Volumes/articles older than two years are open access except editorials which always are open access.

NOMAD – 21(4), 2016
Nummer/Issue
Volume 21, No 4, December 2016
Tamsin Meaney
Locating learning of toddlers in the individual/society and mind/body dividesJulie Sarama, Douglas H. Clements, Christopher B. Wolfe and Mary Elaine Spitler
Professional development in early mathematics: effects of an intervention based on learning trajectories on teachers’ practicesElin Reikerås
Central skills in toddlers’ and preschoolers’ mathematical development, observed in play and everyday activitiesPerEinar Sæbbe and Reidar Mosvold
Initiating a conceptualization of the professional work of teaching mathematics in kindergarten in terms of discourseJorryt van Bommel and Hanna Palmér
Young children exploring probability – with focus on their documentationsCamilla Björklund and Wolmet Barendregt
Teachers’ pedagogical mathematical awareness in diverse childagegroupsTrude Fosse
What characterises mathematical conversations in a Norwegian kindergarten?Ola Helenius, Maria L. Johansson, Troels Lange, Tamsin Meaney and Anna Wernberg
Measuring temperature within the didaktic space of preschoolHanna Palmér and Camilla Björklund
Different perspectives on possible – desirable – plausible mathematics learning in preschoolInnehåll: JH
Skapad: 20161212 kl. 00:00

NOMAD
Central skills in toddlers’ and preschoolers’ mathematical development, observed in play and everyday activities
Elin Reikerås
Abstract
In good mathematical development, it is important to master some central skills at the kindergarten age. Being aware of such skills for each child is useful for facilitating children’s learning and development. The present study examines how kindergarten children master central mathematical skills in toddler age and preschool age. The staff in kindergartens collected data by using structured observation on the basis of observational material The Mathematics, the Individual and the Environments (MIO). The areas examined were Mathematical language, Logical reasoning, Shape and space, Pattern and order, Counting and series of numbers and Enumeration. The children were observed in play and everyday activities in kindergarten in two threemonth periods when they were 2½ years of age (toddlers, n = 1003) and two year later when they were 4 ½ (preschoolers, n = 744). The results show a large dispersion in the children’s skills as toddlers, but as preschoolers, most of the children have a high level of mastery. The percentage of mastery at each of the observation times is reported and discussed in light of earlier findings. In our study, the children had slower development in the numerical area than was found in other research. Reflections about how the Norwegian kindergarten tradition and the method used to collect the data influence the results are included.
Elin Reikerås
Elin Reikerås is associate professor in special needs education at the National centre for reading education and research, University of Stavanger, Norway. Her research interests are on children’s early mathematical development, the relations between early mathematics and other development areas as language, motorlife skills and social skills as well as the relations between arithmetics and reading.
Skapad: 20161212 kl. 00:00

NOMAD
Initiating a conceptualization of the professional work of teaching mathematics in kindergarten in terms of discourse
PerEinar Sæbbe and Reidar Mosvold
Abstract
This study investigates a Norwegian kindergarten teacher’s work of teaching mathematics in an everyday activity involving play with LegoTM bricks. Analysis of the kinder garten teacher’s discourse identifies questioning and affirmation as two core components. We suggest that these are core discursive practices in the work of teaching mathematics in kindergarten. In identifying these practices, a theory of thinking as communicating is applied to investigate what makes these discursive acts of teaching mathematical. Further research is called for to continue investigating kindergarten teachers’ discursive practices in teaching and to continue the efforts to conceptualize the work of teaching mathematics in kindergarten in terms of discourse.
PerEinar Sæbbe
PerEinar Sæbbe is PhD candidate in Educational Science, Department of Early Childhood Education, University of Stavanger, Norway. His research interests are questions related to kindergarten children’s learnings of mathematics, kindergarten teachers ́ professional knowledge in mathematics and general pedagogy in early childhood education and care.
Reidar Mosvold
Reidar Mosvold is Associate Professor of mathematics education at the University of Stavanger, Norway. His research interests are related to the mathematical knowledge required to carry out the work of teaching mathematics at all levels, teacher beliefs, teacher identity and discursive perspectives, as well as use of history of mathematics in mathematics education.
Skapad: 20161212 kl. 00:00

