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Title Transformation-- a fundamental idea of mathematics education / Sebastian Rezat, Mathias Hattermann, Andrea Peter-Koop, editors
Published New York : Springer, 2014
Table of Contents
pt. I Transformations at Transitions in Mathematics Education1
1.How Eighteenth-Century Mathematics Was Transformed into Nineteenth-Century School Curricula / Hans Niels Jahnke5
2.Framework for Examining the Transformation of Mathematics and Mathematics Learning in the Transition from School to University / Stefanie Rach29
3.Knowledge Transformation Between Secondary School and University Mathematics / Kristina Reiss51
4.Student Transition to University Mathematics Education: Transformations of People, Tools and Practices / Birgit Pepin65
5.Overcoming the Gap Between University and School Mathematics / Nils Buchholtz85
6.Mathematical Moments in a Human Life: Narratives on Transformation / Barbro Grevholm107
Discussion of Part I Transitions in Learning Mathematics as a Challenge for People and Institutions / Rolf Biehler127
pt. II Transformations Related to Representations of Mathematics135
7.Constructing Knowledge by Transformation, Diagrammatic Reasoning in Practice / Gert Kadunz141
8.Transforming Images in a DGS: The Semiotic Potential of the Dragging Tool for Introducing the Notion of Conditional Statement / Maria Alessandra Mariotti155
9.Dynamic Representations of Complex Numbers / Reinhard Holzl173
10.Dynamic and Tangible Representations in Mathematics Education / Jean-Marie Laborde187
11.The Role of Social Aspects of Teaching and Learning in Transforming Mathematical Activity: Tools, Tasks, Individuals and Learning Communities / Vince Geiger203
12.Designing a Simulator in Building Trades to Transform Vocational Education / Annie Bessot223
Discussion I of Part II Representing and Meaning-Making. The Transformation of Transformation / Falk Seeger241
Discussion II of Part II Digital Technologies and Transformation in Mathematics Education / Rosamund Sutherland253
pt. III Transformation Related to Concepts and Ideas265
13.From Proof Image to Formal Proof---A Transformation / Ivy Kidron269
14.Elementary Stochastic Seeing in Primary Mathematics Classrooms---Epistemological Foundation and Empirical Evaluation of a Theoretical Construct / Heinz Steinbring291
15.Understanding Geometric Work through Its Development and Its Transformations / Alain Kuzniak311
16.Small Steps to Promote "Mathematical Literacy" / Lothar Profke327
17.Transformation as a Fundamental Concept in Arithmetical Competence Modelling: An Example of Informatical Educational Science / Joost Klep349
Discussion of Part III Fundamental Ideas of Didactics---Reactions to the Suggested Meta-theoretical Construct for Reflecting and Connecting Theories / Susanne Prediger387
 Epilogue / Rudolf Straßer397
 Index403

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Description 1 online resource
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
Summary This book opens up a discussion on fundamental ideas of mathematics education as a means to focus on the overarching core issuesand to reflect upon the identity of the scientific discipline. The concept of transformation is introduced as one fundamental idea in the discipline and examined from different perspectives. Transformations are related to knowledge, to signs and representations of mathematics, to concepts and ideas central to teaching and learning mathematics, andto instruments for the learning of mathematics. With an international pool of authors, this 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? The book is meant for researchers, teacher educators and curriculum designers in the field of Mathematics Education. It is destined tooccupy an important place in current literature on the topic of transformationas a way of uncovering and explaining mathematical practice and the very essence of mathematics as well as a way of creating and maintainingsemantic networks between different content areas
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed December 23, 2013)
Subject Mathematics -- Study and teaching.
Transformative learning.
MATHEMATICS -- Essays.
MATHEMATICS -- Pre-Calculus.
MATHEMATICS -- Reference.
Droit.
Sciences sociales.
Sciences humaines.
Mathematics -- Study and teaching
Transformative learning
Form Electronic book
Author Peter-Koop, Andrea, editor
Rezat, Sebastian, editor
Hattermann, Mathias, editor
ISBN 9781461434894
1461434890
1461434882
9781461434887
1306277744
9781306277747