bluuebunny/crossref_metadata_2025 huggingface dataset:
En flygande start!
Authors: Johansson Bengt
Published: November 2024

Editorial/Ledare
Mediating artifacts and interaction in a computer environment – An exploratory study of the acquisition of geometry concepts
Authors: Wyndhamn Jan
Published: November 2024

Nine dyads of twelve-year old students were engaged in collaborative small-group activity in order to find a way to determine the area of a parallelogram via a computer program. The program introduced two models or metaphors of a parallelogram, one changing the perimeter with a constant area ("the deck-of-cards model"), the other changing the area with a constant perimeter ("the frame model"). By changing the form and size of a displayed parallelogram the students had the opportunity to explore and obtain the characteristics of the parallelogram. The interaction between the students and their interaction with the computer were registered for analysis. After twenty minutes work with the computer, only one dyad failed to obtain the idea of the area determinants. The students' discussion, characterized by active inter- pretation and mutual adoption in combination with the deck-of-cards model as medi- ating artifact, established a situation in which the students acquired the conception that the area remained invariant through a specific kind of transformation. This know- ledge was then used to draw a rectangle with the same area as a given parallelogram.
Att designa för elevers deltagande i ett algebraiskt arbete – elever i årskurs 2 och 3 utforskar visuellt växande mönster
Authors: Fred Jenny
Published: November 2024

Artikelns syfte är att beskriva och analysera vad i olika lektionssekvenser som skapar förutsättningar för att elever ska engageras i ett algebraiskt arbete och därmed urskiljer kritiska aspekter. Artikeln bygger på data från tre forskningslektioner i vilka lärandeverksamhet (learning activity) tillsammans med Radfords arbete om mönster-generaliseringar har utgjort teoretiska utgångspunkter. I analysen har didaktiska principer från lärandeverksamhet samt kritiska aspekter gällande att uttrycka och argumentera för mönstergeneraliseringar fungerat som analysredskap. Resultatet kan bidra till att fördjupa förståelsen gällande på vilka sätt principerna från lärandeverksamhet kan stödja ett etablerande och upprätthållande av ett algebraiskt arbete och därmed möjliggöra för elevers urskiljande av kritiska aspekter.
Kystfiskermatematikk og skolematematikk: to ulike perspektiver på hva ei méd er
Authors: Fyhn Anne Birgitte , Robertsen Håkon
Published: November 2024

Kystens begrep méd er sentralt for blant annet å finne frem på havet og for å lokalisere fiskeplasser. En tradisjonell euklidsk beskrivelse går ut på at ei méd er ei rett linje gitt ved to punkter. Kystens folk har imidlertid utviklet sitt eget funksjonelle språk knyttet til begrepet méd. Der skolematematikken refererer til begreper fra euklidsk geometri, har kystfiskerne utviklet egne begreper og egen terminologi. Artikkelen bidrar til å synliggjøre matematikk i denne delen av vår immaterielle kulturarv. Vi belyser hvordan forskjeller mellom nordnorske kystfiskeres matematikk og skolematematikk kommer til uttrykk gjennom språk og kulturell praksis. Kystfiskernes kontekstavhengige matematikk bruker få ord, men språket er like presist som skolematematikkens mere omstendelige formuleringer.
Potentialer og begrænsninger ved anvendelse af lærebøger i matematikundervisningen: resultater fra et systematisk review
Authors: Steen Natasja , Madsen Matilde Stenhøj , Højgaard Tomas
Published: November 2024

Denne artikel sammenfatter et kvalitativt, systematisk review af hvilke potentialer og begrænsninger der kan identificeres ved anvendelse af lærebøger i matematikundervisningen. Første del af artiklen beskriver den metodiske tilgang og afsluttes med et geografisk og tidsmæssigt overblik over forskningsfeltet. I anden del af artiklen præsenteres anvendelsen af begrebskort som et analyseredskab til at afdække sammenhænge i temaerne i den udvalgte litteratur. Resultatet af reviewet præsenteres som et oversigtsskema over de 59 inkluderede kilder. Disse kilder fordeler sig indenfor ti temaer der overordnet kan placeres i fire kategorier: ”lærebogsbegrebet”, ”lærebogen og eleverne”, ”lærebogen og curriculum” samt ”lærebogen og lærerne”. Disse kategorier udtrykker relationer lærebogen indgår i. Tredje del af artiklen beskriver eksempler på fund indenfor de fire kategorier og går tættere på kvalitative analyser i tre af disse temaer herunder et bud på en definition af begrebet ”lærebog”.
Guidelines for utilizing affordances of dynamic geometry environments to support development of reasoning competency
Authors: Højsted Ingi Heinesen
Published: November 2024

This article reports on guidelines developed based on an extensive research literature review investigating the potentials of dynamic geometry environments (DGEs) when the educational aim is to support students’ development of mathematical reasoning competency. Four types of potentials were identified – feedback, dragging, measuring, and tracing – and used in three dimensions of guidelines: students’ cognition, task design, and the role of the teacher. Using constructs from the Instrumental approach, the Theory of semiotic mediation, and the van Hiele model of levels, affordances and guidelines are elaborated upon and their potentials for reasoning competency are analyzed.
Student conceptions of assessment accommodations in university mathematics: an analysis of power
Authors: Nieminen Juuso Henrik
Published: November 2024