NOMAD
Young children exploring probability – with focus on their documentations
Jorryt van Bommel and Hanna Palmér
Abstract
This article reports on an intervention where possibilities and limitations with problemsolving as a basis for mathematics education in preschool class were studied. In the article we explore how 50 children use nonguided documentation when working with a problemsolving task about probability. The results show that the task was possible to work with for these young children, and in the followup interviews many of the children seemed familiar with the mathematical concepts used, as well as with a relevant sample space. The children’s nonguided documentation showed a diver sity of strategies and contributed positively to their exploration of probability, both during the lesson and in the final discussions.
Jorryt van Bommel
Jorryt van Bommel is Senior lecturer in Mathematics education at Karlstad University. Her research is focused on teacher’s and student teacher’s professional development, as well as mathematics teaching and learning in preschool class, primary and secondary school. Ongoing research is focused on mathematics teacher’s collective work on social media and problem solving in preschool class with a special interest in the role of digital technology.
Hanna Palmér
Hanna Palmér is Senior lecturer in Mathematics education at Linnaeus University. Her research is focused on primary school teacher’s professional identity development, as well as mathematics teaching and learning in preschool, preschool class and primary school. Ongoing research is focused on problem solving, entrepreneurial teaching and learning in mathematics and young children’s learning of mathematics through digital technology.
Skapad: 20161212 kl. 00:00

NOMAD
Teachers’ pedagogical mathematical awareness in diverse childagegroups
Camilla Björklund and Wolmet Barendregt
Abstract
In this study we investigate preschool teachers’ attention to number sense, number sequence, geometrical shapes and patterns, and their pedagogical awareness regarding these areas in their work with younger and older preschool children. The specific research questions are: Are there differences in teachers’ attention to the different mathematical content areas depending on the age group they are teaching? And if mathematical content areas show differences between age groups, what pedagogical awareness levels constitute these differences? The study shows that the frequency of working with mathematical content is higher for all areas regarding older children, but teachers’ choice of mathematical content area is not necessarily depending on the age of the children. Teachers’ frequency of observing and engaging children in mathematics is lower among those working with younger children but the difference is in general quite small. Significant and substantial differences appear in teachers’ attention to children’s mathematizing initiatives and problematizing number sequences, geometrical shapes and patterns.
Camilla Björklund
Camilla Björklund is Associate Professor in Education at the University of Gothenburg. She is involved in preschool teacher education and researches young children’s mathematical learning and the teaching of mathematics in preschool.
Wolmet Barendregt
Wolmet Barendregt is Associate Professor in Interaction Design at the University of Gothenburg. She is involved in teacher education and researches young children’s use of mathematics games as well as other learning technologies.
Skapad: 20161212 kl. 00:00

NOMAD
What characterises mathematical conversations in a Norwegian kindergarten?
Trude Fosse
Abstract
This paper presents a study of young children’s mathematical conversations in a Norwegian kindergarten and provides examples to illustrate some of their characteristics. Using points made in previous research about conversations and mathematics, an analysis of an interaction involving a group of children who are putting a toy together exemplifies what can and what cannot be considered a mathematical conversation. For a conversation to be considered mathematical, it is suggested that it must include not only references to mathematics, but also specific structural elements in the conversation, as well as valuing participants’ contributions and encouraging participants to reflect on the mathematical theme, thereby promoting learning.
Trude Fosse
Trude Fosse is assistant professor at the University of Bergen. Her research interests concern beginners education in mathematics, with a particular interest in mathematical conversations and how mathematics is handled in kindergartens and primary schools. Another interest concerns how the mathematics in teacher education programs can support students’ learning and teaching practices.
Skapad: 20161212 kl. 00:00

