Transformation - A Fundamental Idea of Mathematics Education

ISBN-13: 9781461434887 / Angielski / Twarda / 2013 / 409 str.

Andrea Peter-Koop; Sebastian Rezat; Mathias Hattermann

Opis

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?

Spis treści

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 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

 

Epilogue

Rudolf Sträßer

 

O autorze

Prof. Dr. Andrea Peter-Koop lehrt und forscht am Institut für Didaktik der Mathematik an der Universität Bielefeld. Dort leitet sie die Beratungsstelle für Kinder mit Rechenstörungen. Ihre Forschungsinteressen betreffen die Prozesse des frühen Mathematiklernens, mathematische Diagnostik, die Prävention, Diagnose und Therapie von Kindern mit Rechenstörungen sowie Theorien der Lehrerbildung.

Blurb

This book opens up a discussion on fundamental ideas of mathematics education as a means to focus on the overarching core issues and 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, and to 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 to occupy an important place in current literature on the topic of transformation as a way of uncovering and explaining  mathematical practice and the very essence of mathematics as well as a way of creating and maintaining  semantic networks between different content areas.