Journal of mathematics teacher education, Jun 3, 2024
Mathematics teacher education is often described in terms of the mathematical content and pedagog... more 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.
Thematic working group 10 is interested in discussing diversity and mathematics education within ... more Thematic working group 10 is interested in discussing diversity and mathematics education within the realms of the societal, the cultural, and the political. The working group was established at CERME7 in Rzeszow, Poland, in 2011 (Valero, Crafter, Gellert, & Gorgorio, 2011; see also Pais, Crafter, Straehler-Pohl, & Mesquita, 2013), but was an extension of the language diversity group which had been part of CERME since the first conference. In the work of the group, mathematics education is assumed to refer to more than the encounter between an individual and a mathematical object and to wider contexts than exclusively classroom settings.
The importance of mathematics or its alter ego 'numeracy' has been cemented in the publ... more The importance of mathematics or its alter ego 'numeracy' has been cemented in the public's mind with the instigation of national, high-stakes testing in Australia. As ... In a broader research program, in which we investigated the public discourse around the National Assessment ...
As part of a large research project about supporting preservice teachers to learn about teaching ... more As part of a large research project about supporting preservice teachers to learn about teaching argumentation for critical mathematics education in multilingual classrooms, we outline a framework for considering the knowledge, skills and practices that we, as teacher educators, consider mathematics teachers need. Our objective for describing such a framework is to provide a discussion document for teacher educators, primarily at our institution, but also for others who aim to improve their mathematics teacher education practices and want to determine theoretically how to navigate the complexity of changing our practices.
This chapter explores how politicians’ use of the media can disrupt educational traditions. Analy... more This chapter explores how politicians’ use of the media can disrupt educational traditions. Analysis of the discursive resources that a Norwegian Minister of Education used in a single authored debate article in a Norwegian newspaper shows that he drew on a well-known argument for why schools should teach mathematics, that of the need for socio-economic development of society. The use of this argument, rather than other arguments such as those about civic development, which would be more in alignment with the social pedagogy approach traditionally characterising early childhood education in Norway, seems to indicate that the Minister was promoting a shift in approach to one of preparing children for school. This example of the use of the media to determine how policy shifts are made is explored in relationship to promoting a new kind of “common sense” which does not require public discussion or input from mathematics education researchers.
Homework is an activity done by large numbers of students all over the world. Many concerns have ... more Homework is an activity done by large numbers of students all over the world. Many concerns have been raised including, especially in primary schools, whether any academic benefit is gained and whether parents have appropriate resources to actively support/teach their children. In this paper, we explore the stories that two ten year old girls tell about doing their mathematics homework with family help and the pressures that it puts on them to take control of their own learning. We discuss the opportunities and constraints to students doing homework as a consequence of the social and institutional relations that they operate within.
Although group work is considered beneficial for problem solving, the listening that is needed fo... more Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students' listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, "productive listening," is described which focuses on observable features connected to students' ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker's contribution as being valuable and feeling that one's own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others' mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving. Keywords Listening. Student interactions. Group work. Mathematical problem solving 1 Listening in small group work for mathematical problem solving Although communication in small groups is considered to contribute to collective mathematics learning (Cobb et al., 2001; Walshaw & Anthony, 2008), the role of listening in the work of these groups has been under-researched (Hintz & Tyson, 2015). If listening in mathematical
Māori mathematical practices were excluded from schooling in Aotearoa/New Zealand for over 150 ye... more Māori mathematical practices were excluded from schooling in Aotearoa/New Zealand for over 150 years as a result of explicit policies precluding the use of the Indigenous language and culture. As a consequence of the range of assimilationist policies, by the 1970s, the Māori language was considered endangered. In response to the perilous state of the language, Māori communities set up their own schools, initially outside of the state system, to support the revitalisation of the language and culture. However, the reintroduction of the cultural knowledge in areas such as mathematics has not matched language revitalisation efforts. Many original ethnomathematical practices are no longer in general use in the Indigenous community and the practices valued by the European majority remain the norm in the state-mandated school curricula. Spatial orientation is an example of the mathematics curricula content that is based on Western mathematical perspectives. To provide a Māori perspective, this paper draws on interviews with elders and historical data to examine Māori spatial orientation terms and the spatial frames of references that they are derived from. Students in a Māori-medium school were tested on their understanding of this traditional knowledge. As a consequence, a series of learning activities based on Māori spatial orientation concepts were developed and trialled. The outcomes of these learning activities showed some increased understandings about Māori spatial orientation concepts.
