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  1. NOMAD 21(3), 2016

    The role of semiotic resources when reading and solving mathematics tasks

    Anneli Dyrvold

    Abstract

    One part of being proficient in mathematics is to be able to read and solve mathematics tasks where mathematics is represented using different semiotic resources (i.e. natural language, mathematical notation, and different types of images). In the current study, statistical methods are used to investigate the potential meaning that the presence and co-occurrences of semiotic resources have for how demanding a mathematical task is to read and solve. The results reveal that the number of different semiotic resources in a mathematical task is not related to difficulty, but that difficulty is related to the particular combinations of semiotic resources where pictorial images are one of the resources. The results also indicate that the difficulty related to these semiotic characteristics is not related to an unnecessary reading demand.

    Anneli Dyrvold

    Anneli Dyrvold is a PhD student in mathematics education at the Department of Mathematics and Mathematical Statistics at Umeå University. She is a member of Umeå Mathematics Education Research Centre (UMERC). Her research interest is the affordances, and distinguishing characteristics, of the language of mathematics and what students need to learn in order to master it.

    Skapad: 2016-09-22 kl. 01:00

  2. NOMAD 21(3), 2016

    Lærerarbeidets matematiske undervisningsoppgaver

    Janne Fauskanger og Reidar Mosvold

    Sammanfattning

    Denne artikkelen bidrar til studier og begrepsfesting av det profesjonelle lærerarbeidet i matematikk ved å analysere diskusjoner mellom erfarne matematikklærere. Gjennom slike analyser forsøker vi å komme nærmere et svar på hvilke matematiske undervisningsoppgaver de fremhever som sentrale i sitt lærerarbeid. Utgangspunktet for diskusjonene er en liste med sentrale matematiske undervisningsoppgaver presentert i forskningslitteraturen. Resultatene viser at de erfarne lærerne mener at: 1) listen over matematiske undervisningsoppgaver trenger finpuss og precisering, 2) listen må omstruktureres, og 3) listen mangler matematiske undervisningsoppgaver som er viktige i en norsk kontekst. Vi konkluderer med at studier av erfarne læreres syn på hva som er sentrale matematiske undervisningsoppgaver for matematikklærere kan bidra til videreutvikling av den praksisbaserte teorien om undervisningskunnskap i matematikk.

    Abstract

    Given that it is important to study and conceptualize the professional work of teaching mathematics, discussions between experienced mathematics teachers are analyzed in this article in order to learn more about the mathematical tasks of teaching that they highlight as important for their work of teaching mathematics. The starting point for the discussions was a list of mathematical tasks of teaching mathematics presented in the research literature. The results show that the experienced teachers argue that: 1) the list of mathematical tasks of teaching needs refinement and adjustment, 2) the list must be restructured, and 3) the list lacks mathematical tasks of teaching that are important in a Norwegian context. We conclude that studies of experienced mathematics teachers’ views of important mathematical tasks of teaching can contribute to further development of the practice-based theory of mathematical knowledge for teaching.

    Janne Fauskanger

    Janne Fauskanger er førsteamanuensis i matematikkdidaktikk ved Universitetet i Stavanger, Norge. Hennes forskningsinteresser er i hovedsak rettet mot matematikklæreres undervisningskunnskap og oppfatninger, samt hvordan kunnskaper og oppfatninger kan påvirke lærernes undervisningspraksis og elevers læring av matematikk.

    Reidar Mosvold

    Reidar Mosvold er førsteamanuensis i matematikkdidaktikk ved Universitetet i Stavanger, Norge. Hans forskningsinteresser omfattar læreres undervisningskunnskap i matematikk, læreres oppfatninger, læreridentitet og diskursive perspektiver, samt bruk av matematikens historie i undervisningen.

    Skapad: 2016-09-22 kl. 01:00

  3. NOMAD – 21(3), 2016


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    Volume 21, No 3, September 2016

    Editorial

    Yvonne Liljekvist

    Mathematics teachers’ knowledge-sharing on the Internet: pedagogical message in instruction materials

    [PDF]

    Evangelia Triantafyllou, Morten Misfeldt and Olga Timcenko

    Attitudes towards mathematics as a subject, and mathematics learning and instruction in a trans-disciplinary engineering study

    [PDF]

    Appendix

    Anneli Dyrvold

    The role of semiotic resources when reading and solving mathematics tasks

    [PDF]

    Janne Fauskanger og Reidar Mosvold

    Lærerarbeidets matematiske undervisningsoppgaver

    [PDF]

    Shipra Sacheva, Marit Hvalsøe Schou and Andreas Lindenskov Tamborg

    Reflections on having participated at the Pre-NORMA workshop

    Innehåll: JH

    Skapad: 2016-09-22 kl. 01:00

  4. NOMAD – 21(2), 2016


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    Volume 21, No 2, June 2016

    Editorial

    Florenda Gallos Cronberg

    Learning linear relationships through independent use of the mathematics textbook

    [PDF]

    Nonmanut Pongsakdi, Teija Laine, Koen Veermans, Minna M. Hannula-Sormunen and Erno Lehtinen

    Improving word problem performance in elementary school students by enriching word problems used in mathematics teaching

    [PDF]

    Ida Bergvall, Jenny Wiksten Folkeryd and Caroline Liberg

    Linguistic features and their function in different mathematical content areas in TIMSS 2011

    [PDF]

    Kerstin Larsson

    Finding Erik and Alva: uncovering students who reason additively when multiplying

    [PDF]

    Barbro Grevholm

    Bokanmälan: Fra snublesten til byggesten. Matematikdidaktiske muligheder

    Bokanmälan [PDF]

    Thematic issue of Nomad – call for papers

    Innehåll: JH

    Skapad: 2016-06-09 kl. 01:00

  5. NOMAD 21(2), 2016

    Finding Erik and Alva: uncovering students who reason additively when multiplying

    Kerstin Larsson

    Abstract

    This article presents a study in which grade 5 students’ responses to multiplicative comparison problems, a well-known method for distinguishing additive reasoning from multiplicative, are compared to their reasoning when calculating uncontextualised multiplicative tasks. Despite recognising the multiplicative structure of multiplicative comparison problems a significant proportion of students calculated multiplicative problems additively. Therefore, multiplicative comparison problems are insufficient on their own as indicators of multiplicative reasoning.

    Kerstin Larsson

    Kerstin Larsson is a doctoral student in mathematics education at the Department of Mathematics and Science Education at Stockholm University. Her research interest lies in students’ understanding of arithmetic, especially multiplication.

    Skapad: 2016-06-09 kl. 01:00

  6. NOMAD 21(2), 2016

    Linguistic features and their function in different mathematical content areas in TIMSS 2011

    Ida Bergvall, Jenny Wiksten Folkeryd and Caroline Liberg

    Abstract

    This study investigates how written language is used as a resource to express meaning in different mathematical content areas; algebra, geometry, statistics and arithmetic, in the Swedish version of TIMSS 2011. Based on previous research we identify linguistic features that fulfill the function of expressing four central meaning dimensions of written academic language in general and in language used in school mathematics in particular; Packing, Precision, Personification and Presentation of information. These four meaning dimensions constitute the foundation for the analysis. The results show differences in how the language is used within the different mathematical content areas in TIMSS 2011. These differences consist primarily of to what extent the language is subject specific and used to express the specific mathematics in each of the four content areas. In this way the notion of a single mathematical language is also challenged.

    Ida Bergvall

    Ida Bergvall has a PhD from the Department of Education, Uppsala University, Sweden. Ida has a background as mathematics, science and special education teacher. Her research and thesis, Bokstavligt, bildligt och symboliskt i skolans matematik – en studie om ämnesspråk i TIMSS, focus on language in school mathematics.

    Jenny Wiksten Folkeryd

    Jenny Wiksten Folkeryd is assistant professor at the Department of Education, Uppsala University, Sweden. Her research focuses educational linguistics including reading and writing development, language across the curriculum, text analysis and literacy assessment. She participates in the construction of national tests in Swedish and is a member of the Reading Development Group of PIRLS (Progress in International Reading Literacy Study).

    Caroline Liberg

    Caroline Liberg is a Professor of educational sciences focusing on reading and learning processes at the Department of Education, Uppsala University. Her research has focused on literacy practices in early childhood and in different subject areas in school. Together with her doctoral students and colleagues, Caroline Liberg is currently investigating linguistic and content dimensions of test items in international studies of students’ competences in math and science and furthermore the function, content and form of students’ text-making in different subject areas in early school years.

    Skapad: 2016-06-09 kl. 01:00

  7. NOMAD 21(2), 2016

    Improving word problem performance in elementary school students by enriching word problems used in mathematics teaching

    Nonmanut Pongsakdi, Teija Laine, Koen Veermans, Minna M. Hannula-Sormunen and Erno Lehtinen

    Abstract

    The traditional practice of using word problems in classroom mathematics has been heavily criticized by educators and researchers. Students have an inclination to apply superficial strategies and exclude several important steps of the modeling process. In this study, a Word Problem Enrichment program (WPE) was developed to encourage teachers to use innovative self-created word problems to improve student mathematical modeling and problem solving skills. Participants included 170 fourth-, and sixth-graders and ten teachers from elementary schools in southwest Finland. The intervention effectiveness on student problem solving performance was investigated. The results suggested that the enriching word problems used in mathematics teaching is a promising method to improve student problem solving skills when solving non-routine and application word problems.