This study investigates the power relations that underlie assessment accommodations in the context of university mathematics. Assessment accommodations, such as extended testing time, have been claimed to be controversial and even discriminatory. This study approaches these practices through the viewpoint of power and governmentality to understand their sociocultural nature. Nine mathematics students with special needs were interviewed to give them a voice over their own accommodations. The analysis used three contrasting notions of power (sovereign, epistemological, and disciplinary power). The students understood assessment accommodations as unfair practices, which represents unilateral sovereign power. Epistemological and disciplinary power could be identified when the students normalised mathematical assessment, and in the ways the accommodations constructed exclusion. This study highlights the importance of understanding power in the context of assessment accommodations, to shed light on the power structures that might create inequity and injustice in mathematics assessment.
Educational settings in relation to special educational needs in mathematics
Authors: Roos Helena , Lindfors Maria , Bagger Anette
Published: November 2024

This paper focuses on students in need of special education in mathematics (SEM students) and highlights teachers’ and principals’ reflections upon these students’ construction of knowledge in relation to two educational settings: the regular teaching setting and the test setting. The findings indicate that SEM students’ knowledge is legitimized only when displayed. However, there appear to be differences according to the specific setting. Different settings imply different knowledge representations, norms, and practices that need to be taken into account when reflecting, planning, and carrying out teaching in mathematics in relation to SEM.
Mind the gap between students and their mathematical textbooks
Authors: Segerby Cecilia
Published: November 2024

Reading and comprehending mathematics textbooks means understanding the global meaning and for this to occur successful comprehension strategies are required. Drawing on the results of a pilot study with six grade 3 students, a relationship between the students’ reading skills and their mathematical skills appeared. To examine this relationship further eighteen students from grades 1, 4 and 7, with different achievement levels were interviewed in this study. Both in the pilot study and in the current study the interview questions were inspired by the comprehension strategies of prediction, clarification, questioning and summarization from Palincsar and Brown’s reciprocal teaching model. These strategies are connected to Halliday’s Systemic functional linguistics to better understand how the textbook context affects students’ use of comprehension strategies. The results show that all students had developed reading comprehension strategies that were more or less successful, starting already from grade 1. Furthermore, the results of this study highlights that all students, independent of their achievement level or grade, require explicit teaching concerning efficient comprehension strategies to grasp the mathematical content being presented in mathematics textbooks.
Tasks, tools, and mediated actions – promoting collective theoretical work on algebraic expressions
Authors: Eriksson Inger , Fred Jenny , Nordin Anna-Karin , Nyman Martin , Wettergren Sanna
Published: November 2024

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work.
Variation theory and teaching experiences as tools to generate knowledge about teaching and learning mathematics – the case of pre-service teachers
Authors: Mårtensson Pernilla , Ekdahl Anna-Lena
Published: November 2024

The theory-practice divide in teacher education is commonly viewed as there are two separate entities – theory and practice. However, in practice-based research approaches, theory is commonly integrated with existing practical knowledge with the aim to deepen teachers’ knowledge about practice or to create new knowledge. In this study, we examine 30 pre-service teachers taking part in a 5-week course in a teacher education program in Sweden, in which an action-research approach termed Learning study was used to deepen the pre-service teachers’ thinking and reasoning about mathematics teaching in order to develop primary student learning. Variation theory was used as a tool to support the pre-service teachers’ reflections on how different ways of structuring the mathematical content are related to student learning outcomes. This research aims to illustrate how the integration of theory and teaching experiences from the 5-week mathematics education course supported pre-service teachers’ generation of knowledge about teaching and learning mathematics. In this study, we regard mathematical tasks created by the pre-service teachers and used in the lessons as generated knowledge about the practice of teaching. Data were collected during the course and consist of written reports about task refinements in the pre-service teachers’ lessons. We identified five different ways of re-designing the tasks: expanding tasks, making tasks more explicit, making tasks less explicit, bringing metaphors and representations to the foreground, and creating new tasks.
Teachers’ participation in practice based research – a methodological retrospect
Authors: Palmér Hanna , Van Bommel Jorryt
Published: November 2024

The focus of this article is methodological, on how teachers’ participation in practice-based research coacts with research quality. Educational design research is an example of a practice-based research approach often used in mathematics education with the goal of developing both the theories and the practice of teaching and learning mathematics. In this article, one such educational design research study on problem solving in Swedish preschool class is used as an example of how teachers’ participation in practice-based research can develop and of how different kinds of collaboration between researchers and teachers coact with research quality. One conclusion of the methodological meta-analysis is that there is a challenging tension between ensuring external validity of a study versus enabling internal validity and improvement of practice.
Practice-based research on the teaching of mathematics: progress and imperatives for the future
Authors: Hoover Mark , Ball Deborah Loewenberg
Published: November 2024

Professional fields face persistent challenges in connecting practice and theory. In particular, tensions exist as to how theory and knowledge are developed, as well as what constitutes authority for practice. Together the articles in this issue explore three elements of the turn toward ”practice-based” research and professional education in mathematics education: designing teaching and learning in and for practice, learning mathematics teaching as a practice, and collaborating across professional roles and identities. In this commentary, we interrogate meanings of practice-based research on teaching and discuss themes across this collection of articles. We then argue for three imperatives for future efforts: (i) working on shared understandings of what the term ”practice-based” might mean; (ii) developing more nuanced conceptualizations of ”teaching”; and (iii) attending explicitly to justice in practice.
Creative and algorithmic reasoning – the role of strategy choices in practice and test
Authors: Bergqvist Tomas , Norqvist Mathias
Published: November 2024

