Toril E Rangnes | Western Norway University of Applied Science (original) (raw)

Papers by Toril E Rangnes

Journal of mathematics teacher education, Jun 3, 2024

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

In this paper, interviews with teachers and preservice teachers are analysed to understand their ... more 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.

Routledge eBooks, Sep 29, 2021

Preservice teachers' evaluations on school students' mathematical argumentation are rarely the fo... more 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, we investigate how preservice teachers (PTs) express their awareness about languag... more 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.

Demokratisk danning i skolen, 2019

Dette kapittelet presenterer og drøfter demokrati og medborgerskap i skolen i et tverrfaglig pers... more 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.

En avhandling blir ikke til i ensomhet. Den blir til i dialog med andre. Takk til alle som har va... more 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

Applying Critical Mathematics Education, 2021

This chapter concerns how three teachers in lower secondary school include climate change in scho... more 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.

Hvordan kan demokrati læres og leves i skolen? En sentral del av skolens samfunnsmandat er å utda... more Hvordan kan demokrati læres og leves i skolen? En sentral del av skolens samfunnsmandat er å utdanne til demokratisk deltakelse. I vår samtid blir dette aktualisert, men samtidig også utfordret. I norsk sammenheng har det blitt et stadig økende fokus på skolens demokratimandat, og demokrati og medborgerskap er ett av tre fagovergripende temaer i læreplanen som tas i bruk fra 2020. Forskergruppen Kritisk demokratisk danning, som denne vitenskapelige antologien springer ut fra, representerer et tverrfaglig forskningsmiljø med forskere fra fagene matematikkdidaktikk, naturfag, samfunnsfag, norsk og pedagogikk. Dette gjenspeiles i denne antologien ved at den er utpreget tverrfaglig, og ved at konkrete empiriske eksempler belyses med utgangspunkt i ulike teoretiske rammeverk. Boken viser hvordan elever, lærere og lærerstudenter reflekterer over, fremmer og utvikler demokratisk praksis, og slik bidrar til demokratisk danning og levd demokrati. Antologien retter seg særlig mot forskere i lærerutdanningen, masterstudenter med interesse for demokrati og medborgerskap og forskningsinteresserte lærere i skolen. Redaktører for prosjektet er førsteamanuensis Kjersti Maria Rongen Breivega og førsteamanuensis Toril Eskeland Rangnes, begge ansatt ved Høgskulen på Vestlandet. De øvrige bidragsyterne er tilknyttet Høgskulen på Vestlandet, Aalborg Universitet, Universitetet i Bergen og Universitetet i Sørøst-Norge

Educational Studies in Mathematics, 2017

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

The study presented in this paper focuses on primary school teachers engaging with the Body Mass ... more The study presented in this paper focuses on primary school teachers engaging with the Body Mass Index (BMI) as part of a university course. The BMI is seen as an example of prescriptive modelling where mathematics is used to keep track of the obesity phenomenon. Four categories are developed to characterize the teachers' discussions: the mathematical aspects of the BMI formula, metavalidation, the consequences of the use of the BMI and other indices in society, as well as on their teachability in the classroom. The results can contribute to developing an understanding of prescriptive modelling processes from a critical perspective.

The case study to which this paper refers focuses on 8th grade pupils' conversation in a mathemat... more 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 mathemat... more 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.

Abstract: This paper explores the mathematics learning taking place when a class of 8th grade stu... more 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.