The aim of the study is to describe the semiotic resources that children used in mathematical exp... more The aim of the study is to describe the semiotic resources that children used in mathematical explanations of hypothetical situations. The empirical material consists of a short video from a Norwegian kindergarten, where four 5-year-old children and a kindergarten student teacher discuss real and imaginary page layouts of a photo book. When explaining their reasoning about the amount of photographs in the layouts, the children used oral language, gestures and physical objects like number charts. The use of these resources in different kinds of explanations is discussed. Our results suggest that by using a range of semiotic resources, children are able to provide explanations of hypothetical situations using mathematical ideas at a younger age than previously suggested.
Barn bör ges möjlighet att förstå de begrepp som ligger bakom färdigheten att mäta. Kroppen, flas... more Barn bör ges möjlighet att förstå de begrepp som ligger bakom färdigheten att mäta. Kroppen, flaskor, pennor och chokladpulver kan bli mätinstrument. Vi får här ta del av dialoger mellan barn och vuxna om mätning samt en diskussion om hur problemlösning kan vara en väg till förståelse.
Journal of Mathematics Teacher Education, Aug 16, 2023
As has been the case in many countries around the world, the new Norwegian curriculum from 2020 i... more As has been the case in many countries around the world, the new Norwegian curriculum from 2020 included programming as part of mathematics education. However, little is known about how prospective teachers perceive this addition in regard to their developing professional identities. When the results from an electronic survey of 394 prospective teachers showed unexpected findings, five of the subjects were asked to participate in a focus group interview in order to explore some of these results. The focus group interview was conducted to understand how prospective teachers considered the past, present and future aspects of their professional identities as teachers of mathematics through programming. The results reveal that, although the prospective teachers had little experience of programming, they were positive regarding its implementation in mathematics lessons because they identified themselves as digital natives; they therefore believed that learning to program would be easy. They aligned themselves with their students, as masters of technology, in contrast to their future colleagues, whom they implicitly described as digital immigrants. The findings of this study have implications for teacher education. Even if the prospective teachers have a positive attitude toward programming and consider themselves digitally competent, a limited understanding of how programming can be integrated into their mathematics teaching will affect the identities that they see for themselves as teachers who teach mathematics through programming.
Med gjeninnføring av lek i skolens laereplan er det behov for å vurdere hvordan lek har vaert kny... more Med gjeninnføring av lek i skolens laereplan er det behov for å vurdere hvordan lek har vaert knyttet til matematikk i barnehagen. Vi bruker en modell som kobler sammen barns lek med det å stille og å løse problemer, til å analysere barnehagebarns engasjement med digitale apper og til andreklassingers skriving av regnefortellinger. Analysen viser hvordan lek kan oppstå når barna stiller problemer, og når de prøver ut ulike løsningsstrategier. Vi anser at resultatet av forskningen kan gi innsikt til matematikklaerere i de første skoleårene om lekens potensial i arbeid med problemstilling og problemløsning.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
Using Engeström's third generation of activity theory, we explore three master's students' views ... more Using Engeström's third generation of activity theory, we explore three master's students' views of their completed research projects on children's argumentation in number stories as potentially contributing to their forthcoming teaching of Grade 1 students. Activity theory was chosen because it provided opportunities to consider how two different activity systems, research as part of teacher education and mathematics teaching in Grade 1, might overlap around the shared artefact of mathematical argumentation through number stories. The three interviews are analysed using Engeström's description of four levels of contradictions identified in a matrix of principles and questions. The analysis raised some issues with the use of Activity Theory to understand the master's students' learning from the contradictions between the two activity systems they were in-between.