This study is based on a framework of algorithmic and creative mathematical reasoning and focuses on students’ strategy choices in both practice and test. Previous research indicates that students that practice mathematics with tasks with given solution methods are outperformed in later test by students that have to construct solution methods during practice. Video recordings, students’ written solutions, and student interviews from ten university students provides data on strategy choices. The analysis was carried out to capture students’ strategy choices and reasons for these choices. The results showed that there was no real difference in how the students solved the tasks in the test. Regardless of practice condition, more or less the same solution strategies were used in the test situation.
Students’ reasoning and feedback from a teacher
Authors: Olsson Jan , D’Arcy Denice
Published: November 2024

The present study investigates how to support students’ creative reasoning when they need assistance in solving non-routine tasks. Two groups of 11–12-year-old students solved the same tasks, one group receiving feedback directed at the task solution and the other feedback directed at their thinking processes. The results showed that students who received feedback directed at their thinking processes expressed reasoning based on their attempts to solve tasks while the other group often repeated the researcher’s suggestions for solutions. However, there were some instances in which feedback on task level entailed students engaging in creative reasoning.
Scrutinizing Norwegian kindergarten teachers’ considerations about talk moves
Authors: Justnes Camilla Normann , Mosvold Reidar
Published: November 2024

Talk moves have been used as a communication tool for developing more productive mathematical discussions in school. To avoid uncritical adoption of a tool that was developed in a different context, it is important to consider cultural differences and concerns from the practice field. This study investigates group discussions among 15 Norwegian kindergarten teachers from seven kindergartens to explore how they understand talk moves, and what they consider to be possibilities and limitations of using talk moves in the Norwegian kindergarten context. We argue that kindergarten teachers’ concerns about talk moves do not seem to warrant rejection, but that professional efforts are required for meaningful enactment.
Videreutdanningsstudenters undervisningskunnskap relatert til likhetstegnets betydning i algebra
Authors: Fadum Aleksandra Hara , Tellefsen Helga Kufaas
Published: November 2024

Vi ser på videreutdanningsstudentenes forståelse av algebraiske uttrykk og likhetstegnets betydning og hvilke didaktiske konsekvenser det kan få. Vi presenterer resultatene fra en algebraisk oppgave besvart av 82 norske lærere på videreutdanningskurs i matematikk, 5–10 (aldersgruppe 10–16 år). Vi har sett etter en forståelse av lærernes egne matematiske kunnskap, deres analyse av elevens løsning og tilbakemeldingen de ville gitt eleven. En tematisk analyse av lærernes skriftlige arbeid viste at lærerne sjelden identifiserte misoppfatning om likhetstegnet som et hinder for å løse en oppgave. Resultatene av denne studien kan forhåpentligvis fungere som et framstøt til å forbedre videreutdanning for matematikklærere i algebra.
Methods and key findings in research on conversations in early years mathematics: a review of the literature
Authors: Hågensen Kleven Astrid
Published: November 2024

This qualitative systematic review aims to provide insight into applied research methods and key findings in early years mathematical communication research. This literature review focuses on newly published research reporting on young pupils’ (age 5 to 10) mathematical communication and reasoning. Reporting on 13 studies published between 2016 and 2020, the review found video-recordings as a favourable method for data collection, given its ability to capture verbal and non-verbal communication. Another finding was that implementing classroom norms or rules for conversation could be useful for children learning to communicate productively. The review also reports on several tools for teachers to improve practice related to conversations and mathematical reasoning.
Creative and conceptual challenges in mathematical problem solving
Authors: Jäder Jonas
Published: November 2024

Mathematical problem solving has proven to be valuable for students’ learning. Yet, problem solving is often referred to and discussed without distinguishing between creative and conceptual aspects. The purpose of this study is to advance understanding of mathematical problem solving through the analysis of students’ work with mathematical problems in terms of the creative and conceptual challenges they encounter. It is proposed that the characteristics of creative challenges can be used to obtain a more detailed description of the problem-solving process. Furthermore, the characteristics of conceptual challenges can provide a basis for discussion of what conceptual understanding may entail. Moreover, the analytic framework developed in this study is proven to be of assistance in the visualization of challenges and may be useful in future efforts to investigate challenges and students’ problem solving in mathematics.
Adaptive number knowledge among primary school students of various ages
Authors: Pehkonen Salla , Lehtinen Antti , Nieminen Pasi , Hähkiöniemi Markus
Published: November 2024

Previous studies have highlighted the importance of primary school students’ adaptive number knowledge, which includes knowledge of numerical characteristics and relations. In this study, students from the second (aged 8), fourth (aged 10), and sixth (aged 12) grades (n = 205) answered a modified version of the Arithmetic production task, which has been used to measure primary school students’ adaptive number knowledge. Significant differences among grade levels were found. In addition, a latent profile analysis revealed four profiles based on the students’ answers, with profile membership being associated with grade level. Similar to previous research, the current study found evidence of both age-dependent and individual differences. Furthermore, an analysis of the strategies used by the students to produce solutions revealed differences among the profiles.
Mediating activities in students’ collaborative work on self-explanation prompts
Authors: Bergvall Ida , Dyrvold Anneli
Published: November 2024

