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

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
Studying teachers’ knowledge by the use of multiplechoice 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 multiplechoice MKT items, and in particular where they select the suggested solution ”I’m not sure”, and their written responses to corresponding openended questions (long responses). The findings from our analysis of 15 teachers’ responses indicate that their long responses and their multiplechoice 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: 20141022 kl. 01:00

NOMAD 19(34), 2014
Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDSM study
Hege Kaarstein
Abstract
This paper presents how Norwegian teachers and educational researchers categorized a collection of items used in the international TEDSM 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, multiplechoice 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 TEDSM 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: 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
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. MKUomgrepsapparatet 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 MQIindicators 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: 20141022 kl. 01:00

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

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

NOMAD 19(2), 2014
View of mathematics – an investigation of Estonian university students
Indrek Kaldo
Abstract
This study reports on firstyear Estonian university students’ view of mathematics. The data was collected from 970 university students of different disciplines. The participants filled out a Likerttype 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 nonscience 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: 20140625 kl. 01:00

NOMAD 19(2), 2014
Students’ strategies of expanding fractions to a common denominator – a semiotic perspective
Andreas Lorange and Reinert A. Rinvold
Abstract
The aim of this article is to identify students’ strategies while solving tasks which involve the expansion of fractions to a common denominator. In this case study we follow two groups of 11 year old students and their use of the artifact multilink cubes in the solution process. The analysis of the students’ strategies is based upon a semioticcultural framework. Five different types of strategies are reported: trialanderror, factual, contextual, embodiedsymbolic and symbolic. The concept of semiotic contraction is also used in the analysis.
Andreas Lorange
Andreas Lorange is Assistant Professor at NLA University College in Bergen. His main research interest is related to how physical and visual artefacts can be used in connection with the learning of mathematics.
Reinert A. Rinvold
Reinert A. Rinvold is Associate Professor at Hedmark University College in Hamar. His main research interest is multimodal mathematical thinking and learning.
Skapad: 20140625 kl. 01:00

NOMAD – 19(2), 2014
Nummer/Issue
Volume 19, No 2, June 2014
Indrek Kaldo
View of mathematics – an investigation of Estonian university studentsEugenia Koleza
Students’ conceptions about the formula for a rectangle’s area and some similarities to its historical contextAndreas Lorange and Reinert A. Rinvold
Students’ strategies of expanding fractions to a common denominator – a semiotic perspectiveKristina Juter and JanFredrik Olsen
”Justintime teaching” in undergraduate mathematicsInnehåll: JH
Skapad: 20140625 kl. 01:00

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 2hours 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 VicePresident of the Hellenic Society of History, Philosophy and Didactics of the Sciences.
Skapad: 20140625 kl. 01:00

NOMAD 19(2), 2014
”Justintime teaching” in undergraduate mathematics
Kristina Juter and JanFredrik Olsen
Abstract
We compared five groups of students to investigate the effects of ”Justintime teaching” (JiTT), a method designed to both help students keep up with the often fast pace of undergraduate calculus and to deepen their learning. In total, 137 students participated in the study. The outcome is discussed in terms of conceptual and procedural knowledge in relation to examination and other assessment tasks. We observed an improvement on the assessed items and a shift in study habits.
Kristina Juter
Kristina Juter works as an associate professor in mathematics education at Kristianstad University in Sweden. She got her doctoral degree in mathematics and learning at Luleå University of Technology in 2006. Her research interests are, among others, students’ conceptual development at undergraduate calculus courses and mathematics teacher identity.
JanFredrik Olsen
JanFredrik Olsen has a PhD in pure mathematics from NTNU in Norway (2009), and is currently working as an associate professor in mathematics at Lund University in Sweden. While his research interests lie primarily in the meeting point between complex analysis and Fourier analysis, he has a strong interest in undergraduate mathematics education and the potential of technology to improve student motivation and learning.
Skapad: 20140625 kl. 01:00

NOMAD – 19(1), 2014
Nummer/Issue
Volume 19, No 1, March 2014
Indrek Kaldo and Markku S. Hannula
Gender differences favouring females in Estonian university students’ views of mathematicsHege Kaarstein
A comparison of three frameworks for measuring knowledge for teaching mathematicsRaymond Bjuland, Arne Jakobsen og Elaine Munthe
Muligheter og begrensninger for studenters læring i praksisopplæring – eksempel fra en førveiledningsdialog i matematikkChrister Bergsten
News from Nordic mathematics educationInnehåll: JH
Skapad: 20140320 kl. 00:00

NOMAD – 1(1), 1993
Nummer
Issue
Volume 1, No 1, October 1993Ledare/Editorial
En ny nordisk forskningstidskriftOle Björkqvist
Social konstruktivism som grund för matematikundervisningMorten Blomhøj
Modellerings betydning for tilegnelsen af matematiske begreberInger Wistedt
Elevers svårigheter att formulera matematiska problemBengt Johansson
Matematikdidaktik – nordiskt samarbete i historisk belysningGunhild Nissen
Nordisk Forskernetværk – Initiativet Matematikundervisning og DemokratiOle Björkqvist
Litteraturanmälningar.
Mobilisering av krafter för bättre utvärderingSkapad: 20140319 kl. 00:00

NOMAD 19(1), 2014
A comparison of three frameworks for measuring knowledge for teaching mathematics
Hege Kaarstein
Abstract
This paper presents a comparison of three different frameworks used in research projects aimed at measuring knowledge for teaching mathematics. As the included cases all build on Shulman’s theoretical framework for teacher knowledge, in which the categories subject matter content knowledge (CK) and pedagogical content knowledge (PCK) are central, his framework was used as a reference. To enable comparison across the frameworks, each framework’s categories were analysed and organized taxonomically. The results indicate agreement on a superordinate level. However, important differences were found in the operationalisation of the basic level cat egories mathematics CK and mathematics PCK. As the basic level normally represents clear communication of categories, this paper suggests that more attention to the operationalisation of basic level categories is needed.
Hege Kaarstein
Hege Kaarstein is a PhD student at the Department of Teacher Education and School Research, University of Oslo. Her focus is mathematical knowledge for teaching – the concept, its categorization and operationalization.
Skapad: 20140304 kl. 00:00

NOMAD 19(1), 2014
Gender differences favouring females in Estonian university students’ views of mathematics
Indrek Kaldo and Markku S. Hannula
Abstract
This study reports on firstyear Estonian university students’ views of mathematics. The data were collected from 970 university students of different disciplines. The participants completed a Likerttype questionnaire that was compiled from previously published instruments. The results reveal the importance of Mastery Goal Orientation as central to the structure of their views of mathematics. In this study, in five of six dimensions, females hold a more positive view of mathematics than do male students. PerformanceApproach Goal Orientation was the only dimension in which we found no statistically significant gender difference. In all the other dimensions, the female respondents expressed a more positive affect towards mathematics: They showed a more powerful mastery orientation, valued mathematics more, felt more competent, perceived their teacher more positively, and cheated less frequently.
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.
Markku S. Hannula
Markku S. Hannula is professor in mathematics education at the Department of Teacher Education at the University of Helsinki in Finland. His research interests include motivation, beliefs, emotions, problem solving, and gender in mathematics education. He feels comfortable with both quantitative and qualitative research methods and enjoys the challenges of synthesizing research findings across different research paradigms and theoretical frameworks.
Skapad: 20140304 kl. 00:00

