Mathematical Competencies in the Digital Era

359 Pages·2023·5.544 MB·English

by  Uffe Thomas Jankvist, Eirini Geraniou

Mathematics Education in the Digital Era
Uffe Thomas Jankvist
Eirini Geraniou   Editors
Mathematical
Competencies
in the Digital
Era
Mathematics Education in the Digital Era
Volume 20
Series Editors
Dragana Martinovic, University of Windsor, Windsor, ON, Canada
Viktor Freiman, Faculté des sciences de l’éducation, Université de Moncton,
Moncton, NB, Canada
Editorial Board
Marcelo Borba, State University of São Paulo, São Paulo, Brazil
Rosa Maria Bottino, CNR—Istituto Tecnologie Didattiche, Genova, Italy
Paul Drijvers, Utrecht University, Utrecht, The Netherlands
Celia Hoyles, University of London, London, UK
Zekeriya Karadag, Giresun Üniversitesi, Giresun, Turkey
Stephen Lerman, London South Bank University, London, UK
Richard Lesh, Indiana University, Bloomington, USA
Allen Leung, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Tom Lowrie, University of Canberra, Bruce, Australia
John Mason, Open University, Buckinghamshire, UK
Sergey Pozdnyakov, Saint-Petersburg State Electro Technical University,
Saint-Petersburg, Russia
Ornella Robutti, Università di Torino, Torino, Italy
Anna Sfard, USA & University of Haifa, Michigan State University, Haifa, Israel
Bharath Sriraman, University of Montana, Missoula, USA
Eleonora Faggiano, Department of Mathematics, University of Bari Aldo Moro,
Bari, Bari, Italy
The Mathematics Education in the Digital Era (MEDE) series explores ways in which digital
technologies support mathematics teaching and the learning of Net Gen’ers, paying attention
also to educational debates. Each volume will address one specific issue in mathematics educa-
tion (e.g., visual mathematics and cyber-learning; inclusive and community based e-learning;
teaching in the digital era), in an attempt to explore fundamental assumptions about teaching
and learning mathematics in the presence of digital technologies. This series aims to attract
diverse readers including: researchers in mathematics education, mathematicians, cognitive
scientists and computer scientists, graduate students in education, policy-makers, educational
software developers, administrators and teachers-practitioners. Among other things, the high
quality scientific work published in this series will address questions related to the suitability
of pedagogies and digital technologies for new generations of mathematics students. The
series will also provide readers with deeper insight into how innovative teaching and assess-
ment practices emerge, make their way into the classroom, and shape the learning of young
students who have grown up with technology. The series will also look at how to bridge theory
and practice to enhance the different learning styles of today’s students and turn their motiva-
tion and natural interest in technology into an additional support for meaningful mathematics
learning. The series provides the opportunity for the dissemination of findings that address
the effects of digital technologies on learning outcomes and their integration into effective
teaching practices; the potential of mathematics educational software for the transformation
of instruction and curricula; and the power of the e-learning of mathematics, as inclusive and
community-based, yet personalized and hands-on.
Submit your proposal: Please contact the publishing editor at Springer: Marianna.
[email protected]
Forthcoming titles:
• Mathematics Education in the Age of Artificial Intelligence—Philipe R. Richard, M. Pilar
Velez and Steven van Vaerenbergh (eds.)
• Mathematical Work in Educational Context—Alain Kuzniak, Elizabeth Montoya-
Delgadillo and Philippe R. Richard (eds.)
• The Mathematics Teacher in the Digital Era: International Research on Professional
Learning and Practice (2nd Edition)—Alison Clark-Wilson, Ornella Robutti and Nathalie
Sinclair (eds.)
• Quantitative Reasoning in Mathematics and Science Education—Gülseren Karagöz Akar,
˙Ismail Özgür Zembat, Selahattin Arslan and Patrick W. Thompson (eds.)
• The Evolution of Research on Teaching Mathematics—Agida Manizade, Nils Fredrik
Buchholtz and Kim Beswick (eds.)—Open Access!
·
Uffe Thomas Jankvist Eirini Geraniou
Editors
Mathematical Competencies
in the Digital Era
Editors
Uffe Thomas Jankvist Eirini Geraniou
Danish School of Education Curriculum, Pedagogy and Assessment
Aarhus University UCL Institute of Education
Copenhagen, Denmark London, UK
ISSN 2211-8136 ISSN 2211-8144 (electronic)
Mathematics Education in the Digital Era
ISBN 978-3-031-10140-3 ISBN 978-3-031-10141-0 (eBook)
https://doi.org/10.1007/978-3-031-10141-0
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Switzerland AG 2022
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To all believers and non-believers in the
power, value and impact of digital
technologies for mathematics education and
their influence regarding mathematical
competencies.
Foreword
Mathematical Competencies in the Digital Era, edited by Uffe Thomas Jankvist
and Eirini Geraniou, is a book in the series Mathematics Education in the Digital
Era, edited by Dragana Martinovic and Viktor Freiman. The Digital Era , in this
book, refers to two layers: mathematical digital competencies to be developed, but
even with higher emphasis, the development of mathematical competencies with the
support of digital tools.
The focus on mathematical competencies (also conceptualized as mathematical
practices, in other contexts) has a strong tradition in Denmark, where Mogens Niss
and colleagues not only developed a coherent framework, the mathematics competen-
cies framework, the so-called KOM-framework. Denmark is an interesting curricular
laboratory of international interest, because the KOM framework has been conse-
quently established in the Danish curricula and from there influenced many other
countries and regions and also the previous PISA frameworks. In recent years, digital
technologies have been introduced to classrooms, but the editors and authors are
driven by the main idea that more research is needed to use the digital technolo-
gies productively for supporting the development of mathematical competencies and
mathematical digital competencies.
Thereby, the ambitious book presents design research studies from Denmark
and other countries that develop learning opportunities with digital technologies
to support the development of particular mathematical competencies and that
investigate the initiated teaching–learning processes.
The design as well as the empirical investigations draw upon the KOM framework
as well as upon different theoretical constructs and perspectives in mathematics
education research that were particularly generated for situations involving digital
technologies in the teaching and learning of mathematics. For example, the chapters
refer to the instrumental approach, instrumental orchestration, semiotic mediations,
the anthropological theory of the didactic, mathematics-related beliefs, programming
and computational thinking, mathematical digital competencies and the theory of
conceptual fields. In each of the chapters, the authors find other ways to combine the
KOM framework with one or two other theoretical perspectives or constructs, and
in each of the cases, different strategies are applied for networking the theories. In
vii
viii Foreword
this way, the book documents highly interesting cases of networking experiences on
four levels:
(1) On the practical level, two highly relevant challenges in classrooms practices are
combined in many different ways, each time the development of one competency
and the use of digital technologies, and this networked design work results in
several promising instructional approaches that can enrich classroom practice.
(2) On the theoretical and empirical level, the design research requires coordinating,
local integrating or synthesizing theoretical approaches to make sense of the
investigated teaching–learning processes.
(3) On the personal level, these tasks have been conducted by networking of
researchers from different countries: sustained exchange of ideas and collabo-
rations between Scandinavian researchers familiar with the KOM framework
and a number of international scholars have resulted in an impressive range of
co-authored contributions in the book’s 18 chapters.
(4) On the methodological level, the authors present intriguing ideas about
comparing and contrasting theories in relation to the use of digital technologies
and mathematical competencies and other constructs from the KOM frame-
work. The editors and authors have carried out substantial networking prac-
tices to showcase how KOM’s descriptions of mathematical competencies, etc.,
can be refined and deepened using other frameworks from both inside and
outside of mathematics education research. This in itself is a significant contri-
bution that offers some foundational work for further connections of theo-
ries moving towards a higher level of integration for the KOM framework’s
constructs in the digital era. The audience of this book should recognize the
combined (networked) framework approach suggested in each chapter, as they
provide specific foci for attention and a potential basis for an increasingly unified
discourse of research and practice in mathematics education.
In my view, one of the strongest aspects of the work presented in this book is
the comprehensive exposition of how additional frameworks augment and refine
the KOM framework when digital technologies are in play. Its multi-layer work
reveals a fascinating read for mathematics education researchers, graduate students
and teacher educators worldwide, who are particularly interested in the digital tech-
nologies’ influence on mathematical competencies as presented by different authors
using various educational theories. I congratulate the editors and the authors for this
insightful work!
I hope this compelling book will find many readers who enjoy diving into
Mathematical Competencies in the Digital Era!
Dortmund, Germany Susanne Prediger
Acknowledgements
A big thank you to all contributing authors, without whom this book would not
have been possible. Also a warm thank you to doctoral students Cecilie Carlsen
Bach, Mathilde Kjær Pedersen and Rikke Maagaard Gregersen who efficiently and
effectively assisted in the many practical matters surrounding this book’s coming
into being.
ix
Contents
Mathematical Competencies in the Digital Era: An Introduction ....... 1
Uffe Thomas Jankvist, Eirini Geraniou, Mathilde Kjær Pedersen,
Cecilie Carlsen Bach, and Rikke Maagaard Gregersen
Setting the Scene
On the Mathematical Competencies Framework and Its Potentials
for Connecting with Other Theoretical Perspectives .................. 15
Mogens Niss and Uffe Thomas Jankvist
The Mathematical Competencies Framework and Digital
Technologies ...................................................... 39
Eirini Geraniou and Morten Misfeldt
The Eight Mathematical Competencies
Processes of Mathematical Thinking Competency in Interactions
with a Digital Tool ................................................. 63
Mathilde Kjær Pedersen
Mathematical Competencies Framework Meets Problem-Solving
Research in Mathematics Education ................................. 81
Mario Sánchez Aguilar, Martha Leticia García Rodríguez,
and William Enrique Poveda Fernández
Mathematical Modelling and Digital Tools—And How a Merger
Can Support Students’ Learning .................................... 99
Britta Eyrich Jessen and Tinne Hoff Kjeldsen
Lower Secondary Students’ Reasoning Competency in a Digital
Environment: The Case of Instrumented Justification ................. 119
Rikke Maagaard Gregersen and Anna Baccaglini-Frank
xi