This study concerns mediating activities in student discussions during collaborative work with self-explanation prompts (SEPs). While the aim of most other tasks, from the students’ perspective, can be perceived as finding the correct answer, discussions supported by SEPs require a different approach, because students must engage in mathematical discussions, and explain their insights into the mathematics at hand. In this study, we explore activities that are fostered by SEPs. The analysis of the activities taking place, reveal five mediating activities to promote in teaching, but also potential hinders for the intended discussion to occur.
Thematic issue of Nomad 2025 – call for papers
Authors: Bergman Ärlebäck Jonas , Eyrich Jessen Britta , Frejd Peter , Kacerja Suela
Published: November 2024

The teaching and learning of mathematical modelling in the Nordic and Baltic contexts
Editorial
Authors: Editors The
Published: November 2024

Ledare/Editorial
Towards a technocritical mathematics education
Authors: Jankvist Uffe Thomas , Misfeldt Morten , Geraniou Eirini , Sánchez Aguilar Mario , Baccaglini-Frank Anna
Published: November 2024

Taking its departure point in critical mathematics education, mathematical competencies, and the use of digital technologies in mathematics teaching and learning, the paper sets out to discuss and describe a technocritical mathematics education. Not least this is due to the increase of hidden mathematics in technology of society today, both inside and outside the classroom. It is argued that a technocritical mathematics education must enable students to exercise the processes of ”packing” and ”unpacking” (hidden) mathematics as part of becoming citizens in a modern society. The paper raises the questions of what mathematical cases might enable students to develop competence with regard to these processes, and what might characterise such mathematical cases. Part of the answer to this point is a so-called embedded ”matryoshka doll” feature of such mathematical cases. Two examples of mathematics-based technologies – public-key cryptography and blockchains for cryptocurrency – on which our modern-day society are deeply dependant are displayed and discussed in the light of a technocritical mathematics education.
Allgemeinbildung and digital technologies in mathematics education: a review
Authors: Johansen Stine Gerster
Published: November 2024

The conception of Allgemeinbildung in Danish schools might be influenced by the inclusion of digital technologies in mathematics education. This paper presents the results of a literature review aimed at answering the potential and challenges posed by the inclusion of digital technologies in mathematics education in relation to students’ Allgemeinbildung. The analysis is structured after Heinrich Winter’s basic experiences regarding mathematical Allgemeinbildung. The review reveals both challenges and potentials. In particular, the handling of data, the role of outsourcing, and the lack of empirical research are discussed regarding the aim of Allgemeinbildung in the Danish school.
Teachers’ support for children’s mathematical learning through interactions while playing with a coding toy
Authors: Granone Francesca , Reikerås Elin
Published: November 2024

This study examines how early childhood education and care teachers can support children’s mathematical learning in the context of playing with a coding toy (a robot). Video recordings of the interactions that occurred between a teacher and four 3- to 5-year-old pupils while they played with a robot (three hours per week over the course of a month) were analysed based on the theoretical framework of semiotic mediation for mathematics education. The results highlight the fact that the coding toy can be viewed as an artefact for accomplishing a didactic mathematical objective through teacher support, including factors such as problem-solving, counting and measuring.
The use of DGE and CAS to support mathematical thinking competency: a literature review
Authors: Pedersen Mathilde Kjær
Published: November 2024

Focusing on the potential that dynamic geometry environments (DGE) and computer algebra systems (CAS) offer for mathematical inquiries, this paper presents a literature review of the use of DGE and CAS in relation to the mathematical thinking competency (MTC) of the Danish competency framework (KOM). This specific competency concerns modes of thinking when engaging in mathematical inquiry. The 17 studies included in the review were analysed from the perspective of MTC, resulting in the identification of three ways to use DGE and CAS as tools in activities related to the MTC.
Editorial
Authors: Häggström Johan
Published: November 2024

Editorial
Norwegian student teachers’ perspectives on linear equations
Authors: Larson Niclas
Published: November 2024

The topic of linear equations is part of school mathematics all over the world. Hence, it is important that teachers are proficient in teaching equations, explaining not only the arithmetic operations in the solving process, but also the objectives of the solution, the nature of an unknown and the balance property of an equation. This study employs a set of 16 low-inference codes to analyse 146 Norwegian student teachers’ explanations of the solution of a linear equation. One important result is that a majority of the students explained additive operations rather by ”swap sides swap signs” than by ”do the same to both sides”.
Lärares erfarenheter av Åtgärdsgarantin i matematik: möjligheter att åstadkomma stödinsatser
Authors: Norén Eva , Westerholm Kristin
Published: November 2024

I denna studie intervjuades 14 lärare i årskurs 1 om sina erfarenheter av arbetet med elevers taluppfattning i relation till utbildningsreformen Läsa, skriva, räkna – en garanti för tidiga stödinsatser (Åtgärdsgarantin). Studien undersöker lärares möjligheter att åstadkomma agens som kan leda till att elever tidigt ges stöd, och i vilka avseenden dessa stödinsatser ges. Lärares erfarenheter analyserades tematiskt. Lärare beskriver att deras mål främst är att elevens ska känna sig delaktig ”här och nu” och att undervisningen ska beröra allt centralt innehåll innan nationella proven i årskurs 3. I den ordinarie undervisningen ställs elevers behov av mer tid för träning mot lärarens behov av matematikbokens stöd i undervisningen. Stödinsatserna skapas då främst genom anpassningar av innehåll i matematikboken, samt i kommunikationen med eleven. Studiens resultat pekar på att lärares möjligheter att åstadkomma agens i den ordinarie undervisningen var begränsade. Agensen som åstadkoms syftade till att alla elever ska kunna följa den gemensamma undervisningens takt och innehåll, och då inte i första hand till en uppföljande undervisning som stärker elevens taluppfattning.
Prospective mathematics teachers’ collective identity work: navigating failure experiences and concerns about relating to students
Authors: Lutovac Sonja , Havia Johanna
Published: November 2024

The present study explores the collective identity work of prospective secondary mathematics teachers as they engage with their experiences of failure and success. The findings show how they navigate concerns about relating to students, resulting in failure-provoking or failure-reducing collective identity work. The prospective teachers’ perspectives arising from these distinct types of collective identity work are discussed as they might impact their development and future instruction, especially due to the absence of self-development strategies. This study highlights the need to build prospective mathematics teachers’ ability and confidence to relate to students unlike themselves and to problematise their seemingly unproblematic learning experiences and perspectives they co-construct in the collective identity work.
Professional identities, conflicting positions, and the challenge of conducting mathematical discussions in professional learning communities
Authors: Heyd-Metzuyanim Einat , Nachlieli Talli
Published: November 2024

Our goal in this study is to examine the interweaving of identifying (identity authoring ) and mathematizing of teachers in a Professional learning community (PLC) as they engage with a mathematical challenge. We rely on commognition and positioning theory to examine how storylines of teacher-students interfered with teacher-leaders' ability to hear mathematical ideas that were unfamiliar to them. We focus on one PLC session and show how the conflicts in positions, where the teacher-leader fought to maintain the identity of a mathematical leader, led to ineffectiveness of the mathematical discussion. We argue for the necessity of affording PLC participants alternative roles that would not threaten their professional identity as competent mathematics teachers.
Studying how a mathematics teacher’s professional identity shapes and is shaped by the use of digital resources in the classroom
Authors: Krog Skott Charlotte , Psycharis Giorgos
Published: November 2024

Teachers face many issues when trying to integrate digital resources (DR) into mathematics classes. This article applies an identity-based perspective to understand teachers’ roles in the practices that evolve in such classes. We focus on Victor, a Greek mathematics teacher, who, when viewed from levels beyond the classroom, experienced to become a reform-oriented teacher and a designer of DR. We explore how these experiences of professional identity shapes and is shaped by his work with DR at the classroom level. We show how Victor’s identity changed from ”being a mathematics teacher who struggles with inquiry-based teaching” to ”becoming a mathematics teacher who uses DR to support inquiry-based learning” and outline what fuelled these changes. Our results suggest that it is important to connect an identity perspective with classroom interactions and mathematics.
Review – What is good research?
Authors: Wallén Göran
Published: November 2024

Criteria for Scientific Quality and Relevance in the Didactics of Mathematics. Report from a symposium held in Gilleleje, Denmark, 1992. Editors: Gunhild Nissen and Morten Blomhøj. Danish Research Council for the Humanities. Roskilde University, IMFUFA. 1993. ISBN 87-7349-178-0, ISSN 0906-0103.
A problem-centered alternative to formalistic teaching
Authors: Keranto Tapio
Published: November 2024

Increased attention has been given in recent times to the teacher-centered and formalistic nature of mathematics teaching in schools, and well-founded proposals have been made to change this tradition toward a problem-centered direction which takes into account pupils' previous learning experiences and out-of-school practices. After a historical scrutiny and the criticism of the current formalistic tradition - 'first theory, then practice' - , the article outlines an alternative teaching strategy which provides at least in theory better opportunities for discussive and meaningful teaching-learning processes in school mathematics. Finally, some main results from one of the teaching experiments of the project "Contextual Ap- proach to the Teaching and Learning of Mathematics" are examined. The teaching experiment focused on developing proportional reasoning and ratio concept in the eighth grade of the comprehensive school. Although numerous problems were encountered in the implementation of the "contextual program" designed on the basis of the ideas of Freudenthal's didactical phenomenology and the ideas of the "Vygotskian school" of psychology, the learning results achieved by means of the contextual program were at least equally good and partly better than those achieved in groups taught by the textbook.
Matematikämnets didaktik – ett växande vetenskapsområde
Authors: Emanuelsson Göran , Johansson Bengt
Published: November 2024

Ledare / Editorial
Om kalenderräkning – Aritmetiken, almanackan och fingrarna som beräkningsverktyg
Authors: Wyndhamn Jan
Published: November 2024

I en svensk, nationell studie rörande matematikundervisningen förekom uppgiften
Hur många dagar år det från och med åen 24 mars till och med den 18 juni om mars och maj har 31 dagar och april 30 dagar?
Uppgiften förefaller enkel, men i årskurs 6 var det bara 7 % av eleverna som klarade den. Uppgiften ansågs – i det utvärderingssammanhang den ingick i – mer mäta elevens språkliga förmåga än den individuella matematiska kompetensen. Föreliggande studie belyser betydelsen av några situationsbetingade faktorer vid problemlösningen. Tre olika experiment med den nämnda uppgiften som utgångspunkt genomfördes i årskurs 5. Elever fick gruppvis i två experiment lösa samma uppgift men med olika förutsättningar och i ett tredje experiment två likartade uppgifter. Resultatet blev att eleverna klarade uppgiften utmärkt då de antingen fick ha en almanacka till hands eller blev upplysta om att uppgiften innehöll en svårighet. Omformulering av uppgiften ökade dock inte påtagligt lösningsfrekvensen.
Artikeln är en förkortad och omarbetad version av en rapport om en studie över hur elever löser problem med datumangivelser (Wyndhamn, 1992, 1993).
Konferensrapport – Matematikundervisningens roll och placering i nordisk demokratisk kultur
Authors: Kristjánsdóttir Anna
Published: November 2024

Den 24-28 augusti 1994 hölls i Island ett nordiskt forskarsymposium om matematikundervisningens roll och placering i nordisk demokratisk kultur. Symposiet arrangerades i samarbete mellan Kennaraháskóli Íslands (Islands lärarhögskola), det nordiska forskarnätverket Matematikundervisning och demokrati och det danska initiativet med samma namn under Statens Humanistiske Forskningsråd. Symposiet ägde rum på en kulturhistoriskt mycket känd plats, Reykholt, som på 1200-talet ägdes av Snorri Sturluson, en av sagotidens allra mest framstående författare.
Islands president, Vigdis Finnbogadóttir, var symposiets beskyd- dare och visade sitt intresse bland annat genom att delta i den första dagens program.
Från redaktionen i Mölndal
Authors: Johansson Bengt , Emanuelsson Göran
Published: November 2024

Ledare / Editorial
Stieg Mellin-Olsen in memoriam
Authors: Gjone Gunnar
Published: November 2024

Professor Stieg Theodor Mellin-Olsen døde den 26. januar 1995 nær 56 år gammel. Med ham har Norge og Norden mistet en av sine fremste fagdidaktikere.
Korta bokanmälningar
Authors: Emanuelsson Göran
Published: November 2024

I förra numret gav vi några exempel på den omfattande bokutgivningen inom vårt vetenskapsområde. Vi fortsätter här med ytterligare exempel och förlag.
Från redaktionen i Mölndal
Authors: Johansson Bengt , Emanuelsson Göran
Published: November 2024

Ledare/Editorial
I forlanger for lidt af jer selv
Authors: Alrø Helle
Published: November 2024

Hvorfor forstår eleverne ikke, hvor læreren vil hen, og hvorfor forklarer læreren ikke tingene, så eleverne forstår dem? Disse spørgsmål synes at være centrale, når der er problemer i matematiktimen.
Denne artikel ser på samspillet mellem lærer og elever i en konkret undervisningssituation med henblik på at vise, hvordan kommunikationen kan komme til at virke blokerende i læreprocessen.
Teknologi, kvalifikationer og matematik
Authors: Wedege Tine
Published: November 2024

Almene kvalifikationer er efterspurgte på de dele af arbejdsmarkedet, hvor ny teknik indgår i produktioner med flade ledelsesstrukturer og bredere jobkonstruktioner end i den tayloristiske model. I Danmark bidrager matematikundervisningen i den almene og den erhvervsrettede voksenuddannelse (almen voksenuddannelse og arbejdsmarkedsuddannelserne) hver på sin måde til kvalificeringen. Men én ting er kvalifikationskravet - noget andet kvalificeringsbehovet, som ikke er nogen entydig størrelse. Kan man forestille sig, at matematikundervisningen vil kunne give de kortuddannede voksne mulighed for at (videre) udvikle teknologiske kompetencer med såvel en faglig som en personlig dimension, der stiller dem som subjekt i forholdet til teknologien på deres arbejdsplads?
For at kunne besvare dette spørgsmål, må der arbejdes på tværs af de to forskningsfelter voksenuddannelse og matematikdidaktik Bl.a. på grund af matematikkens skjulte tilværelse i teknologien, skal der nemlig søges svar på et metodisk-didaktisk spørgsmål: Hvordan - og i hvilken grad - er det muligt at konstru- ere en matematikundervisning, der har teknologisk kompetence som mål?
Voksenuddannelsesforskerne har ikke interesseret sig specielt for matematik, og matematikdidaktikerne på universiteterne har fortrinsvis fokuseret på undervisning og læring hos børn og unge. Artiklen skal ses som et forsøg på at opstille nogle begrebslige rammer, der kobler kvalifikationer og matematikviden og der- med åbner mulighed for - i næste omgang - at stille nogle lødige forskningsspørgsmål.
Matematikk i skole og samfunn
Authors: Bekken Otto B.
Published: November 2024