NOMAD 19(1), 2014
Muligheter og begrensninger for studenters læring i praksisopplæring – eksempel fra en førveiledningsdialog i matematikk
Raymond Bjuland, Arne Jakobsen og Elaine Munthe
Sammanfattning
Denne artikkelen presenterer resultater fra en førveiledningsdialog mellom en grunnskolelærerstudent og hennes praksislærer fra en ordinær fjerde semesters praksisopplæringsperiode. Ved hjelp av en dialogisk tilnærming forsøker analysen å identifisere dialogsekvenser som inneholder ytringer som er støttende eller begrensende med tanke på å hjelpe studenten til å rette oppmerksomheten mot elevers læring av likeverdige brøker på 7. trinn. Inspirert av perspektiver som fremmer et positivt læringsmiljø i klasserommet (Bransford, Brown & Cocking, 2000) blir ytringer innenfor en dialogsekvens kategoriserte som elevsentrerte, kunnskapssentrerte og vurderingssentrerte med tanke på å planlegge en undervisningsøkt. Dette danner et grunnlag for å diskutere styrker og svakheter ved førveiledningsdialogen.
Abstract
This article presents results from analyses of a mentoring session between a student teacher and her mentor teacher which took place prior to instruction during a fourth semester field practice placement. Using a dialogic approach, the analyses identify utterances that are perceived as supportive or constraining in relation to enabling the student to direct attention towards pupils’ learning about fractions in grade 7. Bransford mfl.’s (2000) approaches to learning have inspired the development of analytical categories to assess the degree of learner centered, knowledge centered and assessment centered utterances, and thus to discuss strengths and weaknesses in the mentoring session.
Raymond Bjuland
Raymond Bjuland is Professor of Mathematics Education at the Univer sity of Stavanger (UiS), Norway. He is the leader of the research project: Teachers as Students at the Department of Education and Sports Science, University of Stavanger. His interests are related to students’ collaborative problem solving in small groups, the use of gestures in teacherstudent dialogues, classroom research and mathematical knowledge for teaching.
Arne Jakobsen
Arne Jakobsen is Associate Professor of Mathematics at the University of Stavanger, Norway. He has experience from several international research projects in Mathematics Education, and is the leader of the NORHED 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.
Elaine Munthe
Elaine Munthe is Professor of Education and Dean of the Faculty of Education & Arts, University of Stavanger (UiS), Norway. She is Chair of a national panel appointed by the Ministry of Education and Research to follow up the teacher education reform which started in 2010, and is also Chair of the board of a funding program for educational research administered by the Norwegian Research Board. She has led several research projects investigating classroom practices and teachers’ professional work.
Skapad: 20140304 kl. 00:00

NOMAD 18(4), 2013
The first foci of elementary school students dealing with prognosis tasks in interviews
Judith Stanja
Abstract
The nature of stochastics is not only characterized by its relationship as a model of the real phenomena described by it as well as by its usage to find hypotheses to be tested in reality, but also by its peculiar characteristic of modeling the relation between model and real phenomena. Stochastic prognoses can be one key concept for ele mentary school stochastics to implement the fundamental idea of the specific nature of stochastics. Stochastic prognoses may be characterized as reflexive statements containing the structural components focus, evaluation and justification. Examples are given to illustrate these components. The paper outlines some a priori determined conceptional requirements for stochastic prognoses to give a first orientation of what can be expected from primary school children. It is assumed that the topics, ques tions and problems stochastics is concerned with, are part of a culture that a child is just entering. To learn more about the ways in which primary school students under stand and express stochastic prognoses, a series of halfstructured interviews with 3rd graders (age 89) were videotaped and transcribed before and after a series of lessons. This contribution concentrates on the foci that children might adopt when dealing with prognosis tasks in interviews for the first time. An overview of the reconstructed types of foci is given and illustrated by examples. The stochastic foci reconstructed so far may be classified as simple foci that could be further described as sequential or aggregate foci. A case study of one child in a preinterview shows what and how foci might be articulated when being confronted with the new semiotic means of a list.
Judith Stanja
Judith Stanja studied mathematics and history of science at the Georg August University of Göttingen (Germany) and at Lund University (Sweden) with an emphasis on stochastics. Currently, she is working on her Phd in mathematics education at the University of DuisburgEssen (Germany). Her research interests include early stochastic learning, con straints for the development of stochastic knowledge, and representations.
Skapad: 20140109 kl. 00:00

NOMAD 18(4), 2013
Prolifing Swedish teachers’ knowledge base in probability
Per Nilsson and Torsten Lindström
Abstract
This paper aims at profiling Swedish teachers’ knowledge base in probability. 43 teachers in compulsory school answered a questionnaire on probability estimation tasks and concept tasks. In the concept tasks, they were challenged to explain their solutions and the content involved in the probability estimation tasks. We distin guish five patterns in the teachers’ knowledge profile: 1) a basic understanding of the theoretical interpretation of probability, 2) problems with structuring compound events, 3) difficulty with conjunction and conditional probability, 4) a higher degree of common content knowledge than of specialized content knowledge and 5) limited understanding of random variation and principles of experimental probability.
Per Nilsson
Per Nilsson is professor in mathematics education at the School of Science and Technology, Örebro University and associated professor at Linnaeus University. His research interests concern classrooms communication in mathematics, the nature of mathematical reasoning and knowledge for teaching probability.
Torsten Lindström
Torsten Lindström is professor in mathematics at the Department of Mathematics, Linnaeus University. His research interests concern dynamical systems with applications to biology. He has a teacher’s exam in mathematics, physics, and chemistry.
Skapad: 20140109 kl. 00:00

NOMAD – 18(4), 2013
Nummer/Issue
Volume 18, No 4, December 2013
Theodosia Prodromou
A modelling approach to probability – analysing students’ conceptual structuresJudith Stanja
The first foci of elementary school students dealing with prognosis tasks in interviewsPer Nilsson and Torsten Lindström
Prolifing Swedish teachers’ knowledge base in probabilityInnehåll: JH
Skapad: 20140109 kl. 00:00

