Uffe Thomas Jankvist

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• MSc, PhD
• Professor at Aarhus University

This chapter discusses the nature of the Danish mathematical competencies framework (also known as the KOM framework) as a framework for specifying what it means to successfully learn and master mathematics, and how it differs in nature from other mathematics education constructs and frameworks that set out to do similar things. To do so, we first...

This book focuses on the potential interplay between two distinct, yet related paradigm shifts in mathematics education, drawing on the notion of “networking of theories” through illustrative case studies from the Danish educational system and beyond. The first paradigm shift is the massive introduction of digital technology in the teaching and lea...

When students engage with a digital tool to tackle a mathematical task, the interplay between their digital competencies and mathematical abilities gives rise to what is termed mathematical digital competency (MDC). Recognising the significance of MDC as an integral component for contemporary students, the relevance of cultivating mathematical digi...

In mathematics, students’ abilities to make transformations between mathematical representations are fundamental. The recent implementation of digital technologies, such as Dynamic Geometry Environments (DGEs), have changed students’ access to mathematical representations by providing a variety of different representations, available just by pressi...

In February 2024, part of the editorial team of IRME (Uffe Thomas Jankvist, Mario Sánchez Aguilar and Morten Misfeldt) had the pleasure of discussing the development of implementation and replication studies in the context of South American STEAM (Science, Technology, Engineering, Arts, and Mathematics) education. We participated in the 2nd Latin A...

This review paper systematically examines implementation research studies reported in the journals of the Nordic countries focusing on mathematics education innovations implemented in Nordic countries over the past three decades. We aimed to identify the types of innovations reported, the objectives of the research and the scale of the projects. Ou...

Con l’introduzione massiccia delle tecnologie digitali – come gli ambienti di geometria dinamica (DGE) e i sistemi di algebra computerizzata (CAS) – sia nelle scuole secondarie di primo grado che in quelle di secondo grado, oggi una buona parte della matematica rischia di rimanere nascosta agli studenti, poiché è racchiusa nei comandi messi a dispo...

This philosophical essay delves into the role of theories in mathematics curriculum reforms, particularly how theories can contribute to creating and implementing innovations. Using the concepts of discourse and grammar of schooling, we investigate two well-researched Swedish curriculum reforms. With these two concepts, we discuss the possible cont...

We use a key case from implementation research in mathematics education, where results involve a claim of teachers' beliefs influencing the implementation outcome, to argue that alternative interpretations are possible. The case represents how argumentations about teachers' beliefs as an influential factor are carried out in implementation research...

When implementing digital technologies into mathematics teaching and learning situations, new representational and communication infrastructures arise that allow for new speech acts and actions. These new speech acts and actions are also referred to as 'representational expressivity'. Such expressivity arises in the intersection of representational...

This paper concerns the relation between the research fields of implementation research (IR) and professional development (PD). Our main interest is in the concept of innovation and measurement of effects in large scale development projects. The case for our discussion is the Swedish large-scale development project Boost for Mathematics (BM). A pro...

When evaluating large-scale innovation implementation projects, it is of particular interest to identify which characteristics determine the innovation's impact on the target group. By analyzing the projects TRIUMPHS and Boost for Mathematics (BM) by their respective designs of professional development and their designs for scaling innovations, we...

Articles in mathematics education that report on the implementation of innovations do not always report models for how the innovation program is supposed to attain its effects. We analyze an article with no such explicit theory of change with the aim of providing a background case for discussing the role of theories of change in implementation rese...

To get an overview of the characteristics of the studies in mathematics education research that explicitly purport to concern implementation, we have conducted a systematic literature review. We report on a subset of twelve papers investigating and discussing factors of influence that are decisive for implementing curriculum reforms. Results show t...

We report on a study investigating how the notions of large-scale and small-scale projects are interpreted. Some of the methodological procedures of the Delphi technique were used, including posing a couple of scale-related questions to a group of 14 educational researchers who had experience in leading or investigating the large-scale implementati...

