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  1. NOMAD – 23(3-4), 2018

    Volume 23, No 3-4, November 2018

    e-NOMAD

    [PDF] displays the full text pdf. The two most recent volumes are password protected. Use “Open access” in the menu for full text of older articles.

    Editorial

    Tamsin Meaney and Toril Eskeland Rangnes
    Language diversity in mathematics education in the Nordic countries 2008–2018
    [PDF]

    Eva Norén and Petra Svensson Källberg
    Fabrication of newly-arrived students as mathematical learners
    [PDF]

    Petra Svensson Källberg
    Identity formations as mathematical learners in the context of transition
    [PDF]

    Marie Sjöblom
    Developing mathematical reasoning by using questions in a multilingual mathematics classroom
    [PDF]

    Maria Ahlholm and Päivi Portaankorva-Koivisto
    The language factor – what exactly is it? Bilingual speakers of Russian and Finnish solving mathematical tasks
    [PDF]

    Jöran Petersson
    Newly- and early-immigrated second-language students’ knowledge of arithmetic syntax
    [PDF]

    Hilja L. Huru, Anna-Kaisa Räisänen and Anita Movik Simensen
    Culturally based mathematics tasks: a framework for designing tasks from traditional Kven artefacts and knowledge
    [PDF]

    Mette Hjelmborg and Ane Fleischer
    En registeranalyse af centrale matematiske begreber i en grønlandsk kontekst
    [PDF]

    Anne Birgitte Fyhn, Ellen J. Sara Eira, Ole Einar Hætta, Inga Anne Marit Juuso, Siv Ingrid Nordkild og Ellen Margrethe Skum
    Bishop Sámegillii – utfordringer ved oversetting av matematikkdidaktisk fagterminologi
    [PDF]

    Dorota Lembrér
    Polish parents’ views on mathematics activities at home and in Swedish preschools
    [PDF]

    Troels Lange and Tamsin Meaney
    Talking about mathematics in two languages: Can parental views inform the development of digital games for young children?
    [PDF]

    Andrea Eikset and Tamsin Meaney
    When does a difference make a difference? Teaching about language diversity in mathematics teacher education
    [PDF]

    Susanne Prediger
    Multilingual issues in Nordic mathematics education – What is achieved and where to go next?
    [PDF]

    Skapad: 2018-11-06 kl. 11:33

  2. NOMAD 23(3-4), 2018

    Multilingual issues in Nordic mathematics education – What is achieved and where to go next?

    Susanne Prediger

    Abstract
    This Nomad special issue provides eleven highly interesting insights into current research and development projects in mathematics education on multilingual and multicultural issues. It shows the diversity of approaches currently adopted in the Nordic Countries with an impressing richness of perspectives and ideas. I am grateful to have had the opportunity to read and discuss the papers carefully as I learned a lot. In this commentary, I compare and connect the papers with each other and the international state of research and to suggest some directions for further research and development. The commentary is structured in the following steps: Di erent implicit and explicit conceptualization of languages are identi ed in the articles ( rst section); di erent research approaches are summarized with a need to strengthen Design research (second section); and di erent instructional approaches for activating multiple language resources for mathematics learning and further enhancing both languages (third section).

    Susanne Prediger
    Susanne Prediger is full professor for mathematics education research at TU Dortmund University in Germany and currently the vice-director of the German Center for Mathematics Teacher Education. She leads a big research group on language diversity in mathematics education and is interested in fostering language learners’ mathematics learning.

    Skapad: 2018-11-06 kl. 11:22

  3. NOMAD 23(3-4), 2018

    When does a difference make a difference? Teaching about language diversity in mathematics teacher education

    Andrea Eikset and Tamsin Meaney

    Abstract
    There has been little attention in mathematics education research about how to include issues to do with language diversity in teacher education. This paper describes the process used by two teacher educators to examine their own practices of linking multilingual perspectives to mathematics education in their work with preservice teachers. By systematically analysing their discussion about a three-hour, mathematics-teacher-education workshop on proportional thinking, the teacher educators were able to identify a series of Discourses. They considered that these Discourses underlay their decision making about how language diversity could be raised with preservice teachers. The results highlight the complexity connected to raising language diversity issues in mathematics teacher education. For example, deciding what challenging content should be provided to preservice teachers is a ected by the need to develop relationships with them as well as managing their learning. Joint re ection by the teacher educators was needed to ensure that the aim of challenging preservice teachers about how to deal with language diversity issues in mathematics classrooms could be achieved.

    Andrea Eikset
    Andrea Eikset is an assistant professor working at Western Norway University of Applied Sciences in Bergen. Her academic background is in mathematics didactics, and her main research interests are mathematics in early childhood education, diversity and sustainable development. This is also connected to teacher educators own professional development.

    Tamsin Meaney
    Tamsin Meaney is professor in mathematics education at Western Norway University of Applied Sciences in Bergen, Norway. She has written journal articles on language diversity in mathematics education for twenty years.

    Skapad: 2018-11-06 kl. 11:20

  4. NOMAD 23(3-4), 2018

    Talking about mathematics in two languages: Can parental views inform the development of digital games for young children?

    Troels Lange and Tamsin Meaney

    Abstract
    In this article, the results are presented from a survey of parents’ views about the digital games that their young multilingual children play. Previous research has indicated that parents struggled to describe how their children were learning from playing digital games. The results from this study indicate that parents could provide information about the digital games and the mathematical language they invoked. This information could be useful in developing playful, digital games that support multilingual children to talk about mathematics. The survey also provides insights into the follow-up qualitative research studies that are needed to support the development of new digital games.

    Troels Lange
    Troels Lange is professor in mathematics education at Western Norway University of Applied Sciences in Bergen, Norway. He has a long standing interest in children ́s perceptions of mathematics education and societal issues that in uence the views of parents, teachers and politicians about mathematics education for young children.

    Tamsin Meaney
    Tamsin Meaney is professor in mathematics education at Western Norway University of Applied Sciences in Bergen, Norway. She has written journal articles on language diversity in mathematics education for twenty years.