Abstract in english: The aim of this study “Students´mathematical conversations – Learning in a... more Abstract in english:
The aim of this study “Students´mathematical conversations – Learning in and beween practices” is to examine students’ mathematical conversations and the students learning in and between practices. I study what characterizes mathematical conversations, and explore what potential the participation in such conversations in and outside school, have towards critical learning of mathematics. It is an expressed political goal that the subject of mathematics should be more practical in school. The government’s strategic document “Realfag for framtida, [MST for the future] 2010–2014”, describes company as an arena for concretization of school mathematics. This study aims to give teachers and teacher educators research-based insight into the conversations students initiate and are invited into as they move between different objectives for mathematics. It has also been an aim to provide curriculum developers and politicians research-based knowledge about how students learn mathematics through participation in a school-/business collaboration. The study is based on empirical data from an 8th grade class that collaborated with a construction firm to learn geometry. This collaboration was in the form of a school project where the students made physical models of a fisherman’s cabin. Concrete and abstract boundary objects, e.g., construction drawings, physical models and concepts such as scale, were important for the communication, both among the participants at school and between the students and a carpenter.
The study adopts a socio-cultural perspective of learning where learning takes place through participation in practices and dialogues. It is linked to Bakhtinian dialogism and describes how learning takes place in the meeting of different voices, repeatedly in tension with each other. Through struggling with the thoughts of others, one can become more conscious of one´s point of view. This provides opportunities to take a position and make choices. The study is a qualitative study. The empirical data is generated from a group of five students participating in conversations – between the students themselves, between students and teacher and between the students and carpenter. The conversations take place before, during and after visiting the construction firm. The conversation analyses are developed on the basis of Bakhtinian dialogism.
The students meet great complexity as they work practically, learn mathematics and learn how one uses mathematics for different objectives. Their expectations on how to work practically when learning mathematics become a topic of negotiation. The building company has other ways of using mathematics than those the students meet in school. In the company, the students encounter an emphasis on reality and on dealing with rules and regulations. At school, the focus is on the learning of mathematics and on competence aims. At times, the implemented “practical mathematics” is not so practical after all. Other times, the students and the teacher make use of tools and thought processes used in the business. There is a tension between school and business that the students must deal with. There are differences in language, tools and ways of thinking. The study shows how dealing with this tension is about gaining insight into, confronting and forming socio-mathematical norms.
Realized and unrealized potentials for critical mathematical learning are identified. Critical mathematical learning is realized as the students reflect upon and choose among expressions from business and school. The students are genuine participants as they have the opportunity to influence topics, issues and “type” of conversation in interactions with the carpenter and the teacher. Current political themes and tensions among different objectives for mathematics are identified in conversations. These are not explicitly taken up for discussion by the students and the teacher, and are seen as unrealized potential for critical mathematical learning.
The school project provides opportunities for learning mathematics, participation in conversations, engagement, reflection, choice taking and ownership. To make room for outside voices in the mathematics classroom involves taking risks. When different perspectives meet through dialogue, no one can completely predict the course. The study shows that learning in and between practices, is not a matter of transferring or translating from one activity to another, but a hybridization and transformation where the participants together make something new.

Journal of mathematics teacher education, Jun 3, 2024

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

In this paper, interviews with teachers and preservice teachers are analysed to understand their ... more 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.

Routledge eBooks, Sep 29, 2021

Preservice teachers' evaluations on school students' mathematical argumentation are rarely the fo... more 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, we investigate how preservice teachers (PTs) express their awareness about languag... more 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.

Demokratisk danning i skolen, 2019

Dette kapittelet presenterer og drøfter demokrati og medborgerskap i skolen i et tverrfaglig pers... more 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.

En avhandling blir ikke til i ensomhet. Den blir til i dialog med andre. Takk til alle som har va... more 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

Applying Critical Mathematics Education, 2021

This chapter concerns how three teachers in lower secondary school include climate change in scho... more 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.

Hvordan kan demokrati læres og leves i skolen? En sentral del av skolens samfunnsmandat er å utda... more Hvordan kan demokrati læres og leves i skolen? En sentral del av skolens samfunnsmandat er å utdanne til demokratisk deltakelse. I vår samtid blir dette aktualisert, men samtidig også utfordret. I norsk sammenheng har det blitt et stadig økende fokus på skolens demokratimandat, og demokrati og medborgerskap er ett av tre fagovergripende temaer i læreplanen som tas i bruk fra 2020. Forskergruppen Kritisk demokratisk danning, som denne vitenskapelige antologien springer ut fra, representerer et tverrfaglig forskningsmiljø med forskere fra fagene matematikkdidaktikk, naturfag, samfunnsfag, norsk og pedagogikk. Dette gjenspeiles i denne antologien ved at den er utpreget tverrfaglig, og ved at konkrete empiriske eksempler belyses med utgangspunkt i ulike teoretiske rammeverk. Boken viser hvordan elever, lærere og lærerstudenter reflekterer over, fremmer og utvikler demokratisk praksis, og slik bidrar til demokratisk danning og levd demokrati. Antologien retter seg særlig mot forskere i lærerutdanningen, masterstudenter med interesse for demokrati og medborgerskap og forskningsinteresserte lærere i skolen. Redaktører for prosjektet er førsteamanuensis Kjersti Maria Rongen Breivega og førsteamanuensis Toril Eskeland Rangnes, begge ansatt ved Høgskulen på Vestlandet. De øvrige bidragsyterne er tilknyttet Høgskulen på Vestlandet, Aalborg Universitet, Universitetet i Bergen og Universitetet i Sørøst-Norge

