bluuebunny/crossref_metadata_2025 huggingface dataset:
New dissertations in mathematics education by doctoral students in the Nordic Graduate School
Authors: Grevholm Barbro
Published: November 2024

As I wrote in the issue 3-4 of Nomad in 2005, the year 2006 will be exceptional because of the number of doctoral students who will finish their research education in mathematics didactics and defend their dissertations. Already in the first quarter of the year there have been at least five dissertations printed and made public. A short presentation of them will be made here, as they are likely to be of interest to the whole Nordic Graduate School and many Nordic researchers.
Exploring young children’s geometrical strategies
Authors: Gagatsis Athanasios , Elia Iliada , Modestou Modestina , Sriraman Bharath
Published: November 2024

This study explores young children’s strategies while transforming polygons, through the use of geometrical models. Data were collected from 291 children ranging from 4 to 8 years of age in Cyprus. Children were asked to draw a stairway of specific polygons, with each shape being bigger or smaller than its preceding one. Relationships between children’s responses in the transformation tasks, their ability to recognize geometric shapes and their IQ level were investigated. Results showed that children used three alternative strategies in the transformation tasks. Children’s IQ score was directly associated with their transformation strategies, while only a low recognition ability was associated with the use of a defective strategy.
Valg av hoderegning som arbeidsmetode
Authors: Haara Frode Olav
Published: November 2024

Stadig oftere opplever vi at elever bruker kalkulator til å gjøre utregninger som må karakteriseres som enkel hoderegning. Artikkelen omhandler et prosjekt gjennomført på ungdomstrinnet med fokus på å bevisstgjøre elevene i valget av arbeidsmetode, og øke bruken av hoderegning. Sentralt står bruken av et tradisjonelt virkemiddel i en matematikkundervisning preget av lærerens tro på aktive og læringskritiske elever.
Textbooks as instruments – three teachers’ way to organize their mathematics lessons
Authors: Johansson Monica
Published: November 2024

This paper reports a study of three teachers’ way to organize their lessons and how textbooks are incorporated in their work1. Despite the differences between the teachers, it is noticeable that in these three classrooms, the textbooks, to a large degree, guide the teaching. The textbooks are present: (a) in the students’ individual work, (b) in many of the examples presented on the board, (c) as a source for background and motivational discussions, (d) in how mathematics is presented, and (e) for homework.
Children with impairments learning numbers
Authors: Ahlberg Ann
Published: November 2024

This research investigates children’s understanding of numbers when solving addition and subtraction word problems. A comparative approach – studying children who are blind, children with a hearing impairment and children without these impairments aims at illuminating and describing the differences and similarities between the three different groups. Thereby, the investigation contributes to the understanding of critical aspects characterising development of numerical competence in each of the three groups. The design of the study also makes it possible to describe children’s development of number concepts in the context of solving addition and subtraction word problems on a more general level.
The first year of the Danish editorial team
Authors: Blomhøj Morten , Valero Paola
Published: November 2024

Ledare / Editorial
Book review: Mathematical competitions and classroom collaboration: antonyms or a new direction for research on teacher beliefs?
Authors: Sriraman Bharath , Steinthorsdottir Olof
Published: November 2024

Tine Wedege and Jeppe Skott (2006), Changing views and practices: a study of the KappAbel mathematics competition. Research report, Norwegian Center for Mathematics Education & Norwegian University of Science and Technology, Trondheim. ISBN 82-471-6040-4
The Nordic Graduate School
Authors: Grevholm Barbro
Published: November 2024

The third summer school of NoGSME ...
Mathematically productive discourses among student teachers
Authors: Bjuland Raymond
Published: November 2024

This article reports research that focuses on the characteristics of mathematically productive discourses (MPD) while student teachers are working collaboratively on a geometry problem in a problem-solving context. Analyses from the discourses of two groups of students are presented in order to illustrate mathematically non- productive and productive discourses respectively. A definition of MPD is presented and used as an analytical tool to identify critical characteristics of sequences of productive discourses. This definition involves the following five criteria: 1) Student utterances, stimulating a monitoring utterance, 2) the monitoring utterance, 3) student responses, stimulating a second monitoring utterance, 4) the second monitoring utterance, 5) further elaborations, advancing the mathematical discussion among the students. The article also discusses the difficulty of concluding when a discourse is productive or not, especially when students are challenged to work on complex problems in which a solution is not usually reached within a school lesson.
Anmeldelse af Didaktiske elementer – en indføring i matematikkens og naturfagenes didaktik
Authors: Niss Mogens
Published: November 2024

Carl Winsløw (2006). Didaktiske elementer – en indføring i matematikkens og naturfagenes didaktik. Frederiksberg: Bifolia. (254 sider) ISBN: 87-9131-933-1
Some aspects of web-courses in mathematics based on PC screen recorded video lectures
Authors: Lukkassen Dag , Persson Lars-Erik , Sierpinska Anna
Published: November 2024

