Symbols and the bifurcation between procedural and conceptual thinking

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships. In this presentation we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra and calculus, then on to the formalism of axiomatic mathematics. This is taken from a number of research studies recently performed for doctoral dissertations at the University of Warwick by students from the USA, Malaysia, Cyprus and Brazil, with data collected in the USA, Malaysia and the United Kingdom. All the studies form part of a broad investigation into why some students succeed yet others fail

Outcome of hospitalization for COVID-19 in patients with interstitial lung disease. An international multicenter study

Rationale: The impact of coronavirus disease (COVID-19) on patients with interstitial lung disease (ILD) has not been established. Objectives: To assess outcomes in patients with ILD hospitalized for COVID-19 versus those without ILD in a contemporaneous age-, sex-, and comorbidity-matched population. Methods: An international multicenter audit of patients with a prior diagnosis of ILD admitted to the hospital with COVID-19 between March 1 and May 1, 2020, was undertaken and compared with patients without ILD, obtained from the ISARIC4C (International Severe Acute Respiratory and Emerging Infection Consortium Coronavirus Clinical Characterisation Consortium) cohort, admitted with COVID-19 over the same period. The primary outcome was survival. Secondary analysis distinguished idiopathic pulmonary fibrosis from non–idiopathic pulmonary fibrosis ILD and used lung function to determine the greatest risks of death. Measurements and Main Results: Data from 349 patients with ILD across Europe were included, of whom 161 were admitted to the hospital with laboratory or clinical evidence of COVID-19 and eligible for propensity score matching. Overall mortality was 49% (79/161) in patients with ILD with COVID-19. After matching, patients with ILD with COVID-19 had significantly poorer survival (hazard ratio [HR], 1.60; confidence interval, 1.17–2.18; P = 0.003) than age-, sex-, and comorbidity-matched controls without ILD. Patients with an FVC of <80% had an increased risk of death versus patients with FVC ≥80% (HR, 1.72; 1.05–2.83). Furthermore, obese patients with ILD had an elevated risk of death (HR, 2.27; 1.39−3.71). Conclusions: Patients with ILD are at increased risk of death from COVID-19, particularly those with poor lung function and obesity. Stringent precautions should be taken to avoid COVID-19 in patients with ILD