NOMAD 18(4), 2013
A modelling approach to probability – analysing students’ conceptual structures
Theodosia Prodromou
Abstract
This research study investigates how middle school students use probability to model random behaviour in realworld contexts and how they articulated fundamental prob abilistic concepts to show aspects of the mental models that they generated. This article is concerned with the conceptual structures that the students develop when exploring computerbased simulations. The results suggest that the students relied on their experience to provide a context reality from which to construct their mental model of the situation, from which they then defined the probability model. While the students attempted to build mental models, they checked the adequacy of the mapping between their probability models and reality by interrogating the context of their personal experiences. The results also suggest that the way students express this relationship between signal and noise seems to have a particular importance in building comprehensive models that link observed data to modelling distributions.
Theodosia Prodromou
Dr Theodosia Prodromou is a mathematician, statistician and educator. She lectures mathematics education at the University of New England (UNE) in New South Wales, Australia. Her research interests are focused on exploring the relationship between technology and mathematical thinking – especially statistical thinking and probabilistic thinking. She is very interested in statistics education.
Skapad: 20140109 kl. 00:00

Workshop April 17, 2018
NOMAD as a resource for mathematics education research in the Nordic countries
Workshop for doctoral students in mathematics education
The 7th workshop for doctoral students led by the editors of NOMAD will be held in Gothenburg April 17, 2018. PhD students in mathematics education from the Nordic and Baltic countries are invited to submit a draft of a paper for NOMAD, which they will have the opportunity to present and discuss during the workshop.
The deadline for submissions is set to March 15, 2018. The submitted papers will be distributed among the participants shortly after submission, and each participant will be asked to make a review of one other paper before the workshop, according to certain guidelines. Each paper will also be read by one or more of the editors of NOMAD, who during group discussions will give feedback on the paper considering a possible publication in NOMAD.
More information is provided in the InvitationSkapad: 20131128 kl. 00:00

NOMAD 18(3), 2013
An analysis of mathematical modelling in Swedish textbooks in upper secondary school
Peter Frejd
Abstract
A new national curriculum has recently been implemented in the Swedish upper secondary school where one of the goals to be taught is modelling ability. This paper presents a content analysis of 14 ”new” mathematical textbooks with the aim to investigate how the notion of mathematical modelling is presented. An analytic scheme is developed to identify mathematical modelling in the textbooks and to analyse modelling tasks and instructions. Results of the analysis show that there exist a variety of both explicit and implicit descriptions, which imply for teachers to be attentive to complement the textbooks with other material.
Peter Frejd
Peter Frejd is a PhDstudent in mathematics education at the Department of Mathematics, Linköping University, Sweden. His main research interest is on how different actors interpret and work with mathematical modelling in and out of school settings.
Skapad: 20131119 kl. 00:00

NOMAD 18(3), 2013
Arithmetic textbooks in Estonia, Iceland and Norway – similarities and differences during the nineteenth century
Kristín Bjarnadottír, Andreas Christiansen and Madis Lepik
Abstract
This paper identifies similarities and eventual differences in the development of public mathematics education in the nineteenth century in three NorthernEuropean countries: Estonia, Iceland and Norway. Special attention is paid to how these developments were reflected in the first arithmetic textbooks written in the vernacular in these countries. By the end of the century, all three countries had taken serious steps to develop public education, and arithmetic textbooks, meant for selfinstruction or for use in elementary schools, had been published. The content and style of presentation of these textbooks in Estonia, Iceland and Norway are described and compared in the paper, revealing their roots in NorthernEuropean culture: Lutheran Protestantism, Enlightenment and pedagogical currents initiated by Comenius, Pestalozzi and Spencer, emphasizing meaningful learning. Their educational aims were important driving forces in growing national movements in the respective countries by contributing to capability to manage own resources and use of own vernacular, resulting in increased selfesteem.
Kristín Bjarnadóttir
Kristín Bjarnadóttir is associate professor at the School of Education, University of Iceland. Her research interests concern the history of mathematics education and its socioeconomic context.
Andreas Christiansen
Andreas Christiansen is assistant professor at the Department of Teacher Education and Cultural Studies at Stord/Haugesund University College in Norway. His research interests are history of mathematics, and history of mathematics education.
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.
Skapad: 20131119 kl. 00:00

NOMAD 18(3), 2013
Barns bruk av digitale verktøy i barnehagen: muligheter for å gjøre seg matematiske erfaringer
Martin Carlsen
Sammanfattning
Denne artikkelen har som mål å studere hvordan barnehagebarn gjør seg matematiske erfaringer gjennom å bruke digitale verktøy. Ved å ta et sosiokulturelt perspektiv på læring og utvikling studeres den sosiale interaksjonen mellom barn og voksne når disse diskuterer og samhandler med ulike digitale verktøy. Analysene av transkriberte dialoger i to grupper, hver bestående av en voksen og to barn, gir innblikk i det matematiske læringspotensialet som oppstår når barna interagerer med de digitale verktøyene. Dette læringspotensialet knytter seg til de matematiske begrepene telling og tallsymbol, deriblant matematiskteoretiske komponenter som sortering, subitizing, parkobling og kardinalprinsipp. Samtidig viser analysen at interaksjonen med de digitale verktøyene har potensiale til å gi ytterligere næring til approprieringsprosessen av de implisitte matematiske begrepene som finnes i applikasjonene.
Abstract
This study aims at illuminating aspects of how kindergarten children make mathematical experience through the use of digital tools. By taking a sociocultural perspective on learning and development the social inter action amongst children and adults is studied when these discuss and collaborate in using different digital tools. The analyses of transcribed dialogues in two groups comprising one adult and two children show the learning potential that unfolds when the children interact with the digital tools. This learning potential is relative to the mathematical con cepts of counting and number digits, including mathematical theoretical components of sorting, subitizing, onetoone correspondence and cardinality. Furthermore, the analyses show that interaction with the digital tools carries potentials regarding how to further nurture the appropriation process with respect to the implicit mathematical concepts inherent in the applications.
Martin Carlsen
Martin Carlsen er førsteamanuensis i matematikkdidaktikk ved Universitetet i Agder, Norge. Hans forskningsinteresser er innenfor temaet i denne artikkelen, barns læring av matematikk i barnehagen med og uten bruk av digitale verktøy. Hans forskningsinteresse handler også om før skolelæreres orkestrering av matematikkaktiviteter i barnehagen. Han er i tillegg interessert i læring av matematikk gjennom problemløsning i smågrupper. Han identifiserer seg med et sosiokulturelt perspektiv på læring og utvikling, og forskningen hans er situert innen dette teoretiske rammeverket.
Skapad: 20131119 kl. 00:00

NOMAD – 18(3), 2013
Nummer/Issue
Volume 18, No 3, October 2013
Martin Carlsen
Barns bruk av digitale verktøy i barnehagen: muligheter for å gjøre seg matematiske erfaringerKristín Bjarnadottír, Andreas Christiansen and Madis Lepik
Arithmetic textbooks in Estonia, Iceland and Norway – similarities and differences during the nineteenth centuryPeter Frejd
An analysis of mathematical modelling in Swedish textbooks in upper secondary schoolFirst Announcement – NORMA 14, June 3rd–6th 2014
Skapad: 20131119 kl. 00:00