In this paper we will describe and discuss two graduate level web-based mathematics courses based on PC screen recorded video lectures. These courses have been developed by the first author of this paper and followed by master’s students at the Narvik University College since 2001. Comparison to other available courses is made. We argue that the technical solutions, our personal positive experiences and didactical ideas (e.g. concerning the physical presence of students and teachers in addition to instruction by video) in relation to our concept constitute an interesting field for mathematical education research.
The International Commission on Mathematical Instruction: a centenary of history and a future to construct
Authors: Editors The
Published: November 2024

Ledare / Editorial
Växelverkan mellan intuitiva idéer och formella resonemang – en fallstudie av universitetsstudenters arbete med en analysuppgift
Authors: Pettersson Kerstin
Published: November 2024

Studiens syfte är att visa hur en växelverkan mellan intuitiva idéer och formella resonemang kan gestalta sig i en problemlösningsprocess. Studien visar att universitetsstudenter redan under sitt första år av matematikstudier förmår utnyttja en sådan växelverkan. En grupp studenter har arbetat med en analysuppgift som berör begreppen funktion och derivata samt inkluderar ett induktionsbevis. Studenterna utnyttjar i den kreativa processen intuitiva idéer och formella resonemang i ett dynamiskt samspel. Växlingarna har ett flertal funktioner: att kontrollera intuitiva uppfattningar, att skaffa nya utgångspunkter för problemlösningsprocessen, att ekonomisera resonemang och att driva arbetet vidare.
Social konstruktivism som grund för matematikundervisning
Authors: Björkqvist Ole
Published: November 2024

Mot bakgrund av huvudidéerna hos olika konstruktivistiska riktningar väljes den sociala konstruktivismen som utgångspunkt för en härledning av didaktiska prin- ciper för undervisning i matematik. Matematiken ses som en social konstruktion, en särpräglad del av den kollektiva kunskap som människan konstruerat för att överleva som art och som fortlever och utvecklas bunden till en viss kultur. Växel- verkan mellan denna kollektiva kunskap och individens konstruktion av kunskap är central för de didaktiska konsekvenserna. Denna artikel baserar sig på ett bidrag till ett symposium i matematisk och naturvetenskaplig didaktik arrangerat vid Insti- tutionen för lärarutbildning, Åbo Akademi, Vasa, 26 - 27.9. 1991, och har i en något avvikande form publicerats i symposiets proceedings.
Nordisk Forskernetværk – Initiativet Matematikundervisning og Demokrati
Authors: Nissen Gunhild
Published: November 2024

I denna artikel redogörs för tankarna bakom det danska Initiativet Matematik- undervisning och demokrati. Projektet har särskilt betonat vikten av att lära och använda matematik som en grundläggande nödvändighet för alla i en fungerade demokrati. Det nordiska samarbetet har bl a tagit sig uttryck i ett växande nätverk av matematikdidaktiker och forskarkurser om centrala frågeställningar inom det matematikdidaktiska kunskapsområdet.
Multilingual issues in Nordic mathematics education – What is achieved and where to go next?
Authors: Prediger Susanne
Published: November 2024

This Nomad special issue provides eleven highly interesting insights into current research and development projects in mathematics education on multilingual and multicultural issues. It shows the diversity of approaches currently adopted in the Nordic Countries with an impressing richness of perspectives and ideas. I am grateful to have had the opportunity to read and discuss the papers carefully as I learned a lot. In this commentary, I compare and connect the papers with each other and the international state of research and to suggest some directions for further research and deve-lopment. The commentary is structured in the following steps: Different implicit and explicit conceptualization of languages are identified in the articles (first section); different research approaches are summarized with a need to strengthen Design research (second section); and different instructional approaches for activating multiple language resources for mathematics learning and further enhancing both languages (third section).
Literature review of mathematics teaching design for problem solving and reasoning
Authors: Sidenvall Johan
Published: November 2024

To characterize teaching designs intended to enhance students’ problem solving and reasoning skills or to develop other mathematical competencies via problem solving and reasoning, a literature review was conducted of 26 articles published in seven top-ranked journals on mathematics education from 2000 to 2016. Teaching designs were characterized by a) the educational goals of the designs, b) the claims about how to reach these goals, and c) the empirical and theoretical arguments underlying these claims. Thematic analysis was used to analyze the retrieved articles. All but two studies had goals concerned with developing students’ mathematical competencies. The overarching ideas of the identified emergent claims regarding the achievement of stipulated goals, concerned scaffolding students’ learning and letting students construct their own mathematics. Four recurring theoretical arguments were found to support emergent claims: hypothetical learning trajectories, realistic mathematics education, theory of didactical situations and zone of proximal development.
Editorial
Authors: Kilhamn Cecilia , Strømskag Heidi , Hästö Peter , Liljekvist Yvonne , Häggström Johan
Published: November 2024

