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

Specifying and identifying signs of ‘resonance’ in teachers’ professionalization processes as a condition for teacher change

Many studies on professionalization research deal with the question of how teachers actually learn or how teacher change occurs. In this context, Clarke and Hollingsworth (2002) describe a model for capturing teacher change in different domains (external, personal, domain of practice and domain of consequence) and how changes in one domain can affect other domains over time. The present article suggests the notion of resonance for analyzing teachers’ professionalization processes in order to better understand the reasons for teacher change on a micro level in their complexity. The idea was to supplement the model by the dimension of teachers’ professional conditions, to capture and describe the phenomenon that an active process of engagement with the professional development (PD) content is set in motion. We consider teachers’ resonance to be a condition for a successful professionalization process. Insights from two different research projects from Germany and Norway demonstrate the scope of the notion of resonance. Consequences for facilitators and the design of further PD programs are discussed.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

Akupunktur og medikamentelle bivirkninger

Et stadig økende antall krefttilfeller i Norge, gir et stadig økende antall pasienter som må gjennomgå cellegiftbehandling. En vanlig bivirkning ved denne behandlingen er kvalme. Da det per i dag ikke finnes gode nok kvalmestillende medikamenter, søker pasientene alternative metoder for å lindre symptomene. Blant alternative behandlinger for kvalme er akupunktur øverst på listen. Vi ønsker med denne oppgaven å gå i dybden på hvordan akupunktur kan påvirke bivirkninger som følge av cellegiftbehandling, da det også er et personlig ønske for oss å kunne bidra til å lindre symptomer for denne pasientgruppen. I oppgaven har vi tatt for oss problemstillingen: Hvordan kan akupunktur påvirke bivirkninger som følge av cellegiftbehandling? -med fokus på kvalme hos kreftpasienter. For å belyse problemstillingen har vi benyttet dybdeintervju som metode. Det har blitt utført søk i databaser, og benyttet Tradisjonell Kinesisk Medisinsk (TKM) litteratur fra høyskolens pensumliste. I teorikapittelet presenterer vi kvalme sett fra et vestlig medisinsk perspektiv og hva forfatterne sier i TKM. Vi har i tillegg sett på tre forskjellige studier for å se hva forskning sier om temaet, samt intervjuet to informanter for å få høre en akupunktørs erfaring fra klinisk praksis. Det vi konkluderer med i denne oppgaven er at det er nødvendig med flere enn ett akupunkturpunkt for å behandle kvalme som følge av cellegiftbehandling. Denne vurderingen er gjort ut ifra resultatene som er kommet fram av forskning og intervju med informanter

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