    Nonmanut Pongsakdi

    Nonmanut Pongsakdi is a PhD student at the Department of Teacher Education, University of Turku in Finland. She is a part of mathematics learning research group: Cultivating future mathematical minds. Her research is primarily focused on teaching and learning mathematical word problem solving in the elementary school.

    Teija Laine

    Teija Laine is an expert teacher who has many years of experience in teaching elementary school mathematics. Currently, she teaches at Pansio School, and also works for the Center of Teacher Training in Turku. She has been involved in several pre-service and in-service teacher trainings in mathematics.

    Koen Veermans

    Koen Veermans is a senior researcher at the Department of Teacher Education, University of Turku in Finland. His research interests are science learning, computer simulation as well as mathematical problem solving. He specializes in mixed method, and he is also teaching research methodology at the University of Turku.

    Minna M. Hannula-Sormunen

    Minna M. Hannula-Sormunen is adjunct professor at the Department of Teacher Education, University of Turku in Finland. She has been involved in several innovative studies in mathematics. Her main focus is children’s early mathematical development: Spontaneous focusing on numerosity (SFON).

    Erno Lehtinen

    Erno Lehtinen is academy professor at the Department of teacher education at University of Turku in Finland. He has been involved in many different research areas, and he is also a leader of mathematics learning research group: cultivating future mathematical minds.

    Skapad: 2016-06-09 kl. 01:00

  8. NOMAD 21(2), 2016

    Learning linear relationships through independent use of the mathematics textbook

    Florenda Gallos Cronberg

    Abstract

    This paper discusses the participation of one Grade 8 student in a typical Swedish mathematics class as she tried to learn independently about linear relationships, mainly through the mathematics textbook. Since this set-up has the possibility for every student to progress at different rates, only one student, through data from ten consecutive lessons, was considered. Results from an analysis of this student’s use of the textbook showed that the textbook is used independently more as an instrument for learning mathematics rather than an object of learning mathematics. However, further studies are required to determine the extent of learning and the development of mathematical skills.

    Florenda Gallos Cronberg

    Florenda Gallos Cronberg has a PhD in mathematics education and works as senior lecturer at the University of Gothenburg. Her current research interest is on examining student participation in the learning process, particularly during student’s private work in mathematics classrooms.

    Skapad: 2016-06-09 kl. 01:00

  9. NOMAD – 21(1), 2016


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    Volume 21, No 1, March 2016

    Editorial

    Elisabeth Rystedt, Cecilia Kilhamn and Ola Helenius

    What’s there in an n? Investigating contextual resources in small group discussions concerning an algebraic expression

    [PDF]

    Ingvald Erfjord

    Mathematics teachers’ initial implementation of a digital tool package

    [PDF]

    Anette Bagger

    Pressure at stake: Swedish third graders’ talk about national tests in mathematics

    [PDF]

    Johan Prytz and Martin Karlberg

    Nordic school mathematics revisited – on the introduction and functionality of New Math

    [PDF]

    News from Nordic mathematics education

    NORMA 17 – First announcement

    Innehåll: JH

    Skapad: 2016-02-25 kl. 00:00

  10. NOMAD 21(1), 2016

    Mathematics teachers’ initial implementation of a digital tool package

    Ingvald Erfjord

    Abstract

    The study reported in this paper was situated within developmental research and concerns teachers’ initial implementation of a digital tool in mathematics teaching. The paper illuminates two types of implementation processes, and takes an activity theory perspective in the discussion of reasons and the types of issues experienced and addressed in the implementation processes. Using activity theory parlance it is argued that although the teachers appeared to have rather similar objects for the implementation, there were great differences in teachers’ goals and the kinds of issues dealt with in the implementation processes. The schools’ organisation, internal collaboration within each school and how the external requirements for mathematics teaching, such as a curriculum and examination standards, were approached, played a significant role in the different implementation processes.

    Ingvald Erfjord

    Ingvald Erfjord is associate professor in mathematics education at the University of Agder, Norway. He conducts research on learning and teaching mathematics when digital tools are used, as well as on learning of mathematics in kindergarten, with and without the use of digital tools.

    Skapad: 2016-02-25 kl. 00:00

  11. NOMAD 21(1), 2016

    Pressure at stake: Swedish third graders’ talk about national tests in mathematics

    Anette Bagger

    Abstract

    This article presents part of a larger scale ethnographic study1 about Swedish national tests in mathematics in the third grade. Indications concerning possible needs in the test situation are examined through 102 pupils’ talk about pressure and what is at stake. Results imply that this test could be experienced as a high stakes test. Negative pressure is quite common, especially among multilingual pupils in need of support and boys in need of support. There are gendered differences in the talk about what is at stake. The article frames who the pupil in need of support might be from a pupil’s perspective, but also discusses how these possible positions of need might be managed in practice.

    Anette Bagger

    Anette Bagger is Senior lecturer at the Department of Applied Educa- tional Science, Umeå University. Anette has a background as mathema- tics, science and special education teacher. Her thesis, Is school for everyone? The national test in mathematics at grade three in Sweden, deals with students in special needs in the context of assessment. Her research interests are in mathematics didactics, special pedagogics and assessment, as well as combinations of these fields.

    Skapad: 2016-02-25 kl. 00:00

  12. NOMAD 21(1), 2016

    Nordic school mathematics revisited – on the introduction and functionality of New Math

    Johan Prytz and Martin Karlberg

    Abstract

    We investigate the functionality of New Math in order to nuance and deepen our understanding of the process to introduce New Math in Sweden. Our main material is data and statistics from an intervention study conducted during the preparation of the New Math reform in Sweden. In particular we investigate the claim that New Math material had negative effects on students’ learning. Our conclusion is that the claim is, in most parts, incorrect.

    Johan Prytz

    Johan Prytz is senior lecturer at Uppsala University, Department of Education. He is mainly doing research on the history of mathematics education. Other fields of interest are textbook research and the role of language in school mathematics.

    Martin Karlberg

    Martin Karlberg is senior lecturer at Uppsala University, Department of Education. His research is primarily focused on classroom management, behavior management and inclusive education. He specializes mainly in quantitative method.

    Skapad: 2016-02-25 kl. 00:00

  13. NOMAD 21(1), 2016

    What’s there in an n? Investigating contextual resources in small group discussions concerning an algebraic expression

    Elisabeth Rystedt, Cecilia Kilhamn and Ola Helenius

    Abstract

    This small-case study combines a content related and a dialogical approach, in an in-depth analysis of how three 12-year-old pupils in a video recorded small group discussion construe the meaning of the letter n in an algebraic expression. The findings indicate that the pupils used a rich variety of contextual resources in their sensemaking attempt. They also tried out a wide range of interpretations of the letter indicating that their conception of an algebraic letter was rich but unstable and that the dialogue was instrumental in helping them move from primitive to more advanced interpretations. In addition to previously known difficulties of understanding letters as variables, we found that the meaning of the communicative convention ”expressed in n” proved an obstacle, and conclude that learning mathematics is as much about learning a specific communicative genre as learning about mathematical objects and relationships.

    Elisabeth Rystedt

    Elisabeth Rystedt got a licentiate degree in September 2015 and this article is a part of her thesis. As a PhD student she was a member of the The Graduate Research School in Educational Sciences at the University of Gothenburg. Today she is working 50% at the National Center for Mathematics Education (NCM) and 50 % as a teacher educator at the University of Gothenburg. Her research interest concerns how pupils understand introductory algebra.

    Cecilia Kilhamn

    Cecilia Kilhamn is a Dr of Philosophy in Mathematics Education and works as a lecturer and teacher educator at the University of Gothenburg. She is also a mathematics education researcher with an interest in classroom research in primary and lower secondary school.

    Ola Helenius

    Ola Helenius has PhD in mathematics and is a researcher and deputy director at the National Centre for Mathematics Education at the University of Gothenburg. Some of his current research interests include neuroscience perspectives on learning mathematics, socio-cultural perspectives on preschool mathematics and mathematics curriculum design research.