    Skapad: 2018-11-06 kl. 11:18

  5. NOMAD 23(3-4), 2018

    Polish parents’ views on mathematics activities at home and in Swedish preschools

    Dorota Lembrér

    Abstract
    This article describes the results of a digital survey of 41 Polish immigrant parents’ views on mathematics activities at home and at preschool as parents’ views potentially provide a range of perspectives on mathematics activities for young children. Parents were asked to describe and justify their views about how children engage with mathematical ideas and nominate activities that children engage in at home and at preschool. When parents justi ed their views about young children and mathematics, they tended to align themselves with the norms and values of the Swedish preschool curriculum. The ndings suggest that parents, like children, are socialised into Swedish preschools. However, this alignment could limit possibilities for broadening perspectives about mathematics education in preschool, which could be available by incorporating input from immigrant parents’ di erent cultural and linguistic backgrounds.

    Dorota Lembrér
    Dorota Lembrér is a doctoral student at Western Norway University of Applied Sciences in Bergen, Norway. She has a background as a preschool teacher and a lecturer at Malmö University in Sweden. Her main research interests are early childhood mathematics education and aspects of mathematics activities in preschool and home environments.

    Skapad: 2018-11-06 kl. 11:16

  6. NOMAD 23(3-4), 2018

    Bishop Sámegillii – utfordringer ved oversetting av matematikkdidaktisk fagterminologi

    Anne Birgitte Fyhn, Ellen J. Sara Eira, Ole Einar Hætta, Inga Anne Marit Juuso, Siv Ingrid Nordkild og Ellen Margrethe Skum

    Sammenfatning
    I artikkelen belyser vi kulturelle og språklige utfordringer som kan oppstå når teoretiske begreper fra matematikkdidaktisk forskning oversettes til et språk og en kultur som er ernt fra språket og kulturen der begrepene ble utviklet. I samarbeid med forskere oversatte lærere ved Guovdageainnu nuoraidskuvla/Kautokeino ungdomsskole et matematikkdidaktisk rammeverk fra engelsk til nordsamisk. Vi fokuserer på oversetting av aktiviteten locating som inngår i rammeverket. Locating omfatter grunnlaget for elevers utvikling av romlig forståelse. Vi bidrar også til diskusjonen om hvorvidt hovedområdene i matematikklæreplanen skal utformes som verb eller substantiver.

    Abstract
    In this article we enlighten cultural and linguistic challenges that may occur when concepts from mathematics education are translated into a language and a culture that is far from the language and the culture where the concepts were developed. In cooperation with researchers, teachers at Guovdageainnu nuoraidskuvla/Kautokeino lower secondary school translated a mathematics education framework into North Sámi. We focus on translations of the activity locating, which is part of this framework. Locating constitutes the basis for students’ development of spatial understanding. We also contribute to the discussion about whether the national mathematics curriculum’s content areas should be verbs or nouns.

    Anne Birgitte Fyhn
    Anne Birgitte Fyhn is professor in mathematics education at UiT, the Arctic University of Norway, Tromsø. She holds a professor II position at Sámi Allaskuvla/ Sámi University of Applied Sciences. Her main research interests are relations between mathematics education and culture.

    Ellen J. Sara Eira
    Ellen J. Sara Eira is principal of Guovdageainnu nuoraidskuvla. She has taught mathematics in Sámi for 35 years and she taught Sámi at Sámi Allaskuvla/Sámi University of Applied Sciences for two years. Since 2010, she is mathematics sensor for the national compulsory school exam. From 1983–1998 she was member of the national exam group in Sámi at upper and lower secondary level.

    Ole Einar Hætta
    Ole Einar Hætta is mathematics teacher at Guovdageainnu nuoraidskuvla. He has been sensor at the Sámi mathematics exam for the compulsory school for ten years. He was member of the 2017 national curriculum group that worked out core elements in mathematics. He is master student in mathematics education at UiT, the Arctic University of Norway.

    Inga Anne Marit Juuso
    Inga Anne Marit Juuso is mathematics teacher at Guovdageainnu nuoraidskuvla. She also teaches duodji (Sámi handicraft). She is master student in mathematics education at UiT, the Arctic University of Norway.

    Siv Ingrid Nordkild
    Siv Ingrid Nordkild is Ph.D. student at UiT-The Arctic University of Norway, Campus Tromsø. Her Ph.D. is based in mathematics education in the North Sámi area in Norway. Her research interests are culture based mathematics education and indigenous related issues in education. She is educated as an electrical engineer with Master’s degree in pedagogy.

    Ellen Margrethe Skum
    Ellen Margrethe Skum is vice principal of Guovdageainnu nuoraidskuvla. She teaches Sámi language and duodji (Sámi handicraft). She uses her competencies in Sámi tradition and culture, among others from reindeer husbandry, in her teaching.

    Skapad: 2018-11-06 kl. 11:12

  7. NOMAD 23(3-4), 2018

    En registeranalyse af centrale matematiske begreber i en grønlandsk kontekst

    Mette Hjelmborg and Ane Fleischer

    Sammenfatning
    Denne artikel beskriver resultaterne af en registeranalyse af grønlandske matematiske begreber. Fokus for analysen er de karakteristiske træk, der opstår når man genererer et matematisk register i et polysyntetisk sprog. Vores teoretiske ramme er faglige registre og registerkontinuum i et systemisk funktionelt lingvistisk perspektiv. Metodisk foretages dokumentanalyser, der mættes af interviewsvar fra semistrukturerede interviews. Vores analyse indikerer, at der som oftest benyttes samtlige tre teknikker når grønlandske matematiktermer genereres: omskrivninger, nominaliseringer og metaforer. Det matematiske register knytter sig dermed i høj grad og på mange og varierede måder til det grønlandske dagligdagssprog.

    Abstract
    This article describes the results of an analysis of the mathematical register in Greenland concerning the characteristics for developing terms for mathematical concepts in a polysynthetic language. The theoretical frame is registers, register continuum with respect to systemic functional linguistic. The analysis indicates that three techniques (gerunding, circumlocutions, and metaphors) are used simultaneously when generating new terms in Greenlandic. The mathematical concepts in Greenlandic thereby have a direct link to everyday meanings of similar concepts.