Ledare / Editorial
Developing a frame for analysing different meanings of the concept of variable mediated by tasks in elementary-school mathematics textbooks
Authors: Partanen Anna-Maija , Tolvanen Pieti
Published: November 2024

Pupils’ studies in arithmetic can support the development of their algebraic thinking if arithmetic is taken as a starting point for generalising in sense-making discussions. One of the most prominent concepts in algebra is that of the variable, which can have many different meanings, depending on its context. In this paper, we develop a frame for content analysis of tasks in elementary-school mathematics textbooks. New categories for the meaning of variable are added to previous summaries, based on the literature review and the analysis. The developed frame can be used for analysing curricular materials, especially at the elementary-school level.
Algebraic thinking and level of generalisation: students’ experiencing of comparisons of quantities
Authors: Eriksson Helena
Published: November 2024

This article explores grade 1 students’ different ways of experiencing quantity comparisons after participating in teaching designed as a learning activity using tasks from the Davydov curriculum. A phenomenographic analysis generated three hierarchical ways of experiencing comparisons: counting numerically, relating quantities, and conserving relationships. The first category comprises arithmetic ways of thinking, whereas the second and third categories comprise algebraic ways of thinking. Algebraic thinking was identified as reflections on relationships between quantities at different levels of generalisation. The implications of these results in relation learning activity theory are discussed.
Algebra teachers’ questions and quandaries – Swedish and Finnish algebra teachers discussing practice
Authors: Kilhamn Cecilia , Röj-Lindberg Ann-Sofi
Published: November 2024

Taking the teachers’ own practices as a point of departure, this study investigates what areas of mathematical knowledge algebra teachers brought up in collegial discussions and how they used their knowledge in acts of decompressing, trimming and bridging. The discussions centered around aspects of teaching and learning school algebra previously shown to be problematic, but gave rise to mathematical quandaries, revealing gaps in the teachers’ own understanding of the mathematical content. The study implies that the ability to unpack a mathematical concept is essential in algebra teaching and that teachers may need external input concerning mathematical knowledge to enable development in pedagogical content knowledge.
Exploring engineering students’ participation in flipped mathematics classroom: a discursive approach
Authors: Fredriksen Helge , Hadjerrouit Said
Published: November 2024

This paper explores first-year engineering students’ participation in flipped mathematics classroom. The work uses Sfard’s commognitive framework both as a lens for conceptualizing learning as participation in mathematical discourse and as a methodology for analysing the data generated by the activities that build the mathematical discourse. Data was collected mainly by video recording of classroom activities of first-year engineering students enrolled in several mathematics courses at a Norwegian university in 2016/2017. The aim of the study is to add to the lack of research on participation in flipped mathematics classrooms at the university level. The paper argues that engagement in the videos out-of-class enhances students’ participation in the mathematical discourse. The commognitive analysis comparing out-of-class videos and in-class activities show that there are indications of student learning through expansion of the discourse in the videos and enhanced participation in mathematical activities.
A logical model for interventions for students in mathematics difficulties – improving professionalism and mathematical confidence
Authors: Lindenskov Lena , Tonnesen Pia Beck
Published: November 2024

This article describes elements in a Danish model for interventions in mathematics for students in mathematics difficulties. The authors have been core members of the intervention development team for the last decade. The aim of the interventions is to support the students and teachers involved and to be an instrument for municipalities and schools to improve mathematics culture. In the article, we start by sketching a couple of political level incentives and by outlining the pilot study and two large-scale experiments in which the model was implemented and expanded. We then present the research question that guides the article. In the main section, we present the logical model, which consists of nine boxes of inputs, processes and outputs. In order to illustrate viewpoints and ideas behind the boxes and their implementation, we have chosen to include some extracts from identification and teaching materials and some data collected through the pilot study and the experiments. We only address the many other existing intervention models to the extent that comparing characteristics helps to clarity characteristics in our own model. We conclude the article by claiming that an open standard to deal with students’ mathematics diffi- culties, and which is based on high expectations for students, teachers and schools, has been developed.
What the teachers and the students do and how they interact – a comparison of special education teaching and ordinary teaching in mathematics
Authors: Skorpen Leif Bjørn
Published: November 2024

In this article, I compare three teaching situations: ordinary mathematics teaching, special education teaching in mathematics located within the ordinary class, and special education teaching in mathematics located outside the ordinary class, in order to find the main differences between them with respect to what the teacher and the students do. The findings are discussed in light of various aspects of the inclusion concept. The empirical material has been collected in the SPEED-project and consists of observations throughout an entire school day of 108 individual students, their teachers and the classes they belong to. The discussion reveals that the special education teaching is more individual, the student is more frequently engaged in subject-related activities and in communication with the teacher, and that each of the two different organizational forms of the special education teaching in mathematics separately seem to fulfil different aspects of the concept of inclusion in a best way.
Exploring student explanations: What types can be observed, and how do teachers initiate and respond to them?
Authors: Drageset Ove Gunnar
Published: November 2024

