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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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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This paper is a summary paper of the Thematic Working Group (TWG) on Adult Mathematics Education (AME). As the only thematic working group that focuses on adults’ lived experiences of mathematics, the research makes an important contribution to the field of Mathematics Education. The main themes in this group identify that adult numerical behaviour goes beyond the mathematics skills, knowledge, and procedures taught in formal education It is multifaceted, requiring the use of higher order skills of analysis and judgement, applied within a broad array of life’s contexts, experienced through a range of emotions. The research in this group points to the need to raise the profile of research that shows the benefits to adults of learning mathematics but also the long term economic disbenefits in the neglect of teaching and teacher training for this group.
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This paper analyses the impact of two structural context factors on mathematics teacher students. First, the Netherlands is coping with a massive mathematics teacher shortage. Second, the Dutch knowledge-economy feeds the private tutoring sector. The impact on young teacher-students is tremendous; they start working as a teacher too early. Besides successful studying, broader professionalization and quality of mathematics education are in jeopardy. A quick-fix for mathematics education might do more damage than foreseen.
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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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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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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 paper we describe values in mathematics education in the Netherlands, in a context where both government and teachers are merely focused on test results. At the same time, newly proposed core goals emphasise mathematics education’s socializing function. These new core goals also focus on mathematical attitudes and relating mathematics and the world outside school. This paper describes an exploration to come to a model that can be used to both clarify the role of values in mathematics education and can be used to design education that aligns with this value-oriented character. We present the development of this model as it evolved in discussions with experts such as teacher educators, mathematics specialists, and primary school teachers. It developed from a linear model, via an adapted version making it too complex, to a model that is more focused on the relation between the main elements. The final model represents relations between ‘mathematics’, ‘values’, and ‘the world’ and names the connections between these aspects ‘mathematical literacy’, ‘citizenship’, and ‘value-based mathematics’. By developing this model, we experienced that its use shifted from a descriptive model, via a model that helps communicating about value based mathematics to a mental model. The final model can be used for future design research, where the first step will be establishing the present status of values in mathematics education.
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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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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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