    Mette Hjelmborg
    Mette Hjelmborg er lektor på UCL Erhvervsakademi og Professionshøjskole, læreruddannelsen på Fyn. De vigtigste interesser er: sprog og begrebsdannelse, Dansk som andetsprog, elever med særlige behov, læremiddelanalyse.

    Ane Fleischer
    Ane Fleischer underviser på læreruddannelsen i Grønland, efteruddanner, lærebogsforfatter. De vigtigste interesser er: matematiklæring og især sprog og matematikbegreber på grønlandsk, elever med særlige behov.

    Skapad: 2018-11-06 kl. 11:04

  8. NOMAD 23(3-4), 2018

    Culturally based mathematics tasks: a framework for designing tasks from traditional Kven artefacts and knowledge

    Hilja L. Huru, Anna-Kaisa Räisänen and Anita Movik Simensen

    Abstract
    This article discusses mathematical and cultural task design to support minority and endangered languages and cultures. More precisely, we propose a theoretical framework to design mathematical tasks for language immersion in mathematics for Kven students. Drawing on previous studies, we suggest that traditional tools have the potential to support the learning of mathematics, language, and culture. One challenge for endangered languages and cultures is that the younger generations may have lost connections with their traditional language and culture. We argue that the older generations can mediate authentic aspects of Kven culture to students, which then become historical-cultural authentic (HiCuA) aspects.

    Hilja L. Huru
    Hilja L. Huru is a professor in mathematics at OsloMet – Oslo Metropolitan Univerity and UiT – The Arctic University og Norway. Her background is in pure mathematics with a PhD in non-commutative algebra connected to mathematical physics. Her research interest also includes multicultural classrooms with a focus on pressured minorities and indegenous mathematics.

    Anna-Kaisa Räisänen
    Anna-Kaisa Räisänen is a language advisor at the Kainun institute – Kvensk institutt, Norway and a doctoral student at the University of Oulu, Finland. She is involved with language education programs for Kven language and leads Kven language nests projects in northern Norway. Her main research interests are sociolinguistics and language policy as well as language revitalization and language vitality.

    Anita Movik Simensen
    Anita Movik Simensen is assistant professor of mathematics education at UiT – The Arctic University of Norway. Her research interests include mathematics education in inclusive classrooms, indigenous mathematics, and the use of natural outdoor learning environments as setting for young children’s (age 1–6) mathematical experiences.

    Skapad: 2018-11-06 kl. 10:55

  9. NOMAD 23(3-4), 2018

    Newly- and early-immigrated second-language students’ knowledge of arithmetic syntax

    Jöran Petersson

    Abstract
    The present study investigated how 259 Swedish, grade 9 students, of whom 90 had an immigrant background, achieved on twelve written test items in the content area of number. Four of the twelve test items required good knowledge of arithmetic syntax, such as when it was appropriate to apply order-of-operation rules and the associative and distributive laws of arithmetic operations. On these four test items, the most-recently arrived students showed on average signi cantly more knowledge than the students who had immigrated when they were younger and had participated in Swedish schools for longer periods of time. The outcome suggests that these two groups of immigrant students in later school years should be considered as separate sub-categories of second-language students when it comes to teaching, assessment and research.

    Jöran Petersson
    Jöran Petersson is a senior lecturer at Stockholm University, Sweden. He wrote his PhD-dissertation on test achievement of second language students in the last year of compulsory school. Presently he is doing postdoctoral research on how foundational number sense appears in textbooks and homework in the rst year of compulsory school. Jöran also has an interest in mathematical modelling.

    Skapad: 2018-11-06 kl. 10:52

  10. NOMAD 23(3-4), 2018

    The language factor – what exactly is it? Bilingual speakers of Russian and Finnish solving mathematical tasks

    Maria Ahlholm and Päivi Portaankorva-Koivisto

    Abstract
    A lack of knowledge of the language of instruction is often believed to be the main reason for low achievement among students with an immigrant background. We regard language as a tripartite unit comprising aspects of concept formation, pragmatic language usage and the linguistic form. In this theoretical framework, we report two case studies of bilingual, Russian and Finnish speaking students’ explanations of their procedures while solving mathematical tasks. The students’ linguistic processing varied in terms of conceptualization, pragmatic meaning-making and grammatical form. In a bilingual context, the labelling of concepts and meaning-making through argumentation are simultaneously processed in two languages.

    Maria Ahlholm
    Maria Ahlholm is a University lecturer (PhD) in the Faculty of Educational Sciences at the University of Helsinki, and an adjunct professor in Finnish language, especially applied linguistics. Ahlholm is interested in the multilingual socialisation process of emerging second language.

    Päivi Portaankorva-Koivisto
    Päivi Portaankorva-Koivisto is a University lecturer (PhD) of mathematics didactics in the Faculty of Educational Sciences at the University of Helsinki. Portaankorva-Koivisto is interested in developing mathematics teacher education and teachers’ awareness of the language factor in teaching and learning mathematics.

    Skapad: 2018-11-06 kl. 10:49

  11. NOMAD 23(3-4), 2018

    Developing mathematical reasoning by using questions in a multilingual mathematics classroom

    Marie Sjöblom

    Abstract
    In this paper, students’ questions while working in small groups on mathematical problem-solving tasks are investigated. In order to improve students’ reasoning and communication abilities in mathematics, an intervention study was designed in a multilingual upper secondary mathematics classroom in Sweden. In their discussions students used Swedish, which was their second language and also the language of instruction. The changes in students’ ways of using questions across the three cycles of the intervention were analysed. The results showed how students over the cycles changed their ways of framing questions from looking for the correct answer towards clarifying other students’ meaning in order to understand each other’s reasoning. The implication from the study is that it is important to promote interactions between students rather than focusing on students’ need to develop their second language competencies.