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...

We are pleased to introduce the 2023 thematic issue of Nordic Studies in Mathematics Education (NOMAD) on Digital resources in mathematics education. Digital resources seem to play an ever-increasing role in mathematics education and are now part of the teaching and learning of most mathematical topics. While resources that are no longer new, such...

We present the results of a systematic literature review of research articles that self-identify as describing the implementation of innovations from mathematics education research in educational practice. We classified 103 articles according to study type, the type of teaching/learning phenomenon the implementation targeted, and whether the innova...

The development of middle-grade students' fraction schemes is challenging while also necessary for students in the later development of their ability to reason with reciprocals. In this theoretical paper, we display a method for designing and sequencing tasks in an online assignment portal to develop schemes that provide the necessary prior knowled...

Posing problems that are based on given real-world situations is important for teaching mathematical modelling. However, little is known about the posing process and the corresponding roles that teachers play. To help fill this gap, the current study examined the roles that preservice teachers adopt when they pose problems based on given real-world...

Scale and scaling are central concepts in projects aimed at implementing innovations for improving mathematics education. This study aims to provide conceptual clarity on the notions of scale and scaling in mathematics education research. The meanings of these terms are handled tacitly, and there is diversity in how they are used in the literature....

When we launched Implementation and Replication Studies in Mathematics Education (IRME) two years ago, it was in a sense a culmination of several years of work trying to increase the focus on implementation (and replications) in mathematics education research (Jankvist et al., 2021). Our feeling at the time was that improvement of mathematics teach...

This chapter focuses on the KOM-framework’s aids and tools competency and investigates its application in the digital era for mathematical learning. The aids and tools competency may be viewed as distinguishing between more classical material or physical tools (e.g., centicubes, rod systems, abacuses, rulers, compasses, protractors, specially lined...

Using three theoretical lenses, we investigate a teacher’s practice in a dynamic geometry teaching sequence aiming to support students’ development of mathematical reasoning. These lenses are the Danish KOM framework’s description of mathematics teacher competencies, the Theory of Instrumental Orchestration (TIO) and the theoretical construct of Ju...

Mathematics education has been experiencing two rather distinct, yet related, ‘paradigm shifts’. The first is to do with the massive introduction of digital technologies (DT) in the teaching and learning of the subject (e.g., Trouche et al., 2013); the second is to do with a shift from the traditional focusing on mastering of skills and knowledge t...

In this article, we compare two disciplinary competency descriptions of mathematics. More precisely, we describe and compare the Core Mathematics Competencies (CMC) framework in the Chinese mainland with the Danish mathematics competencies framework (KOM). We look for similarities and differences in the conceptualization of “competency”, the struct...

The history of mathematics education is an interdisciplinary research area that is experiencing a significant development and this book presents recent work in this area. This book is the result of the seventh conference ICHME (International Conference on the History of Mathematics Education) that took place at Erbacher Hof, Mainz (Germany) from 19...

This paper examines the experience of three teachers who participated in developing teaching resources for programming and computational thinking (PCT) as part of a project that integrates mathematics and PCT. Using interviews, we explore the teachers’ understanding of this integration and their approach to transmitting it through teaching sequence...

The international trend towards young people learning programming and computational thinking in compulsory school has led to different developments in mathematics teaching. In this paper, we view this as a case of interdisciplinarity and explore what the interplay between mathematics and computational thinking in K-9 schools in Denmark, Sweden and...

The symposium series Mathematics and its Connections to the Arts and Sciences (MACAS) has been held since 2005. The vision which the MACAS initiative is based upon is to develop a humanistic approach to education that combines various disciplines in a single curriculum. According to this vision, the aim is to educate students by enabling them to pu...

