ICME-13 Monographs. Series editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany

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1 ICME-13 Monographs Series editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany

2 Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volume is based on the discussions and presentations during the ICME-13 Congress and includes the best papers from one of the ICME-13 Topical Study Groups or Discussion Groups. More information about this series at

3 Florence Mihaela Singer Editor Mathematical Creativity and Mathematical Giftedness Enhancing Creative Capacities in Mathematically Promising Students 123

4 Editor Florence Mihaela Singer Faculty of Letters and Science Oil & Gas University of Ploiești Ploiești Romania ISSN ISSN (electronic) ICME-13 Monographs ISBN ISBN (ebook) Library of Congress Control Number: Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 Contents 1 Enhancing Creative Capacities in Mathematically-Promising Students. Challenges and Limits... 1 Florence Mihaela Singer Part I Frameworks for Studying Mathematical Creativity and Giftedness 2 Mathematical Creativity: Product, Person, Process and Press Demetra Pitta-Pantazi, Maria Kattou and Constantinos Christou 3 Mathematical Giftedness and Creativity in Primary Grades Daniela Assmus and Torsten Fritzlar 4 Cognitive Variety in Rich-Challenging Tasks Cristian Voica and Florence Mihaela Singer 5 Mathematical Creativity and Its Subdomain-Specificity. Investigating the Appropriateness of Solutions in Multiple Solution Tasks Maike Schindler, Julia Joklitschke and Benjamin Rott Part II Characteristics of Students with Exceptional Mathematical Promise 6 Characteristics of Mathematical Giftedness in Early Primary School Age Daniela Assmus 7 The Cognitive Demand of a Gifted Student s Answers to Geometric Pattern Problems Angel Gutierrez, Clara Benedicto, Adela Jaime and Eva Arbona v

6 vi Contents 8 Twice-Exceptional Students: Students with Special Needs and a High Mathematical Potential Marianne Nolte Part III Teaching Strategies to Foster Creative Learning 9 Flexibility of Pre-services Teachers in Problem Posing in Different Environments Wajeeh Daher and Ahlam Anabousy 10 Ornaments and Tessellations: Encouraging Creativity in the Mathematics Classroom Hana Moraová, Jarmila Novotná and Franco Favilli 11 Instances of Promoting Creativity with Procedural Tasks Michal Tabach and Alex Friedlander Part IV Tasks and Techniques to Enhance Creative Capacities 12 Gifted Students Approaches When Solving Challenging Mathematical Problems Andreas Poulos and Joanna Mamona-Downs 13 Repeated Participation at the Mathematical Olympiads: A Comparative Study of the Solutions of Selected Problems Ingrida Veilande, Liga Ramana and Sandra Krauze 14 Complex and Open-Ended Tasks to Enrich Mathematical Experiences of Kindergarten Students Viktor Freiman Commentary Paper: A Reflection on Mathematical Creativity and Giftedness Linda Jensen Sheffield Author Index Subject Index

7 Introduction What are the relationships between mathematical creativity and mathematical giftedness? How could mathematical creativity contribute to a balanced development of the child? What are the characteristics of mathematical giftedness in early ages? What about these characteristics at university level? What teaching strategies might enhance creative learning? How mathematical promise of young children can be maintained and extended towards a variety of professions? These are some of the questions addressed by this book. The book offers, among others: analyses of substantial learning environments for supporting creativity in mathematics lessons, discussions of a variety of strategies in problem-solving and posing, investigations of students progress along years of training, and examinations of technological tools and virtual resources meant to enhance learning with understanding. Multiple perspectives in the interdisciplinary fields of mathematical creativity and giftedness are developed to offer a springboard for further research. The theoretical and empirical studies included in the book offer consistent data useful for researchers, as well as for the teachers of the gifted in specialized or inclusive settings, at various levels of education. vii