NOMAD
Measuring temperature within the didaktic space of preschool
Ola Helenius, Maria L. Johansson, Troels Lange, Tamsin Meaney and Anna Wernberg
Abstract
The informal character of preschool mathematics, engaged in during children’s play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the ”didaktic space”, is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher’s contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.
Ola Helenius
Ola Helenius has PhD in mathematics and is a researcher and deputy director at the National Center for Mathematics Education, University of Gothenburg. Some of his current research interests include neuroscience perspectives on learning mathematics and mathematics curriculum design research. Another interest is sociocultural perspectives on preschool mathematics and he is a member of the research group Young children’s mathematics.
Maria L. Johansson
Maria L. Johansson has a PhD in mathematics and one in mathematics education. Her PhD in mathematics education focused on issues related to mathematics in preschool, particularly to professional development of preschool teachers and childcare workers. She is an associate professor at Luleå University where she works in teacher education. Her research interests are wide ranging, covering both mathematics and mathematics education for a range of ages. She has also published extensively with the research group, Young children’s mathematics.
Troels Lange
Troels Lange has been a mathematics teacher educator for twenty years, first in Denmark, then Australia and Sweden. He currently works at Bergen University College in Norway and in 2016 became Professor in mathematics education. His research interests centre on how children experience learning mathematics, but he has published on a range of different issues regarding mathematics education. Since 2011, he is part of and publishes with the research group Young children’s mathematics.
Tamsin Meaney
Tamsin Meaney is professor of mathematics education at Bergen University College, having previously been professor at Malmö University. She has worked in teacher education in New Zealand, Australia, Sweden and Norway. Her research interests are varied but centre around the need for mathematics education to support social justice concerns. Whilst in Sweden she started the research group, Young children’s mathematics, with researchers from Norway, Sweden and USA.
Anna Wernberg
Anna Wernberg is associate professor in mathematics teacher education in the Faculty of Education and Society, Malmö University. She has previously worked at Kristianstad University and Borås University, also in Sweden. Her research interests focus on the use of Learning studies in mathematics classrooms for young children. She has also published extensively with other members of the research group Young children’s mathematics.
Skapad: 20161212 kl. 00:00

NOMAD
Different perspectives on possible – desirable – plausible mathematics learning in preschool
Hanna Palmér and Camilla Björklund
Abstract
This article addresses the question of what is considered possible – desirable – plausible in preschool mathematics. On the one hand, there is a growing consensus that preschool mathematics matters, on the other hand, there are different opinions about how it should be designed and what constitutes an appropriate content. In the article we provide an overview of similarities and differences found in eight articles published in a thematic issue of Nomad on preschool mathematics. The overview is based on Bernstein’s notions vertical and horizontal discourses, and how content for learning is described as basic or advanced mathematics. The aim is not to evaluate or rate the articles but to illustrate diversity regarding possible – desirable – plausible in current research of preschool mathematics.
Hanna Palmér
Hanna Palmér is senior lecturer in Mathematics Education at Linnaeus University in Växjö. Her research is focused on mathematics teaching and learning in preschool, preschool class and primary school.
Camilla Björklund
Camilla Björklund is Associate Professor in Education at the University of Gothenburg. She is involved in preschool teacher education and researches young children’s mathematical learning and the teaching of mathematics in preschool.
Skapad: 20161212 kl. 00:00

NOMAD
Mathematics teachers’ knowledgesharing on the Internet: pedagogical message in instruction materials
Yvonne Liljekvist
Abstract
This article reports on a study of teachershared documents containing matematical tasks published on the Internet. The aim was to identify the goals, metods and pedagogical justifications presented in the documents and what was needed to solve the tasks. Content analysis was used to define their pedagogical message. The results show that the documents mainly involve content goals for younger pupils that are not consistent with the explicit descriptions. The conceptual goals are communicated to a great extent, but are not supported by task features. The reasons for why the tasks given are expected to lead to a certain goal are very often implicit, and, as a result, the content of the documents and the quality of the tasks are somewhat unclear to other teachers.
Yvonne Liljekvist
Yvonne Liljekvist is senior lecturer in mathematics education at the Department of Mathematics and Computer Science at Karlstad University, Sweden. One of her research interests is mathematics teachers’ use of Internet to improve their own teaching and to support colleagues. Liljekvist and her colleagues have an ongoing research project in this area that examines how teachers use social network sites to develop their pedagogical content knowledge.
Skapad: 20160922 kl. 01:00