    Skapad: 2015-12-02 kl. 00:00

  14. NOMAD – 20(3-4), 2015


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    Volume 20, No 3-4, November 2015

    Editorial

    Kristín Bjarnadóttir

    Tölur og mengi – Numbers and sets. A New Math textbook in Iceland in the 1960s

    [PDF]

    Andreas Christiansen

    An analysis of two 19th century Norwegian geometry books, and the reactions they caused

    [PDF]

    Marc van Zanten and Marja van den Heuvel-Panhuizen

    Past and current approaches to decimal numbers in Dutch primary school mathematics textbooks

    [PDF]

    Tom Rune Kongelf

    Introduksjon av algebra i matematikkbøker for ungdomstrinnet i Norge

    [PDF]

    Rannveig Halldórsdóttir

    Comparison of three textbooks published for 8th grade in Iceland

    [PDF]

    Madis Lepik, Barbro Grevholm and Antti Viholainen

    Using textbooks in the mathematics classroom – the teachers’ view

    [PDF]

    Antti Viholainen, Miia Partanen, Jani Piiroinen, Mervi Asikainen and Pekka E. Hirvonen

    The role of textbooks in Finnish upper secondary school mathematics: theory, examples and exercises

    [PDF]

    Linda Ahl, Guðný Helga Gunnarsdóttir, Tuula Koljonen and Guðbjörg Pálsdóttir

    How teachers interact and use teacher guides in mathematics – cases from Sweden and Iceland

    [PDF]

    Ingvild Lambert Grave and Birgit Pepin

    Teachers’ use of resources in and for mathematics teaching

    [PDF]

    Ragnhild Johanne Rensaa and Barbro Grevholm

    A textbook in linear algebra – the use and views of engineering students

    [PDF]

    Sebastian Rezat and Rudolf Sträßer

    Methodological issues and challenges in research on mathematics textbooks

    [PDF]

    Thematic issue of Nomad – call for papers

    Innehåll: JH

    Skapad: 2015-12-02 kl. 00:00

  15. NOMAD 20(3-4), 2015

    An analysis of two 19th century Norwegian geometry books, and the reactions they caused

    Andreas Christiansen

    Abstract

    Bernt Michael Holmboe (1795–1850), professor in mathematics, wrote several textbooks on mathematics, and his presentation of geometry was traditional and in conformity with Euclidean ideas. Christopher Hansteen (1784–1873), professor in applied mathematics, wrote a textbook on geometry where he challenged the traditional Euclidean geometry. This paper analyses two very different approaches to basic definitions in the two geometry textbooks written by Holmboe and Hansteen, and what reactions this caused in the contemporary society. The main focus will be on the understanding of basic concepts in geometry, and of parallel lines and Euclid’s parallel postulate.

    Andreas Christiansen

    Andreas Christiansen is associate professor at the Department of teacher education and cultural studies at Stord/Haugesund university college in Norway where he is teaching mathemtics and didactics. He is also teaching mathematics and didactics at Bergen university college, and history of mathematics at the University of Bergen. His research interests are history of mathematics, and history of mathematics education.

    Skapad: 2015-12-02 kl. 00:00

  16. NOMAD 20(3-4), 2015

    Past and current approaches to decimal numbers in Dutch primary school mathematics textbooks

    Marc van Zanten and Marja van den Heuvel-Panhuizen

    Abstract

    In the Netherlands, most contemporary textbook series for primary school mathematics education are influenced by the so-called Realistic mathematics education (RME) reform. This reform dates back to the 1970s. In the study described in this paper we investigated what this reform means for the approach to decimal numbers. We analyzed how this content domain is treated in a contemporary RME-oriented textbook series and two pre-RME textbook series. Our study revealed that most, although not all, of the RME characteristics included in our analysis framework were found to be present in the researched contemporary RME-oriented textbook The world in numbers (2009). Furthermore, it was found that onsets of several RME characteristics were already present in the two older textbooks, New arithmetic (1958) and Functional arithmetic, (1969) that date from before the RME reform started.

    Marc van Zanten

    Marc van Zanten works at the National Dutch Institute for Curriculum Development and is a PhD student at the Freudenthal Institute, Faculty of Science & Faculty of Social and Behavioral Sciences of Utrecht University, the Netherlands. His research interests lie in mathematics curricula and textbooks.

    Marja van den Heuvel-Panhuizen

    Marja van den Heuvel-Panhuizen is Professor of Mathematics Education at the Freudenthal Institute, Faculty of Science & Faculty of Social and Behavioral Sciences of Utrecht University, the Netherlands. Her research interests are in learning and teaching of mathematics of the age group 4–14.

    Skapad: 2015-12-02 kl. 00:00

  17. NOMAD 20(3-4), 2015

    Introduksjon av algebra i matematikkbøker for ungdomstrinnet i Norge

    Tom Rune Kongelf

    Sammanfattning

    I denne artikkelen presenterer vi funnene fra en analyse av introduksjonskapitlet i algebra i seks ulike lærebøker. Introduksjonen til bokstaver som symbol for variable størrelser varierer med hensyn til klassetrinn, mengde og kontekst. Gjennom en induktiv kvalitativ innholdsanalyse karakteriserer vi mangelfulle sider ved kapitlene. Hovedfunnene er at variabelaspektet ikke kommer tydelig frem, og at en i liten gradbenytter mulighetene til å bygge videre på tallære. I tillegg inneholder lærebøkene feilaktige formuleringer, illustrasjoner og matematiske resonnement, som lägger forholdene til rette for utvikling av misoppfatninger.

    Abstract

    In this paper we present findings from an analysis of the chapters introducing algebra in six mathematics textbooks used in lower secondary schools in Norway. The introduction of letters as symbols for variables varies with respect to grade, quantity and context. Through an inductive qualitative content analysis we characterise insufficient aspects of the different chapters. The main findings are that the variable aspect is not clear, and that the textbooks hardly use the opportunities to build on arithmetic. In addition we find erroneous formulations, illustrations and mathematical reasoning, which facilitates the development of misconceptions.

    Tom Rune Kongelf

    Tom Rune Kongelf er en Ph.D.-student tilknyttet doktorgradsprogrammet ved Universitetet i Agder, og arbeider som foreleser ved Høgskulen i Sogn og Fjordane. Han forsker på lærebøker i matematikk som blir brukt på ungdomstrinnet, med vekt på problemløsning, algebra og oppgaver.

    Skapad: 2015-12-02 kl. 00:00

  18. NOMAD 20(3-4), 2015

    Comparison of three textbooks published for 8th grade in Iceland

    Rannveig Halldórsdóttir

    Abstract

    This study compares characteristics of three Icelandic mathematics textbooks for grade 8, used over a period of 25 years. The textbooks’ structure, content, attitudes to mathematics and mathematical competences were compared and portrayed in the light of official curricula. The purpose of the study is to investigate through the focal point of textbooks the implementation of new curricular policy including new topics as well as mathematical competences and attitudes to mathematics. Our findings show that the textbooks differ considerably with respect to the characteristics studied. The objectives of mathematics formulated in the national curriculum are reflected to a great extent in the most recent textbook Átta – tíu, but the widely used translated textbook, Almenn stærðfræði I, deviates in important ways from the curriculum and much more than the Talnaspegill/Hornalína books that only stayed in use for a short while.

    Rannveig Halldórsdóttir

    Rannveig Halldórsdóttir is a teacher in Reykjavík, Iceland. She teaches mathematics and information technology, primarily at secondary level. Her main research interests are related to implementation of new curricular policy through textbooks.

    Skapad: 2015-12-02 kl. 00:00

  19. NOMAD 20(3-4), 2015

    Using textbooks in the mathematics classroom – the teachers’ view

    Madis Lepik, Barbro Grevholm and Antti Viholainen

    Abstract

    Mathematics teachers’ self-reported practices of textbook use were investigated by a survey of more than 400 teachers in Estonia, Finland and Norway. Do they have different approaches in their use of textbooks and to what extent do they rely on textbooks in planning and preparing their lessons? What kinds of patterns characterize teachers’ practice when using textbooks in mathematics lessons? The answers to these questions indicate that in Estonia and Finland teachers have similar attitudes towards textbooks. They are responsible for the choice of book and the textbook has a strong effect on their didactical choices. In Norway the teachers are less dependent on the textbook. In Finland the textbook is the crucial resource for exercises while in Estonia and Norway teachers use other resources more often. The study reveals the limited use of the full potential of the textbook. Almost 45 % of the teachers use the textbook simply as an exercise book. As a result the pupils do not get the opportunity to fully exploit the book as a multifaceted learning resource.

    Madis Lepik

    Madis Lepik is Associate Professor of mathematics education at the Department of Mathematics, Tallinn University, Estonia. His research interests include teachers’ beliefs and professional development, textbook studies, and proof and proving.

    Barbro Grevholm

    Barbro Grevholm is Professor Emerita in didactics of mathematics at University of Agder in Norway and at Kristianstad University. She has been active in creating and developing the doctoral programmes in both universities and at Luleå University of Technology. She currently supervises doctoral students and has published in books and journals. From 2006 she was the leader of the network for research on mathematics textbooks in the Nordic and Baltic countries (supported by NordForsk).

    Antti Viholainen

    Antti Viholainen (Ph. D) is a Senior Lecturer at the Department of Physics and Mathematics, University of Eastern Finland. He has taught several courses in the mathematics teacher education program. His main research interests are mathematical orientations, mathematical reasoning and use of learning materials.