This article presents different types of student explanations that can were observed, and how these were initiated and responded to. The research is based on the practice of five teachers, with all interactions having been analysed and categorized to develop the concepts. First, three distinct types of student explanation were found: explaining actions, explaining reasons, and explaining concepts. Secondly, the teachers’ initiations were inspected, by studying the turn before each student explanation. Strong connections were found between the initiation and each type of student explanation. Thirdly, teachers’ responses to the students’ explanations were inspected, with three main types of response being found to all three types of student explanation: pointing out what to notice, requesting further detail, and confirming and moving on. The main contribution of this article is the conceptualization of students’ explanations and the explanation of how these are initiated and responded to.
Dekomponering av planleggingspraksis i en syklus av utforsking og utprøving i lærerutdanning
Authors: Valenta Anita , Rø Kirsti , Persdatter Ødegaard Reidun , Langfeldt Marit Buset
Published: November 2024

I lærerutdanningsforskning pekes det stadig oftere på et behov for å organisere arbeid med studenter rundt sentrale undervisningspraksiser, og syklusen av utforsking og utprøving er en av tilnærmingene som er blitt brukt til det formålet. I denne studien ser vi nærmere på planleggingsfasen i syklusen og identifiserer hvordan en lærerutdanner dekomponerer praksisen ”planlegging av matematisk diskusjon mot et gitt faglig mål” mens han leder planleggingen i tre studentgrupper. Ved å identifisere og beskrive lærerutdannerens handlinger åpnes det for videreutvikling av arbeid med praksisen i lærerutdanning. Vi sammenligner våre resultater med tidligere studier som omhandler dekomponering av planlegging for å diskutere lærerstudenters muligheter for utvikling av en planleggingspraksis innen arbeid med syklusen.
Designing a game-based environment for enhancing rational number knowledge
Authors: Kärki Tomi , McMullen Jake , Lehtinen Erno
Published: November 2024

Rational number knowledge is an important factor in students’ mathematical development. However, many students face difficulties with rational number concepts. This study describes a new educational game, NanoRoboMath, which has been designed to support students’ rational number knowledge. Our goal is to examine the design and the nature of the mathematical practice in the game. Four comprehensive school students aged between 11 and 13 years individually played a prototype version of the game. Video recordings and log data of these game sessions revealed that the game was able to elicit mathematical activities related to rational numbers. This version of the game seemed to enable a variety of strategies matching different skill levels and supported arithmetic activities related to different aspects of rational number conceptual knowledge.
Effective mathematical communication in play-based activities: a case study of a Norwegian preschool
Authors: Nergård Beate , Wæge Kjersti
Published: November 2024

This article focuses on effective mathematical communication in preschool. Based on a qualitative case study of a Norwegian preschool, we explore how visual mediators, gestures and mathematical concepts support effective mathematical communication in play-based activities. The article shows how these modes, and the links between them, were crucial for establishing effective communication. Visual mediators, gestures and mathematical concepts functioned as means for making the focal projects and the contexts explicit in the conversations, and thus for communicating effectively.
Languaging in mathematics classrooms – space for students’ varied language repertoires in the Language introduction program in Sweden
Authors: Wedin Åsa
Published: November 2024

The aim for this article is to investigate how languaging in mathematics classrooms for recently arrived students may or may not support students’ development of mathematics language and thinking. The study builds on classroom observations with four teachers in upper secondary school in Sweden, and the analysis is based on languaging as a source of meaning. Generally, students did not ask many questions and it was only in two classrooms that students were required to talk mathematics and to move between different representations. A space open for students’ use of their varied linguistic repertoires appeared. However, whether teachers themselves took part in the ongoing translanguaging practices or not influenced what value these practices were attributed. The article highlights the need for teachers to be educated in the role of languaging in mathematics and in conditions for learning among recently arrived students and students who study school subjects through a second language that they are in the beginning of learning.
Editorial
Authors: Kullberg Angelika , Björklund Camilla , Mosvold Reidar
Published: November 2024

Ledare / Editorial
Learning to teach mathematics in preschool through theory-driven interventions
Authors: Björklund Camilla , Ekdahl Anna-Lena
Published: November 2024

In this paper we aim to highlight how teachers’ ways of experiencing mathematics teaching for preschoolers is reflected in their teaching acts. The specific research question is how one teacher’s way of experiencing the task of teaching numbers to preschool children change when participating in a professional development project informed by Variation theory principles. We analyze the teaching of one teacher participating in a professional development project during one preschool year with particular interest in how principles for teaching numbers in preschool are implemented in the teacher’s teaching. Observations from authentic teaching situations and an interview with the teacher are data for analysis. From a variation theoretical analysis, we draw conclusions of how the teacher’s ways of experiencing mathematics teaching to preschoolers is reflected in her teaching acts and what challenges there are to implement theory-driven mathematics education in preschool.
Initiating teacher-researcher collaboration to support students’ mathematical problem-solving
Authors: Säfström Anna Ida , Palmberg Björn , Granberg Carina , Sidenvall Johan , Lithner Johan
Published: November 2024