NOMAD 18(2), 2013
Preparing future teachers for interdisciplinarity: designing and implementing a course for preservice upper secondary teachers
Uffe Thomas Jankvist, Jan Alexis Nielsen and Claus Michelsen
Abstract
Educational researchers and policymakers have for some time touted the need for interdisciplinary teaching. But while there are many educational, democratic, and economic arguments for bringing an increased attention to interdisciplinary teaching, there has been a striking lack of exposure of the question of how future teachers, who are largely educated in a monodisciplinary fashion, can best become equipped to introduce genuinely interdisciplinary teaching activities to their future students. This article presents some preliminary reflections upon a graduate course at the University of Southern Denmark, which aims to prepare future science and mathematics teachers for interdisciplinary teaching, and which has been designed on the basis of influential theoretical expositions of the concept of interdisciplinarity.
Uffe Thomas Jankvist
Uffe Thomas Jankvist is associate professor of mathematics education at Aarhus University, Department of Education, Campus Emdrup, Denmark. In addition to the topic of interdisciplinarity, 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. Besides being an editor of Nomad, he is currently involved in a new initiative at Roskilde University to design and implement an educational program for inservice upper secondary school mathematics teachers to become ”math counselors”.
Jan Alexis Nielsen
Jan Alexis Nielsen is postdoc at Department of Science Education, University of Copenhagen. His research focus lies in student argumentation in interdisciplinary contexts and in competence assessment – in particular assessment of competencies that are illdefined and manifest in processes. He has taught several courses in education and communication at bachelor, master and postgraduate levels.
Claus Michelsen
Claus Michelsen is associate professor of mathematics education at University of Southern Denmark, Department of Mathematics and Computer Science. He is associate dean and head of the Ph.D.school at The Faculty of Science at University of Southern Denmark. In addition to the topic of interdisciplinarity, his research interests include students’ interest in science and mathematics, informal learning in mathematics and science, teacher education and inservice teacher training.
Skapad: 20131015 kl. 01:00

NOMAD 18(2), 2013
Teacherassisted open problem solving
Markus Hähkiöniemi, Henry Leppäaho and John Francisco
Abstract
Previous research has developed several problemsolving models and suggested that the teacher plays a crucial role in guiding students’ problem solving. However, less is known about the particularities of problem solving and teacher guidance when dealing with open problems which include multiple possible solution pathways. The aim of this study is to understand students’ open problemsolving processes and teachers’ ways of supporting them. Data collection involved videotaping one 9th grade mathematics lesson with two video cameras and capturing the screens of the students’ computers. Seven student pairs worked on an open problem using GeoGe bra under the guidance of a teacher trainee. We found that students had various kinds of problemsolving processes and that the teacher had a crucial role in guiding them. We elaborate on 9 ways how the teacher guided students to change between phases in open problem solving.
Markus Hähkiöniemi
Dr. Markus Hähkiöniemi is university lecturer in the Department of Teacher Education, University of Jyväskylä, Finland. He is interested in classroom interaction and students’ mathematical thinking. His current project focuses on preservice mathematics teachers’ technologyenriched inquirybased mathematics teaching in grades 7 to 12.
Henry Leppäaho
Dr. Henry Leppäaho is university lecturer on the pedagogy of mathematics in the Department of Teacher Education, University of Jyväskylä, Finland. His research is focused on mathematical problem solving.
John Francisco
Dr. John Francisco is assistant professor in mathematics education in the School of Education at the University of Massachusetts at Amherst, USA. His research interests include students’ development of mathematical ideas and reasoning, personal epistemological beliefs and teacher learning.
Skapad: 20131015 kl. 01:00

NOMAD 18(2), 2013
Nummer/Issue
Volume 18, No 2, June 2013
Dagmar Neuman
Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningenMarkus Hähkiöniemi, Henry Leppäaho and John Francisco
Teacherassisted open problem solvingUffe Thomas Jankvist, Jan Alexis Nielsen and Claus Michelsen
Preparing future teachers for interdisciplinarity: designing and implementing a course for preservice upper secondary teachersChrister Bergsten
News from Nordic mathematics educationSkapad: 20131015 kl. 01:00

NOMAD 18(2), 2013
Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen
Dagmar Neuman
Sammanfattning
Utgående från den holistiska kunskapssyn som representerar fenomenologin och den fenomenografiska forskningsansatsen diskuterar jag i den här artikeln observationer redovisade i min nu drygt tjugosex år gamla avhandling, i boken Räknefärdighetens rötter samt i en senare studie av hur barn dividerar. Observationerna gäller dels elever som deltar i specialundervisning i matematik i grundskolan, samt elever i gymnasieskolan som anser sig lida av matematiksvårigheter, och dels skolnybörjare som ännu inte har undervisats i matematik. De visar
– att det som främst tycks förorsaka grava eller specifika matematiksvårigheter är att eleverna saknar talföreställningar samt förståelse för sambandet mellan de fyra räknesätten
– att sådana begrepp och föreställningar knappast utvecklas genom skolans tabellträning
– att många barn intuitivt börjar utveckla talföreställningar före skolstarten, samtidigt med att de formar konkreta representationer som blir till abstrakta föreställningar om tal.
Avslutningsvis ställer jag frågan: skulle den stora andel elever som nu lämnar grundskolan utan godkänt betyg i matematik möjligen kunna reduceras genom ett paradigmskifte inom den kultur som styr hur den grundläggande aritmetiken behandlas under de första skolåren?
Abstract
Setting out from the holistic view of knowledge representing pheno menology and the phenomenographic research approach, I have in this article revisited the observations presented in my now twentysix year old dissertation The origin of arithmetic skills, the Swedish book Räknefärdighetens rötter and a later study of how children divide. One side of the observations concerns elementary and middle school pupils who take part in special education as well as high school pupils who believe they suffer from severe math difficulties; the other concerns seven year old first year pupils without any formal education in the field of mathematics. These observations show
– that the primary cause of severe or specific math difficulties seems to be the absence of numerical representations and of the concep tual understanding of the inverse relation between addition and subtraction
– that those concepts and representations are probably not developed through the tabletraining usually used at school; but
– that many children intuitively begin to use those concepts or arith metic laws before they enter school, whilst simultaneously crea ting numerical representations, which in due time become tools for thinking in numerical terms.
Finally, the question is posed: would a shift of paradigm within the culture now ruling the ways in which arithmetic is introduced to first year pupils possibly reduce the great number of pupils who now fail mathematics when leaving school at the end of grade nine?
Dagmar Neuman
Dagmar Neuman doktorerade vid Göteborgs universitet år 1987, avgick med pension från universitetet år 1991 och har därefter huvudsakligen ägnat sig åt fortbildning inom ämnet matematik, med inriktning mot förskollärare och lärare för de första skolåren.
Skapad: 20131015 kl. 01:00