    Skapad: 2015-12-02 kl. 00:00

  20. NOMAD 20(3-4), 2015

    The role of textbooks in Finnish upper secondary school mathematics: theory, examples and exercises

    Antti Viholainen, Miia Partanen, Jani Piiroinen, Mervi Asikainen and Pekka E. Hirvonen

    Abstract

    Textbooks are written mainly for students, but they can also be seen as mediators between the intended curriculum and teachers’ practices. The focus of the present study is on how students and teachers at Finnish upper secondary schools perceive and describe their use of the theory, examples, and exercises presented in their mathematics textbooks. Seventy-one students participated in a short survey, and six of them and three of their teachers were interviewed. The results indicate that the theory, examples, and exercises presented in their textbooks have a strong influence on teachers’ work, but for the students the textbooks primarily represent a source of exercises.

    Antti Viholainen

    Senior lecturer at the Department of Physics and Mathematics, University of Eastern Finland. He has taught several courses in the mathematics teacher education program. His main research interests are mathematical orientations, mathematical reasoning and use of learning materials.

    Miia Partanen

    Lecturer in mathematics, physics, chemistry and computer science in Kontiolahti school, Finland.

    Jani Piiroinen

    Lecturer in mathematics, physics, chemistry and computer science in Suininlahti school, Finland.

    Mervi A. Asikainen

    Senior lecturer at the Department of Physics and Mathematics, University of Eastern Finland. She has taught physics in various in-service teacher education courses for both primary and secondary schoolteachers and has also worked as a schoolteacher herself. Her main research interests are the methodology of science education research, teacher knowledge in physics and mathematics, and the teaching and learning of university physics.

    Pekka E. Hirvonen

    Associate professor at the Department of Physics and Mathematics, University of Eastern Finland. He is the leader of the Physics and Mathematics Education Research Group at the University of Eastern Finland and the educational unit of the Department of Physics and Mathematics. At the present time he is also serving as the chair of the LUMA Centre Finland board. His research interests include the teaching and learning of different topics of physics and mathematics and the research-based development work of physics and mathematics teacher education.

    Skapad: 2015-12-02 kl. 00:00

  21. NOMAD 20(3-4), 2015

    How teachers interact and use teacher guides in mathematics – cases from Sweden and Iceland

    Linda Ahl, Guðný Helga Gunnarsdóttir, Tuula Koljonen and Guðbjörg Pálsdóttir

    Abstract

    Recent research findings show that curriculum resources have a potential to support teachers’ design of lessons. The aim of this study is to investigate how Icelandic and Swedish teachers interact with and use teacher guides while planning their teaching. Five teachers in each country teaching lower grade levels (1–6) were interviewed about their utilization of teacher guides. The analytical tool used to analyse the teacher guides and the interviews focused on the different features of the guides and shed light on what the teachers were looking for in the guides and for what purpose. Our findings showed that teachers using educative teacher guides were more likely to use a wider range of lesson design considerations in contrast to teachers using traditional teacher guides.

    Linda Ahl

    Linda Ahl holds a licentiate degree in didactics from the graduate school Developing mathematics education. She works as a lecturer in Kriminalvården, [The Swedish prison and probation service] Section for adult education. Her research interests are proportional reasoning, support for teaching and learning from curriculum resources and ways to put research findings back to teaching practice.

    Guðný Helga Gunnarsdóttir

    Guðný Helga Gunnarsdóttir is a senior lecturer in mathematics education at the University of Iceland, School of Education. Her research interests include mathematics teacher education, teachers’ professional development and teachers’ interactions with curriculum resources.

    Tuula Koljonen

    Tuula Koljonen is a lecturer in special needs education and PhD student in mathematics education at the University of Mälardalen in Sweden. Her research interests include mathematics teacher education, mathematics difficulties and support in and for teaching and learning from curriculum resources.

    MGuðbjörg Pálsdóttir

    Guðbjörg Pálsdóttir is an associate professor in mathematics education at the University of Iceland, School of Education. Her research interests include mathematics teacher education, curriculum resources and the development of mathematical ideas in early childhood.

    Skapad: 2015-12-02 kl. 00:00

  22. NOMAD 20(3-4), 2015

    Teachers’ use of resources in and for mathematics teaching

    Ingvild Lambert Grave and Birgit Pepin

    Abstract

    Over the past decades the amount of available resources for mathematics teaching has vastly increased, in particular the availability of resources on the web. However, we know very little about how teachers select and use the available resources. In this paper we investigate how four primary school teachers used curriculum resources in and for their mathematics teaching. Grounded in a case study approach, we have analysed lessons, teacher interviews, and documents they used for their lesson preparation and instruction. Subsequently, we identified five ”usage categories”: (1) resources to manage the teaching objectives; (2) resources to ”inspire” teaching; (3) resources for student work; (4) resources to adapt the teaching to indivi-dual students’ needs (differentiation); and (5) resources to organize the teaching. In this article we explain and discuss these five categories, and argue that the ”lens of resources” offers an opportune window into teachers’ work, in particular their work as mathematics teachers.

    Ingvild Lambert Grave

    Ingvild Lambert Grave is a primary school teacher in mathematics. She works at Grav primary school, Bærum, Norway. In addition to her work as a teacher she has a position as a mathematics supervisor in Bærum kommune, where she supervises mathematics teachers and organizes mathematics projects and workshops between schools. Ingvild completed her master degree in mathematics didactics at the university college in Sør-Trøndelag (HiST), Norway, in 2013.

    Birgit Pepin

    Birgit Pepin is professor of Mathematics/STEM education at the Technische Universiteit Eindhoven, Netherlands. Previously, she has worked as a professor of mathematics education at Sør-Trøndelag University College (HiST), Norway. Her research interests and expertise include the education (and professional development) of mathematics/STEM teachers, international and comparative studies in mathematics/STEM education and mathematics/STEM teaching and learning in higher education. In particular, she has investigated mathematics/STEM teacher interaction with ”resources”, including textbooks and other curriculum materials.

    Skapad: 2015-12-02 kl. 00:00

  23. NOMAD 20(3-4), 2015

    A textbook in linear algebra – the use and views of engineering students

    Ragnhild Johanne Rensaa and Barbro Grevholm

    Abstract

    This paper has a twofold aim. One is to analyse parts of a linear algebra textbook to seek for its relevance to engineering students. Another is to present an analysis of engineering students’ views about this textbook. Results from the textbook analysis indicate that characteristics like motivating examples and visual design of text and pictures may appeal to engineering students. This is confirmed by analysis of students’ views, showing that the textbook is appreciated, with examples as the most valued part. The textbook’s design with theory presented in small portions, often in examples using specific values to illustrate theoretical arguments, seems to be a success factor.

    Ragnhild Johanne Rensaa

    Ragnhild Johanne Rensaa is an associate professor at Narvik University College, where she teaches mathematics to engineering students. She has her Ph.D in mathematics, but has had a research interest in didactics of mathematics for a number of years. Her main interest is investigating different aspects about engineering students’ studies and learning of mathematics.

    Barbro Grevholm

    Barbro Grevholm is professor emerita in didactics of mathematics at University of Agder in Norway and at Kristianstad University. She has been active in creating and developing the doctoral programmes in both places and at Luleå University of Technology. She currently supervises doctoral students and publishes in books and journals. From 2006 she was the leader of the Network for research on mathematics textbooks in the Nordic and Baltic countries (supported by NordForsk).

    Skapad: 2015-12-02 kl. 00:00

  24. Kopia av NOMAD 20(3-4), 2015

    Methodological issues and challenges in research on mathematics textbooks

    Sebastian Rezat and Rudolf Sträßer

    Abstract

    The growing field of research on mathematics textbooks can be divided into three areas: 1) Research that focuses on the influences on textbooks; 2) Research that focuses on the mathematics textbook itself; 3) Research on the use of mathematics textbooks and its impact. Concentrating on research done in the Nordic countries, the paper provides an overview of methods used in all three areas. Based on an analysis of 24 papers, the findings are that whereas research related to area 1) and 2) usually relies on surveys or content analysis of textbooks – well-established methods from the social sciences –, research in area 3) has to face the methodological challenges of gathering valid data and of generalization of its results. Triangulation and typologies are presented as possible ways to tackle these challenges.

    Sebastian Rezat

    Sebastian Rezat is professor for mathematics education at the University of Paderborn (Germany). His main research interest relates to instruments of teaching and learning mathematics with a focus on traditional and digital textbooks and language.

    Rudolf Sträßer

    Rudolf Sträßer is retired professor for mathematics education at the University of Giessen (Germany). His main research interest relates to mathematics in workplace contexts and instruments for teaching and learning mathematics.

    Skapad: 2015-12-02 kl. 00:00

  25. NOMAD 20(2), 2015

    School mathematical practices as experiences of identity work: the learning journeys of three students

    Ann-Sofi Röj-Lindberg

    Abstract

    This paper illuminates, through stories, how three students’ school mathematical practices accumulate over the years into descriptions of identity in relation to school mathematics. The stories are based on semi-structured interviews with students who were successful during lower secondary school from the perspective of their mathematics teachers’ reform objectives and according to formal assessments. There was not, however, parallel successes in their personal identifications with the school mathematical enterprise as a whole. The study shows that, from the perspective of the student taking part in school mathematical practices, a sense of belonging to learning communities considered as legitimate is of uttermost importance.

