What are the essential components of a doctorate program in mathematics education or didactics of mathematics concerning research, coursework, seminars, and collaboration? The purpose of this study was to learn from doctoral students across the world about how their programs in mathematics education are preparing them for research and teaching in mathematics education; how their programs provide academic research and writing support; and what they view as missing from their experiences. Online surveys, along with follow-up interviews from a subset of survey respondents, indicated that doctoral students from 17 different countries stressed the importance of international collaboration, examining fundamental theories of learning mathematics, and identified a need for more support with academic writing.
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The purpose of this study was to learn from university faculty with a doctorate in mathematics education from across the world about how programs in mathematics education should prepare doctoral students for research and teaching in mathematics education. Online survey responses indicated that 99 mathematics education university faculty from 33 different countries stressed the importance of providing doctoral students with opportunities to examine and compare fundamental theories of learning mathematics; examine current and historical research in the field of mathematics education; and develop broad and deep knowledge of the big ideas ages 2-20 years (i.e., grades preK-14) mathematics.
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Nowadays, digital tools for mathematics education are sophisticated and widely available. These tools offer important opportunities, but also come with constraints. Some tools are hard to tailor by teachers, educational designers and researchers; their functionality has to be taken for granted. Other tools offer many possible educational applications, which require didactical choices. In both cases, one may experience a tension between a teacher’s didactical goals and the tool’s affordances. From the perspective of Realistic Mathematics Education (RME), this challenge concerns both guided reinvention and didactical phenomenology. In this chapter, this dialectic relationship will be addressed through the description of two particular cases of using digital tools in Dutch mathematics education: the introduction of the graphing calculator (GC), and the evolution of the online Digital Mathematics Environment (DME). From these two case descriptions, my conclusion is that students need to develop new techniques for using digital tools; techniques that interact with conceptual understanding. For teachers, it is important to be able to tailor the digital tool to their didactical intentions. From the perspective of RME, I conclude that its match with using digital technology is not self-evident. Guided reinvention may be challenged by the rigid character of the tools, and the phenomena that form the point of departure of the learning of mathematics may change in a technology-rich classroom.
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