    Marie Sjöblom
    Marie Sjöblom is a PhD-student in mathematics education at Malmö University. She is also a mathematics teacher, and work as senior lecturer with school development in Malmö, supporting teachers and school leaders on collegial learning processes. Key research interests are interaction in multilingual mathematics classrooms and educational design research.

    Skapad: 2018-11-06 kl. 10:46

  12. NOMAD 23(3-4), 2018

    Identity formations as mathematical learners in the context of transition

    Petra Svensson Källberg

    Abstract
    This paper explores the relation between discourses and identity formations as mathematical learners in a context of transition. The data consists of an interview with two 16 year-old immigrant girls, who were relocated when their school, in a multicultural and socio-economically disadvantaged area in Sweden, was closed. The girls showed dynamic and unstable identities by drawing on di erent discourses. Social relational discourses, more than mathematical pedagogical discourses, governed their actions as learners of mathematics; enabling identities as noisy, un-engaged, but able students in the old school, and as engaged and accepted, but also as strangers, in the new school.

    Petra Svensson Källberg
    Petra Svensson Källberg has a doctoral degree in mathematics education from Stockholm University, the department of mathematics and science education. She works at Pedagogisk Inspiration, a department which works with school development and research in the muncipality of Malmö, Sweden. Her main research interests concern socio-political issues in mathematics education and are related to multilingual and multicultural issues in mathematics education.

    Skapad: 2018-11-06 kl. 10:44

  13. NOMAD 23(3-4), 2018

    Fabrication of newly-arrived students as mathematical learners

    Eva Norén and Petra Svensson Källberg

    Abstract
    As a response to recent laws on how to support newly-arrived students’ schooling, new policy texts have been released in Sweden. By analyzing policy texts we show how a particular kind of human, ”the newly-arrived student as a mathematical learner” is fabricated through discursive processes. We show how the policy texts are framed within an including discourse that encourages multiculingualism and views students’ mother tongue and backgrounds as resources. However, simultaneously the newly-arrived student is thought of, in a more excluding discourse, as being in need of rescue and as lacking the most valuable asset, the Swedish language.

    Eva Norén
    Eva Norén is senior lecturer in mathematics education at the department of mathematics and science education, Stockholm University. Her main research interest is multilingual students in mathematics classrooms. She defended her PhD thesis, Flerspråkiga matematikklassrum [Multilingual mathematics classrooms] in 2010. She has also researched gender issues related to mathematics teaching and learning. Since 2017 she is involved in a development and research project on programming in subject didactics.

    Petra Svensson Källberg
    Petra Svensson Källberg has a doctoral degree in mathematics education from Stockholm University, the department of mathematics and science education. She works at Pedagogisk Inspiration, a department which works with school development and research in the muncipality of Malmö, Sweden. Her main research interests concern socio-political issues in mathematics education and are related to multilingual and multicultural issues in mathematics education.

    Skapad: 2018-11-06 kl. 10:41

  14. NOMAD 23(3-4), 2018

    Language diversity in mathematics education in the Nordic countries 2008–2018

    Tamsin Meaney and Toril Eskeland Rangnes

    Abstract
    A paper in which the guest editors introduce this thematic issue of NOMAD.
    “The aim of the thematic issue is to provide an overview of what was being done and from this to determine what still needed to be done on language diversity in mathematics classrooms and early childhood centres in the Nordic countries.”

    Tamsin Meaney
    Tamsin Meaney is professor in mathematics education at Western Norway University of Applied Sciences in Bergen, Norway. She has written journal articles on language diversity in mathematics education for twenty years.

    Toril Eskeland Rangnes
    Toril Eskeland Rangnes is associate professor in mathematics education at the Faculty of Education, Arts and Sports at Western Norway University of Applied Sciences, campus Bergen. Her main research interest are critical mathematics education, teacher professional development and language diversity in mathematics classrooms.

    Skapad: 2018-11-06 kl. 10:35

  15. NOMAD 23(2), 2018

    Scrutinizing teacher-learner interactions on volume

    Anita Tyskerud and Reidar Mosvold

    Abstract
    This study adds to research on volume and spatial reasoning by investigating teacher-learner interactions in the context of Lesson study. Our analysis illustrates how the mathematical object of volume is realized, and what metarules of discourse that can be observed over two iterations of a research lesson. The study unpacks the mathematical work of teaching volume in terms of discourse, and shows how an undesirable and unexpected result from the first research lesson can be attributed to the communicational work of teaching rather than to lack of skills among students.

    Anita Tyskerud
    Anita Tyskerud is a PhD candidate in Educational Science, Department of Education and Sports Science, University of Stavanger, Norway. Her research interests are related to teachers’ professional development in mathematics and Lesson study.

    Reidar Mosvold
    Reidar Mosvold is Professor of Mathematics Education at the Department of Education and Sports Science, University of Stavanger, Norway. His research interests are related to mathematics teaching and developing mathematics teachers.

    Skapad: 2018-08-22 kl. 16:08

  16. NOMAD 23(2), 2018

    Læreres utbytte av kunnskap om hjernen

    Jan Roksvold

    Sammandrag
    Konkrete klasseromsanvendelser av hjerneforskning har latt vente på seg. I denne oversiktsartikkelen undersøkes det potensielle utbyttet for lærerstudenter ved å kjenne til ulike temaer knytta til hjernens befatning med tall og aritmetikk – uavhengig av hvorvidt slike en-til-en-anvendelser eksisterer eller kan eksistere. Av potensiell verdi for lærere framheves blant annet kunnskap om hvilke vanskeligheter et assosiativt minne forårsaker i forbindelse med aritmetiske tabeller. Med bakgrunn i moderne hjerneforskning belyses ei tallbehandling som kan deles opp i en medfødt ”tallsans” og et kultur- og utdanningsavhengig eksakt tallsystem, hvordan ulike binæroperasjoner behandles på grunnleggende forskjellig vis av hjernen, og hvordan innlæringsstrategi kan påvirke lagringa av aritmetisk kunnskap. Temaer som barnets ”logaritmiske indre tallinje” og dyskalkuli blir også belyst. Jeg konkluderer med at denne typen kunnskap om hjernen vil utvide lærerstudentenes forståelse av det lærende barnet, og dermed kunne påvirke deres praksis.