This chapter explores the notion of historical awareness in relation to using primary historical sources in the teaching and learning of mathematics. It does so through the analysis of two teaching experiments originally designed from different, yet related perspectives. We present an analytic framework for identifying historical awareness and use...

In this chapter, we describe and analyse the design of a teaching and learning activity between mathematics and arts and crafts, centred round the making of a skirt. The context is a collaboration between two teachers and a professional seamstress in a lesson organized with relation to the “Open School Program” in Denmark, which allows for non-teac...

Is it possible to communicate abstract mathematical thinking to children? This is what the Danish picture books “Fermat’s last theorem” and “Twin primes” attempt to do. This chapter discusses their educational potential from both a literary and a didactical perspective, basing the latter on the Danish framework for mathematical competencies and its...

To get an overview of how many and which studies in the literature specifically address the implementation of innovations from mathematics education research, we have conducted a systematic literature review. We report on the subset of 19 studies from the review, dealing with the implementation of instructional sequences aiming to enhance students'...

The word ‘fidelity’ regularly pops up in mathematics education research and practice. This is in particular when dealing with matters of digital technologies, instructional interventions and replications. The experience shows that it is not always clear what is meant by fidelity. That it may have slightly different meanings in different situations....

In this study, we investigate how the results of the Swedish PUMP project (1973–1977) influenced the content of mathematics textbooks in Sweden. Through analyses of 26 mathematics textbooks and interviews with three key informants, we identified a large impact on textbooks and six different channels for spreading innovations to textbooks, but also...

The paper addresses the role of educational task design in implementation research. Its point of departure is the first revision of a task developed for 4th grade in collaboration with a Danish school teacher. The authors informed the task from a hypothetical learning trajectory that requires students to draw on their knowledge both of mathematics...

In this paper, we present a mathematics teacher's reflections on the design and experimentation of an activity sequence involving transitions from 'pen-and-paper' mathematical explorations to mathematical explorations within three different digital environments: GeoGebra, the Scratch programming environment and Excel. We look at her arguments for s...

Recently the construct of mathematical digital competency (MDC) was put forward in which mathematical competency and digital competency are seen as a connected whole. This entails that student understanding of mathematical concepts may be almost inseparable from digital tools. We report on a quantitative study with n=238 preservice teachers (PSTs)...

In this paper, we study the external didactical transposition of programming and computational thinking (PCT) into the Danish compulsory school mathematics curriculum. Taking an anthropological theory of the didactic approach, we focus on the nature of mathematical and PCT knowledge being transposed into the new curriculum as prescribed praxeologie...

To get an overview of the characteristics of the studies in mathematics education research that explicitly state that they deal with implementation, we have conducted a systematic review. In this paper, we report on a subset of the identified studies from the review, dealing with large-scale professional development for teachers. For the subset of...

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854–1912), Felix Klein (1849–1925), and Hans Freudenthal (1905–1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears without...

In this paper, we investigate the implementation strategies related to bringing programming and an increased focus on the use of digital tools into the mathematics curriculum in Sweden. Drawing on implementation theory, we take a starting point in two teacher training in-service modules that constitute a central aspect in the Swedish effort of impl...

The Danish national curriculum, the so-called Common Goals, for mathematics in primary and lower secondary school is based on the Danish mathematics competencies framework (KOM), which describes eight different mathematical competencies. Two of these, the thinking competency and the reasoning competency, were merged together in the Common Goals. Fr...

The Fifteenth International Conference on Technology in Mathematics Teaching (ICTMT 15) took place on September 13–16, 2022, in the Danish School of Education, Aarhus University, located on campus Emdrup, in the Northwestern district of Copenhagen, Denmark.

In the present editorial, we will first describe the evolution of the work on IR in the context of CERME, and then we will describe the contributions at CERME12’s TWG23. Afterwards we will describe three overarching themes that were discussed at this year’s meeting in TWG23: (1) the role of change and theory of change; (2) matters of scaling; and (...