MiSS (Matematikk i Skole og Samfunn) är ett treårigt projekt som leds från Høgskolen i Agder, Kristiansand av førsteamanuensis Dr Otte B. Bekken. Arbetsgruppen är tillsattav Kirke-, utdannings-og forskningsdepartementet Den består av 12 medlemmar från skolor och högskolor i Norge och skall göra en översyn av matematiken i det norska utbildningsväsendet mot bakgrund av de förändringar som skett i samhället de senaste åren.
Vi har bedömt att uppdraget har stort intresse för NOMADs läsare och publicerar det därför i sinhelhet Den första rapporten är under tryckning och kommer att anmälas i kommande nummer av NOMAD.
Hva skjer med matematikkpedagogiske samhandlinger når tester tas i bruk?
Authors: Johnsen Høines Marit
Published: November 2024

Artikkelen er skrevet fordi testbegrepet kan se ut til å få en slags rennesanse i Norge. Stor satsing på TIMSS og KIM gir oss på mange måter bilde av en pedagogisk og samfunnspolitisk trend. Det handler om styring, oversikt og «harmonisering» og det handler om stimulering av utdanningsmiljø. Nye typer tester tar form. I TIMSS og KIM-miljø refereres det til et vidt testbegrep der en tar mål av seg til å teste matematikk-kunnskap som noe mer enn rette og gale svar på regnestykker. Det kan f.eks. handle om elevers evne til problemløsing og til å gjøre undersøkelser. Det kan handle om elevers kunnskaper om egen matematikkforståelse. I den samme tidsperioden utvikles det ny læreplan for grunnskolen i Norge. Læreplanens høringsutkast er detaljert og formulert gjennom «elevene skal ... ved å ...». Jeg mener det er naturlig å se disse tingene i sammenheng. Vi går fra en læreplan med målformuleringer som er retningsgivende, og som ikke er målbare, til en plan med formuleringer som er mer håndterlige dersom en ønsker å bruke tester som styringsredskap. Tester og «assessments» har hatt liten plass i norsk skolekultur. Som iakttager ser jeg ulike spørsmål aktualisert: Hva skjer med slike viktige felter når en lar dem inngå i en test-tradisjon? Vil det skje en fattiggjøring ved at f.eks. problemløsing får snevrere rammer? Vil en, dersom en f.eks. retter fokus mot «childrens awareness», gjennom testprosesser definere hva en mener med «childrens awareness» og vil det så være til berikelse?
De nordiske landene har ulike tradisjoner når det gjelder tester, prøver og eva- luering. Jeg vil likevel tro at mange av problemstillingene som reises i Norge er aktuelle i de andre landene. Det kan synes som om et forskningsfelt åpner seg: Hva skjer i matematikkpedagogiske samhandlinger når ulike tester tas i bruk, hvilke innsnevringer og hvilke berikelser? I denne artikkelen knytter jeg testproblematikken opp mot barns mangfoldige tallbegrep. Jeg forsøker å gi et bilde av trekk ved barns tal/begrepsutvikling (og dergjennom trekk ved matematikk-peda- gogiske samhandlinger) som jeg mener bør være med som bakgrunn for å vurdere testmaterialers legitimitet.
On pupils' reactions to the use of open-ended problems in mathematics
Authors: Pehkonen Erkki
Published: November 2024

This article will focus on the preliminary results of one experimental class from the three-year research project "Open tasks in mathematics", which has been carried out in junior high schools during the years 1989-92 in Helsinki (Finland). The experiment groups used open-ended problems (problem fields) regularly, i.e. once a month, within their normal teaching. The main results from one class (N = 18) were as follows: The pupils liked most of the problem fields used. Their mathematical views did not change statistically significantly, but the non-significant changes in questionnaire ratings, classroom observations and the teacher's evaluations indicate that there was a change, and the change was in most cases positive.
Review – Didactics of mathematics. A scientific discipline
Authors: Gjone Gunnar
Published: November 2024

Review

Biehler, R., Scholz, R.W., Strässer, R. & Winkelmann, B. (eds.) (1994). Didactics of Mathematics as a Scientific Discipline. (Mathematics Education Library, Volume 13). Dordrecht, NL: Kluwer Academic Publishers, 467p.
Læring som sprogspilsoverskridelse
Authors: Dahl Bettina
Published: November 2024

Matematik har fællestræk med sprog, men jeg benytter begrebet 'sprogspil' for at afspejle, at et sprog er en del af en livsform og en social proces. Læring sker ved en forhandling, hvori vigtige variable er individernes Formål med dialogen, deres Referenceramme, Ordforråd, Metafysik og holdning til den Ydre ramme de befinder sig i (FROMY-variable). Læring af matematik er at kunne bevæge sig til dette matematiksprogspil, udspændt af en mængde FROMY-variable, fra sit naturlige sprogspil, udspændt af en anden mængde FROMY-variable. Dvs. individerne har udviklet deres FROMY-variable, og de kan nu deltage i begge sprogspil.
Hva er en vinkel?
Authors: Johnsen Veslemøy
Published: November 2024