NOMAD 17(34), 2012.
Research on mathematical beliefs. The birth and growth of the MAVI group in 1995–2012
Erkki Pehkonen
Abstract
In the 1980s the meaning of beliefs for teaching and learning aroused also to the con sciousness of mathematics educators. Therefore, here it is firstly sketched the research field of mathematical beliefs, in order to understand why belief research has been a topic for an international research group for more than 30 years. The aim of the paper is to have a look at the history of MAVI and to describe its development within the years 1995–2012. A special look is given at the birth of the MAVI group in the middle of the 1990s and then its development through the last 18 years will be described. Also some statistics on the MAVI meetings and their participants are presented. And in the appendix the total list of the MAVI proceedings is documented.
Erkki Pehkonen
Dr. Erkki Pehkonen is a full professor (retired) in the field of mathematics and informatics education in the Department of Applied Sciences of Education at the University of Helsinki in Finland. He is interested in problem solving with a focus on motivating middle grade pupils, as well as in understanding pupils’ and teachers’ beliefs and conceptions about mathematics teaching.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Stability of beliefs in mathematics education: a critical analysis
Peter Liljedahl, Susan Oesterle and Christian Bernèche
Abstract
The field of mathematics education has assumed for too long that stability is an inherent and definable characteristic of beliefs. In this article we explore the validity of this claim through the critical analysis of 92 journal articles, conference papers, and book chapters. Using a stringent definition of what it means for a belief to be stable, we conclude that the body of research on mathematical beliefs is inconsistent in its use of this construct. The aggregated results of our analysis also indicate that stability and instability are not mutually exclusive characteristics of beliefs.
Peter Liljedahl
Dr. Peter Liljedahl is an Associate Professor of Mathematics Education in the Faculty of Education at Simon Fraser University in Vancouver, Canada. He is a former high school mathematics teacher who has kept his research interests and activities close to the classroom. He regularly works closely with teachers, schools, school districts, and ministries of education on issues pertaining to the improvement of teaching and learning. His primary research interests are teacher beliefs, teacher education, and creativity in mathematics.
Susan Oesterle
Dr. Susan Oesterle is a Mathematics instructor in the Faculty of Science & Technology at Douglas College in New Westminster, Canada. Over the last few years she has been heavily involved in developing and teaching in a Graduate Diploma Program for Mathematics and Science Teaching, a twoyear program which provides an opportunity for practicing elementary and middle school teachers to build their knowledgebase and improve their teaching of these subjects. Her current research interests include preservice and inservice teacher education, teacher beliefs, and issues concerning mathematics teacher educators.
Christian Bernèche
Christian Bernèche is a PhD student in Mathematics Education at Simon Fraser University in Vancouver, Canada. He has been teaching for over two decades and is presently teaching Grade 6. He is a member of his local Professional Development Committee and strongly believes in selfdirected professional growth plans. His area of interest in research is student perceptions about learning and teaching mathematics.
Skapad: 20130820 kl. 01:00

