Spin-off learning about epidemics from modelling with differential equations

This article presents a case study of students modelling epidemics with differential equation systems. The study introduces spin-off learning as a process intertwined with learning mathematics and examines the conditions for ‘spin-off’ learning to occur when modelling epidemics. Learning mathematics is conceptualised in terms of emergent modelling and models and identified by the associated progressive, horizontal and vertical mathematising in textual analysis. Signs of ‘spin-off’ learning are linked with the mathematising. Furthermore, the ‘spin-off’ learning is related to the direction of modelling being either expressive or explorative. As a result, the stratification of students’ mathematising activities and the introduction of the notion of direction served to pinpoint a variety of conditions for ‘spin-off’ learning internal to the modelling processes. In addition, the results showed the huge potential in mathematical modelling for ‘spin-off’ learning which might be realised and utilised at a societal level for preparation against new crises.publishedVersio

Meningsfuld begynderundervisning i matematisk analyse

This article presents a study of a minor reversion of a first year course in calculus at Mathematics Department, University of Bergen, Norway. The lecturer’s goal was to force the students to take responsibility for their own learning. The article brings reflections upon the lecturer’s professional autonomy and background for the revision of the course. The study was neither quantitative nor comparative. Data do not suggest that the students’ working habits had changed. The rate of passing students, though, had increased.Artiklen præsenterer studiet af en mindre ændring i organiseringen af undervisningen på et førsteårskursus, gennemført i efteråret 2013 på Matematisk Institut, UiB (Universitetet i Bergen, Norge). Underviseren ønskede at omorganisere kurset, så de studerende blev mere ansvarlige for deres egen læring. Artiklen bringer didaktiske refleksioner over underviserens belæg for den gennemførte omorganisering. Studiet, som præsenteres, var hverken kvantitativt eller komparativt. Det indsamlede datamateriale tyder ikke på, at de studerendes arbejdsformer eller indbyrdes samarbejde adskilte sig fra tidligere år. Men de studerende på kurset fik bedre resultater til eksamen end tidligere år, idet gennemførelsesprocenten var højere.publishedVersio

The influence of ready-made tools on students’ learning by modelling with differential equations systems

This article discusses the role played by the tool when students learn about differential equations systems (DE) by modelling. The discussion was based on a three-case sub-study of an ongoing study of group-reports from experienced mathematics teachers participating in a masters’ program in mathematics education. In the teaching sequences, setting the scene for the students’ modelling of authentic problems by DE, it was indispensable to include a variety of digital resources such as databanks and software for numerical solutions, graphical representations, and some sorts of simulations. Apps with simulations of commonly used DE models are widespread on the internet, some of them are user-friendly and elaborated to a degree that justify use of the term ready-made tools. The issue addressed in this article is whether such ready-made tools constitute shortcuts to the students’ modelling process and thereby obstacles in their learning of mathematics. For the analysis, the term direction of modelling was used to make a distinction between expressive and explorative modelling, respectively. Direction of modelling proved useful for the analysis of students’ learning not only with relation to the ready-made tool but also more generally. In line with the author’s previous research, students’ learning of mathematics by modelling was conceptualised in terms of emergent models and modelling and detected by textual analysis of students’ written reports. The study gave new insight into the students’ learning processes in the form of a variety of patterns for interplay between the tool use and the learning of mathematics. This variety seems to be pivotal for the designs of modelling sequences in general and particularly in the case of DE due to their dependence on digital resources

Breakthrough infections with the omicron and delta variants of SARS-CoV-2 result in similar re-activation of vaccine-induced immunity

Background: Results showing that sera from double vaccinated individuals have minimal neutralizing activity against Omicron have been interpreted as indicating the need for a third vaccine dose for protection. However, there is little information about early immune responses to Omicron infection in double vaccinated individuals. Methods: We measured inflammatory mediators, antibodies to the SARS-CoV-2 spike and nucleocapsid proteins, and spike peptide-induced release of interferon gamma in whole blood in 51 double-vaccinated individuals infected with Omicron, in 14 infected with Delta, and in 18 healthy controls. The median time points for the first and second samples were 7 and 14 days after symptom onset, respectively. Findings: Infection with Omicron or Delta led to a rapid and similar increase in antibodies to the receptor-binding domain (RBD) of Omicron protein and spike peptide-induced interferon gamma in whole blood. Both the Omicron- and the Delta-infected patients had a mild and transient increase in inflammatory parameters. <p<Interpretation: The results suggest that two vaccine doses are sufficient to mount a rapid and potent immune response upon infection in healthy individuals of with the Omicron variant

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Correction to: Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

The original version of this article unfortunately contained a mistake

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Spin-off learning about epidemics from modelling with differential equations

This article presents a case study of students modelling epidemics with differential equation systems. The study introduces spin-off learning as a process intertwined with learning mathematics and examines the conditions for ‘spin-off’ learning to occur when modelling epidemics. Learning mathematics is conceptualised in terms of emergent modelling and models and identified by the associated progressive, horizontal and vertical mathematising in textual analysis. Signs of ‘spin-off’ learning are linked with the mathematising. Furthermore, the ‘spin-off’ learning is related to the direction of modelling being either expressive or explorative. As a result, the stratification of students’ mathematising activities and the introduction of the notion of direction served to pinpoint a variety of conditions for ‘spin-off’ learning internal to the modelling processes. In addition, the results showed the huge potential in mathematical modelling for ‘spin-off’ learning which might be realised and utilised at a societal level for preparation against new crises

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat