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 learning of the subject; the second is a shift from the traditional focusing on mastering of skills and knowledge to being concerned with the possession and development of mathematical competencies.
This book builds on the Danish KOM (Competencies and the Learning of Mathematics) project, which sources its description of mathematical mastery primarily on the notion of a mathematical competency rather than on lists of topics, concepts, and results. This allows for an overarching framework, which captures the perspectives of mathematics teaching and learning at whichever educational level. While the KOM framework does not in detail address the role of digital technologies in relation to its description of different types of mathematical competencies, etc., the chapters of this book set out to do exactly this, while in the process also drawing on a selection of other theoretical constructs and frameworks from mathematics education research.
Starting with introductory chapters by key researchers in the area, the book brings forth chapters for each of the KOM frameworks eight mathematical competencies, authored by Nordic researchers in combination with international scholars. The KOM framework also operates with three types of overview and judgement, which are specifically addressed in relation to the role of digital technologies in the third part of the book. The fourth and final part of the book broadens the scene and provides chapters of a more perspective nature in relation to mathematical competencies in the digital era. The books preface is by Susanne Prediger.
Part I: Setting the Scene.
Chapter
1. Introduction(Uffe Thomas
Jankvist, Eirini Geraniou & Rikke Maagaard Gregersen).
Chapter
2. About the
Mathematical Competencies Framework and Potential Networking(Mogens Niss &
Uffe Thomas Jankvist).
Chapter
3. The Mathematical Competencies Framework
and Digital Technologies(Eirini Geraniou & Morten Misfeldt).- Part II:
Examples of networking around the eight competencies.
Chapter
4.
Mathematical Thinking Competency(Mathilde Kjęr Pedersen & Paul Drijvers).-
Chapter
5. Mathematical Problem Handling Competency(Tomas Hųjgaard & Thomas
Kaas).
Chapter
6. Mathematical Modelling Competency(Tinne Hoff Kjeldsen &
Kasper Bjerring & Britta Jessen).
Chapter
7. Mathematical Reasoning
Competency(Rikke Maagaard Gregersen & Anna Baccaglini-Frank).
Chapter
8.
Mathematical Representation Competency(Ingi Heinesen Hųjsted & Maria
Allesandra Mariotti).
Chapter
9. Mathematical Symbols and Formalism
Competency(Ola Helenius & Linda Ahl).
Chapter
10. Mathematical Communication
Competency(Cecilie Carlsen Bach & Angelika Bikner-Ahsbahs).
Chapter
11.
Mathematical Tools and Aids Competency(Morten Misfeldt, Eirini Geraniou &
Uffe Thomas Jankvist).- Part III: Examples of networking around the three
types of overview and judgment.
Chapter
12. The actual application of
mathematics(Raimundo José Elicer & Morten Blomhųj).
Chapter
13. The
historical development of mathematics(Marianne Thomsen & Kathy Clark).-
Chapter
14. The nature of mathematics as a discipline(Maria Ųstergaard &
Dandan Sun).- Part IV: Broadening the Scene.
Chapter
15. KOMs six teacher
competencies - in the digital era(Charlotte Krog Skott & NN).
Chapter
16.
The KOM framework and PISA - in the digital era(Ross Turner & NN).
Chapter
17. Mathematical competencies and computational thinking(Andreas Tamborg &
Jonas Dreyųe & Boris Koichu).
Chapter
18. Summary and suggested uses for the
book(Mario Sįnchez Aguilar).
Uffe Thomas Jankvist is professor of mathematics education at Danish School of Education, Aarhus University, Denmark. His research interests involve the use of history of mathematics in mathematics education, digital technologies in the teaching and learning of mathematics, the role of interdisciplinarity when teaching mathematics, students mathematics specific learning difficulties, and implementation research related to mathematics education. In collaboration with E. Geraniou, he has also done research on students and teachers mathematical digital competencies.
Eirini Geraniou is associate professor of mathematics education at the UCL Institute of Education, University College London, London, United Kingdom. Her research interests involve the use of digital technologies for the learning and teaching of mathematics, the design and implementation of bridging resources and media for mathematical learning with digital technologies, and students mathematical thinking and computational thinking. In collaboration with U. T. Jankvist, she has also done research on students and teachers mathematical digital competencies.