NOMAD – 17(34), 2012
Nummer/Issue
Volume 17, No 34, December 2012
Erkki Pehkonen
Research on mathematical beliefs. The birth and growth of the MAVI group in 1995–2012Peter Liljedahl, Susan Oesterle and Christian Bernèche
Stability of beliefs in mathematics education: a critical analysisAnu Laine, Liisa Näveri, Maija Ahtee, Markku S. Hannula and Erkki Pehkonen
Emotional atmosphere in thirdgraders’ mathematics classroom – an analysis of pupils’ drawingsInés Mª GómezChacón
Affective pathways and interactive visualization in the context of technological and professional mathematical knowledgeChiara Andrà and Guido Magnano
Interplay of cognition and affect in undergraduate math students’ careers: insights from recursive partitioningFulvia Furinghetti, Chiara Maggiani and Francesca Morselli
How mathematics students perceive the transition from secondary to tertiary level with particular reference to proofCristina Coppola, Pietro Di Martino, Tiziana Pacelli and Cristina Sabena
Primary teachers’ affect: a crucial variable in the teaching of mathematicsSonja Lutovac and Raimo Kaasila
Dialogue between past and future mathematical identitiesHanna Palmér
(In)consistent? The mathematics teaching of a novice primary school teacherPäivi PortaankorvaKoivisto
Prospective mathematics teachers’ metaphors for mathematics, teaching, and the teacher’s roleMadis Lepik, Anita Pipere and Markku S. Hannula
Comparing mathematics teachers’ beliefs about good teaching: the cases of Estonia, Latvia and FinlandIgor’ Kontorovich and Boris Koichu
Feeling of innovation in expert problem posingSkapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Emotional atmosphere in thirdgraders’ mathematics classroom – an analysis of pupils’ drawings
Anu Laine, Liisa Näveri, Maija Ahtee, Markku S. Hannula and Erkki Pehkonen
Abstract
The aim of this study is to find out what kind of emotional atmosphere dominates in thirdgraders’ mathematics lessons. The analysis is based on pupils’ drawings. In total 133 drawings were analyzed by looking for content categories related to a holistic evaluation of emotional atmosphere during mathematics lesson. As a summary we can conclude that the emotional atmospheres in the mathematics lessons are mainly positive even though the differences between the classes are large. Furthermore, it can be said that asking pupils to do drawings is a good and manysided method to collect data about the emotional atmosphere of a class.
Anu Laine
Anu Laine is adjunct professor in mathematics education and she is working as university lecturer at the Department of Teacher Education at the University of Helsinki in Finland. Her research interests include affects, communication and problem solving in mathematics education.
Liisa Näveri
Liisa Näveri is Ph.D. and working as a researcher at the Department of Teacher Education at the University of Helsinki in Finland. Her research interests include learning and problem solving in mathematics education.
Maija Ahtee
Maija Ahtee is professor emerita in mathematics and science education at the University of Jyväskylä, Finland. Her research interests have been more in science education.
Markku S. Hannula
Markku S. Hannula is professor in mathematics education at the Department of Teacher Education at the University of Helsinki in Finland. His research interests include motivation, beliefs, emotions, problem solving, and gender in mathematics education.
Erkki Pehkonen
Erkki Pehkonen is a full professor (emeritus) in the field of mathematics and informatics education in the Department of Teacher Education at the University of Helsinki in Finland. He is interested in problem solving with a focus on motivating middle grade pupils, as well as in understanding pupils’ and teachers’ beliefs and conceptions about mathematics teaching.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Affective pathways and interactive visualization in the context of technological and professional mathematical knowledge
Inés Mª GómezChacón
Abstract
This article reports the findings for a qualitative study on the use of dynamic geometry systems (DGS) and their impact on students’ affective pathways. The approach adopted is to view affect through the lens of a representational system. The participants, mathematics teacher trainees, were asked to solve geometric locus exercises using GeoGebra software. The results reveal a number of features that characterize subjects’ local and global affect. Future teachers’ local affect when using imagery in computerized environments was found to be impacted by the balance between their analyticalalgebraic and graphic reasoning and their understanding of the tools at their avail and their use in the instrumental deconstruction of geometric figures. Evidence was observed that linked student teachers’ global affect, in turn, to their motivation as defined by their goals and selfconcept.
Inés Mª GómezChacón
Inés Mª GómezChacón is Professor of Mathematics Education in the Faculty of Mathematics in Complutense University where she is Vicedean and Director of Cátedra Miguel de Guzmán about Mathematic Education. She develops basic research and applied research in different topics: relationship between knowledge and affectivity in mathematics, Sociology of mathematical education (the sociocultural environments and identity) and the development of new technologies as part of the curriculum and teacher training in these areas.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Interplay of cognition and affect in undergraduate math students’ careers: insights from recursive partitioning
Chiara Andrà and Guido Magnano
Abstract
Data collected in entrance tests for undergraduate curricula in mathematics at the University of Turin are analysed using the recursive partition method, to obtain classification trees for different ”response variables” describing academic achievement or dropout. The input factors include both math abilities and several affective and motivational factors, the latter having being assessed using internationally validated questionnaires. We argue that classification trees can provide unexpected insight into the interplay of such factors for academic success or failure, specifically for math students.
Chiara Andrà
Chiara Andrà is Lecturer at the University of Torino. She teaches Mathematics Education at the Department of Philosophy and Education in Torino, and Statistics at the Department of Mathematics. Her research interests regard early probabilistic thinking, undergraduate students’ difficulties about mathematics and its learning, and semiotics. Her research is framed within the paradigm of the embodied cognition.
Guido Magnano
Guido Magnano is associate professor of Mathematical Physics at the University of Torino. Since 2001 he has supervised the design and the administration of student entrance tests at his university, and participated to various research projects, both at regional and at national level, aimed at measuring mathematical ability and other relevant dimensions in students’ transition from high school to undergraduate studies. A significant part of his recent research activity is devoted to Item response theory, in connection with item validation and reliability issues in multiplechoice testing.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
How mathematics students perceive the transition from secondary to tertiary level with particular reference to proof
Fulvia Furinghetti, Chiara Maggiani and Francesca Morselli
Abstract
This paper reports on a research project concerning the difficulties met by undergraduate students in mathematics during the first year of university. Our aim is to provide elements for studying the transition from secondary to tertiary level as perceived by the students who live it. The combination of different analytical tools (questionnaires, interviews, problem solving and proving activities) allows shedding light on aspects which are not purely cognitive, but also pertain to the affective domain.
Fulvia Furinghetti
Fulvia Furinghetti is full professor (retired) in the University of Genoa. She teaches Mathematics Education in the Department of Mathematics of this University. Her research concerns beliefs, images of mathematics in society, proof, problem solving, use of history of mathematics in teaching, teacher professional development, and history of mathematics education. In 2000–2004 she chaired HPM (the International Study Group on the relations between History and Pedagogy of Mathematics affiliated to ICMI).
Chiara Maggiani
Chiara Maggiani graduated in Mathematics at the University of Genoa discussing a dissertation on the problems encountered by mathematics students in the transition from secondary school to university. At present she is going to obtain her specialization in mathematics teaching.
Francesca Morselli
Francesca Morselli is assistant professor at the Department of Philosophy and Education of the University of Turin. She teaches Mathematics Education to prospective primary teachers. Her research interests concern the intertwining of affect and cognition in mathematics teaching and learning, and the teaching and learning of mathematical proof.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Primary teachers’ affect: a crucial variable in the teaching of mathematics
Cristina Coppola, Pietro Di Martino, Tiziana Pacelli and Cristina Sabena
Abstract
Mathematics education is strongly interested in defining ”what is necessary for teaching mathematics effectively”. The main directions of research emphasize the cognitive side of the answer to this question, trying to describe what kind of knowledge is needed in order to teach mathematics effectively. Starting from the point that teachers’ affect plays a crucial role in determining the quality of teaching, we discuss this issue from a theoretical point of view, introducing the construct of ”attitude towards mathematics teaching”. Within this theoretical framework we conducted a study with 189 primary school preservice teachers, investigating teachers’ emotions, beliefs and attitudes. In this paper, we analyze and discuss the relationship among the participants’ emotional disposition towards mathematics and towards the idea of having to teach it, their past experiences as mathstudents and the current perceived competence in mathematics.
Cristina Coppola
Cristina Coppola has got a research fellowship at Dipartimento di Matematica of Università degli Studi di Salerno. Her main research interests are: future teachers’ attitudes and emotions towards mathematics; the study of different aspects regarding the relationship between mathematical logic and language, with particular attention to the development of logical tools in primary school children, to the semiotic coordination with secondary school children in mathematical learning processes and to undergraduate students’ reasoning in logical tasks; the use of elearning in mathematics education.
Pietro Di Martino
Pietro Di Martino is a Researcher in Mathematics Education at Dipartimento di Matematica of Università degli Studi di Pisa. His main research interests regard: the role of affective factors in the teaching/learning of mathematics, with particular attention to the theoretical aspects related to the definition of the construct ”attitude towards mathematics”; the study of the difficulties related to the transition between secondary and tertiary transition in mathematics; mathematics teachers development, with particular attention to the development of future primary teachers, and the study of their emotions beliefs and attitudes towards mathematics.
Tiziana Pacelli
Tiziana Pacelli has got a research fellowship at Dipartimento di Matematica of Università degli Studi di Salerno. Her main research interests are: analysis of emotions, beliefs and attitudes towards mathematics in future primary teachers; the exploration of the relationship between language and the development of logical tools in students at different school levels, in particular through cooperative and linguisticmanipulative activities with primary school children, through activities about semiotic coordination with secondary school children, through logical tasks with undergraduate students; analysis of the use of elearning in mathematics education.
Cristina Sabena
Cristina Sabena is a researcher in Mathematics Education at Dipartimento di Filosofia e Scienze dell’Educazione of Università degli Studi di Torino. Her main research interests regard: the multimodality of mathematics learning and teaching, with particular attention to the role of gestures, analysed with a semiotic lens; the argumentation processes from primary to secondary school; teachers’ and future teachers’ attitudes and emotions towards mathematics.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Feeling of innovation in expert problem posing
Igor’ Kontorovich and Boris Koichu
Abstract
This paper is one of the reports on a multiplecase study concerned with the intertwining between affect and cognition in the mechanisms governing experts when posing new mathematical problems. Based on inductive analysis of a single case of an expert poser for mathematics competitions, we suggest that the desire to experience the feeling of innovation may be one of such mechanisms. In the case of interest, the feeling was realized through expert’s reflections on the problems he created in the past, by systematically emphasizing how a new problem was innovative in comparison with other familiar problems based on the same nesting idea. The findings are discussed in light of past research on expert problem posers and expert problem solvers.
Igor’ Kontorovich
Igor’ Kontorovich is a mathematics educator and a researcher, who has recently (in 2013) completed his Ph.D. studies at the Department of Education in Science and Technology at the Technion – Israel Institute of Technology. Assistant Professor Boris Koichu was his academic adviser. The Ph.D. research, of which this paper is a part, is concerned with mental mechanisms involved in expert problem posing.
Boris Koichu
Boris Koichu is an Assistant Professor at the Department of Education in Science and Technology at the Technion – Israel Institute of Technology. His research domain is mathematical problem solving and problem posing, with special attention to learning and teaching mathematics at secondary school and university. Some of his work concerns a question of how insights on problem solving and problem posing by the gifted and experts can be implemented in promoting regular students and in mathematics teacher education.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Comparing mathematics teachers’ beliefs about good teaching: the cases of Estonia, Latvia and Finland
Madis Lepik, Anita Pipere and Markku S. Hannula
Abstract
The article presents results from a crosscultural NorBa project Mathematics teachers’ educational beliefs. We report on Estonian, Latvian and Finnish lower secondary mathematics teachers’ espoused beliefs about good teaching. A principal component analyses identified a twocomponent structure of teachers’ beliefs about good teaching: (1) Reasoning and conceptual understanding and (2) Mastery of skills and facts. Crosscultural differences were identified in both of these dimensions. Latvian teachers indicated the strongest agreement with reasoning and conceptual understanding, Estonian teachers with mastery of skills and facts, while Finnish teachers scored lowest on both dimensions. Moreover, we analysed the amount of teachers with different profiles with regard to these two dimensions. The results suggest both common conceptual core of teachers’ beliefs on mathematics teaching and certain cultural influence on the profile of these beliefs.
Madis Lepik
Madis Lepik is associated 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.
Anita Pipere
Anita Pipere is professor of educational psychology at the Institute of Sustainable Education, Faculty of Education and Management, Daugavpils University, Latvia. Her research interests include professional identity, teachers’ beliefs and teaching approaches, dialogical self, and education for sustainable development.
Markku S. Hannula
Markku S. Hannula is professor in mathematics education at the Department of Teacher Education at the University of Helsinki in Finland. His research interests include motivation, beliefs, emotions, problem solving, and gender in mathematics education.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Prospective mathematics teachers’ metaphors for mathematics, teaching, and the teacher’s role
Päivi PortaankorvaKoivisto
Abstract
This study sheds light on Finnish preservice mathematics teachers’ (n = 16) views of mathematics, teaching, and the teacher’s role. Data was gathered via metaphors at three time points during teacher students’ pedagogical studies, in academic year 2011–2012. The analysis was conducted inductively, but based on categories found in previous studies. The results indicated that prospective mathematics teachers’ metaphors for mathematics mostly involved picturing the selfexistent quality of mathematics. Their metaphors for teaching referred to the ups and downs in teaching, and their metaphors for the teacher’s role were involved with the characteristics of the teacher’s personality. One possible explanation for these results centres round mathematics student teachers’ life situations. They have studied mathematics as their major at the department of mathematics for 2–3 years just before they started their pedagogical studies, and they have just experienced their very first and overwhelming lessons as teachers.
Päivi PortaankorvaKoivisto
Päivi PortaankorvaKoivisto is university lecturer (PhD) at the University of Helsinki. Her research interests are Experiential mathematics teaching; Teachers’ professional development; Metaphors in teacher education context; and Using photos and pictures to support reflective thinking in teacher education.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
(In)consistent? The mathematics teaching of a novice primary school teacher
Hanna Palmér
Abstract
This article focuses on the mathematics teaching of Helena, a Swedish novice teacher. Helena is one of seven teachers in a case study of primary school mathematics teachers’ professional identity development. She is also an example of a teacher whose mathematics teaching, from an observer’s perspective, may appear inconsistent with her talk about mathematics teaching. However, in this article a conceptual framework aimed at analysing professional identity development will be used making the process of her mathematics teaching visible and then her mathematics teaching appear as consistent.
Hanna Palmér
Hanna Palmér is a postgraduate student in mathematics education at Linnaeus University, Sweden. Her main research interest is the professional identity development of mathematics teachers and the work with and learning of mathematics of children in preschool, preschool class and lower primary school.
Skapad: 20130820 kl. 01:00