    Ann-Sofi Röj-Lindberg

    Ann-Sofi Röj-Lindberg is university teacher in the didactics of mathematics at Åbo Akademi University in Vasa, Finland. Before working in teacher education she was a teacher in mathematics, physics and chemistry. In the course of her career she has had a commitment to promote the voices of students in the mathematics classroom and through research.

    Skapad: 2015-06-22 kl. 01:00

  26. NOMAD 20(2), 2015

    Sociofaglig inklusion og elevfællesskaber. Til didaktiseringen af kammerathjælp i matematikundervisning på folkeskolens begyndertrin

    Maria Christina Secher Schmidt

    Sammanfattning

    Artiklen tager udgangspunkt i et casestudie, der undersøger matematikundervisningen i fire indskolingsklasser (1.–3. klasse). Gennem historier, baseret på elevinterviews og observationer, giver artiklen eksempler på, hvordan elever i matematikvanskeligheder iværksætter strategier med henblik på at blive legitime deltagere i elevfællesskabet. Når eleverne samarbejder om matematik, anvender de deres sociale kapital i form af, at de byder sig til som ven eller dominerende partner. Det synliggøres i artiklen, at det ikke er nok, at matematiklæreren har blik for at organisere samarbejdsstrukturen – der skal også støttes matematikfagligt. Analyserne illustrerer behovet for et nyt inklusionsbegreb: ”sociofaglig inklusion”. Artiklen afsluttes med konkrete fagdidaktiske opmærksomhedspunkter som anledning til at udnytte læringspotentialet i kammerathjælp.

    Abstract

    This article is based on a case study investigating mathematics teaching and learning in four classrooms (1–3 grade) at two different primary schools. Using narratives constructed on pupil interviews and observations of mathematics teaching, the article gives examples of how pupils – for whom mathematics is extensively difficult – implement strategies for gaining acceptance as legitimate participants in pupil communities. Pupils engaged in collaborative mathematics activities draw on their social capital by offering themselves as a friend or dominant partner. The study indicates that mathematics teachers must not only have an eye for organizing cooperative structures, but also provide specific academic support. The analyses illustrate the need for a new notion of inclusion: ”socioacademic inclusion”. The article concludes with some didactic points of attention for maximizing the learning potential inherent in peer support.

    Maria Christina Secher Schmidt

    Maria Christina Secher Schmidt is Ph.D. and associate professor at Metropolitan University College in Copenhagen. Her research interest is cross-disciplinary: inclusive education, special education, didactics (general and subject-related education), mathematics education and sociological professions research. The resent scientific effort is to contribute theoretically and empirically to the didactic research by bringing together classroom leadership and didactics through a focus that grasps both academic and social aspects in mathematics teaching.

    Skapad: 2015-06-22 kl. 01:00

  27. NOMAD 20(2), 2015

    Conceptualising a university teaching practice in an activity theory perspective

    Stephanie Treffert-Thomas

    Abstract

    In this article I present a theorisation of a university mathematics teaching practice, based on a research study into the teaching of linear algebra in a first year mathematics undergraduate course. The research was largely qualitative and consisted of data collected in interviews with the lecturer and in observations of his lectures. Using Leontiev’s (1981) activity theory framework I categorised the teaching of linear algebra on three levels: activity-motive, actions-goals and operations-conditions. Each level of analysis provided insights into the lecturer’s teaching approach, his motivation, his intentions and his strategies in relation to his teaching. I developed a model of the teaching process that relates goals as expressed by the lecturer in interviews to the strategies that he designed for his teaching.

    Stephanie Treffert-Thomas

    Stephanie Treffert-Thomas is a lecturer at Loughborough University (UK) and based in the Mathematics Education Centre. She has a MSc in applied mathematics, with research in fluid dynamics. She has recently completed a PhD in mathematics education with a focus on mathematics teaching at the university level. She has taught mathematics at secondary, tertiary and undergraduate levels. Her research interests lie within socio-cultural approaches to teaching and learning mathematics beyond compulsory schooling.

    Skapad: 2015-06-22 kl. 01:00

  28. NOMAD 20(2), 2015

    En metodisk studie av innholdsanalyse – med analyser av matematikklæreres undervisningskunnskap som eksempel.

    Janne Fauskanger and Reidar Mosvold

    Sammanfattning

    Innholdsanalyse brukes i hovedsak som begrep i tilknytning til den systematiske prosessen forskere går gjennom når de skal analysere innholdet i et skriftlig datamateriale. Muligheter og begrensninger ved tre ulike tilnærminger til kvalitativ innholdsanalyse diskuteres i artikkelen, med datamateriale fra en studie av læreres undervisningskunnskap i matematikk som eksempel. Konvensjonell innholdsanalyse synes å være velegnet til å få en dybdeforståelse av datamaterialets mening, summativ innholdsanalyse er en noe mer strukturert tilnærming som ved en kombinasjon av manifest og latent analyse kan gi en god oversikt over datamaterialets struktur og innhold, mens teoridreven innholdsanalyse synes å egne seg til å teste hypoteser knyttet til teori.

    Abstract

    The concept of content analysis is mainly used with reference to the systematic process of analyzing the content of written data material. Possibilities and constraints of three different approaches to qualitative content analysis are discussed in this article. Data material from a study on assessing and accessing teachers’ mathematical knowledge for teaching is used as example. Conventional content analysis seems to be well suited for developing an in-depth understanding of the data material. Summative content analysis is a more structured approach including manifest as well as latent analysis, and it gives an overview of the structure and content of the data material. Directed or theory driven content analysis seems well suited for testing theoretical hypotheses.

    Janne Fauskanger

    Janne Fauskanger er førsteamanuensis i matematikkdidaktikk ved Universitetet i Stavanger, Norge. Hennes forskningsinteresser er i hovedsakrettet mot matematikklæreres undervisningskunnskap og matematikklæreres oppfatninger, samt hvordan kunnskaper og oppfatninger kan påvirke lærernes undervisningspraksis og elevers læring av matematikk.

    Reidar Mosvold

    Reidar Mosvold er førsteamanuensis i matematikkdidaktikk ved Universitetet i Stavanger, Norge. Hans forskningsinteresser omfatter læreres undervisningskunnskap i matematikk, læreres oppfatninger, læreridentitet og diskursive perspektiver, samt bruk av matematikkens historie i undervisningen.

    Skapad: 2015-06-22 kl. 01:00

  29. NOMAD – 20(2), 2015


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 20, No 2, June 2015

    Editorial

    Ann-Sofi Röj-Lindberg

    School mathematical practices as experiences of identity work: the learning journeys of three students.

    [PDF]

    Maria Christina Secher Schmidt

    Sociofaglig inklusion og elevfællesskaber. Til didaktiseringen af kammerathjælp i matematikundervisning på folkeskolens begyndertrin.

    [PDF]

    Stephanie Treffert-Thomas

    Conceptualising a university teaching practice in an activity theory perspective

    [PDF]

    Janne Fauskanger and Reidar Mosvold

    En metodisk studie av innholdsanalyse – med analyser av matematikklæreres undervisningskunnskap som eksempel

    [PDF]

    Mario Sánchez Aguilar

    Where’s the ”math” in ”mathematics education”? Review of ”Mathematics and mathematicseducation: searching for common ground”

    Book review [PDF]

    Mette Andresen

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2015-06-22 kl. 01:00

  30. NOMAD 20(1), 2015

    Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency

    Anneli Dyrvold, Ewa Bergqvist and Magnus Österholm

    Abstract

    This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.

    Anneli Dyrvold

    This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.

    Ewa Bergqvist

    Ewa Bergqvist is an assistant professor in mathematics education at the Department of Science and Mathematics Education at Umeå University. She is a member of Umeå Mathematics Education Research Centre (UMERC) and teaches mathematics education for pre-service mathematics teachers. Her research focuses mainly on aspects of reasoning and language in upper secondary and university level mathematics.

    Magnus Österholm

    Magnus Österholm is a docent (associate professor) in mathematics education and works at the Department of Science and Mathematics Education at Umeå University. He is also a member of Umeå Mathematics Education Research Centre (UMERC). His research interests deal primarily with mathematics education at the upper secondary and university levels, where cognitive and metacognitive perspectives are of special interest, together with studying language and communication in the learning and teaching of mathematics.

    Skapad: 2015-03-04 kl. 00:00

  31. NOMAD 20(1), 2015

    Systemic functional linguistics as a methodological tool in mathematics education research

    Andreas Ebbelind and Cecilia Segerby

    Abstract

    The aim of this article is to illustrate how Systemic functional linguistics (SFL) can be used as methodological tool for analysing the meaning of texts from two different studies. An analysis using SFL provides insights into how different concepts of mathematical literacy operate in the text. SFL considers language to be a resource used for expressing meaning in specific contexts that accomplishes specific communication purposes. Therefore, SFL contains opportunities for highlighting different aspects of mathematics education which are of interest to researchers. In Sweden, the SFL approach has been used in other research areas but references to it in mathematics education research have been limited.

