Morten Misfeldt

University of Copenhagen · Center for Digital Education - Department of Science Education and Department of Computer Science

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...

In this chapter, we introduce the section “Politics of Digital Resources,” which focuses on the relationship between politics and digital resources in teaching and learning mathematics. We explore the politics surrounding digital resources in mathematics education, including the rules and regulations imposed by the political and bureaucratic system...

In this chapter, we ask whether digital resources in the mathematics classroom can be said to have a political agenda or political consequences. Of course, resources can be used for political purposes – but do they serve a political goal? We theoretically explore this question by relating to mainstream trends in mathematics education literature as...

Teknologiforståelse har siden dets lancering som en ny dansk faglighed været valplads for en række aktørers forsøg på at definere og afgrænse faget indadtil og udadtil. I denne artikel analyseres tre kompetenceudviklingsforløb i teknologiforståelse, der fandt sted inden for rammerne af projekt ”Teknologiforståelse i uddannelse af lærere og andet pæ...

Over five decades, the field of mathematics education research has generated a wealth of innovations aimed at improving the teaching and learning of mathematics. However, while mathematics education research has produced solid findings related to fundamental phenomena in teaching and learning mathematics, has constructed elaborate theoretical frame...

In this paper, we study the relationship between the content and goals of curriculum revisions toward the integration of computational thinking (CT) in compulsory schools in Denmark, Sweden, and England. Our analyses build on data consisting of a combination of official documents such as new curricula, white papers, and implementation strategies an...

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...

This chapter discusses the influence of the increased use of digital technologies for mathematical teaching and learning and their relevance to the Danish mathematical competencies framework (KOM) (Niss & Højgaard, 2011, 2019), and how the different types of digital technologies may influence different components of the KOM framework. Inspired by t...

Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their abilit...

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 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...

This introduction offers an overview of the eighteen contributions (15 papers and three posters) to the TWG23 at CERME12. The three thematic discussions that took place in this Thematic Working Group are addressed, namely: the role of change, matters of scaling, and the conception of stakeholders.

In this study, we investigate how students undertaking an elective programming course experience the connection between programming and mathematics. Based on stimulated recall interviews with six Grade 8 students who have solved test items from PISA 2003, we identify various experiences among the students regarding how they draw on programming skil...

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 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...

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 paper takes a quantitative ethnographic approach to understand how the lockdown in the spring of 2020 affected the teachers’ work situation at a large university in Denmark. Based on free-text responses from survey data, we create epistemic networks to explore how teachers articulate changes, longings, and potentials for their own future digit...

Når Teknologiforståelse rammer klasseværelset, står lærere og elever overfor et nyt fag, de endnu ikke er bekendte med. Faget er defineret igennem læreplan og fælles mål blandt andet gennem kompetenceområdet computationel tankegang . I denne artikel sætter vi fokus på, hvilke kompetencer der knytter sig til computational thinking ved at undersøge,...

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.

In this article, we explore an emerging organization that unfolds during the implementation of a collaborative and practice-oriented professional development program ( PD ) called Action Learning. In Action Learning, local mathematics supervisors facilitate meetings where mathematics teachers collaboratively discuss and develop interventions in the...

Implementation has always been a paramount concern of mathematics education, but only recently has the conceptualizing and theorizing work on implementation as a phenomenon begun in our field. In this survey paper, we conduct a hermeneutic review of mathematics education research identified as related to the implementation problematics. The first c...

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...

Responsartikel til Morten Blomhøjs tekst: “Samspil mellem fagdidaktisk forskning og udvikling af matematikundervisning - Belyst gennem erfaringer fra et udviklingsprojekt om undersøgende matematikundervisning”

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...

Variables included in cross-crountry comparison on the relation between mathematics teachers' training problem solving, intgration of digital technology, a combination thereof and none at all for their students TIMMS scores in DK, ENG and SE.

Bidrag til DUT Tidskapsel Her er mine indtryk fra digital undervisning i år 2020. Jeg synes det blev et alvorens år for pædagogisk it.

Quantitative Ethnography (QE) is an emerging methodological approach that combines ethnographic and statistical tools to analyze both Big Data and smaller data to study human behavior and interactions. This paper presents a methodological scoping review of 60 studies employing QE approaches with an intention to characterize and establish where the...

Topic model of technology in mathematics education

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...

Mathematicians’ use of external representations, such as symbols and diagrams, constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical b...

This workshop explores quantitative ethnography as a framework for discussing network approaches to learning analysis. In many learning contexts, we increasingly have access to large amounts of rich process data. To make meaning of this evidence, our goal is to develop a qualitatively "thick" description of the data and thus of learning. However, t...

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...

In this introduction, we briefly present the origin of a young Thematic Working Group 23 (TWG23) on implementation of research findings in mathematics education, and its development from CERME 10 to CERME 11. We then address the construct “implementation research” by looking at the model proposed by Century and Cassata (2016). Drawing from this mod...

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...

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...

Denne artikel afsøger den seneste internationale engelsksprogede forskningslitteratur om anvendelse af digitale læringsplatforme. Reviewet behandler forskning fra i alt 21 studier og sammenfatter resultaterne i tre hovedkategorier, der hhv. omfatter implementering af læringsplatforme, kompetenceudviklingsbehov i forbindelse med platforme og relatio...