    Abstract
    Concrete applications of neuroscience to the classroom are yet to be confirmed. The topic of this research article is the potential gains to be had for trainee teachers in knowing about various topics concerning the brain’s processing of numbers and arithmetic – regardless of whether one-to-one applications exist or can exist. Highlighted as potentially valuable to teachers, is knowledge about: the dichotomy between an inborn ”number sense” and a culturally and educationally dependant exact number system; how different binary operations are processed; how learning strategy can affect the encoding of arithmetic facts; the difficulties caused by an associative memory in relation to arithmetic tables; the child’s ”logarithmic inner number line”; dyscalculia, and the neuromyth pertaining to it. I conclude that this type of knowledge will expand trainee teachers’ understanding of the learning child, and thereby possibly in uence their practice.

    Jan Roksvold
    Jan Roksvold er førsteamanuens i matematikkdidaktikk ved UiT Norges arktiske universitet. Hans forskningsinteresser omfatter anvendelse av funn fra kognitiv psykologi i matematikkundervisning, hjernens befatning med matematikk, samt bruk av matematikkhistorie og historie-fortelling i undervisning.

    Skapad: 2018-08-22 kl. 16:02

  17. NOMAD 23(2), 2018

    Disciplinary competence descriptions for external use

    Jens Højgaard Jensen and Uffe Thomas Jankvist

    Abstract
    The article addresses the need for competence descriptions of disciplines as a means for fostering more productive communication between different disciplines and between the disciplines and their surroundings. It is argued that the usual competence descriptions devised for use within a discipline itself, e.g. in relation to teaching and learning of the discipline – so-called competence descriptions for internal use – are not the best means to achieve this. The same is true for the general, non-disciplinary competence descriptions. Instead, specially devised disciplinary competence descriptions for external use are called for. Our main illustration is a competence description of mathematics for external use devised so that it can support the dialogue about justi cation of mathematics education between the discipline’s practitioners and its recipients. This description for external use is counterposed with one for internal use i.e. that of the Danish KOM project. It is also counterposed with a competence description for external use for physics, taking into account the different justification problem of physics education. Together these two descriptions showcase how competence descriptions of disciplines for external use may support interdisciplinary collaboration and division of labor in the educational system.

    Jens Højgaard Jensen
    Jens Højggard Jensen is associate professor in physics at Roskilde University. For many years he was involved in the governing of Roskilde University in various positions. Besides publications with more specific physics content he has published on university politics, general didactics, science didactics, and interdisciplinarity.

    Uffe Thomas Jankvist
    Uffe Thomas Jankvist is professor with special responsibilities in mathematics education at the Danish School of Education, Aarhus University. He has published on the use of history of mathematics in mathematics education, technology in mathematics education, interdisciplinarity, and students’ learning difficulties in mathematics. Besides teaching and supervising future mathematics teacher educators at the Danish School of Education, he is also part of the Danish research-based “maths counsellor” upper secondary teacher program at Roskilde University.

    Skapad: 2018-08-22 kl. 15:56

  18. NOMAD – 23(2), 2018

    Volume 23, No 2, June 2018

    e-NOMAD

    [PDF] displays the full text pdf. The two most recent volumes are password protected. Use “Open access” in the menu for full text of older articles.

    Editorial

    Jens Højgaard Jensen and Uffe Thomas Jankvist
    Disciplinary competence descriptions for external use
    [PDF]

    Jan Roksvold
    Læreres utbytte av kunnskap om hjernen
    [PDF]

    Anita Tyskerud and Reidar Mosvold
    Scrutinizing teacher-learner interactions on volume
    [PDF]

    Skapad: 2018-08-22 kl. 15:48

  19. NOMAD 23(1), 2018

    The gap between school mathematics and university mathematics: prospective mathematics teachers’ conceptions and mathematical thinking

    Jani Hannula

    Abstract
    In Finland, both prospective and in-service mathematics teachers report a discontinuity between university-level mathematics and mathematics taught at comprehensive and secondary school. In this study, ten prospective mathematics teachers (PMTs) were interviewed to examine their conceptions of the nature of this gap as well as their mathematical thinking. The study’s findings support research that has revealed difficulties experienced by PMTs in the secondary–tertiary transition and in connecting formal and informal components of mathematical thinking. Additionally, the study provides new insight into PMTs’ conceptions of teacher knowledge, such as the relationship between knowledge of advanced mathematics and the knowledge needed in teaching situations. The findings offer guidelines for further studies that could help the development of mathematics teacher education.

    Jani Hannula
    Jani Hannula is a doctoral student at the University of Helsinki, Finland. He is involved with mathematics teacher education at the Department of Mathematics and Statistics. He has a background as a lecturer of mathematics and information technology at Helsinki Metropolia University of Applied Sciences. His main research interests are teacher knowledge and beliefs as well as cognitive aspects of mathematical thinking.

    Skapad: 2018-03-20 kl. 15:50

  20. NOMAD 23(1), 2018

    Discourses in school algebra: the textbooks’ different views on algebra and the positioning of students

    Kristina Palm Kaplan

    Abstract
    The purpose of this study is to understand the school algebra offered in Swedish mathematic textbooks for grade 8. Using a social semiotic perspective, textbook tasks are analysed with a method inspired by Systemic Functional Linguistics. Five school algebra discourses are identified: symbolic discourse, geometrical discourse, arithmetical discourse, (un)realistic discourse and the scientific discourse. It is argued that these offer different views on the nature of algebra and the positioning of students.

    Kristina Palm Kaplan
    Kristina Palm Kaplan is a doctoral student at Uppsala University since September 2014. The main research interests are mathematics and language, especially algebra and social semiotics.