Implementing teaching through mathematical problem-solving entails substantial challenges and calls for sustained teacher-researcher collaboration. The joint research and development project ”Teaching that supports students’ creative mathematical problem-solving” has a fundamental ambition to be symmetric in that both teachers’ and researchers’ needs and conditions are attended to and complementary in that their different areas of expertise are utilised and valued. In this paper we show how the interplay and development of symmetry and complementarity can function as a means for studying teacher-researcher collaborations.
Utvikling av matematikk-undervisning – en kommognitiv analyse av rutiner i klasserommet
Authors: Tyskerud Anita
Published: November 2024

Denne studien undersøker utvikling av undervisning hos en gruppe matematikklærere som deltar i lesson study for første gang. Utvikling av undervisning i et kommognitivt perspektiv defineres som endring i rutiner. Analysene av seks forskningstimer fra tre lesson study-sykluser identifiserer rutiner i klasserommet når lærerne presenterer oppgaver. En sammenlikning av funnene viser at endringer i rutiner forekommer, men det er vanskelig å spore mønster eller tegn til varige endringer. Rutinene knytter undervisning og elevers mulighet for læring sammen, to komplekse dynamiske prosesser.
Practice-based research on mathematics teaching: A developmental turn?
Authors: Venkat Hamsa
Published: November 2024

When I began my career in mathematics education research in the early 2000s, I was fascinated by a number of what were, at the time, recent and emerging studies of mathematics teaching ...
Mathematical modelling in textbook tasks and national examination in Norwegian upper secondary school
Authors: Berget Ingeborg Katrin Lid
Published: November 2024

Modelling competence is defined as the ability to carry through all steps of a mathematical modelling process, to solve a non-mathematical problem by mathematics. In this study, Norwegian textbook modelling tasks and tasks from the national exam are analyzed through the lens of a modelling cycle. The findings discussed as the enacted curriculum (textbook tasks) and assessed curriculum (exam tasks) are seen in relation to the intended curriculum. The results show different starting points of the modelling process in the intended curriculum and the tasks from textbooks and exam. The findings indicate different perspectives on mathematical modelling in the curriculum (modelling for developing modelling competence) and the textbook tasks and the national exam, where only parts of the modelling process are included.
Computational thinking as a tool in primary and secondary mathematical problem solving: a literature review
Authors: Stavenæs Refvik Kim André , Bjerke Annette Hessen
Published: November 2024

In this systematic literature review, we investigate the connections between computational thinking and problem solving in the context of primary and secondary mathematics education. We do this by exploring how and at which steps in the mathematics problem-solving process seven peer reviewed studies report on the inclusion of computational thinking concepts, practices and perspectives. Overall, the studies show that it is possible and at times beneficial to include computational thinking in mathematics problem solving. However, more research is needed to see whether simply including computational thinking and its programming tools enhances students’ problem-solving skills in mathematics.
Students’ reasoned dialogs during problem solving in a Norwegian thinking classroom
Authors: Valbekmo Ingunn , Bjuland Raymond
Published: November 2024

This study explores students’ collective mathematical problem-solving processes. Grade-seven Norwegian students were observed during regular problem-solving sessions to discover how reasoned dialogs might develop in a thinking-classroom context. An analytical framework associated with sociocultural discourse analysis was used to identify utterances (dialog moves) that were essential in revealing a dynamic and continuous scaffolding process with symmetrical interaction between the students, and where the vertical whiteboards supported students during the reasoned dialogs. The context of a thinking classroom created an environment suitable for highly interactive learning where students constructed and refined their ideas in collaboration with each other. The findings also point to the crucial role of the teacher as a facilitator of classroom dialogs to get students to dig deeper into the ideas of others.
A set of design principles for exercising mathematical communication competency when using a DGE
Authors: Bach Cecilie Carlsen
Published: November 2024

In design research, design principles involve the development of theory and practice. This paper refines a set of humble design heuristics into a set of design principles in the third iteration of a design research project. The set of design principles aims to exercise (meaning ”to put into practice”) students’ mathematical communication competency when using a dynamic geometry environment (DGE). Based on an analysis, which includes perspectives on the instrumental approach, semiotic registers and mathematical language, the set of design principles is refined by transforming an analysis of two 9th grade (15–16 years old) students’ interactions with the task design into prescriptive principles. The overall principle of separate – join – new separate indicates that it is crucial to relate mathematical representations across registers in the different steps, individually and in collaboration.
From policy to resources: programming, computational thinking and mathematics in the Danish curriculum
Authors: Elicer Raimundo , Lindenskov Tamborg Andreas
Published: November 2024