NOMAD
Attitudes towards mathematics as a subject, and mathematics learning and instruction in a transdisciplinary engineering study
Evangelia Triantafyllou, Morten Misfeldt and Olga Timcenko
Abstract
This article explores student attitudes and preferences in learning and teaching of mathematics in engineering studies that transcend the division between technical, scientific and artistic disciplines. For observing such attitudes, we have developed a model that relates the attitude towards mathematics as a subject with the attitude towards mathematics learning and instruction. Data comes from a study at the Media technology educational program of Aalborg university. The study used attitude and preference questionnaires, and observations and interviews with students. The results show that media technology students are not confident in mathematics and consider mathematics to be a difficult subject. Nevertheless, they recognize the importance of mathematics both in their studies and in general. Moreover, students favour learning on their own or together with their peers over learning supported by a teacher. We propose that these findings inspire reforming mathematical education for such engineering students.
AppendixEvangelia Triantafyllou
Evangelia Triantafyllou has a M.A. degree in Electrical and computer engineering and a professional doctorate in Engineering design. She received her Ph.D. on ICTbased teaching methods for improving university mathematics learning at Aalborg University in 2015. In February 2016, Evangelia was appointed as a postdoc fellow in the department of Media technology at Aalborg University, Copenhagen. Her research interests include technologyenhanced learning in mathematics, active learning and university mathematics education.
Morten Misfeldt
Morten Misfeldt is professor and research manager of the research lab for ICT and design for learning, Aalborg University in Copenhagen. His research interests includes technology enhanced learning, university mathematics education, the use of ICT in primary level mathematics education, the influence of ICT on mathematics curriculum and mathematical practices in various areas of society. Morten is also research manager of the Danish GeoGebra Institute.
Olga Timcenko
Olga Timcenko is associate professor at the department of Media technology at Aalborg University. She holds a PhD in Robot control and her research interests concern virtual environments and user interfaces for educational purposes, and technology enhanced teaching and learning, especially of mathematics at university level. She is a member of the Research center for creative and immersive learning environments at Aalborg University.
Skapad: 20160922 kl. 01:00

NOMAD
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 cooccurrences 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: 20160922 kl. 01:00

NOMAD
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 practicebased 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: 20160922 kl. 01:00

NOMAD – 21(3), 2016
Nummer/Issue
Volume 21, No 3, September 2016
Yvonne Liljekvist
Mathematics teachers’ knowledgesharing on the Internet: pedagogical message in instruction materialsEvangelia Triantafyllou, Morten Misfeldt and Olga Timcenko
Attitudes towards mathematics as a subject, and mathematics learning and instruction in a transdisciplinary engineering studyAnneli Dyrvold
The role of semiotic resources when reading and solving mathematics tasksJanne Fauskanger og Reidar Mosvold
Lærerarbeidets matematiske undervisningsoppgaverShipra Sacheva, Marit Hvalsøe Schou and Andreas Lindenskov Tamborg
Reflections on having participated at the PreNORMA workshopInnehåll: JH
Skapad: 20160922 kl. 01:00

NOMAD – 21(2), 2016
Nummer/Issue
Volume 21, No 2, June 2016
Florenda Gallos Cronberg
Learning linear relationships through independent use of the mathematics textbookNonmanut Pongsakdi, Teija Laine, Koen Veermans, Minna M. HannulaSormunen and Erno Lehtinen
Improving word problem performance in elementary school students by enriching word problems used in mathematics teachingIda Bergvall, Jenny Wiksten Folkeryd and Caroline Liberg
Linguistic features and their function in different mathematical content areas in TIMSS 2011Kerstin Larsson
Finding Erik and Alva: uncovering students who reason additively when multiplyingBarbro Grevholm
Bokanmälan:
Fra snublesten til byggesten. Matematikdidaktiske mulighederThematic issue of Nomad – call for papers
Innehåll: JH
Skapad: 20160609 kl. 01:00

NOMAD
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 wellknown 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: 20160609 kl. 01:00

NOMAD
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’ textmaking in different subject areas in early school years.
Skapad: 20160609 kl. 01:00

NOMAD
Improving word problem performance in elementary school students by enriching word problems used in mathematics teaching
Nonmanut Pongsakdi, Teija Laine, Koen Veermans, Minna M. HannulaSormunen 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 selfcreated word problems to improve student mathematical modeling and problem solving skills. Participants included 170 fourth, and sixthgraders 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 nonroutine 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 preservice and inservice 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. HannulaSormunen
Minna M. HannulaSormunen 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: 20160609 kl. 01:00

NOMAD
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 setup 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: 20160609 kl. 01:00

