Contents

Introduction

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 Transfor-mation 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

Fundam