Educational Studies in Mathematics, 2017

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

The study presented in this paper focuses on primary school teachers engaging with the Body Mass ... more The study presented in this paper focuses on primary school teachers engaging with the Body Mass Index (BMI) as part of a university course. The BMI is seen as an example of prescriptive modelling where mathematics is used to keep track of the obesity phenomenon. Four categories are developed to characterize the teachers' discussions: the mathematical aspects of the BMI formula, metavalidation, the consequences of the use of the BMI and other indices in society, as well as on their teachability in the classroom. The results can contribute to developing an understanding of prescriptive modelling processes from a critical perspective.

The case study to which this paper refers focuses on 8th grade pupils' conversation in a mathemat... more 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 mathemat... more 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.

Abstract: This paper explores the mathematics learning taking place when a class of 8th grade stu... more 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.

Abstract in english: The aim of this study “Students´mathematical conversations – Learning in a... more Abstract in english:
The aim of this study “Students´mathematical conversations – Learning in and beween practices” is to examine students’ mathematical conversations and the students learning in and between practices. I study what characterizes mathematical conversations, and explore what potential the participation in such conversations in and outside school, have towards critical learning of mathematics. It is an expressed political goal that the subject of mathematics should be more practical in school. The government’s strategic document “Realfag for framtida, [MST for the future] 2010–2014”, describes company as an arena for concretization of school mathematics. This study aims to give teachers and teacher educators research-based insight into the conversations students initiate and are invited into as they move between different objectives for mathematics. It has also been an aim to provide curriculum developers and politicians research-based knowledge about how students learn mathematics through participation in a school-/business collaboration. The study is based on empirical data from an 8th grade class that collaborated with a construction firm to learn geometry. This collaboration was in the form of a school project where the students made physical models of a fisherman’s cabin. Concrete and abstract boundary objects, e.g., construction drawings, physical models and concepts such as scale, were important for the communication, both among the participants at school and between the students and a carpenter.
The study adopts a socio-cultural perspective of learning where learning takes place through participation in practices and dialogues. It is linked to Bakhtinian dialogism and describes how learning takes place in the meeting of different voices, repeatedly in tension with each other. Through struggling with the thoughts of others, one can become more conscious of one´s point of view. This provides opportunities to take a position and make choices. The study is a qualitative study. The empirical data is generated from a group of five students participating in conversations – between the students themselves, between students and teacher and between the students and carpenter. The conversations take place before, during and after visiting the construction firm. The conversation analyses are developed on the basis of Bakhtinian dialogism.
The students meet great complexity as they work practically, learn mathematics and learn how one uses mathematics for different objectives. Their expectations on how to work practically when learning mathematics become a topic of negotiation. The building company has other ways of using mathematics than those the students meet in school. In the company, the students encounter an emphasis on reality and on dealing with rules and regulations. At school, the focus is on the learning of mathematics and on competence aims. At times, the implemented “practical mathematics” is not so practical after all. Other times, the students and the teacher make use of tools and thought processes used in the business. There is a tension between school and business that the students must deal with. There are differences in language, tools and ways of thinking. The study shows how dealing with this tension is about gaining insight into, confronting and forming socio-mathematical norms.
Realized and unrealized potentials for critical mathematical learning are identified. Critical mathematical learning is realized as the students reflect upon and choose among expressions from business and school. The students are genuine participants as they have the opportunity to influence topics, issues and “type” of conversation in interactions with the carpenter and the teacher. Current political themes and tensions among different objectives for mathematics are identified in conversations. These are not explicitly taken up for discussion by the students and the teacher, and are seen as unrealized potential for critical mathematical learning.
The school project provides opportunities for learning mathematics, participation in conversations, engagement, reflection, choice taking and ownership. To make room for outside voices in the mathematics classroom involves taking risks. When different perspectives meet through dialogue, no one can completely predict the course. The study shows that learning in and between practices, is not a matter of transferring or translating from one activity to another, but a hybridization and transformation where the participants together make something new.