NOMAD
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: 20160225 kl. 00:00

NOMAD
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: 20160225 kl. 00:00

NOMAD
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: 20160225 kl. 00:00

NOMAD – 21(1), 2016
Nummer/Issue
Volume 21, No 1, March 2016
Elisabeth Rystedt, Cecilia Kilhamn and Ola Helenius
What’s there in an n? Investigating contextual resources in small group discussions concerning an algebraic expressionIngvald Erfjord
Mathematics teachers’ initial implementation of a digital tool packageAnette Bagger
Pressure at stake: Swedish third graders’ talk about national tests in mathematicsJohan Prytz and Martin Karlberg
Nordic school mathematics revisited – on the introduction and functionality of New MathNews from Nordic mathematics education
Innehåll: JH
Skapad: 20160225 kl. 00:00

NOMAD
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 smallcase study combines a content related and a dialogical approach, in an indepth analysis of how three 12yearold 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, sociocultural perspectives on preschool mathematics and mathematics curriculum design research.
Skapad: 20151202 kl. 00:00

NOMAD
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: 20151202 kl. 00:00

NOMAD – 20(34), 2015
Nummer/Issue
Volume 20, No 34, November 2015
Kristín Bjarnadóttir
Tölur og mengi – Numbers and sets. A New Math textbook in Iceland in the 1960sAndreas Christiansen
An analysis of two 19th century Norwegian geometry books, and the reactions they causedMarc van Zanten and Marja van den HeuvelPanhuizen
Past and current approaches to decimal numbers in Dutch primary school mathematics textbooksTom Rune Kongelf
Introduksjon av algebra i matematikkbøker for ungdomstrinnet i NorgeRannveig Halldórsdóttir
Comparison of three textbooks published for 8th grade in IcelandMadis Lepik, Barbro Grevholm and Antti Viholainen
Using textbooks in the mathematics classroom – the teachers’ viewAntti Viholainen, Miia Partanen, Jani Piiroinen, Mervi Asikainen and Pekka E. Hirvonen
The role of textbooks in Finnish upper secondary school mathematics: theory, examples and exercisesLinda Ahl, Guðný Helga Gunnarsdóttir, Tuula Koljonen and Guðbjörg Pálsdóttir
How teachers interact and use teacher guides in mathematics – cases from Sweden and IcelandIngvild Lambert Grave and Birgit Pepin
Teachers’ use of resources in and for mathematics teachingRagnhild Johanne Rensaa and Barbro Grevholm
A textbook in linear algebra – the use and views of engineering students
Sebastian Rezat and Rudolf Sträßer
Methodological issues and challenges in research on mathematics textbooksInnehåll: JH
Skapad: 20151202 kl. 00:00

NOMAD
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: 20151202 kl. 00:00

NOMAD
Past and current approaches to decimal numbers in Dutch primary school mathematics textbooks
Marc van Zanten and Marja van den HeuvelPanhuizen
Abstract
In the Netherlands, most contemporary textbook series for primary school mathematics education are influenced by the socalled 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 RMEoriented textbook series and two preRME 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 RMEoriented 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 HeuvelPanhuizen
Marja van den HeuvelPanhuizen 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: 20151202 kl. 00:00

NOMAD
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: 20151202 kl. 00:00

NOMAD
Using textbooks in the mathematics classroom – the teachers’ view
Madis Lepik, Barbro Grevholm and Antti Viholainen
Abstract
Mathematics teachers’ selfreported 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: 20151202 kl. 00:00

NOMAD
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. Seventyone 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 inservice 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 researchbased development work of physics and mathematics teacher education.
Skapad: 20151202 kl. 00:00

NOMAD
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: 20151202 kl. 00:00

NOMAD
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 individual 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 SørTrøndelag (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 SørTrøndelag 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: 20151202 kl. 00:00

NOMAD
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: 20151202 kl. 00:00

NOMAD
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 – wellestablished 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: 20151202 kl. 00:00

NOMAD
School mathematical practices as experiences of identity work: the learning journeys of three students
AnnSofi RöjLindberg
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 semistructured 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.
AnnSofi RöjLindberg
AnnSofi RöjLindberg 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: 20150622 kl. 01:00

NOMAD
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 crossdisciplinary: inclusive education, special education, didactics (general and subjectrelated 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: 20150622 kl. 01:00