    Andreas Ebbelind

    Andreas Ebbelind is a lecturer and doctoral student at the department of mathematics education, Linnaeus University, Växjö, Sweden. His research focus how generalist student teachers, who are to teach mathematics among other subjects, perceive becoming mathematics teachers of children ten to twelve years old and how this perception changes during teacher education.

    Cecilia Segerby

    Cecilia Segerby is a doctoral student in mathematics education at Malmö University, Sweden. Her research is related to mathematics and language with special focus on examining how specific writing activities connected to reading strategies can support the students´ understanding in mathematics.

    Skapad: 2015-03-04 kl. 00:00

  32. NOMAD 20(1), 2015

    Disciplined by tests

    Gunnar Sjöberg and Eva Silfver, Anette Bagger

    Abstract

    This article reports on a Swedish research project on the reintroduction of national tests in mathematics for nine- to ten-year-old pupils. Data were collected over a period of three years (2010–2012) by video recording test situations in different classrooms and by conducting video-stimulated recall interviews with children. The aim is to explore and analyse the testing situation and how it creates different positions for children. We conclude that discourses of testing, caring and competition, sometimes strengthening and sometimes shadowing each other and thereby, produce knowledge in children about success and failure in mathematics, positioning children as ”winners” or ”losers”. The tests are interpreted as a technology – a form of disciplinary power that functions at the level of the body (Foucault, 1980).

    Gunnar Sjöberg

    Gunnar Sjöberg is senior lecturer at the Department of science and mathematics education at Umeå University and also teaches in the compulsory school. His research interests concerns special needs issues in mathematics education and the development of special needs education.

    Eva Silfver

    Eva Silfver is senior lecturer at the Department of science and mathematics education at Umeå University. Her research interests concerns special needs education and gender issues in mathematics and science education.

    Anette Bagger

    Anette Bagger is a doctoral student at the Department of science and mathematics education at Umeå University. Her research interests concerns special needs education in mathematics.

    Skapad: 2015-03-04 kl. 00:00

  33. NOMAD 20(1), 2015

    Lektionsstudier i dansk læreruddannelse

    Charlotte Krog Skott og Camilla Hellsten Østergaard

    Sammendrag

    Reformtendenserne har generelt svært ved at slå igennem i grundskolens matematikundervisning. Der er derfor behov for metoder, der kan støtte lærerstuderende i at arbejde med tendenserne på måder, der rækker ud over retoriske inddragelser i uddannelsens sædvanlige undervisning. Ved at være baserede på praksisnære, kollektive praksisser (Murata, 2011), er lektionsstudier et eksempel på en sådan metode. Lektionsstudier understøtter et socialt syn på lærerviden, såsom begrebet ”knowing” (Hodgen, 2011). Ud fra analyser af en empirisk case, argumenterer vi for, at sådanne metoder er vigtige i læreruddannelsen, hvis studerende skal udvikle ”knowing” i og om reformorienteret matematikundervisning.

    Abstract

    In general, the reform is having difficulty gaining acceptance in school mathematics teaching. Methods are needed which make it possible for student teachers to work with the reform movement in ways beyond the rhetorical in Teacher Education. Lesson study (Murata, 2011) represents a promising approach by being based on practice-related, collaborative practices. The method supports a social perspective on teacher knowledge such as the concept of ”knowing” (Hodgen, 2011). Based on analysis of an empirical case, we argue that such methods are important in Teacher Education if student teachers are to develop ”knowing” in and of reform-oriented mathematics teaching.

    Charlotte Krog Skott

    Charlotte Krog Skott, Ph.D., er lektor i afdelingen for forskning og udvikling på Professionshøjskolen UCC, København. Hun er tilknyttet forskningsprogrammet Didaktik og Læringsrum. Omdrejningspunktet for hendes forskning er udvikling af læreres og lærerstuderendes professionelle kompetencer. I øjeblikket er hun involveret i udviklings- og forskningsprojekter, der undersøger forskellige metoder og tilgange til professionel kompetence udvikling.

    Camilla Hellsten Østergaard

    Camilla Hellsten Østergaard, MA, er lektor på Professionshøjskolen Metropol, København. Hun underviser lærerstuderende go professionelle lærere i matematik og matematikkens didaktik. Hendes forskningsinteresse er studerendes udvikling til lærere gennem læreruddannelsen og særligt, hvordan nyuddannede lærere udvikler deres deltagelse i sociale praksisser i deres første år som lærere.

    Skapad: 2015-03-04 kl. 00:00

  34. NOMAD 20(1), 2015

    Message from the Chair of the NoRME board

    I was appointed as the new Chair of the NoRME board at NORMA14 in Turku. I want to continue the good job of the former Chairs of NoRME and NoGSME, and therefore I invite everybody to send me notifications and information of general concern for NOMAD’s audience. I shall do my best, then, to collect and present information in the Nordic News column, starting in the second issue of NOMAD 2015.
    Kind regards,

    Mette Andresen

    Associate professor, Department of Mathematics, University of Bergen.
    mette.andresen@math.uib.no

    Skapad: 2015-03-04 kl. 00:00

  35. NOMAD – 20(1), 2015


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 20, No 1, March 2015

    Editorial

    Anneli Dyrvold, Ewa Bergqvist and Magnus Österholm

    Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency

    [PDF]

    Andreas Ebbelind and Cecilia Segerby

    Systemic functional linguistics as a methodological tool in mathematics education research

    [PDF]

    Gunnar Sjöberg and Eva Silfver, Anette Bagger

    Disciplined by tests

    [PDF]

    Charlotte Krog Skott og Camilla Hellsten Østergaard

    Lektionsstudier i dansk læreruddannelse

    [PDF]

    Mette Andresen

    Message from the Chair of the NoRME board

    Mario Sánchez Aguilar

    Where’s the ”math” in ”mathematics education”? Review of ”Mathematics and mathematicseducation: searching for common ground”

    Book review [PDF]

    Due to unfortunate circumstances the book review will be published in print in no. 2 this volume

    Innehåll: JH

    Skapad: 2015-03-04 kl. 00:00

  36. NOMAD 19(3-4), 2014

    Common tasks of teaching as a resource for measuring professional content knowledge internationally

    Mark Hoover, Reidar Mosvold and Janne Fauskanger

    Abstract

    In the United States, extensive time and money has been invested in developing and validating measures of mathematical knowledge for teaching (MKT). Although studies of adaptation of these measures generally conclude that they are useable in other countries, cultural differences in teaching prompt questions about whether theories and measures of knowledge for teaching are culturally specific. This article argues that the issue turns on the meaning of ”teaching” and ”tasks of teaching” and it recommends increased efforts to identify professionally defensible mathematical tasks of teaching that can serve as a common foundation for conceptualizing and measuring mathematical knowledge for teaching internationally.

    Mark Hoover

    Mark Hoover is Assistant Research Scientist in Educational Studies at the University of Michigan, Ann Arbor, MI. His research investigates the practice of teaching mathematics, including research on equitable teaching, measures of teacher knowledge and designs for collective work on teaching.

    Reidar Mosvold

    Reidar Mosvold is Associate Professor in mathematics education at the University of Stavanger, Norway. His research interests are related to mathematical knowledge for teaching, teacher beliefs and use of history of mathematics in mathematics education.

    Janne Fauskanger

    Janne Fauskanger is Assistant Professor in mathematics education at the University of Stavanger, Norway. Her main research interests are related to teachers’ beliefs and mathematical knowledge for teaching and their influence on teaching practice.

    Skapad: 2014-10-22 kl. 01:00

  37. NOMAD – 19(3-4), 2014


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 19, No 3-4, October 2014

    Editorial

    Mark Hoover, Reidar Mosvold and Janne Fauskanger

    Common tasks of teaching as a resource for measuring professional content knowledge internationally

    [PDF]

    Björg Jóhannsdóttir and Berglind Gísladóttir

    Exploring the mathematical knowledge of prospective elementary teachers in Iceland using the MKT measures

    [PDF]

    Janne Fauskanger and Reidar Mosvold

    Studying teachers’ knowledge by the use of multiple-choice items: the case of ”I’m not sure”

    [PDF]

    Hege Kaarstein

    Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study

    [PDF]

    Cecilia Kilhamn

    When does a variable vary? Identifying mathematical content knowledge for teaching variables

    [PDF]

    Frode Opsvik og Leif Bjørn Skorpen

    Matematisk kvalitet i undervisning

    [PDF]

    Bodil Kleve and Ida Heiberg Solem

    Aspects of a teacher’s mathematical knowledge in his orchestration of a discussion about rational numbers

    [PDF]

    Arne Jakobsen, C. Miguel Ribeiro and Maria Mellone

    Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task

    [PDF]

    Ove Gunnar Drageset

    Knowledge used when orchestrating mathematical discourses – doing, guiding and requesting

    [PDF]

    Bjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark

    Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teaching

    [PDF]

    Jorryt van Bommel

    The teaching of mathematical knowledge for teaching – a learning study of primary school teacher education

    [PDF]

    Innehåll: JH

    Skapad: 2014-10-22 kl. 01:00

  38. NOMAD 19(3-4), 2014

    Exploring the mathematical knowledge of prospective elementary teachers in Iceland using the MKT measures

    Björg Jóhannsdóttir and Berglind Gísladóttir

    Abstract

    This article reports findings from a study carried out with prospective teachers at the University of Iceland. The study explores the mathematical content knowledge of participants, with a special focus on the understanding of numbers, operations, patterns, functions, and algebra. The mathematical knowledge is measured with interviews and a survey, translated and adapted from the MKT measures designed by Ball and the research team at the University of Michigan. The findings indicate that prospective teachers’ knowledge is procedural and related to the ”standard algorithms” they learned and used in elementary school. Findings also indicate that prospective teachers have difficulty evaluating alternative solution methods, and working with and understanding fractions.

