Waiting times and socioeconomic status. Evidence from Norway

We investigate whether socioeconomic status, measured by income and education, affects waiting time when controls for severity and hospital specific conditions are included. We also examine which aspects of the hospital supply (attachment to local hospital, traveling time, or choice of hospital) that matter most for unequal treatment of different socioeconomic groups, and how different behavior responses can create discrimination. The study uses administrative data from all somatic elective inpatient and outpatient hospital stays in Norway. The main results are that we find very little indication of discrimination with regard to income. This result holds both for males and females. We find some indication of discrimination of men with low education as these men have a lower probability of zero waiting time. We also find a pro educational bias for women; as women with only primary education wait about 9 % (13 %) longer than women with upper secondary (tertiary) education.Health Care Markets; Regulations: Public Health

Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups

The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students’ use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students’ multimodal reasoning was characterized by the ways their utterances, inscriptions, and gestures emerged and supplemented each other. The students’ pointing gestures mediated the intended mathematical meaning solely when combined with inscriptions displaying all possible combinations. Sliding gestures, on the other hand, did mediate the intended mathematical meaning when their inscriptions were not displaying all possible combinations. In this latter case, the shortcomings of their inscriptions were complemented and compensated by the sliding gestures. The students’ multimodal mathematical reasoning made explicit their combinatorial thinking, mediated the intended mathematical meaning, and facilitated their solving of the given combinatorial problems.publishedVersio

Qualities in mathematical discourses in kindergartens

In this study we investigated qualities of the mathematical discourse in four kindergarten classes in which kindergarten teachers and 5-year-old children engaged in mathematical learning activities. We analysed differences in the mathematical discourses in two experimental kindergarten classes and two control kindergarten classes, in a research and development project. The overarching research question guiding our study was as follows: what characterises the mathematical discourse unfolding in kindergarten classes? In our study we drew on the theoretical framework Mathematical Discourse in Instruction coined by Adler and Ronda, as we quantified the collected qualitative data. Our analyses identified significant characteristics of mathematical discourse with respect to the children’s opportunities to contribute with ideas and arguments. The discourse in the kindergartens differed both with respect to the extent and nature of verbal utterances among the participants, as well as the mathematical engagement nurtured amongst the children. Moreover, the mathematical discourse within the experimental kindergarten classes, to a greater extent than that in the control kindergarten classes, initiated opportunities for the participating children’s mathematical learning.publishedVersio

Mathematical learning opportunities in kindergarten through the use of digital tools: Affordances and constraints

Accepted version of an article in the journal: Nordic Journal of Digital Literacy. Also available from the publisher at: http://www.idunn.no/ts/dk/2013/03/mathematical_learning_opportunities_in_kindergarten_throughThis study aims at scrutinising the mathematical learning opportunities of children engaging with digital tools and the emerging affordances and constraints faced in such settings. By adopting a sociocultural perspective on learning and development, the multimodal analysis of the adult-child interaction shows that the children are participants in processes of appropriating the mathematical concepts of sorting and counting. Affordances are taken advantage of by the adults and constraints causing didactical dissonance are overcome and transformed into didactical harmony

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

Article from the journal: Mathematics Education Research Journal. Also available from the journals homepage: http://www.merga.net.au/node/41?volume=21&number=1The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students make use of inscriptions, self-made as well as ones provided by text books and teachers, and the role these played in the co-ordination of their learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning

Grunnskolelærerstudenters erfaring med eBok-basert undervisning i matematikk

I denne artikkelen analyserer vi grunnskolelærerstudenters respons på en eBok-basert undervisningsform i matematikk. Denne eBoka besto av oppgaver med både skriftlige og videobaserte løsningsforslag. Oppgavene ble hentet fra tidligere gitte eksamensoppgaver knyttet til nasjonal deleksamen i matematikk. Formålet var å undersøke: a) hvordan studentene benyttet de ulike læringsressursene i eBoka, og b) på hvilke måter studentens bruk av læringsressursene hadde pragmatisk og epistemisk verdi (Artigue, 2002). Analysene bygger på kvantitative og kvalitative data fra en spørreundersøkelse (N = 60) om bruk av eBoka og viser at nesten alle studentene benyttet de videobaserte løsningsforslagene, mens litt under halvparten benyttet de skriftlige løsningsforslagene. Studentenes respons gir uttrykk for den pragmatiske verdien av bruken av læringsressursene. De fikk tips både i begynnelsen av løsningsprosessen og underveis om hvordan oppgavene kan løses, samt en sjekk på om de hadde løst oppgavene korrekt. Studentenes respons gir også uttrykk for den epistemiske verdien av bruken av læringsressursene. De fikk hjelp til å forstå hva oppgavene spurte om, de fikk hjelp til å forstå sin egen løsningsprosess, og de oppdaget andre måter å løse oppgavene på. Dette viser at eBoka ga grunnlag for matematisk meningsskaping blant grunnskolelærerstudentene.publishedVersio

Kindergarten teachers’ accounts of their developing mathematical practice

Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0422-1This study explores kindergarten teachers’ accounts of their developing mathematical practice in the context of their participation in a developmental research project. Observations and interviews were analysed to elaborate the accounts as regards orchestrating mathematical activities in the kindergarten. A co-learning agreement was established as collaboration between the kindergarten teachers and researchers. The study reveals that the kindergarten teachers argue that they have been empowered in developing an inquiry stance towards mathematics and mathematical activities. Taking an inquiry stance, they claim, has increased their awareness of the mathematics involved in activities, and enabled them to be more explicit when communicating mathematical ideas to children. An adjusted didactic triangle within the kindergarten setting is proposed based on these results

Kindergarten teachers’ orchestration of mathematical activities afforded by technology: agency and mediation

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