Full Description
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline's lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
Contents
Introduction to Part I.- How 18th Century Mathematics was Transformed into 19th Century School Curricula.- A Framework for Examining the Transformation of Mathematics and Mathematics Learning in the Transition from School to University: An Analysis of German Textbooks from Upper Secondary School and the First Semester.- Knowledge Transformation between Secondary School and University Mathematics.- Student Transition to University Mathematics Education: Transformations of People, Tools and Practices.- Overcoming the Gap between University and School Mathematics: The Impact of an Innovative Programme in Mathematics Teacher Education at the Justus-Liebig-University in Giessen.- Mathematical Moments in a Human Life: Narratives on Transformation.- Transitions in Learning Mathematics as a Challenge for People and Institutions.- Introduction to Part II.- Constructing Knowledge by Transformation: Diagrammatic Reasoning in Practice.- Transforming Images in a DGS: The Semiotic Potential of the Dragging Tool for Introducing the Notion of Conditional Statement.- Dynamic Representations of Complex Numbers: Opportunities to Learn in Teacher Training.- Dynamic and Tangible Representations in Mathematics Education.- The Role of Social Aspects of Teaching and Learning in Transforming Mathematical Activity: Tools, Tasks, Individuals and Learning Communities.- Designing a Simulator in Building Trades to Transform Vocational Education.- Discussion I from an Epistemological Point of View: Representing and Meaning-making: The Transformation of Transformation.- Discussion II from a Technological Point of View: Digital Technologies and Transformation in Mathematics Education.- Introduction to Part III.- From Proof Image to Formal Proof - a Transformation.- Elementary Stochastic Seeing in Primary Mathematics Classrooms - Epistemological Foundation and Empirical Evaluation of a Theoretical Construct.- Understanding Geometric Work through its Development and its Transformations.-Small Steps to Promote "Mathematical Literacy".- Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science.- Fundamental Ideas of Didactics - Reactions to the Suggested Meta-Theoretical Construct for Reflecting and Connecting Theories.- Epilogue.
