We highlight how each of these themes is addressed by the chapter authors, either explicitly or more implicitly, to draw out the important interconnections within and between the respective texts. By doing so, we aim to highlight not only the complex nature of the field but also the advancements in theoretical and practical knowledge that is enabling the mathematics education community to continue to learn in this increasingly digital age.
Mathematics teacher education and professional development in the digital age
Since the 1980s and 1990s and the introduction of the early mathematical computer applications to mathematics classrooms (i.e. LOGO, spreadsheets, dynamic graphing and dynamic geometry software), teachers of mathematics have been challenged to explore how these new tools impact on the curriculum and its pedagogy. In the intervening years, the mathematics education research field has expanded to consider the teacher in all of his/her roles within the context of both pre-service and in-service teacher education, with increasing emphasis on how to prepare and support teachers to conduct their professional lives in this fast-moving digital age.
The chapter by Faggiano, Rocha, Sacristán and Santacruz-Rodríguez adopts a historical approach to the analysis of major national or regional professional development initiatives in Colombia, Italy, Mexico and Portugal to aim at making explicit the “pragmatic theories” that have underpinned their design, implementation and (in some cases) evaluation. Their resulting methodological frame develops and expands five interconnected themes: the vision and goals of the initiative, its focus, the strategies and methods employed, constraints and incentives and the approaches to evaluation. This frame offers a useful analysis tool to inform the design of teacher professional development interventions that address digital technology use in school mathematics education – and take account of important international differences.
Sacristán, Rahaman, Srinivas and Rojano provide the important perspectives from developing countries in their chapter, which offers insights from Mexico and India on technology integration in mathematics education. Within this, they consider the contextual factors that influence teachers’ attitudes to and uptake of technology, alongside the nature of associated professional development design.
Gueudet, Pepin, Courtney, Kock, Misfeldt and Lindenskov Tamborg also adopt an international perspective as they compare the affordances and constraints of digital education platforms offered as resource banks for teachers of mathematics to support them to design lessons. Drawing on the documentational approach, the authors conclude a number of factors that differentiate such platforms, which link to national education policies and perspectives on the nature of teachers’ work, in particular the important aspect of the role of the teacher as a designer of lessons. Their chapter highlights the developing complexity of this role in the digital age.
Aspects of the role of the teacher are addressed less explicitly in the chapter by Jankvist, Dreyøe, Geraniou, Weigand and Misfeldt (concerning teachers’ roles as formative assessors of students’ learning), that by Albano, Kondratieva and Telloni (reflecting the multiple roles of undergraduate mathematics’ lecturers as designers, teachers and researchers of students’ digital experiences) and the chapter by Leung and Donevska-Todorova (offering pedagogical insights into how the pragmatic to abstract continuum is addressed within digital task design).
Finally, three chapters produce tools and frameworks that may prove useful for teachers in aspects of their roles as curriculum and lesson designers.
Donevska-Todorova, Trgalova, Schreiber and Rojano compare the analysis of selected digital mathematics tasks to develop a set of criteria that might indicate a sense of their quality.
Koch, Confrey, Clark-Wilson, Jameson and Suurtamm describe and analyze three digital maps of the mathematics curriculum, which offer different ways to conceive its design and construction. The resulting maps offer opportunities to reflect on the design and enactment of the mathematics curriculum in dynamic ways.
Skott, C., Psycharis and Skott, J. adopt a social perspective to help understand how the use of digital resources affects one teacher’s professional by using the Patterns of Participation (PoP) framework.
Research on aspects of initial teacher education and teachers’ ongoing professional learning is evolving rapidly to incorporate aspects of digital technological tools beyond only training activities with particular digital tools. However, the geographical and cultural diversity of technology integration within mathematics education, as brought to the fore by several chapters in this book, indicates that the dissemination of existing research, with further validation of the theories and methods adopted, may support more research-informed approaches. However, as new mathematical technological tools emerge, alongside the increased interoperability of the existing tools, there will always be the continued need for related research. There is still much to be understood about the components of more effective teaching practices involving technological tools and how these relate to the evolution of teachers’ knowledge.