This article investigates the relations between mathematics and programming and computational thinking (PCT). In scholarly knowledge, PCT is juxtaposed as an aid to mathematical problem solving, but also integrated as a collection of practices common to both domains. This knowledge is being turned into curriculum and teaching resources developed for Danish compulsory schools (students aged 6–15), in the context of a pilot project to embed a new technology comprehension subject into mathematics. In the curriculum, PCT is being juxtaposed to mathematics. The teaching resources are predominantly integrated, but lacking connections to mathematical problem solving and modelling. These misalignments are both missed opportunities and a leeway for a cautious integration in teaching practice.
Anna Sierpinska död
Authors: Grevholm Barbro
Published: November 2024

Minnesord av Barbro Grevholm
Teaching mathematics with high cognitive activation: instructional formats and connection-making interactions in high-level Nordic lessons
Authors: Sigurjónsson Jóhann Örn
Published: November 2024

Cognitive activation is a dimension of teaching quality which considers to what extent the teacher addresses the educational goal of student understanding, such as through successful implementation of demanding tasks. This study aimed to enrich empirical understandings of instructional formats and teacher-student interactions in cognitively activating lessons. Eight lessons were purposefully selected from a Nordic video database containing 125 lessons. The interactions in the lessons were analysed using reflexive thematic analysis and instructional formats using content analysis. Whole-class discussions and group work were the dominant formats. Four types of connection-making interactions were observed, connecting both within mathematics and to non-mathematical experience.
Researching mathematics teachers’ professional identities: complexities and ways ahead
Authors: Skott Jeppe , Lutovac Sonja , Bjuland Raymond
Published: November 2024

Editorial
Analyzing teachers’ narratives to identify potential impediments of professional development in mathematics
Authors: Bjuland Raymond , Fauskanger Janne , Mosvold Reidar
Published: November 2024

This study explores two experienced teachers’ identifying narratives on teaching mathematics with problems in professional development. Data is from the Partners in practice project, which aims to support transition from traditional to progressive educational practices. The study investigates narratives of these teachers and how they align with dominant discourses of teaching in the field. Analysis suggests that both teachers are squeezed between their specific pedagogical discourses and more official pedagogical Discourses. Secondly, there is an unclear connection between the teachers’ discourses as learners and as teachers of mathematics.
Conceptualising (mathematics teacher educator) identity work: an enactivist-informed approach
Authors: Helliwell Tracy , Ebbelind Andreas
Published: November 2024

Research suggests that engaging in identity work is a vital part of a process of becoming a mathematics teacher and that mathematics teacher educators (MTEs) are key to supporting this process, yet we currently know very little about the identity work of MTEs themselves. In this paper, we contribute to this dearth of literature whilst exploring what the perspective of enactivism has to offer identity research given its emphasis on relationships and embodied action. We formulate our conceptualisation of MTE identity work as a set of seven methodological principles informed by the enactivist theory of cognition.
The first issue in English
Authors: Johansson Bengt
Published: November 2024

Editorial / Ledare
Assessing authentic tasks: alternatives to mark-schemes
Authors: Wiliam Dylan
Published: November 2024

The kinds of authentic tasks that have been used in national assessments in Eng- land and Wales over the last thirty years - typically open-ended, 'pure' investigative tasks - are described, and the marking schemes used for their assessment are classified as either task-specific or generic. Generic schemes are further classified according to whether the 'degree of difficulty' of the task or the 'extent of progress' through the task is given most emphasis. A view of validation is presented that requires consideration of the value implications and social consequences of imple- menting assessment procedures, and it is argued that both task-specific and generic schemes will have the effect of stereotyping student approaches to these tasks. An alternative paradigm to norm-referenced and criterion-referenced interpretations of assessments, entitled 'construct-referenced' assessment, is proposed as being more consistent with the rationale behind such authentic assessments. Suggestions for the implementation of such a system are made and indices derived from signal- detection theory are suggested as appropriate measures for the evaluation of the accuracy of such assessments.
Matematikundervisning i en demokratisk kultur
Authors: Nissen Gunhild
Published: November 2024

Vi har svårigheter att få den förståelse för matematik som ett demokratiskt samhälle kräver. Varför har inte ämnet fått plats vid sidan av historia och litteratur i en folklig upplysningstradition? Hör inte matematiken hemma i en skola för livet?
I artikeln belyses hur olika grupper i samhället har ett problematiskt förhållande till matematik och vilka konsekvenser detta har för ämnets ställning i och utanför skolan. Förslag ges på åtgärder för att bryta matematikämnets isolering.
Artikeln baserar sig på ett föredrag, som hölls vid den 8:e Matematikbiennalen 26-28 januari, 1994 i Göteborg.
Algorismus i Hauksbók
Authors: Bekken Otto B.
Published: November 2024