    Skapad: 2018-03-20 kl. 15:47

  21. NOMAD – 23(1), 2018

    Volume 23, No 1, March 2018

    e-NOMAD

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    Editorial

    Anna Ida Säfström
    Preschoolers exercising mathematical competencies
    [PDF]

    Magnus Fahlström and Lovisa Sumpter
    A model for the role of the physical environment in mathematics education
    [PDF]

    Kristina Palm Kaplan
    Discourses in school algebra: the textbooks’ different views on algebra and the positioning of students
    [PDF]

    Jani Hannula
    The gap between school mathematics and university mathematics: prospective mathematics teachers’ conceptions and mathematical thinking
    [PDF]

    Skapad: 2018-03-20 kl. 12:27

  22. NOMAD 23(1), 2018

    Preschoolers exercising mathematical competencies

    Anna Ida Säfström

    Abstract
    The mathematical ideas that emerge in children’s free and guided play can be both complex and sophisticated, and if they are linked to formal mathematics, they can be a powerful basis for mathematical development. To form such links, one needs knowledge of how children use and express these ideas. This is especially true in the intersection of arithmetic and geometry, where the intermingling of numerical and spatial concepts and skills is not yet fully understood. This study aims to gain understanding of children’s mathematical practices by describing the interplay of key mathematical ideas, and more specifically how young children exercise mathematical competencies in the intersection of early arithmetic and geometry. The results show that children can use spatial representations when reasoning about numbers, and that they are able to connect spatial and numerical structures. Furthermore, it is shown that children not only use and invent effective procedures, but also are able to explain, justify and evaluate such procedures.

    Anna Ida Säfström
    Anna Ida Säfström is associate professor in mathematics education at Halmstad University. Her main research interests are mathematical competence, mathematics as conceptual fields, design research and teachers’ professional development.

    Skapad: 2018-03-19 kl. 15:22

  23. NOMAD 23(1), 2018

    A model for the role of the physical environment in mathematics education

    Magnus Fahlström and Lovisa Sumpter

    Abstract
    In this paper, we develop an analytical tool for the role of the physical environment in mathematics education. We do this by extending the didactical triangle with the physical environment as a fourth actor and test it in a review of literature concerning the physical environment and mathematics education. We find that one role played by the physical environment, in relation to mathematical content, is to portray the content in focus, such as geometry and scale. When focusing on teachers, students, and the interaction between them, the role of the physical environment appears to be a precondition, either positive (enabling) or negative (hindering). Many of the findings are valid for education in general as well, such as the importance of building status.

    Magnus Fahlström
    Magnus Fahlström is PhD-student in Microdata Analysis and a mathematics teacher educator at Dalarna University. Key research interests are physical school environment and mathematics education.

    Lovisa Sumpter
    Lovisa Sumpter is Senior Lecturer and Associate Professor in Mathematics Education at Stockholm University. Key research interests are mathe-matical reasoning, affect and gender.

    Skapad: 2018-03-19 kl. 15:16

  24. NOMAD 22(4), 2017

    Mathematics lecturers’ views on the teaching of mathematical modelling

    Stephanie Treffert-Thomas, Olov Viirman, Paul Hernandez-Martinez and Yuriy Rogovchenko

    Abstract
    The paper reports on the views and use of mathematical modelling (MM) in university mathematics courses in Norway from the perspective of lecturers. Our analysis includes a characterisation of MM views based on the modelling perspectives developed by Kaiser and Sriraman (2006). Through an online survey we aimed to identify the main perspectives held in higher education by mathematics lecturers and the underlying rationale for integrating (or not) MM in university courses. The results indicated that most respondents displayed a realistic perspective on MM when it came to their professional practice. There was a more varied response when it came to their views on MM in teaching. Regarding conditions influencing the use or non-use of MM in teaching, these mainly concerned the mathematical content and the institutional practices.

    Stephanie Treffert-Thomas
    Stephanie Treffert-Thomas is a lecturer at Loughborough University (UK) with experience of teaching mathematics at school level, tertiary (college) level and at university, mainly to engineering students. Her research interests are in university level mathematics teaching and learning using socio-cultural educational theories. She has a particular interest in the mathematical teaching practices of lecturers, including the use of mathematical modelling in teaching.

    Olov Viirman
    When the research reported on in this paper was conducted, Olov Viirman was a postdoctoral researcher within the MatRIC centre at the University of Agder, Norway. He has recently taken up a position as senior lecturer at the University of Gävle, Sweden. His research is in university mathematics education, mainly focusing on the discursive practices of lecturers and students, and on the teaching and learning of mathematics, for instance mathematical modelling, in other academic disciplines.

    Paul Hernandez-Martinez
    Paul Hernandez-Martinez is a senior lecturer in the Department of Mathematics at Swinburne University of Technology, Australia, and a visiting fellow in the Mathematics Education Centre at Loughborough University, UK. His research is in post-compulsory Mathematics Education, where he uses socio-cultural educational theories to investigate teaching-learning practices (e.g. Mathematical Modelling) that have the potential to develop in students rich mathematical meanings while at the same time create in them positive dispositions towards the subject.

    Yuriy Rogovchenko
    Yuriy Rogovchenko is a Professor of Mathematics at the University of Agder, Kristiansand, Norway. His research interests include qualitative theory of ordinary, functional and impulsive differential equations, mathematical modelling, and mathematics education related to teaching and learning of differential equations and mathematical modelling at university level.

    Skapad: 2018-01-04 kl. 00:00

  25. NOMAD – 22(4), 2017

    Volume 22, No 4, December 2017

    Volume 22, No 4, December 2017

    e-NOMAD

    [PDF] displays the full text pdf. The two most recent volumes are password protected. Use “Open access” in the menu for full text of older articles.