    Björg Jóhannsdóttir

    Björg Jóhannsdóttir graduated with a PhD in Mathematics Education from Teachers College, Columbia University in May 2013. Dr. Jóhannsdóttir is an assitant professor of mathematics at California State University Stanislaus. Her main research interests lie within elementary mathematics education, especilly elemenatry teacher education, and in ways to assist students in experiencing mathematics as alive and creative subject.

    Berglind Gísladóttir

    Berglind Gísladóttir is a researcher at Reykjavík University, where she focuses on research. She got her PhD in Mathematics Education from Teachers College, Columbia University 2013. Dr. Gísladóttir’s research interests are, among others, teacher education and mathematics education, inparticular how social factors affect mathematics learning.

    Skapad: 2014-10-22 kl. 01:00

  39. NOMAD 19(3-4), 2014

    Studying teachers’ knowledge by the use of multiple-choice items: the case of ”I’m not sure”

    Janne Fauskanger and Reidar Mosvold

    Abstract

    The mathematical knowledge for teaching (MKT) measures have been widely adopted by researchers in several countries. This article reports on a study on the connection between teachers’ responses to multiple-choice MKT items, and in particular where they select the suggested solution ”I’m not sure”, and their written responses to corresponding open-ended questions (long responses). The findings from our analysis of 15 teachers’ responses indicate that their long responses and their multiple-choice responses do not always correspond. Some teachers who selected ”I’m not sure” showed uncertainty also in their long responses, whereas other teachers revealed instrumental and even relational understanding of the content.

    Janne Fauskanger

    Janne Fauskanger is Assistant Professor in mathematics education at the University of Stavanger, Norway. Her main interest is related to primary school teachers’ mathematical knowledge for teaching and their practice.

    Reidar Mosvold

    Reidar Mosvold is Associate Professor in mathematics education at the University of Stavanger, Norway. His interests are related to teachers’ beliefs and knowledge of mathematics, and their influence on practice.

    Skapad: 2014-10-22 kl. 01:00

  40. NOMAD 19(3-4), 2014

    Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study

    Hege Kaarstein

    Abstract

    This paper presents how Norwegian teachers and educational researchers categorized a collection of items used in the international TEDS-M study. The teachers categorized the items according to their own prototype understanding of mathematical content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK), while the researchers categorised them after discussing how to understand MCK and MPCK and agreeing on what categorisation criteria to use. The results show that the item categorisation depended on the item characteristics. For example, multiple-choice items were associated with MCK and items asking the respondents to rewrite or reword a mathematical task were associated with MPCK. Furthermore, the results indicate a common Norwegian understanding of MPCK as the teachers’ and researchers’ categorisation largely coincided.

    Hege Kaarstein

    Hege Kaarstein was a member of the Norwegian TEDS-M group and she is currently working as a researcher for the Norwegian TIMSS 2015 group at the Department of Teacher Education and School Research, University of Oslo. The focus of her research is measurement of mathematical knowledge for teaching.

    Skapad: 2014-10-22 kl. 01:00

  41. NOMAD 19(3-4), 2014

    When does a variable vary? Identifying mathematical content knowledge for teaching variables

    Cecilia Kilhamn

    Abstract

    In what sense is x in the expression x + 2 a variable? What do teachers need to know about variables in order to create optimal learning conditions for students? The aim of this study is to understand the mathematical issues and demands of teaching the concept of variables, to outline a body of Specialized content knowledge for teaching (SCK). Data from two lessons in two Swedish grade 6 classrooms, with complimentary focus group interviews, were analysed using the Mathematical knowledge for teaching framework. Findings suggest some aspects of SCK to be an awareness of the different roles of the algebraic letter x in the expression x + 3, the equation x + 3 = 8 and the formula x + 3 = y, an appropriate use of the terms unknown and variable, and the importance of mathematical contexts for expressions.

    Cecilia Kilhamn

    Cecilia Kilhamn is a teacher and a senior lecturer in Mathematics Education in the Faculty of Education at Gothenburg University.

    Skapad: 2014-10-22 kl. 01:00

  42. NOMAD 19(3-4), 2014

    Matematisk kvalitet i undervisning

    Frode Opsvik og Leif Bjørn Skorpen

    Sammanfattning

    Vi vil i denne artikkelen studere kvalitetar ved matematikkundervisning. Dette gjer vi ved å ta i bruk omgrepet Matematisk kvalitet i undervisning (MKU) som byggjer på Mathematical quality of instruction (MQI) og eit tilhøyrande observasjons- go analyseinstrument som er utvikla av ei forskargruppe i USA. Vi vil arbeide med følgjande forskingsspørsmål: Korleis kan ein tilpasse og utvikle omgrepet MKU med tilhøyrande omgrepsapparat til bruk i rettleiingssituasjonar? På kva måtar kan ein bruke MKUindikatorane som ein reiskap til å fokusere på ulike kvalitetar ved det matematikkfaglege innhaldet i undervisninga? Analyseinstrumentet (MQI) er opphavleg etablert for å gje eit kvantitativt mål på den matematiske kvaliteten i ein lærar si undervisning, basert på videoopptak av undervisninga. I rettleiingssituasjonar har vi bruk for å fokusere på kvalitative sider ved undervisninga. Artikkelen viser korleis vi har tilpassa analyseinstrumentet til kvalitativ bruk. Døme på bruk av omgrepsapparatet er henta frå eige videomateriale innsamla i prosjektet ”Kvalitet i opplæringa” ved Høgskulen i Volda. MKU-omgrepsapparatet vil etter vårt syn vere nyttig ved til dømes observasjon og rettleiing av lærarstudentar i praksis.

    Abstract

    In this article we show how mathematics instruction can be studied by applying a modified version of the concept Mathematical quality of instruction (MQI), and its related observation and analysis instrument, developed by a U.S. research team. Our research questions are: How can we adapt and develop the concept of MQI and its associated structure of concepts for use in tutoring situations? And how can we use the adapted MQI-indicators as a tool to focus on various mathematical qualities in mathematics instruction. The MQI instrument was originally developed for making quantitative studies based on videotapes of mathematics lessons. We have translated and adapted the key concepts of this instrument to Norwegian, and show how these can be used in qualitative analyses of mathematics instruction. Examples of this usage are taken from our own video material collected in the project ”Kvalitet i opplæringa” (Quality in education) financed by The Research Council of Norway and Volda University College. Our adapted instrument is, in our opinion, useful when observing and tutoring student teachers.

    Frode Opsvik

    Frode Opsvik er høgskulelektor i matematikk og har undervist i lærarutdanningane ved Høgskulen i Volda sidan 1998. Forskingsinteressa hans er klasseromsstudier av matematikkundervisning som grunnlag for kvalifisering av lærarar.

    Leif Bjørn Skorpen

    Leif Bjørn Skorpen er førstelektor i matematikk og har undervist ved lærarutdanningane ved Høgskulen i Volda sidan 1992. Hans interesser er i hovudsak knytt til klasseromsforsking, matematikkvanskar og matematikk i tverrfaglege samanhengar, spesielt matematikk og musikk.

    Skapad: 2014-10-22 kl. 01:00

  43. NOMAD 19(3-4), 2014

    Aspects of a teacher’s mathematical knowledge in his orchestration of a discussion about rational numbers

    Bodil Kleve and Ida Heiberg Solem

    Abstract

    In this article we discuss how aspects of a mathematics teacher’s knowledge surfaced in a whole class discussion about decimal numbers, percentages and fractions. Our focus is the teacher’s orchestration of the discussion in order to unpack the mathematical content for the students. His interactive teaching which included questioning and probing students’ contributions in order to make the students take part in the discussion, were important features of this lesson. A range of aspects of the teacher’s mathematical knowledge was revealed in studying the teacher’s pedagogical moves, and we suggest that the interplay between the aspects of his knowledge was crucial in this lesson.

