergetic pathways in Chlamydomonas, we compared growth rates, iron content, and photosynthetic parameters systematically in acetate versus CO2-grown cells. Acetate-grown cells have, predictably (2-fold) greater abundance of respiration components but also, counter-intuitively, more chlorophyll on a per cell basis. We found that phototrophic cells are less impacted by iron deficiency and this correlates with their higher iron content on a per cell basis, suggesting a greater capacity/ability for iron assimilation in this metabolic state. Phototrophic cells maintain both photosynthetic and respiratory function and their associated Fe-containing proteins in conditions where heterotrophic cells lose photosynthetic capacity and have reduced oxygen evolution activity. Maintenance of NPQ capacity might contribute to protection of the photosynthetic apparatus in iron-limited phototrophic cells. Acetate-grown iron-limited cells maintain high growth rates by suppressing photosynthesis but increasing instead respiration. These cells are also able to maintain a reduced plastoquinone pool

LEARN: A multi-centre, cross-sectional evaluation of Urology teaching in UK medical schools

OBJECTIVE: To evaluate the status of UK undergraduate urology teaching against the British Association of Urological Surgeons (BAUS) Undergraduate Syllabus for Urology. Secondary objectives included evaluating the type and quantity of teaching provided, the reported performance rate of General Medical Council (GMC)-mandated urological procedures, and the proportion of undergraduates considering urology as a career. MATERIALS AND METHODS: LEARN was a national multicentre cross-sectional study. Year 2 to Year 5 medical students and FY1 doctors were invited to complete a survey between 3rd October and 20th December 2020, retrospectively assessing the urology teaching received to date. Results are reported according to the Checklist for Reporting Results of Internet E-Surveys (CHERRIES). RESULTS: 7,063/8,346 (84.6%) responses from all 39 UK medical schools were included; 1,127/7,063 (16.0%) were from Foundation Year (FY) 1 doctors, who reported that the most frequently taught topics in undergraduate training were on urinary tract infection (96.5%), acute kidney injury (95.9%) and haematuria (94.4%). The most infrequently taught topics were male urinary incontinence (59.4%), male infertility (52.4%) and erectile dysfunction (43.8%). Male and female catheterisation on patients as undergraduates was performed by 92.1% and 73.0% of FY1 doctors respectively, and 16.9% had considered a career in urology. Theory based teaching was mainly prevalent in the early years of medical school, with clinical skills teaching, and clinical placements in the later years of medical school. 20.1% of FY1 doctors reported no undergraduate clinical attachment in urology. CONCLUSION: LEARN is the largest ever evaluation of undergraduate urology teaching. In the UK, teaching seemed satisfactory as evaluated by the BAUS undergraduate syllabus. However, many students report having no clinical attachments in Urology and some newly qualified doctors report never having inserted a catheter, which is a GMC mandated requirement. We recommend a greater emphasis on undergraduate clinical exposure to urology and stricter adherence to GMC mandated procedures

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Strategies for controlling testlet exposure rates in computerized adaptive testing systems

textExposure control procedures in computerized adaptive testing (CAT) systems protect item pools from being compromised, however, this impacts measurement precision. Previous research indicates that exposure control procedures perform differently for dichotomously scored versus polytomously scored CAT systems. For dichotomously scored CATs, conditional selection procedures are often the optimal choice, while randomization procedures perform best for polytomously scored CATs. CAT systems modeled with testlet response theory have not been examined to determine optimal exposure control procedures. This dissertation examined various exposure control procedures in testletbased CAT systems using the three-parameter logistic testlet response theory model and the partial credit model. The exposure control procedures were the randomesque procedure, the modified within .10 logits procedure, two levels of the progressive restricted procedure, and two levels of the Sympson-Hetter procedure. Each of these was compared to a baseline no exposure control procedure, maximum information. The testlets were reading passages with six to ten multiple-choice items. The CAT systems consisted of maximum information testlet selection contingent on an exposure control procedure and content balancing for passage type and the number of items per passage; expected a posteriori ability estimation; and a fixed length stopping rule of seven testlets totaling fifty multiple-choice items. Measurement precision and exposure rates were examined to evaluate the effectiveness of the exposure control procedures for each measurement model. The exposure control procedures yielded similar results for measurement precision within the models. The exposure rates distinguished which exposure control procedures were most effective. The Sympson-Hetter conditions, which are conditional procedures, maintained the pre-specified maximum exposure rate, but performed very poorly in terms of pool utilization. The randomization procedures, randomesque and modified within .10 logits, yielded low maximum exposure rates, but used only about 70% of the testlet pool. Surprisingly, the progressive restricted procedure, which is a combination of both a conditional and randomization procedure, yielded the best results in its ability to maintain and control the maximum exposure rate and it used the entire testlet pool. The progressive restricted conditions were the optimal procedures for both the partial credit CAT systems and the threeparameter logistic testlet response theory CAT systems.Educational Psycholog