Mathematics education

As the pupils move between school and commercial workplace, they meet different norms as to what can be acceptable ways of working with mathematics. This paper explores how different norms for working with scaling in school and in building company can give different support for learning mathematics. Conversations are analysed and discussed in relation to Gorgorió, Planas & Vilella´s (2001) definition of sociomathematical norms.

Abstract: This paper explores the mathematics learning taking place when a class of 8th grade students in Norway  cooperated with a carpenter in a construction company. Working with mathematics in different practices, such as school and enterprise, can make students aware of similarities and differences between doing mathematics in different contexts. Students´ conversations have been analysed and discussed in relation to Bakhtin’s dialogism. The findings indicate that learning in and between practices has the potential to facilitate pupils´ critical reflections in relation to how mathematics is performed inside and outside school.

The case study to which this paper refers focuses on 8th grade pupils' conversation in a mathematics learning situation related to a building company. The paper illustrates how school and company, having different goals for the use of mathematics, create a field of tension where the pupils meet differing languages and modes of thought. Taking mathematics conversations in and out of school as a starting point, the polyphony of this field of tension is analysed and discussed on the basis of Bakhtin's ideas of dialogicity and how the encounter with different voices influences the pupils' positioning and strengthens their participation in making decisions.

The case study to which this paper refers focuses on 8th grade pupils' conversation in a mathematics learning situation related to a building company. The paper illustrates how school and company, having different goals for the use of mathematics, create a field of tension where the pupils meet differing languages and modes of thought. Taking mathematics conversations in and out of school as a starting point, the polyphony of this field of tension is analysed and discussed on the basis of Bakhtin's ideas of dialogicity and how the encounter with different voices influences the pupils' positioning and strengthens their participation in making decisions.

This chapter concerns how three teachers in lower secondary school include climate change in school mathematics. Data was collected over a one-year period, where the teachers organised several teaching activities such as fieldwork, posters, contribution to an exhibition, and dialogue and debates, to facilitate students' critical mathematics competences through working with climate change. We apply a teacher perspective and focus on the role mathematics can play in formatting the understanding of climate change. A formatting power of mathematics is identified at three levels: (1) in teachers' meta-reflections, (2) when the teachers use mathematics to format students' understanding, and (3) when teachers facilitate students' awareness of the formatting power of mathematics. The findings suggest that a complex issue like climate change brings forth an awareness of the formatting powers of mathematics.

En avhandling blir ikke til i ensomhet. Den blir til i dialog med andre. Takk til alle som har vaert med i dialoger fram til resultatet! Noen må nevnes spesielt. Takk til elevene, laereren og byggefirmaet som slapp meg inn slik at jeg fikk empirien jeg trengte for å studere matematikksamtaler og laering i og mellom praksiser. Jeg møtte en raushet som jeg har satt utrolig stor pris på. Takk til forskergruppen «Laeringssamtalen i matematikkfagets praksis» (LIMP) ledet av professor Marit Johnsen-Høinesuten dere hadde jeg ikke våget å starte. Kollegaer, både i matematikkseksjonen og i stipendiatgrupper på HiB, NLA og UiAdere har gitt meg styrke til å fortsette når jeg har trengt det. Kollegaer ved Aalborg universitet, blant andre professor Paola Valero, professor Helle Alrø, Poul Nørgård Dahl, Søren Friman som jeg fikk møte på studieopphold, dere har satt spor. Takk også til min gamle arbeidsplass, NLA, Høgskolen, som gav meg permisjon og dermed trygghet til å ta fatt på en stipendiatperiode. Takk til min nye arbeidsplass Høgskolen i Bergen som sammen med Norges forskningsråd har gjort denne reisen økonomisk mulig ved å gi meg stipend. To personer, mine veiledere professor Marit Johnsen-Høines og professor Simon Goodchild, har fulgt meg gjennom tykt og tynt. Takk for tålmodighet, utfordrende spørsmål, støtte når det har røynet på, gode råd og for at dere åpnet for muligheter jeg selv ikke umiddelbart så. Til slutt: Takk Odd Kjetil! For tålmodighet, for oppbakking, for hjelp med engelsken (uten den hadde jeg ikke kommet meg på konferanser), for korrekturlesning og for at du er den du er! Toril Eskeland Rangnes Kristiansand, Norway 25.09.12 6 Elevers matematikksamtaler-Laering i og mellom praksiser Elevers matematikksamtaler-Laering i og mellom praksiser 15 9.3.2 Anvendelsesområde for sosiomatematiske normer 9.4 Diskusjon og konsekvenser 9.4.1 Spenninger i matematikkfaget 9.4.2 Realfagssatsingen 9.5 Implikasjoner for undervisning og forskning 10 Referanser