    Bodil Kleve

    Bodil Kleve is associate professor at Oslo and Akershus University College of Applied Sciences. She was a teacher in school for many years before she started working with mathematics teacher education in 1994. Through classroom research, Kleve has investigated teachers’ implementations of a curriculum reform and teachers’ mathematical knowledge in and for teaching. Related to the research program Utdanning 2020, financed by the Norwegian Research Council, Kleve took part in the large research project, The Didactic Challenge of New Literacies in School and Teacher Education. Kleve has many national and international publications.

    Ida Heiberg Solem

    Ida Heiberg Solem is associate professor at Oslo and Akershus University College of Applied Science. She was a teacher in upper secondary school and a school leader before she started working with mathematics teacher education in 1993. In her work as a teacher educator, she is involved with in service training of teachers, and she has written several textbooks for teacher education. Her research interest is mainly communication in the mathematics classroom.

    Skapad: 2014-10-22 kl. 01:00

  44. NOMAD 19(3-4), 2014

    Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task

    Arne Jakobsen, C. Miguel Ribeiro and Maria Mellone

    Abstract

    This paper focuses on Norwegian prospective primary teachers’ mathematical knowledge for teaching (MKT) when interpreting and making sense of pupils’ answers. We named such knowledge interpretative knowledge and we consider it to be linked with common content knowledge and specialized content knowledge. In order to deepen these links and to access and develop such knowledge in prospective teachers, we designed a suitable set of tasks on a problem concerning fractions in order to investigate this particular kind of knowledge and clarify its features and dimensions. The results reveal the importance of developing such types of knowledge as a basis for teachers to effectively make sense and interpret pupils’ productions and to make it possible to provide effective and meaningful feedback.

    Arne Jakobsen

    Arne Jakobsen is Associate Professor of Mathematics at the University of Stavanger, Norway. He has experience from many international research projects in Mathematics Education, and is currently leader of the project: Improving quality and capacity of mathematics teacher education in Malawi. His interests are mathematics, mathematical knowledge for teaching, and quantitative studies in mathematics education.

    C. Miguel Ribeiro

    C. Miguel Ribeiro is Associate Professor of Mathematics Education at the University of Algarve, Portugal and in the present year he has a postdoc position at São Paulo State University (UNESP-Rio Claro), Brazil. His main interests are teachers’ specialized knowledge for teaching, students’ knowledge and reasoning and the role of representations in and for learning.

    Maria Mellone

    Maria Mellone is researcher in Mathematics Education at Dipartimento di Matematica e Applicazioni ”R. Caccioppoli”, University Federico II of Naples, Italy. Her main research interests are the development of arithmetic and algebra in young children, semiotic mediation and mathematics teacher education.

    Skapad: 2014-10-22 kl. 01:00

  45. NOMAD 19(3-4), 2014

    Knowledge used when orchestrating mathematical discourses – doing, guiding and requesting

    Ove Gunnar Drageset

    Abstract

    There is a need to understand more about which types of knowledge teachers use when orchestrating mathematical discourses. This article combines models for mathematical knowledge for teaching with a recent framework that describes the actions that teachers typically use during classroom discourses in mathematics. By looking into what knowledge each action demands from the teacher, three areas related to mathematical knowledge for teaching are described: doing, guiding and requesting. Doing describes different ways the teachers are doing the mathematical work themselves. Guiding describes how the teachers help, while leaving most of the work to the students. Requesting describes different ways teachers asked the students to explain or contribute to the discourse.

    Ove Gunnar Drageset

    Ove Gunnar Drageset has a PhD in Mathematics Education from the University of Oslo (2013) and is currently working as associate professor at UiT ( The Arctic University of Norway) and as a program leader for master of teacher education for grades 5 to 10. The main research interests are communication in the classroom, mathematical knowledge for teaching, and teaching and learning of numbers and operations at grades 1 to 10.

    Skapad: 2014-10-22 kl. 01:00

  46. NOMAD 19(3-4), 2014

    Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teaching

    Bjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark

    Abstract

    This article discusses how the inclusion of history of mathematics in mathematics education draws heavily on a teacher’s mathematical knowledge for teaching, in particular horizon content knowledge, in the context of curricular changes. We discuss the role of history of mathematics in school curricula, its inclusion in textbooks and its consequences for the mathematical knowledge needed for teaching. We address the matter from three national settings (Denmark, Norway and the United States). These settings exemplify how, in particular, teachers’ horizon content knowledge needs to be broader than what is necessary for only the current curriculum.

    Bjørn Smestad

    Bjørn Smestad is an associate professor of mathematics education at Oslo and Akershus University College of Applied Sciences, Department of Primary and Secondary Teacher Education. His main research interests are the role of history of mathematics in teaching and teacher education, ICT in teaching mathematics and school placement as part of teacher education.

    Uffe Thomas Jankvist

    Uffe Thomas Jankvist is an associate professor of mathematics education at Aarhus University, Department of Education, Campus Emdrup, Denmark. His research interests include the use of history of mathematics, applications of mathematics, and philosophy of mathematics in mathematics education, both from a theoretical and an empirical point of view, including also students’ beliefs about and images of mathematics as a (scientific) discipline, as well as interdisciplinary teaching and learning. Also, he is involved in educating Danish ”maths counsellors” for upper secondary school at Roskilde University.

    Kathleen Clark

    Kathleen Clark is an associate professor in the College of Education at Florida State University. Her primary research interests lie in two fields, mathematics education and history of mathematics. In the former, her research investigates ways in which prospective and in-service mathematics teachers use history of mathematics in teaching and the ways in which the study of history of mathematics impacts mathematical knowledge for teaching. In the latter, her historical research is focused on 17th and 18th century mathematics, with a particular emphasis on the early development of logarithms.

    Skapad: 2014-10-22 kl. 01:00

  47. NOMAD 19(3-4), 2014

    The teaching of mathematical knowledge for teaching – a learning study of primary school teacher education

    Jorryt van Bommel

    Abstract

    A group of Swedish teacher educators conducted a learning study in order to identify critical features concerning the teaching and learning of Mathematical knowledge for teaching (MKT). Three seminars and 300 tests were analysed using variation theory revealing four critical features to take into account in teaching student teachers in mathematics education: namely their need to i) formulate proper goals for a lesson, ii) outline the lesson plan in detail, iii) shift perspective from the role of being a teacher to being a mathematics teacher, and iv) understand the underlying mathematics of the lesson topic at hand. Thus, these are the four features of importance to the learning and teaching of MKT.

    Jorryt van Bommel

    Jorryt van Bommel is a lecturer at Karlstad University and works mainly with in-service and pre-service teacher training. Her research interests concern mathematics teacher training and professional development of mathematics teachers.

    Skapad: 2014-10-22 kl. 01:00

  48. NOMAD 19(2), 2014

    View of mathematics – an investigation of Estonian university students

    Indrek Kaldo

    Abstract

    This study reports on first-year Estonian university students’ view of mathematics. The data was collected from 970 university students of different disciplines. The participants filled out a Likert-type questionnaire that was developed using previously published instruments. This paper documents and analyses the data from the study. In this study students agreed that mathematics is an important and valuable subject. Female students have a more positive view of mathematics than male students. Science students have a more positive view of mathematics than non-science students.

    Indrek Kaldo

    Indrek Kaldo is a PhD student in mathematics education at the Institute of Educational Sciences, Tallinn University. His research interests are students’ beliefs, attitudes and motivation towards the teaching and learning of mathematics, particularly at the university level. He has also 14 years experiences as lecturer in mathematics at university level.

    Skapad: 2014-06-25 kl. 01:00

  49. NOMAD – 19(2), 2014


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 19, No 2, June 2014

    Editorial

    Indrek Kaldo

    View of mathematics – an investigation of Estonian university students

    [PDF]

    Eugenia Koleza

    Students’ conceptions about the formula for a rectangle’s area and some similarities to its historical context

    [PDF]

    Andreas Lorange and Reinert A. Rinvold

    Students’ strategies of expanding fractions to a common denominator – a semiotic perspective

    [PDF]

    Kristina Juter and Jan-Fredrik Olsen

    ”Just-in-time teaching” in undergraduate mathematics

    [PDF]

    Innehåll: JH

    Skapad: 2014-06-25 kl. 01:00

  50. NOMAD 19(2), 2014

    Students’ conceptions about the formula for a rectangle’s area and some similarities to its historical context

    Eugenia Koleza

    Abstract

    In this paper, we focus on a debate between grade 6 students about the formula for a rectangle’s area, emerging during a 2-hours teaching, and raising questions about the possibility of using history in order to design a hypothetical learning/teaching trajectory of rectangle’s area, and we analyse students’ conceptions/misconceptions in relation to the historical context of area measurement.

    Eugenia Koleza

    Eugenia Koleza is Professor of Mathematics Education at the Department of Primary Education, University of Patras, Greece. She is member of the International Scientific Committee of the International Journal for Mathematics in Education and of the Editorial Board of the journal Mathematical Review. She is one of the Editors of the journal Critical Science & Education and Vice-President of the Hellenic Society of History, Philosophy and Didactics of the Sciences.

    Skapad: 2014-06-25 kl. 01:00

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