The design and use of online materials for blended learning have been in the spotlight of educational development over the last decade. With respect to didactical courses, however, the potential of online and blended learning seems to be underexplored; little is known about its affordances for teacher education, and for domain specific didactical courses in particular. To investigate this potential, as well as the ways to organize the co-design of such learning units, we carried out a small and short-term research project in which teacher educators in the Netherlands engaged in a co-design process of developing and field-testing open online learning units for mathematics and science didactics. We focused on the features of the designed online learning units, on the organization of the co-design process, and on the experiences with the learning units in teacher education practice. A first conclusion was that it was most fruitful to design building blocks rather than ready-to-use courses, and that students should have play a role in the materials. With respect to the co-design process, intensive meetings of small design teams seemed an efficient approach. The experiences in the field tests revealed that the learning units were inspiring, but needed finalization, and educators needed time to prepare the incorporation in their existing educational practices. In the future, the resulting learning units will be maintained and extended, and are expected to contribute to a community of practice of mathematics and science educators.
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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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In this chapter, we discuss the education of secondary school mathematics teachers in the Netherlands. There are different routes for qualifying as a secondary school mathematics teacher. These routes target different student teacher populations, ranging from those who have just graduated from high school to those who have already pursued a career outside education or working teachers who want to qualify for teaching in higher grades. After discussing the complex structure this leads to, we focus on the aspects that these different routes have in common. We point out typical characteristics of Dutch school mathematics and discuss the aims and challenges in teacher education that result from this. We give examples of different approaches used in Dutch teacher education, which we link to a particular model for designing vocational and professional learning environments.We end the chapter with a reflection on the current situation.
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Mathematics teacher educators in primary teacher education need expert knowledge and skills in teaching in primary school, in subject matter and research. Most starting mathematics teacher educators possess only part of this knowledge and skills. A professional development trajectory for this group is developed and tested, where a design based research is used to evaluate the design. This paper describes the professional development trajectory and design. We conclude that the professional development design should focus on mathematical knowledge for teaching, should refer to both teacher education and primary education, should offer opportunities for cooperative learning, and need to use practice based research as a developmental tool.
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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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Blended learning, a teaching format in which face-to-face and online learning is integrated, nowadays is an important development in education. Little is known, however, about its affordances for teacher education, and for domain specific didactical courses in particular. To investigate this topic, we carried out a design research project in which teacher educators engaged in a co-design process of developing and field-testing open online learning units for mathematics and science didactics. The preliminary results concern descriptions of the work processes by the design teams, of design heuristics, and of typical ways of collaborating. These findings are illustrated for the case of two of the designed online units on statistics didactics and mathematical thinking, respectively.
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Social robots have been introduced in different fields such as retail, health care and education. Primary education in the Netherlands (and elsewhere) recently faced new challenges because of the COVID-19 pandemic, lockdowns and quarantines including students falling behind and teachers burdened with high workloads. Together with two Dutch municipalities and nine primary schools we are exploring the long-term use of social robots to study how social robots might support teachers in primary education, with a focus on mathematics education. This paper presents an explorative study to define requirements for a social robot math tutor. Multiple focus groups were held with the two main stakeholders, namely teachers and students. During the focus groups the aim was 1) to understand the current situation of mathematics education in the upper primary school level, 2) to identify the problems that teachers and students encounter in mathematics education, and 3) to identify opportunities for deploying a social robot math tutor in primary education from the perspective of both the teachers and students. The results inform the development of social robots and opportunities for pedagogical methods used in math teaching, child-robot interaction and potential support for teachers in the classroom
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In this chapter, I look back at the implementation of W12-16, a major reform of mathematics education in the lower grades of general secondary education and pre-vocational secondary education in the Netherlands including all students aged 12–16. The nationwide implementation of W12-16 started in 1990 and envisioned a major change in what and how mathematics was taught and learned. The content was broadened from algebra and geometry to algebra, geometry and measurement, numeracy, and data processing and statistics. The learning trajectories and the instruction theory were based on the ideas of Realistic Mathematics Education (RME): the primary processes used in the classroom were to be guided re-invention and problem solving. ‘Ensuring usability’ in the title of this chapter refers to the aim of the content being useful and understandable for all students, but also to the involvement of all relevant stakeholders in the implementation project, including teachers, students, parents, editors, curriculum and assessment developers, teacher educators, publishers, media and policy makers. Finally, I reflect on the current state of affairs more than 20 years after the nationwide introduction. The main questions to be asked are: Have the goals been reached? Was the implementation successful?
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Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
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This paper explores the contributions of research to the field of adults learning mathematics (ALM) in the last twenty years. The results of the review of the literature on ALM show that the most cited studies that have been published in the last twenty years tend to focus on the field of numeracy to understand health data (such as understanding how to dose a medicine in a medical treatment). However, we know little about key aspects of how adults learn mathematics, what obstacles they encounter, and how they overcome them. This paper identifies the main gaps that ALM research faces in the coming years.
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