NOMAD 17(34), 2012.
Dialogue between past and future mathematical identities
Sonja Lutovac and Raimo Kaasila
Abstract
Preservice teachers’ schooltime experiences have been addressed much in mathematics
education research. These experiences have been shown to have a central meaning for preservice teachers’ views of mathematics and their present mathematical identities. However, the identity is not only bound to the past and present, but it also extends to the future. Further, preservice teachers’ anticipations of the future have been overlooked in the research on identity in a mathematics education context. We focus here on the mathematical identity work of two preservice teachers and its dialogue between the past and the future. We compare the cases of one Finnish and one Slovenian preservice teacher, who reported having had negative experiences with mathematics during their school years. Based on the results, two different types of mathematical identity work were identified; resulting from the different facilitators used in mathematics education courses.
Sonja Lutovac
Sonja Lutovac is a doctoral candidate in Education at the University of Maribor (Slovenia) and University of Lapland (Finland). Her research interests are in the field of elementary teacher education, especially in mathematics education and in the use of qualitative research methods, such as narrative and rhetorical approaches. She is mostly interested in preservice teachers’ identity and identity work in mathematics education context.
Raimo Kaasila
Ph.D. Raimo Kaasila is a Professor of Education, especially studying and developing teacher education at the University of Oulu (Finland). His main research areas are preservice teachers’ identity formation and reflective processes during teacher education, especially in the mathematics education context. He has also studied affective domain in teacher education and mathematics education, and the use of narrative, rhetorical and discursive approaches in teacher education.
Skapad: 20130820 kl. 01:00