This article is a review of the literature on the use of history of mathematics in combination with use of digital technologies in the teaching and learning of mathematics. The review identifies 33 peer-reviewed publications (book chapters, journal articles, and papers in conference proceedings) that address an actual interplay between use of histo...

This article is a review of the literature on the use of history of mathematics in combination with use of digital technologies in the teaching and learning of mathematics. The review identifies 33 peer-reviewed publications (book chapters, journal articles, and papers in conference proceedings) that address an actual interplay between use of histo...

In this second editorial of Implementation and Replication Studies in Mathematics Education (IRME), we address the question of what to look for in research results and findings from mathematics education research in terms of sources for replication studies.

This paper first introduces and reviews the existing research on the well-known “students–professors (S/P) problem”, which was first formulated in 1979. Next, it presents an empirical study of Danish upper secondary students’ answers to two mathematical modeling versions of the S/P-problem; a mathematization version (296 students), and a de-mathema...

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering—or whiteboxing—the content of a mathematical proof, in this case that of Proposition 41 from Euclid’s Elements. In the discussion of the example, we look into the impact of GeoGebra’s “dragging” functionality on stude...

Taking as its point of departure, situations arising in classrooms exposed to a heavy use of CAS, exemplified by the Danish upper secondary school mathematics program, the paper discusses the use of “old” cognitive frameworks of mathematics education as an alternative to more recent theoretical developments in the field. The paper draws on three ri...

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of lit...

We are launching a new international research journal in mathematics education. “What?”, you might ask, “Doesn’t mathematics education already have a myriad of journals?” Yes, this is indisputable. A quick count will easily reveal more than a hundred, counting also regional and national journals. Yet, as the title of this journal reveals, Impleme...

In this paper, we report on a finding in an ongoing literature review on Networking of theories. As theories are the focus of networking practices, discussion of what is meant by theory is an ongoing debate. In our reading of these discussions, we experience a discrepancy in the use of the notion of background theories and foreground theories, whic...

Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic online environments for mathematics teaching and...

Representations are crucial to mathematical activity, both for learners and skilled mathematicians. Digital technologies (DT) to support mathematical activity offer a plethora of new possibilities, not least in the context of mathematics education. This paper presents a literature review on representations and activation of students' representation...

The purpose of this study is to present the need for stakeholders to share an agreed-on Theory of Change (ToC) during the various phases of an implementation process. To this end, we draw on the Swedish Boost for Mathematics (BM), a large-scale national educational initiative, and its intrinsic ‘algebra’ instructional module. More precisely, we ana...

In this paper, we analyze and discuss an empirical example related to students’ socalled techno-authoritarian proof schemes, i.e. when digital technologies come to play the authority of establishing mathematical truth. The example stems from a pilot study concerning the interplay between the uses of original historical sources, in this case Euclid’...

In this paper we juxtapose and give examples of mathematical aspects of how programming is included in teaching in three different countries; Denmark, Sweden and England. We look at cases of both curriculum standards and resources in order to describe the nature of the relations between programming and mathematics. The methodology consists of a cas...

What mathematical knowledge is required for teaching has been researched by many, with Ball et al. (J Teach Educ 59(5):389–407, 2008) and their practice-based theory of mathematical knowledge for teaching (MKT) primary among them. However, what is required in terms of mathematical knowledge for teacher educator training has been researched much les...

The gap between research and practice is a well-known problem (and topic) in educational research, and not least in mathematics education research. This empirically based article discusses the effects of a particular attempt to foster a closer connection between research and practice by involving mathematics education research findings in the activ...

Often mathematics teachers are reluctant to use even free digital tools, such as GeoGebra and Scratch, due to their lack of insight and conviction about how tools impact learning, but also other contextual and personal factors, involving their own digital competencies and confidence in their technological pedagogical knowledge. In this paper, we ta...