Journal of mathematics teacher education, Jun 3, 2024
Mathematics teacher education is often described in terms of the mathematical content and pedagog... more 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.
Thematic working group 10 is interested in discussing diversity and mathematics education within ... more Thematic working group 10 is interested in discussing diversity and mathematics education within the realms of the societal, the cultural, and the political. The working group was established at CERME7 in Rzeszow, Poland, in 2011 (Valero, Crafter, Gellert, & Gorgorio, 2011; see also Pais, Crafter, Straehler-Pohl, & Mesquita, 2013), but was an extension of the language diversity group which had been part of CERME since the first conference. In the work of the group, mathematics education is assumed to refer to more than the encounter between an individual and a mathematical object and to wider contexts than exclusively classroom settings.
The importance of mathematics or its alter ego 'numeracy' has been cemented in the publ... more The importance of mathematics or its alter ego 'numeracy' has been cemented in the public's mind with the instigation of national, high-stakes testing in Australia. As ... In a broader research program, in which we investigated the public discourse around the National Assessment ...
As part of a large research project about supporting preservice teachers to learn about teaching ... more As part of a large research project about supporting preservice teachers to learn about teaching argumentation for critical mathematics education in multilingual classrooms, we outline a framework for considering the knowledge, skills and practices that we, as teacher educators, consider mathematics teachers need. Our objective for describing such a framework is to provide a discussion document for teacher educators, primarily at our institution, but also for others who aim to improve their mathematics teacher education practices and want to determine theoretically how to navigate the complexity of changing our practices.
This chapter explores how politicians’ use of the media can disrupt educational traditions. Analy... more This chapter explores how politicians’ use of the media can disrupt educational traditions. Analysis of the discursive resources that a Norwegian Minister of Education used in a single authored debate article in a Norwegian newspaper shows that he drew on a well-known argument for why schools should teach mathematics, that of the need for socio-economic development of society. The use of this argument, rather than other arguments such as those about civic development, which would be more in alignment with the social pedagogy approach traditionally characterising early childhood education in Norway, seems to indicate that the Minister was promoting a shift in approach to one of preparing children for school. This example of the use of the media to determine how policy shifts are made is explored in relationship to promoting a new kind of “common sense” which does not require public discussion or input from mathematics education researchers.
Homework is an activity done by large numbers of students all over the world. Many concerns have ... more Homework is an activity done by large numbers of students all over the world. Many concerns have been raised including, especially in primary schools, whether any academic benefit is gained and whether parents have appropriate resources to actively support/teach their children. In this paper, we explore the stories that two ten year old girls tell about doing their mathematics homework with family help and the pressures that it puts on them to take control of their own learning. We discuss the opportunities and constraints to students doing homework as a consequence of the social and institutional relations that they operate within.
Although group work is considered beneficial for problem solving, the listening that is needed fo... more Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students' listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, "productive listening," is described which focuses on observable features connected to students' ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker's contribution as being valuable and feeling that one's own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others' mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving. Keywords Listening. Student interactions. Group work. Mathematical problem solving 1 Listening in small group work for mathematical problem solving Although communication in small groups is considered to contribute to collective mathematics learning (Cobb et al., 2001; Walshaw & Anthony, 2008), the role of listening in the work of these groups has been under-researched (Hintz & Tyson, 2015). If listening in mathematical
Māori mathematical practices were excluded from schooling in Aotearoa/New Zealand for over 150 ye... more Māori mathematical practices were excluded from schooling in Aotearoa/New Zealand for over 150 years as a result of explicit policies precluding the use of the Indigenous language and culture. As a consequence of the range of assimilationist policies, by the 1970s, the Māori language was considered endangered. In response to the perilous state of the language, Māori communities set up their own schools, initially outside of the state system, to support the revitalisation of the language and culture. However, the reintroduction of the cultural knowledge in areas such as mathematics has not matched language revitalisation efforts. Many original ethnomathematical practices are no longer in general use in the Indigenous community and the practices valued by the European majority remain the norm in the state-mandated school curricula. Spatial orientation is an example of the mathematics curricula content that is based on Western mathematical perspectives. To provide a Māori perspective, this paper draws on interviews with elders and historical data to examine Māori spatial orientation terms and the spatial frames of references that they are derived from. Students in a Māori-medium school were tested on their understanding of this traditional knowledge. As a consequence, a series of learning activities based on Māori spatial orientation concepts were developed and trialled. The outcomes of these learning activities showed some increased understandings about Māori spatial orientation concepts.