    Editorial

    Simon Goodchild and Barbara Jaworski

    Developing practice through research into university mathematics education

    [PDF]

    Angeliki Mali and Georgia Petropoulou

    Characterising undergraduate mathematics teaching across settings and countries: an analytical framework

    [PDF]

    Suela Kacerja, Toril Eskeland Rangnes, Rune Herheim, Meinrad Pohl, Inger Elin Lilland and Ragnhild Hansen

    Stimulating critical mathematical discussions in teacher education: use of indices such as the BMI as entry points

    [PDF]

    Mervi A. Asikainen, Antti Viholainen, Mika Koponen and Pekka E. Hirvonen

    Finnish entry-level students’ views of teacher knowledge and the characteristics of a good mathematics teacher

    [PDF]

    Sinéad Breen, Niclas Larson, Ann O’Shea and Kerstin Pettersson

    A study of students’ concept images of inverse functions in Ireland and Sweden

    [PDF]

    Margrethe Naalsund and Joakim Skogholt

    Oral presentations as a tool for promoting metacognitive regulation in real analysis

    [PDF]

    Stephanie Treffert-Thomas, Olov Viirman, Paul Hernandez-Martinez and Yuriy Rogovchenko

    Mathematics lecturers’ views on the teaching of mathematical modelling

    [PDF]

    Ian Jones and David Sirl

    Peer assessment of mathematical understanding using comparative judgement

    [PDF]

    Barbro Grevholm

    Bokanmälan

    Innehåll: JH

    Skapad: 2018-01-04 kl. 00:00

  26. NOMAD 22(4), 2017

    Oral presentations as a tool for promoting metacognitive regulation in real analysis

    Margrethe Naalsund and Joakim Skogholt

    Abstract
    Real Analysis is for many students their first proof-based mathematics course, and many find it challenging. This paper studies how oral presentations of mathematical problems for peers can contribute to students’ metacognitive reflections. The paper discusses several aspects tied to preparing for, and carrying out, oral presentations, that seem to spur important sub-components of metacognitive regulation such as planning, monitoring, and evaluating. Thoughtful guidance from an expert encouraged the students to further monitor their cognition, and evaluate their arguments and cognitive processes when expressing their reasoning to their peers.

    Margrethe Naalsund
    Margrethe Naalsund is associate professor in Mathematics Education. She works at Faculty of Science and Technology (Section for Learning and Teacher Education) at Norwegian University of Life Sciences (NMBU). Her main research interests are learning and teaching algebra at primary and secondary school, and learning and teaching real analysis at university level.

    Joakim Skogholt
    Joakim Skogholt is PhD-student in Mathematics. He works at Faculty of Science and Technology (Section for Applied Mathematics) at Norwegian University of Life Sciences (NMBU). His main research interests are applied linear algebra, and learning and teaching real analysis at university level.

    Skapad: 2018-01-04 kl. 00:00

  27. NOMAD 22(4), 2017

    A study of students’ concept images of inverse functions in Ireland and Sweden

    Sinéad Breen, Niclas Larson, Ann O’Shea and Kerstin Pettersson

    Abstract
    In this paper we focus on first-year university students’ conceptions of inverse function. We present results from two projects, conducted in Ireland and Sweden respectively. In both countries, data were collected through questionnaires, as well as through student interviews in Sweden. We draw on the notion of concept image and describe the components of students’ evoked concept images. The students’ responses involved e.g. ”reflection”, ”reverse”, and concrete ”examples”, while just a few students gave explanations relating to the definition of inverse functions. We found that the conceptions of inverses as reflections and reverse processes are important and relatively independent of local factors, and the data seemed to suggest that a ”reverse” conception is linked to an appreciation of injectivity more than a ”reflection” conception.

    Sinéad Breen
    Sinéad Breen holds a PhD in Mathematics (on Asymptotic Analysis) from Dublin City University and has recently returned there as an Assistant Professor in the School of Mathematical Sciences. She conducts research in mathematics education, her main interest being in the teaching and learning of mathematics at undergraduate level.

    Niclas Larson
    Niclas Larson is an associate professor at the Department of Mathematical Sciences, University of Agder, Kristiansand, Norway. His research interest lies in the teaching and learning of mathematics at secondary or university level. Current projects, both comparative, deal with students’ understanding of proof by mathematical induction and student teachers’ explanations of solutions to linear equations respectively. His methodological and theoretical standpoints are varied and driven by current research questions.

    Ann O’Shea
    Ann O’Shea is a Senior Lecturer in the Department of Mathematics and Statistics at the Maynooth University in Ireland. She received a PhD in Mathematics from the University of Notre Dame, Indiana in 1991. Currently her research interests lie in Mathematics Education, especially at undergraduate level.

    Kerstin Pettersson
    Kerstin Pettersson is an associate professor at the Department of Mathe-matics and Science Education, Stockholm University, Sweden. Her research interests concern university students’ conceptions of thres-hold concepts. Current projects deal with students’ learning in small groups teaching and students’ understanding of proof by mathematical induction.

    Skapad: 2018-01-04 kl. 00:00

  28. NOMAD 22(4), 2017

    Finnish entry-level students’ views of teacher knowledge and the characteristics of a good mathematics teacher

    Mervi A. Asikainen, Antti Viholainen, Mika Koponen and Pekka E. Hirvonen

    Abstract
    This paper reports a study of the views held by Finnish students at the start of their university studies concerning their understanding of the knowledge and characteristics of a good mathematics teacher. A total of 97 students following a basic university course responded to a questionnaire. The results showed that a knowledge of teaching mathematics was more often used to describe the good mathematics teacher than a knowledge of mathematics. According to the students’ views, mathematics teachers need to be able to take the level of understanding of individual students into account in their teaching. Good mathematics teachers were also considered to be skilled in explaining, simplifying and transforming mathematical contents for their students. A good mathematics teacher was often described by the respondents as a patient, clear, inspiring and consistent person. On the other hand, characteristics such as humorous, likeable, empathetic, or fair were seldom used in the students’ responses to describe a good mathematics teacher. Those respondents who planned to become teachers demonstrated a more learner-centred concept of a good mathematics teacher than did those who were aiming at some other subject specialist profession than that of teaching.

    Mervi A. Asikainen
    Docent Mervi A. Asikainen is a senior lecturer at the UEF Department of Physics and Mathematics. Asikainen directs the UEF physics and mathematics education research group. Her current field of interest include teacher knowledge of mathematics and physics teachers, teaching and learning of physics in higher and secondary education, and research-based development of STEM education.