Dette kapittelet presenterer og drøfter demokrati og medborgerskap i skolen i et tverrfaglig perspektiv. I vår tilnaerming står danningsperspektivet sentralt, og i første halvdel av kapittelet drøfter vi, med utgangspunkt i dannings-og demokratipedagogiske tilnaerminger, hvordan demokratisk danning kan forstås. Vi konseptualiserer vår forståelse av demokratisk danning som levd demokrati. I dette ligger et fokus på det daglige, faglige arbeidet i alle fag der målsettingen først og fremst er en opplaering gjennom-og ikke om og for-demokratisk deltakelse. Vi presenterer dessuten bokens datamaterialer og kapitler, og viser hvordan disse på ulike måter anskueliggjør og konkretiserer vår tilnaerming med vekt på kontroversielle temaer, uenighet, muntlig samhandling og argumentasjon. NØKKELORD demokratisk danning, levd demokrati, empiriske tilnaerminger ABSTRACT This chapter presents and explains democracy and citizenship in schools from a transdisciplinary perspective. With our approach we follow an educational theoretical perspective on Bildung. Building on a discussion based on theory of Bildung (Klafki) and democratic pedagogy, the first part of the chapter investigates the question of what can be understood as democratic education today. In doing so we conceptualize our understanding of democratic education as lived democracy. We attach particular importance to the daily, professional work in schools that aims at education throughand not for or by-democratic participation. In addition, we present the data material used as well as the individual chapters. Further, we outline how we operationalize our approach on the subject of controversial issues, disagreement, oral cooperation and argumentation.

In this paper, we investigate how preservice teachers (PTs) express their awareness about language diversity in mathematics classrooms. We use "language as resource" and "language as a problem" as theoretical constructs. The data is taken from PTs´ group assignments, including transcriptions of dialogues between the PTs and multilingual students, and from PTs´ written reflections about teaching in multilingual classrooms. We found that in the dialogues, PTs and multilingual students produced meanings together through negotiating a shared repertoire from out-of-school and in-school mathematics context. Nevertheless, the students' home languages were not evident as resources in PT´s dialogues and reflections. A deficit perspective was present in their reflections. These findings lead us to rethink our teacher education courses so that language as a resource becomes more prominent.

Preservice teachers' evaluations on school students' mathematical argumentation are rarely the focus of mathematics education research. Yet, understanding how they evaluate the quality of their future students' mathematical argumentation is important. In this paper, a discussion by a group of multilingual preservice teachers is analysed to determine the properties they considered to be connected to high-quality mathematical argumentation. The preservice teachers, who had two different dominant languages, discussed whether examples of Grade Four students' work, written in those two languages, displayed the qualities of being clearly written, mathematically correct and complete. From an analysis of this discussion, we identify how the preservice teachers' multilingual backgrounds provided potential and realised learning opportunities about students' mathematical argumentation.

In this paper, interviews with teachers and preservice teachers are analysed to understand their views about using digital tools in mathematics classrooms, connected to language-diverse students': communication; potential for learning; and available identities. When digital tools were seen only as providing ways to utilise the home language so that existing mathematical knowledge could be used to complete tasks in the language of instruction, then language-diverse students' available identities were reduced to becoming like their non-immigrant peers. In contrast, when digital tools were considered as providing opportunities for utilising a wider range of their language resources, then preservice teachers broadened their views about language-diverse students' potentials for learning and available identities.

Mathematics teacher education is often described in terms of the mathematical content and pedagogy that teachers need. However, recent calls for equity in mathematics education demand a broadening of this view. In this article, we articulate a theoretical description of what the role of being an advocate in language-diverse classrooms could involve and some of the practical challenges that mathematics teacher educators may have when introducing it, using empirical examples from our teacher education courses for teachers of Grades 1-7 in Norway. In the theoretical description of the role of being an advocate into mathematics teacher education, we distinguish between in-class advocacy and advocacy beyond the classroom and what these different kinds of advocacy might entail in languagediverse classrooms. The practical issues that we identified in raising different aspects of the role indicate the need for further research into how to raise preservice teachers' awareness about the role of being an advocate, in and outside of the classroom, in different cultural settings and how this knowledge could be used in teacher education to challenge preservice teachers' language ideologies and raise non-trivial issues.