When school students reach a certain age, say when they become teenagers and reach middle school, the mathematics teaching they encounter has often become rather non-material. At the same time, it is well-known that students may experience mathematics as more relevant, if it takes it's departure point in their own reality (Skovsmose, 1990, 2011). F...

Is it possible to communicate abstract mathematical thinking to children? This is what the Danish picture book “Fermat’s last theorem” attempts to do. Our paper discusses the mathematics educational potential from both a literary and a didactical perspective, basing the latter on the Danish mathematics competencies framework and its characterizatio...

Although there have always been investigations in the field of mathematics education that concern implementation research, it is not yet clear how to structure such a research area. In this paper, we take a step towards this. Taking as reference frameworks elaborated in other fields where implementation research is more advanced, we attempt to outl...

The paper addresses the potential of using history of mathematics in combination with ICT to illustrate the notion of proof and proving, including also the role of examples and counterexamples, to undergraduate students and relates such use to research findings regarding students’ difficulties. The historical case used to illustrate this is Tschirn...

In this paper, we argue for the use of digital technologies in making original sources more accessible to students. W digital technologies 005) framework of instrumental genesis, and a. The combination of original sources and use of digital technologies appears to be a somewhat overlooked area in the HPM research, not least in terms of empirical in...

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are i...

Due to the embeddedness of digital technologies in mathematics education of today, we often see examples of students simultaneously using their mathematical competencies and digital competencies. In relevant literature, however, these are not seen as a connected whole. Based on reviewing existing competency frameworks, both mathematical and digital...

Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands “solve” and “desolve,” it is asked what happens when such CAS procedures are objectified in...

This article reports on a combined quantitative and in-depth qualitative study of 315 Danish upper secondary (grades 10–12) mathematics students’ answers to six modelling tasks that place emphasis on the early phases of the so-called modelling cycle. In order to focus attention on the extra-mathematical aspects of modelling, the technical mathemati...

In this paper, we identify a number of implementation enablers and barriers in the Swedish ‘Boost for Mathematics’ (BM). Through an analysis of two selected BM modules’ use of sensitizing and prescriptive theoretical constructs from mathematics education research, we attempt to link the existence of enablers and barriers to identified policy dimens...

Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education

Proceedings presentation

This paper explores how the use of computer algebra systems affects students identity in the mathematical classroom. The theoretical outset is a combination of the instrumental approach in mathematics education (studying the cognitive influence of computational tools), and literacy research (looking at writing as "identity work" actively shaping ho...

This paper addresses mathematically gifted students and their capacity to express themselves in regard to their mathematical problem tackling when in dialogue with a teacher. Through a case study of a student in 3rd grade-Celeste-it is argued that a well-developed communication competency may indeed be an indicator of mathematically giftedness. In...

In this paper, we investigate the use of CAS in Danish upper secondary school from a norms perspective. The construct of sociomathematical norms is used to understand the potential influence that CAS may have on the rules (and values) in the mathematics classroom. We focus on a situation of teacher change, where the different teachers enact differe...

The paper points to the emergence of the phenomenon "mixed notation" as a result of the use of Computer Algebra Systems (CAS) in upper secondary education. We provide an illustrative example or "existence proof" of mixed notation consisting in a student's written answer to an exam question from the Danish national mathematics exam as an instance of...

This paper focuses on the KOM framework for mathematical competencies and in particular its aids and tools competency and investigates its application to digital technologies used for mathematical learning. Very little has been done on networking the KOM's mathematics competencies framework to internationally established theories and theoretical co...

The article addresses the need for competence descriptions of disciplines as a means for fostering more productive communication between different disciplines and between the disciplines and their surroundings. It is argued that the usual competence descriptions devised for use within a discipline itself, e.g. in relation to teaching and learning o...

Two conference papers - the plenary lecture in section 4 (pp. 515-530) on "The art and architecture of mathematics education: A study in metaphors", and a workshop summary in section 1 (p. 65) on "What can art teach us about mathematics?".