Deepening students' understanding of multiplication and division by exploring divisibility by nine

This paper explores how a focus on understanding divisibility rules can be used to help deepen students’ understanding of multiplication and division with whole numbers. It is based on research with seven Year 7–8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a way of proving why the divisibility rule for nine works, using materials grouped in tens and hundreds. After the lesson, students’ understanding of multiplication and division was considerably deepened

The mathematical content knowledge and attitudes of New Zealand pre-service primary teachers

This paper presents data on the mathematical content knowledge and attitudes of pre-service primary teacher education students. The assessment consisted of nine tasks, including 2-digit computations and proportional reasoning. Students rated their liking for mathematics at three time points: primary, secondary, .and when assessed. Fewer than half the students liked mathematics, currently. Those with positive attitudes tended to perform well on mathematics tasks, but some low scorers were positive and some high' scorers were negative about mathematics. Most students used algorithmic procedures to solve problems and several consistent misconceptions were identified. Performance was noticeably poor on adding common fractions and converting fractions to percentages using knowledge of common factors. The implications of these findings for Initial Teacher Education (ITE) providers are presented

Supporting students' additive thinking: The use of equal additions for subtraction

This paper looks at how teachers can support students' additive thinking. It reports on a study of a lesson designed to teach the equal additions strategy for subtraction, contained in Numeracy Development Project (NDP) Book 5. Nine teachers were observed teaching mathematics. Despite having a strong commitment to promoting conceptual understanding, many teachers struggled with various aspects of the material and resorted to teaching procedurally. We concluded that teachers need to have a deeper, more connected understanding of addition and subtraction in order to develop their pedagogical content knowledge in mathematics

In-hospital and 6-month outcomes in patients with COVID-19 supported with extracorporeal membrane oxygenation (EuroECMO-COVID): a multicentre, prospective observational study

Extracorporeal membrane oxygenation (ECMO) has been widely used in patients with COVID-19, but uncertainty remains about the determinants of in-hospital mortality and data on post-discharge outcomes are scarce. The aims of this study were to investigate the variables associated with in-hospital outcomes in patients who received ECMO during the first wave of COVID-19 and to describe the status of patients 6 months after ECMO initiation

Stratified analyses refine association between TLR7 rare variants and severe COVID-19

Summary: Despite extensive global research into genetic predisposition for severe COVID-19, knowledge on the role of rare host genetic variants and their relation to other risk factors remains limited. Here, 52 genes with prior etiological evidence were sequenced in 1,772 severe COVID-19 cases and 5,347 population-based controls from Spain/Italy. Rare deleterious TLR7 variants were present in 2.4% of young (<60 years) cases with no reported clinical risk factors (n = 378), compared to 0.24% of controls (odds ratio [OR] = 12.3, p = 1.27 × 10−10). Incorporation of the results of either functional assays or protein modeling led to a pronounced increase in effect size (ORmax = 46.5, p = 1.74 × 10−15). Association signals for the X-chromosomal gene TLR7 were also detected in the female-only subgroup, suggesting the existence of additional mechanisms beyond X-linked recessive inheritance in males. Additionally, supporting evidence was generated for a contribution to severe COVID-19 of the previously implicated genes IFNAR2, IFIH1, and TBK1. Our results refine the genetic contribution of rare TLR7 variants to severe COVID-19 and strengthen evidence for the etiological relevance of genes in the interferon signaling pathway

ILC Reference Design Report Volume 1 - Executive Summary

The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization.The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization

Mortality after surgery in Europe: a 7 day cohort study

Background: Clinical outcomes after major surgery are poorly described at the national level. Evidence of heterogeneity between hospitals and health-care systems suggests potential to improve care for patients but this potential remains unconfirmed. The European Surgical Outcomes Study was an international study designed to assess outcomes after non-cardiac surgery in Europe.Methods: We did this 7 day cohort study between April 4 and April 11, 2011. We collected data describing consecutive patients aged 16 years and older undergoing inpatient non-cardiac surgery in 498 hospitals across 28 European nations. Patients were followed up for a maximum of 60 days. The primary endpoint was in-hospital mortality. Secondary outcome measures were duration of hospital stay and admission to critical care. We used χ² and Fisher’s exact tests to compare categorical variables and the t test or the Mann-Whitney U test to compare continuous variables. Significance was set at p&lt;0·05. We constructed multilevel logistic regression models to adjust for the differences in mortality rates between countries.Findings: We included 46 539 patients, of whom 1855 (4%) died before hospital discharge. 3599 (8%) patients were admitted to critical care after surgery with a median length of stay of 1·2 days (IQR 0·9–3·6). 1358 (73%) patients who died were not admitted to critical care at any stage after surgery. Crude mortality rates varied widely between countries (from 1·2% [95% CI 0·0–3·0] for Iceland to 21·5% [16·9–26·2] for Latvia). After adjustment for confounding variables, important differences remained between countries when compared with the UK, the country with the largest dataset (OR range from 0·44 [95% CI 0·19 1·05; p=0·06] for Finland to 6·92 [2·37–20·27; p=0·0004] for Poland).Interpretation: The mortality rate for patients undergoing inpatient non-cardiac surgery was higher than anticipated. Variations in mortality between countries suggest the need for national and international strategies to improve care for this group of patients.Funding: European Society of Intensive Care Medicine, European Society of Anaesthesiology