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The almost universal rejection of the notion of symbols as carriers of meaning' has created the need to find an alternative for the use of models as embodiments of mathematical concepts. By taking its point of departure as a concern for the way students actually use tools and symbols, and for what these signify for them, this book explores the option of building on symbolizing, modelling and tool use as personally meaningful activities of students. This theme is approached from different angles and different perspectives. One dimension is that of setting, varying from the study of informal,...

Educational design research is the systematic study of designing, developing and evaluating educational programs, processes and products. It can be an invaluable process, yielding considerable insight into how to optimize educational interventions and better understand teaching and learning. However, the fact that such investigations are typically carried out in naturalistic settings - with all the color and complexity that accompanies real classrooms and schools - presents researchers with significant methodological challenges, and scientific rigor can be difficult to maintain. This book...