I Kongespeilet fra 1260 sies det som kjent, at kunnskap i regning er nyttig for kjøpmannen, men vi vet ellers lite om hvordan regningen foregikk før 1300-tallet her i Norden. I den norsk-islandske Hauksbok fra ca. 1310 finner vi imidlertid en innføring i regning medhindu-arabiske tall. I denne artikkelen søker vi svar på følgende spørsmål: Hva er kildene for dette? Hvor original er den? Hva sier den oss om læring og forståelse av matematikk i 1300-tallets Island-Norge i forhold til ellers i Europa?
Single-sex mathematics classes: Who benefits?
Authors: Forgasz Helen J. , Leder Gilah C.
Published: November 2024

A co-educational high school in Melbourne, Australia, introduced an innovative program of single-sex mathematics classes for grade 10 students. Of particular concern to the school was the impact of the program on enrolments in mathematics courses in grade 11. The requested evaluation of the program is reported in this paper. Students' and parents' reactions, the effects on students' achievements and their beliefs about themselves as learners of mathematics are presented. Implications of the findings and recommendations to the school for future action are discussed.
Om problemlösning, laborativa material och test
Authors: Johansson Bengt , Emanuelsson Göran
Published: November 2024

Ledare/Editorial
Staking Claims
Authors: Kilpatrick Jeremy
Published: November 2024

The field of mathematics education has both scholarly and professional aspects. On the scholarly side, the question of what counts as research is still being debated. An examination of two proposed sets of criteria for evaluating the quality of research in mathematics education reveals that, interpreted appropriately, criteria borrowed from the natural and social sciences are relevant to a field that is attempting to be scientific. On the professional side, mathematics education must inevitably be concerned with the application of specialized knowledge to assist the students and teachers who are its clients. Teacher education remains a major function of mathematics education, parallel to the search for reliable knowledge to be applied. University mathematics educators need to work closely with mathematicians and with classroom teachers in developing both theory and practice. Mathematics education has flourished in countries in which institutional structures have supported it as an identifiable academic field.
Ett nytt dubbelnummer
Authors: Johansson Bengt , Emanuelsson Göran
Published: November 2024

Ledare/editorial
Graphing calculators and students' interpretations of results: a study in four upper secondary classes in Sweden
Authors: Dahland Göte
Published: November 2024

Thanks to a drastic change in the availability of graphing tools in the teaching and learning of mathematics, a similar change in written and oral ways to communicate the subject can be expected. In several reports students' participation in mathematics and students' views of the use of electronic tools like graphing calculators are discussed. A study in upper secondary classes in Sweden confirms that test items can be classified according to how students tend to record their written solutions. Logical solutions recorded in a traditional way are not mastered sufficiently, and when a modern approach with graphing calculators is used, at least two difficulties must be taken into account. The student must have technical insight to be able to interpret the information given on a graphics screen, and the student must also have a sufficiently good mathematical understanding to realize the connection between the current problem and the possibilities given by the tool. Some consequences for mathematics education are discussed.
Utvecklingsarbete i en skola inspirerat av NOMAD och Nämnaren
Authors: Svensson Bengt
Published: November 2024

Här beskrivs hur studium av artiklar i NOMADoch Nämnaren inspirerat lärarna på en svensk skola till ett utvecklingsarbete, som omfattar bl a kompetensutveckling, arbetsformer, undervisningens innehåll och matematikens integrering i andra ämnen. Arbetet har påverkat den lokala arbetsplanen, som i sin tur inspirerat till fortsatt utvecklingsarbete.
A review of recent research on cognitive, metacognitive and affective aspects of problem solving
Authors: Barkatsas Anastasios N. , Hunting Robert P.
Published: November 2024

Mathematical problem solving is a complex activity that necessitates thoughtful consideration about the best ways to teach it, since any two individuals can arrive at the same solution to a problem using different, but correct methods.
An identification of common traits that expert problem solvers possess, instruction related problem solving research, the contribution of cognition, meta-cognition and belief systems, are presented in this research review in an effort to weave a coherent picture of the state of the art of problem solving in mathematics today.
Some unrepresented and underrepresented issues are also considered, in order to provide evidence of the diversity and multiplicity of issues concerning mathematical problem solving research and the need for collaboration between researchers in this field of study.
Announcements – Literature
Authors: Emanuelsson Göran
Published: November 2024

Announcements – Literature
Funktionsbegrebet og 9. klasse elevers begrebsforståelse
Authors: Blomhøj Morten
Published: November 2024

Elevers vanskeligheder med at tilegne sig funktions-begrebet som et teoretisk begreb med et net af relationer til andre begreber som variabel, ligning og graf er velkendte både i matematikdidaktisk forskning og i undervisningens praksis. I det danske skolesystem viser de sig mest markant ved overgangen fra folkeskolens til gymnasiets matematikundervisning. Denne problemstilling belyses i artiklen ud fra en empirisk undersøgelse af begrebsforståelsen hos en 9. klasse. Analysen afdækker fællestræk ved nogle elevers forståelse, der viser at de har meget vanskeligt ved at tilegne sig afgørende begrebssammenhænge mellem f.eks. ligning og funktion. Analyse af to kvalitative elevinterview viser endvidere, at elevernes forståelse kan være både sammenhængende og modstandsdygtig over for udfordringer, selvom den ikke er i overensstemmelse med de objektiverede matematiske betydninger af begreberne. Artiklen fremdrager enkelte undervisningsmæssige konsekvenser af analysen.
Litteraturanmeldelse – Approaches to Algebra Perspectives for Research and Teaching
Authors: Breiteig Trygve
Published: November 2024

