Transformation - A Fundamental Idea of Mathematics Education
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Transformation - A Fundamental Idea of Mathematics Education

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Sebastian Rezat
788 g
244x162x30 mm

This book addresses transformation as a fundamendal idea in mathematics education, in relation to knowledge, to signs and representations of mathematics, to concepts and ideas and to instruments for the learning of mathematics.

Sebastian Rezat, Mathias Hattermann

Part I

Introduction to Part I

Sebastian Rezat, Mathias Hattermann

1 How 18 th Century Mathematics was Transformed into 19 th Century School Curricula

Heike Renate Biermann, Hans Niels Jahnke

2 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

Maike Vollstedt, Aiso Heinze, Kristin Gojdka and Stefanie Rach

3 Knowledge Transformation between Secondary School and University Mathematics

Oliver Deiser, Kristina Reiss

4 Student Transition to University Mathematics Education: Transformations of People, Tools and Practices

Birgit Pepin

5 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

Gabriele Kaiser, Nils Buchholtz

6 Mathematical Moments in a Human Life: Narratives on Transformation

Barbro Grevholm

Discussion to Part I

Transitions in Learning Mathematics as a Challenge for People and Institutions

Rolf Biehler

Part II

Introduction to Part II

Sebastian Rezat, Mathias Hattermann

7 Constructing Knowledge by Transformation: Diagrammatic Reasoning in Practice

Gert Kadunz

8 Transforming Images in a DGS: The Semiotic Potential of the Dragging Tool for Introducing the Notion of Conditional Statement

Maria Alessandra Mariotti

9 Dynamic Representations of Complex Numbers: Opportunities to Learn in Teacher Training

Reinhard Hölzl

10 Dynamic and Tangible Representations in Mathematics Education

Colette Laborde, Jean-Marie Laborde

11 The Role of Social Aspects of Teaching and Learning in Transforming Mathematical Activity: Tools, Tasks, Individuals and Learning Communities

Vince Geiger

12 Designing a Simulator in Building Trades to Transform Vocational Education

Annie Bessot

Discussion to Part II

Discussion I from an Epistemological Point of View: Representing and Meaning-making: The Transformation of Transformation

Falk Seeger

Discussion II from a Technological Point of View: Digital Technologies and Transformation in Mathematics Education

Rosamund Sutherland

Part III

Introduction to Part III

Sebastian Rezat, Mathias Hattermann

13 From Proof Image to Formal Proof - a Transformation

Tommy Dreyfus, Ivy Kidron

14 Elementary Stochastic Seeing in Primary Mathematics Classrooms - Epistemological Foundation and Empirical Evaluation of a Theoretical Construct

Judith Stanja, Heinz Steinbring

15 Understanding Geometric Work through its Development and its Transformations

Alain Kuzniak

16 Small Steps to Promote "Mathematical Literacy"

Lothar Profke

17 Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science

Josephus Klep

Discussion to Part III

Fundamental Ideas of Didactics - Reactions to the Suggested Meta-Theoretical Construct for Reflecting and Connecting Theories

Susanne Prediger


Rudolf Sträßer
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?