NOMAD 18(1), 2013.
Making sense of a ”misleading” graph
Oduor Olande
Abstract
Given the importance of a criticalanalytical disposition in the case of graphical artefacts, this paper explores graphicacy based on students’ answers to an item from PISA survey test. Primarily, results from the written test were analyzed using PISA’s doubledigit rubrics or coding. In evaluating these categories, it is observed that just a small percentage of students are able to produce answers that reflect a criticalanalytical approach with respect to the use of statistical/mathematical operators and forms of expressions. Secondly, video observation shows that students tend to employ what is perceived as an ”identification approach” while discussing the task. Whereas elements of mathematical and statistical ideas can be identified in the students’ discussion, these are not explicitly stated and are largely submerged in everyday concerns and forms of expression.
Oduor Olande
Oduor Olande is a Ph. D. candidate in the didactics of mathematics at the Department of Applied Science and Design, Mid Sweden University (Mittuniversitetet), Sweden. His special research interest is in interactions (sense making and analysis) with graphical artefacts. He is also interested in issues concerning stochastic thinking.
Skapad: 20130515 kl. 01:00

NOMAD – 18(1), 2013
Nummer/Issue
Volume 18, No 1, March 2013
Oduor Olande
Making sense of a ”misleading” graphAnita Valenta and Ole Enge
Student teachers’ work on instructional explanations in multiplication – representations and conversions between themIda Friestad Pedersen
”I need advanced mathematics to pursue the career of my choice”. Norwegian students’ motivations for enrolling in mathematics and plans for postsecondary studiesSkapad: 20130515 kl. 01:00

NOMAD 18(1), 2013.
I need advanced mathematics to pursue the career of my choice”. Norwegian students’ motivations for enrolling in mathematics and plans for postsecondary studies
Ida Friestad Pedersen
Abstract
Participation in advanced science and mathematics courses in upper secondary school is a gateway to tertiary education and career opportunities in the STEM fields (Science, Technology, Engineering, and Mathematics). The purpose of this study is to investigate Norwegian finalyear upper secondary school students’ motivations for choosing to enroll in the most advanced mathematics course offered (3MX), as well as to ascertain their plans for postsecondary education. Since females are underrepresented in mathematics and mathematicsrelated fields of study, special attention is paid to the gender perspective. The analyses are based on questionnaire data from the largescale international achievement study TIMSS Advanced, and are framed by the expectancyvalue model developed by Eccles and her colleagues (1985). Results show that the subject’s utility value was the primary reason for students’ enrollment in mathematics; that interest in mathematics as a school subject is somewhat more important to the girls than to the boys; and that there are some gender differences in students’ plans for postsecondary studies in the STEM fields.
Ida Friestad Pedersen
Ida Friestad Pedersen is a PhDstudent in the doctoral program at the University of Oslo, and works as a lecturer at the University of Tromsø. Her research interests include students’ mathematical competence, with an emphasis on algebra, and their motivations for choosing mathematics in upper secondary school and beyond.
Skapad: 20130515 kl. 01:00

NOMAD 18(1), 2013.
Student teachers’ work on instructional explanations in multiplication – representations and conversions between them
Anita Valenta and Ole Enge
Abstract
In this study we are analysing student teachers’ instructional explanations. The study is based on student teachers’ written work on two different tasks about different strategies and properties in multiplication and explaining these. Our research questions concern the type of representation registers student teachers use in their explanations. In explanations where several representation registers are used, we analyse what can be challenges in conversions between representations. Data is analysed using the framework of Duval’s cognitive analysis, and analyses and discussions are related to development of mathematical knowledge for teaching.
Anita Valenta
Anita Valenta is Associate Professor in mathematics education at SørTrøndelag University College in Trondheim, Norway. Her main interest is in developing a knowledge base for mathematics teacher education, research in student teachers’ mathematical knowledge for teaching and algebra in the early grades.
Ole Enge
Ole Enge is Associate Professor in mathematics education at SørTrøndelag University College in Trondheim, Norway. He is interested in developing a knowledge base for mathematics teacher education, research on instructional routines in mathematics teaching and students’ proportional reasoning.
Skapad: 20130515 kl. 01:00

NOMAD 17(2), 2012. Innovative approaches to teaching mathematics in higher education: a review and critique
Innovative approaches to teaching mathematics in higher education: a review and critique
Mahmoud Abdulwahed, Barbara Jaworski and Adam R. Crawford
Abstract
This paper provides a snapshot of emerging trends in mathematics teaching in higher education for STEM subjects (Science, Technology, Engineering and Mathematics). Overwhelmingly, papers identify a focus on conceptual understandings of mathematics in comparison to understanding that is instrumental or procedural. Calls for reform of mathematics teaching have been the basis for a range of studies; responses to these calls have embraced innovative methods for implementing changes in learning and teaching of mathematics, sometimes rooted in constructivist ideology. Observed trends have been categorised in six groups. In many studies, technology is being used as an enabler of reforms. Constraints to implementing new approaches in mathematics teaching are indicated. Discussion of contemporary research questions that could be asked as a result of the shift towards teaching mathematics in innovative ways is provided and is followed by a critique of the underlying theoretical positions, essentially that of constructivism.
Mahmoud Abdulwahed
Mahmoud Abdulwahed is Assistant Professor and Acting Head of the College Requirement Unit at the College of Engineering, Qatar University, Qatar. He was formerly a researcher and developer in ICT, STEM Education, and Innovation at Loughborough University, where he earned his PhD.
Barbara Jaworski
Barbara Jaworski is a Professor of Mathematics Education and Director of Research at the Mathematics Education Centre, Loughborough University, UK, formerly a Professor of Mathematics Education at the University of Agder, Norway, where she recently was awarded an Honorary Doctorate.
Adam Crawford
Adam Crawford is based within the School of Civil and Building Engineering at Loughborough University, UK, formerly Manager of the Engineering Centre for Excellence in Teaching and Learning at the University.
Skapad: 20130213 kl. 00:00

NOMAD 17(2), 2012. Upper secondary school students’ gendered conceptions about affect in mathematics
Upper secondary school students’ gendered conceptions about affect in mathematics
Lovisa Sumpter
Abstract
This study explores upper secondary school students’ conceptions about gender and affect in mathematics. Two groups of students from Swedish Natural Science Programme each answered a questionnaire; the first with a focus on boys and girls in general and the other with a focus on individuals themselves. The results from two questionnaires were compared. The first questionnaire revealed a view of rather traditional femininities and masculinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between traits students ascribed as gender different and traits students ascribed to themselves.
Lovisa Sumpter
Lovisa Sumpter is lecturer and researcher at Dalarna University, Falun, Sweden. Her research interests are mathematical reasoning, affect and gender.
Skapad: 20130213 kl. 00:00

NOMAD – 17(2), 2012
Nummer/Issue
Volume 17, No 2, June 2012
Indrek Kaldo and Markku S. Hannula
Structure of university students’ view of mathematics in EstoniaLovisa Sumpter
Upper secondary school students’ gendered conceptions about affect in mathematicsMahmoud Abdulwahed, Barbara Jaworski and Adam R. Crawford
Innovative approaches to teaching mathematics in higher education: a review and critiqueChrister Bergsten
News from Nordic mathematics educationSkapad: 20130213 kl. 00:00