Bednarz, N., Kieran, C. & Lesley, L. (eds.) (1996) Approaches to Algebra. Perspectives for Research and Teaching. (Mathematics Education Library, Volume 18). Dordrecht, NL: Kluwer Academic Publishers, 345 p. https://doi.org/10.1007/978-94-009-1732-3_1
Et matematikkdidaktisk tidsskrift
Authors: Brekke Gard , Gjone Gunnar
Published: November 2024

Ledare / Editorial
Rethinking the role of context in mathematics education
Authors: Patronis Tasos
Published: November 2024

In this paper the role of context in teaching and learning mathematics is considered from a «local» and then from a «global» point of view. The «local» viewpoint focuses on context as a «scene» providing meaning to the mathematical content, while the «global» one addresses the problem of transformation of a given context, which arises when the teacher intends to put the students into a new perspective of mathematical knowledge. Both these viewpoints are used in an attempt to relate context to the metonymic transformation of the meaning of words used in mathematics. From this point of view various mathematical and empirical (classroom) examples are discussed and reinterpreted in the paper.
Matematikkens sproglighed som didaktisk potentiale
Authors: Winsløw Carl
Published: November 2024

Med udgangspunkt i klassiske og nyere matematikfilosofiske synspunkter redegøres kort for hvorledes matematik som fænomen kan beskrives i sprogteoretiske termer. Derpå diskuteres konsekvenserne af en sådan beskrivelse for to grundlæggende matematikdidaktiske problemkredse: Hvordan begrundes matematikundervisning? Hvordan kan matematikundervisning sætte den lærende i stand til at udvikle kreative (i modsætning til automatiske) kompetencer i udøvelse og anvendelse af faget?
The International Congress on Mathematical Education in 2008 - a task for the Nordic countries?
Authors: Brekke Gard , Gjone Gunnar
Published: November 2024

Ledare / Editorial
Computer support for diagnostic teaching – the case of decimal numbers
Authors: Fuglestad Anne Berit
Published: November 2024

Computers with different kinds of software were used in mathematics teaching during one school year with Norwegian students of age 10–14. The development of students' understanding of decimal numbers was investigated, using computers to support a diagnostic teaching approach. In particular some spreadsheet tasks were used to stimulate mathematical investigations and to generate discussions exhibiting conflict. An item analysis of pre-test data revealed a common pattern of misconceptions on decimal numbers. As the students worked on the spreadsheet tasks, their concepts seemingly were in conflict with what they observed. This led the students into lively discussions. The test results indicated that the computer group improved significantly by comparison with the control group on part of the test, with the greatest improvement from the 'high' spreadsheet users in the research group.
Engagement with task context of applications tasks: student performance and teacher beliefs
Authors: Stillman Gloria
Published: November 2024

This study investigated the impact of engagement with the task context by upper secondary students on their performance on applications tasks and teacher beliefs about the effects of students' engagement with task context. Moderate to high engagement with a task context was not often associated with poor performance which was more likely to be associated with no to low engagement. High engagement with task context was not a necessary condition for success as the degree of engagement necessary for success may be task specific. Engagement with task context alone was not of sufficient explanatory power to account for all the patterns in the data and it is acknowledged other factors need to be considered. Students identified a sense of realism and having an objective to work towards as facilitators of their engaging with task context. Amongst the teachers interviewed, there was support for the following beliefs: (a) students' preferred degree of contextualisation determines whether success is accompanied by engagement with the task context; (b) if the mathematics is not integrated with the task context, students will not engage with the context and will develop the habit of ignoring it; (c) if the two are integrated, students will engage with the task context; (d) the setting of tasks where the context transcends reality is problematic. The last of these was not supported by all teachers, however.
Internasjonale undersøkelser
Authors: Brekke Gard , Gjone Gunnar
Published: November 2024

Ledare / Editorial
Integration, a genetic introduction
Authors: Burn Robert P.
Published: November 2024

The genetic method of O.Toeplitz is a structuring of conventional instructional material using historical insights and historical problems, not for a history course, but for the better understanding of modern mathematics by students today. The paper which follows describes an introduction to integration suitable for a first course in analysis, in the style of Toeplitz. After two examples of the Greek method of exhaustion (intended for lecturers rather than students), historical developments from the 17th and 19th centuries pinpoint the conceptual steps which a student must take in a conventional first course in analysis up to the Riemann integral.