NOMAD
Conceptualising a university teaching practice in an activity theory perspective
Stephanie TreffertThomas
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: activitymotive, actionsgoals and operationsconditions. 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 TreffertThomas
Stephanie TreffertThomas 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 sociocultural approaches to teaching and learning mathematics beyond compulsory schooling.
Skapad: 20150622 kl. 01:00

NOMAD
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 indepth 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: 20150622 kl. 01:00

NOMAD – 20(2), 2015
Nummer/Issue
Volume 20, No 2, June 2015
AnnSofi RöjLindberg
School mathematical practices as experiences of identity work: the learning journeys of three students.Maria Christina Secher Schmidt
Sociofaglig inklusion og elevfællesskaber. Til didaktiseringen af kammerathjælp i matematikundervisning på folkeskolens begyndertrin.Stephanie TreffertThomas
Conceptualising a university teaching practice in an activity theory perspectiveJanne Fauskanger and Reidar Mosvold
En metodisk studie av innholdsanalyse – med analyser av matematikklæreres undervisningskunnskap som eksempelMario Sánchez Aguilar
Where’s the ”math” in ”mathematics education”? Review of ”Mathematics and mathematicseducation: searching for common ground”Mette Andresen
News from Nordic mathematics educationInnehåll: JH
Skapad: 20150622 kl. 01:00

NOMAD
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 preservice 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: 20150304 kl. 00:00

NOMAD
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 tenyearold pupils. Data were collected over a period of three years (2010–2012) by video recording test situations in different classrooms and by conducting videostimulated 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: 20150304 kl. 00:00

NOMAD
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: 20150304 kl. 00:00

NOMAD
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 practicerelated, 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 reformoriented 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: 20150304 kl. 00:00

NOMAD
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.noSkapad: 20150304 kl. 00:00

NOMAD – 20(1), 2015
Nummer/Issue
Volume 20, No 1, March 2015
Anneli Dyrvold, Ewa Bergqvist and Magnus Österholm
Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequencyAndreas Ebbelind and Cecilia Segerby
Systemic functional linguistics as a methodological tool in mathematics education researchGunnar Sjöberg, Eva Silfver and Anette Bagger
Disciplined by testsCharlotte Krog Skott og Camilla Hellsten Østergaard
Lektionsstudier i dansk læreruddannelseMette Andresen
Message from the Chair of the NoRME boardMario Sánchez Aguilar
Where’s the ”math” in ”mathematics education”? Review of ”Mathematics and mathematicseducation: searching for common ground”Due to unfortunate circumstances the book review will be published in print in no. 2 this volume
Innehåll: JH
Skapad: 20150304 kl. 00:00

NOMAD – 19(34), 2014
Nummer/Issue
Volume 19, No 34, October 2014
Mark Hoover, Reidar Mosvold and Janne Fauskanger
Common tasks of teaching as a resource for measuring professional content knowledge internationallyBjörg Jóhannsdóttir and Berglind Gísladóttir
Exploring the mathematical knowledge of prospective elementary teachers in Iceland using the MKT measuresJanne Fauskanger and Reidar Mosvold
Studying teachers’ knowledge by the use of multiplechoice items: the case of ”I’m not sure”Hege Kaarstein
Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDSM studyCecilia Kilhamn
When does a variable vary? Identifying mathematical content knowledge for teaching variablesFrode Opsvik og Leif Bjørn Skorpen
Matematisk kvalitet i undervisningBodil Kleve and Ida Heiberg Solem
Aspects of a teacher’s mathematical knowledge in his orchestration of a discussion about rational numbersArne Jakobsen, C. Miguel Ribeiro and Maria Mellone
Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction taskOve Gunnar Drageset
Knowledge used when orchestrating mathematical discourses – doing, guiding and requestingBjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark
Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teachingJorryt van Bommel
The teaching of mathematical knowledge for teaching – a learning study of primary school teacher educationInnehåll: JH
Skapad: 20141022 kl. 01:00

NOMAD 19(34), 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: 20141022 kl. 01:00

NOMAD 19(34), 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: 20141022 kl. 01:00

NOMAD 19(34), 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 inservice and preservice teacher training. Her research interests concern mathematics teacher training and professional development of mathematics teachers.
Skapad: 20141022 kl. 01:00

NOMAD 19(34), 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 inservice 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: 20141022 kl. 01:00