Det har vært gjort mange undersøkelser om elevers utvikling av matematiske begreper. Hensikten med denne artikkelen er å beskrive elevers utvikling av vinkelbegrepet i en bestemt klasse. Vinkler kan oppfattes dynamisk som rotasjoner, statisk som stråler eller de kan analyseres ved måling.
Forskning viser at elever har begrepsmessige problemer med å oppfatte vinkler der ingen av vinkelbeina er orientert horisontalt, sammenlikne vinkler med samme måltall, men med ulik lengde på vinkelbeina, oppfatte vinkler som er større enn 180 grader, og at de har enda større problemer med å oppfatte en vinkel på 180 grader.
Undervisningen som vi observerte, viste at læreren la vekt på elevenes egen utforsking og at samspillet mellom dynamiske og statiske erfaringer med vinkler var grunnlaget for begrepslæringen. Læreren fokuserte på de vanskelige vinklene (0, 180 og 360 grader), på hvor stor en vinkel kan bli og på hvor mange vinkler vi kan finne.
Elevene arbeidet også med hvilken vinkel som skal måles (v eller 360° - v), når vinkelen er større enn 180 grader. Elevene hadde problemer med det statiske perspektivet på vinkler, med måling av vinkler, og med vinkler større enn 180 grader - særlig når konteksten ikke var praktisk. Men det var få elever som hadde problemer med å gjenkjenne vinkler med forskjellig orientering eller å sammenlikne vinkler med ulik lengde påvinkelbeina.
Alternatives to traditional algorithms in elementary mathematics instruction
Authors: Hedrén Rolf
Published: November 2024

The purpose of the research project has been to find out what changes ought to take place in elementary mathematics teaching, if we want to consider the changing need of mathematical knowledge and skill in a society with calculators and computers.
The project is and will be carried out in one class followed through years 2 - 5. The children are now (May 1996) in year 3. Traditional algorithms for the four arithmetic operations are not taught, instead the children are encouraged to invent their own methods for written computation and, besides, to use mental arithmetic and estimation whenever appropriate. Each child has also access to a calculator of her/ his own.
The project is mainly evaluated by qualitative methods, e. g. clinical interviews and observations of groups of children. The results that are discussed, are mainly from year 3. They show that the children, when given the chance, invent a lot of different methods to cope with exercises in addition and subtraction, and in so doing they exhibit signs of increasing number sense. However, many children still have difficulties with regrouping in subtraction.
Litteraturanmälan – Tänk så många kompetenta kvinnor det finns ...
Authors: Grevholm Barbro
Published: November 2024

Wistedt, I. (1996). Gender-inclusive Higher Education in Mathematics, Physics and Technology. Five Swedish Development Projects. Stockholm: Högskoleverket. (75 sidor)
Using a journal to engage teachers in developmental work
Authors: Emanuelsson Göran , Johansson Bengt , Reys Barbara J. , Reys Robert E.
Published: November 2024

Professional journals provide a fresh and stimulating source of ideas and serve as both a lifeline and a conduit for professional growth for many teachers. Journals have the potential to address timely issues and reach teachers regularly. Furthermore, journals represent a significant resource to promote dialogue about teaching and learning as well as to chronicle historical developments within professional fields.
This article details how a Swedish journal for mathematics teachers, Nämnaren, was used to focus on a timely issue and stimulate awareness and involvement of mathematics teachers throughout the country. Nämnaren was founded over 20 years ago and established with the stated purpose of helping Swedish teachers: keep informed of current issues and happenings in mathematics education; and learn more effective ways to learn and teach mathematics at all levels. Nämnaren is published four times a year and has a circulation that reaches nearly all elementary and secondary schools in Sweden. Several issues of Nämnaren were used recently to bring the mathematical theme of number sense to the attention of Swedish teachers *).
NOMAD over Kjølen
Authors: Brekke Gard , Gjone Gunnar
Published: November 2024

Ledare / Editorial
Diagnoser i matematik år 2. Varför – hur – vad ger resultatet?
Authors: Neuman Dagmar
Published: November 2024

I denna artikel presenteras teorier och tankar bakom de svenska nationella diagnoserna i matematik för år 2 och exempel på hur dessa tar sig uttryck i det färdiga i materialet. Innehållet i diagnoserna avser att spegla det som är nytt inom ämnet i den svenska läroplanen, Lpo 94, och i den syn på kunskap, inlärning och undervisning den utgår ifrån. Diagnosernas viktigaste motiv är emellertid att avslöja hur barn upplever matematiken under sitt andra skolår. Hur teorier och tankar reflekteras i materialet exemplifieras med elevlösningar som visar hur barn upplever det tidigaste bråktalet "en halv". Exemplen antyder också hur problemlösning som sker i interaktion mellan elev-elev-lärare i meningsfulla situationer kan bli en drivkraft i utveckling av matematisk kunskap.
Preservice teachers' perceptions of gender equity issues in the mathematics classroom
Authors: Mewborn Denise S. , Gober Deborah A.
Published: November 2024

The purpose of the study was to identify preservice teachers' perspectives on gender equity and to explore how they process the information they receive about gender issues. Data were collected through written surveys administered to 225 preservice and inservice teachers enrolled in mathematics and science education (methods) courses at the university. Data were analyzed using Paine's (1990) categories of orientations to diversity: individual difference, categorical difference, contextual difference, and pedagogical difference. The study suggests that most preservice teachers have an individual difference view of gender equity in which they strive to treat all students the same to avoid discrimination. Some students hold a categorical view of gender equity in which they strive to overcome stereotypes about boys and girls. A small number of students actively denied that gender issues have any relevance to education.
Forskning og forskningens organisering
Authors: Brekke Gard , Gjone Gunnar
Published: November 2024

Ledare / Editorial