    Antti Viholainen
    Antti Viholainen is a senior lecturer in mathematics / mathematics education at University of Eastern Finland. His research areas are mathematical beliefs, mathematics teacher education, learning materials (textbooks etc.) in mathematics, and mathematical argumentation.

    Mika Koponen
    Mika Koponen is a postdoctoral researcher at the University of Eastern Finland. He has used Mathematical Knowledge for Teaching (MKT) framework for evaluating and improving mathematics teacher education. In his dissertation study, he presented a novel approach for investigating teacher knowledge and its interconnections by making use of network analysis methods. His postdoctoral research continues from this work by focusing on how the components of teacher knowledge are interconnected.

    Pekka E. Hirvonen
    Docent Pekka E. Hirvonen is a senior lecturer at the UEF Department of Physics and Mathematics. Hirvonen has published more than 30 peer-reviewed articles in international journals, books, and proceedings.

    Skapad: 2018-01-04 kl. 00:00

  29. NOMAD 22(4), 2017

    Stimulating critical mathematical discussions in teacher education: use of indices such as the BMI as entry points

    Suela Kacerja, Toril Eskeland Rangnes, Rune Herheim, Meinrad Pohl, Inger Elin Lilland and Ragnhild Hansen

    Abstract
    The main purpose of our research project is to gain insight into, and develop teaching on indices and their applications in society. In this paper, the focus is to present insights into teachers’ reflections when discussing the Body Mass Index (BMI). Skovsmose´s concept of mathemacy, and source criticism, are chosen as conceptual framework. The data analysed were collected in a numeracy across the curriculum class with practising teachers. The findings show that the practising teachers engaged in meaning making of the index formula, and they critically discussed how BMI is used in society and the role the BMI index can have in our lives. We gain insight into the potential of such an index for developing teachers’ awareness of the application of mathematics­ to the real world and the issues it raises, both for the teachers and for ourselves.

    Suela Kacerja
    Suela Kacerja has a postdoc position in mathematics education at the Western Norway University of Applied Sciences. She has a background as mathematics teacher educator from Albania and Norway. Her research interests are: developing critical mathematics education possibilities in teacher education and in schools, in intersection with real-life contexts in learning mathematics, as well as pre-service teachers’ reflections about their own practice.

    Toril Eskeland Rangnes
    Toril Eskeland Rangnes is associate professor in mathematics education. She works at the Department of Teacher Education Study in Mathematics, Western Norway University of Applied Sciences. Rangnes has a background as primary school teacher, textbook author and editor for Tangenten. Her main research interests are critical mathematics education, teacher professional development and language diversity in mathematics classrooms.

    Rune Herheim
    Rune Herheim is associate professor at Western Norway University of Applied Sciences. His research focuses on connections between communication qualities and learning in mathematics with a particular focus on argumentation and agency in real-life contexts and when students use digital learning tools. Herheim is the Editor in chief for Tangenten, a Norwegian journal on mathematics teaching.

    Meinrad Pohl
    Meinrad Pohl is associate professor in history. He works at the Department of Social Science, Western Norway University of Applied Sciences, Bergen. His main research interests are early modern economic theory and economic policy, trade history and mining history.

    Inger Elin Lilland
    Inger Elin Lilland is associate professor at the Western Norway University of Applied Sciences, where she works at the Department of Teacher Education Study in Mathematics. She has previous experience as mathematics teacher at the upper secondary school level. Her main research interests are critical mathematics education and mathematics teacher professional development.

    Ragnhild Hansen
    Ragnhild Hansen is associate professor at the Department of Teacher Education Study in Mathematics at Western Norway University of Applied Sciences (HVL). She received her master and PhD degrees from the University of Bergen within applied mathematics. Hansen has a background in as a researcher in different modelling projects. Her main research interests are critical mathematics education and teacher professional development.

    Skapad: 2018-01-04 kl. 00:00

  30. NOMAD 22(4), 2017

    Developing practice through research into university mathematics education

    Simon Goodchild and Barbara Jaworski

    Abstract
    The paper provides a very brief outline review of research into some key issues that affect students’ performance in mathematics in higher education. Community of practice theory is used to frame and focus the discussion. Policies regarding the recruitment of students, institutional practices for grouping students and the cultures of teaching and learning mathematics are considered. The research reviewed provides a context for examining the contributions of the research reports included within this thematic issue of NOMAD. The reports address three themes: regular approaches adopted in teaching mathematics in higher education, innovative approaches to teaching and learning, with emphasis on student participation in the educational process, and the characteristics of mathematical knowledge students appropriate. The paper endorses calls for large scale studies, especially those which relate teaching approaches, both regular and innovative, to the qualities and characteristics of students’ learning. The absence of a single overarching theoretical framework that embraces all the studies is also perceived as an obstacle that interferes with scientific developments in the field of researching university mathematics education. However, the value of teachers researching their own practice and their students’ learning is argued to be crucial for developing knowledge ”in practice” and this underscores the value of the papers included in this issue of NOMAD, both for the authors and the inspiration of other higher education mathematics teachers who, it is hoped, will be inspired to engage in similar studies.

    Simon Goodchild
    Simon Goodchild is Professor of Mathematics Education at the University of Agder, he is also leader of MatRIC, Centre for Research Innovation and Coordination of Mathematics Teaching. MatRIC is one of eight Norwegian centres for excellence in higher education. He has over two decades of experience of school classroom research and school mathematics teaching development. In his role leading MatRIC he is using and extending his experience of mathematics teaching development in the context of university mathematics education.

    Barbara Jaworski
    Barbara Jaworski is Professor of Mathematics Education at Loughborough University and coordinates research, including a group of eight PhD research fellows, within MatRIC. She has held positions of Chair of the British Society for Research into Learning Mathematics; President of the Congress of European Researchers in Mathematics Education; and President of the International Group for the Psychology of Mathematics Education. She has been research mathematics teaching and teaching development for over three decades.

    Skapad: 2018-01-04 kl. 00:00

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