Denne artikel undersøger, hvilke muligheder og begrænsninger der er for at planlægge undersøgende STEM undervisning i digitale platforme, og hvad der har betydning for dette. Det empiriske grundlag er to forløb, der er udviklet i samme læringsplatform, hvor det ene af disse forløb har været målrettet en undersøgende tilgang. Det teoretiske udgangsp...

Previous research has emphasized the importance and potential of actively involving teachers in the design and implementation of educational technologies in schools. However, only a few studies have explored the development of methodologies for engaging teachers in the appropriation of digital technologies, as the increased digitalization of many e...

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...

In this paper, we investigate mathematics teachers' conception of the relationship between mathematics and programming. The context of the investigation is a recent curriculum reform in Sweden that makes programming a compulsory element of the national mathematics standards. Following up on an in-service training initiative, we conducted a pilot su...

This book constitutes the refereed proceedings of the First International Conference on Quantitative Ethnography, ICQE 2019, held in Madison, Wisconsin, USA, in October 2019. It consists of 23 full and 9 short carefully reviewed papers selected from 52 submissions. The contributions come from a diverse range of fields and perspectives, including le...

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...

In this article, we explore the relationship between teacher practice, technological infrastructure, and national curriculum standards using one teacher's experience as outset for theoretical exploration of relations between curriculum and technology in digital learning platforms. We present a project testing a learning platform that connects natio...

Using games for learning tends to blur boundaries across across in- and out-of-school domains. In this way, it becomes difficult to describe and understand the meaning-making processes involved in game-oriented learning. In this chapter, we present the analytical framework of scenario-based education, which can be used to explore the translation pr...

"Games and Education" explores new designs in and for learning and offer inspiraton to teachers, technologists and researchers interested in changing educational practices.

https://connectedlearningsummit.org/cls2018/proceedings/

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...

A game based learning approach may work wonderfully in one school, and then very differently in another, shortly after. This paper reports how one intervention lead to different outcomes depending on school setting. We combine statistical and qualitative lenses to analyze differential impact based on the social and cultural characteristics of four...

Can the challenges encountered in cooperative video games encourage classroom inclusion? And can this experience be translated into curriculum engagement? This study describes a 3 week intervention with game-based learning activities in eight lower secondary classrooms (N=190). The intervention combined the use of the coop action role-playing game...

In this chapter we investigate the role of Computer Algebra Systems (CAS) in textbook proofs. We describe two cases of CAS use in textbook proofs and use the instrumental approach, and in particular the distinction between epistemic and pragmatic mediations, to understand the consequences of the so-called CAS-assisted proofs. We end with a discussi...

This paper reports a Design-Based Research project developing a tool (the Process Tab) that supports teachers' interventions with students in virtual internships. The tool uses a networked approach and allows insights into the discourse of groups and individuals based on contributions in chat fora and assignments. In the paper, we present the tool...

This paper reports on an exploratory trial of developing pedagogical visualizations of 16 students' written assignments on literary analysis using two sets of keywords and Epistemic Network Analysis (ENA). The visualizations are aimed at summative evaluation as a tool for the professor to support assessment and understanding of subject learning. Re...

I disse år implementeres læringsplatforme på de danske folkeskoler som en del af et stort nationalt initiativ. Disse platforme griber ind i og skaber nye betingelser for læreres arbejde med undervisning og skolernes kommunikation og samarbejde.Denne artikel undersøger, hvordan skolerne forholder sig til læringsplatformene og implementeringen af dem...

I folkeskolen spiller en 3. klasse Minecraft i dansktimen, mens to 7. klasser forestiller sig, hvordan danmarkshistorien havde set ud, hvis Stauning var gået i krig mod Hitler. På sygeplejeuddannelsen behandler tre studerende den koldsvedende dukke Anne™, samtidig med at deres medstuderende overværer det dramatiske scenarie. Hvad gør de, hvis pulse...

Mathematical models have a substantial impact at all levels of society, and hence mathematical modelling stands as an important topic in mathematics education. Mathematical modelling has a particular pedagogical/didactical discourse as modelling continues to garner attention in educational research. Diagrammatic representations of mathematical mode...

This paper emerges from our research focusing on mathematics education in trans-disciplinary engineering programs and presents a case study in such an engineering discipline, namely the Media Technology program at Aalborg University Copenhagen, Denmark. In this case study, we substituted traditional mathematics assignments with a programming projec...

In this paper we investigate the role of the local supervisor when implementing a mathematics teacher training program based on Action Learning (Misfeldt et al. 2014, Plauborg et al. 2007). Using data from interviews of teachers, local supervisors and school managers we examine the arising expectations on the local supervisor and how these expectat...

Forenklede Fælles Mål trådte i kraft i skoleåret 2015/2016 og er karakteriseret ved at sætte elevers læring i forgrunden. De lægger op til en øget detailstyring af elevernes læring, samtidigt med at styring og valg af aktiviteter stadig er overladt til de enkelte lærere. Mange pædagogiske tanker og tendenser lægger vægt på eleverog læreres udforskn...

The article discusses three empirical examples of Computer Algebra System (CAS) use in Danish upper secondary school mathematics class with a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students’ mathematical skills and confiden...

Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has...

In this article, we address how the design of educational scenarios can support teachers’ adoption of both technology and open-ended projects indorsing creativity and innovation. We do that by describing how groups of teachers develop digital learning environments supporting using a combination of GeoGebra and Google sites. Both teachers and pupils...