It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
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.
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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