The aim of the study is to describe the semiotic resources that children used in mathematical exp... more The aim of the study is to describe the semiotic resources that children used in mathematical explanations of hypothetical situations. The empirical material consists of a short video from a Norwegian kindergarten, where four 5-year-old children and a kindergarten student teacher discuss real and imaginary page layouts of a photo book. When explaining their reasoning about the amount of photographs in the layouts, the children used oral language, gestures and physical objects like number charts. The use of these resources in different kinds of explanations is discussed. Our results suggest that by using a range of semiotic resources, children are able to provide explanations of hypothetical situations using mathematical ideas at a younger age than previously suggested.
Barn bör ges möjlighet att förstå de begrepp som ligger bakom färdigheten att mäta. Kroppen, flas... more Barn bör ges möjlighet att förstå de begrepp som ligger bakom färdigheten att mäta. Kroppen, flaskor, pennor och chokladpulver kan bli mätinstrument. Vi får här ta del av dialoger mellan barn och vuxna om mätning samt en diskussion om hur problemlösning kan vara en väg till förståelse.
Journal of Mathematics Teacher Education, Aug 16, 2023
As has been the case in many countries around the world, the new Norwegian curriculum from 2020 i... more As has been the case in many countries around the world, the new Norwegian curriculum from 2020 included programming as part of mathematics education. However, little is known about how prospective teachers perceive this addition in regard to their developing professional identities. When the results from an electronic survey of 394 prospective teachers showed unexpected findings, five of the subjects were asked to participate in a focus group interview in order to explore some of these results. The focus group interview was conducted to understand how prospective teachers considered the past, present and future aspects of their professional identities as teachers of mathematics through programming. The results reveal that, although the prospective teachers had little experience of programming, they were positive regarding its implementation in mathematics lessons because they identified themselves as digital natives; they therefore believed that learning to program would be easy. They aligned themselves with their students, as masters of technology, in contrast to their future colleagues, whom they implicitly described as digital immigrants. The findings of this study have implications for teacher education. Even if the prospective teachers have a positive attitude toward programming and consider themselves digitally competent, a limited understanding of how programming can be integrated into their mathematics teaching will affect the identities that they see for themselves as teachers who teach mathematics through programming.
Med gjeninnføring av lek i skolens laereplan er det behov for å vurdere hvordan lek har vaert kny... more Med gjeninnføring av lek i skolens laereplan er det behov for å vurdere hvordan lek har vaert knyttet til matematikk i barnehagen. Vi bruker en modell som kobler sammen barns lek med det å stille og å løse problemer, til å analysere barnehagebarns engasjement med digitale apper og til andreklassingers skriving av regnefortellinger. Analysen viser hvordan lek kan oppstå når barna stiller problemer, og når de prøver ut ulike løsningsstrategier. Vi anser at resultatet av forskningen kan gi innsikt til matematikklaerere i de første skoleårene om lekens potensial i arbeid med problemstilling og problemløsning.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
Using Engeström's third generation of activity theory, we explore three master's students' views ... more Using Engeström's third generation of activity theory, we explore three master's students' views of their completed research projects on children's argumentation in number stories as potentially contributing to their forthcoming teaching of Grade 1 students. Activity theory was chosen because it provided opportunities to consider how two different activity systems, research as part of teacher education and mathematics teaching in Grade 1, might overlap around the shared artefact of mathematical argumentation through number stories. The three interviews are analysed using Engeström's description of four levels of contradictions identified in a matrix of principles and questions. The analysis raised some issues with the use of Activity Theory to understand the master's students' learning from the contradictions between the two activity systems they were in-between.
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Papers by Tamsin Meaney