Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond

261 Pages·2017·6.008 MB·English

by  Roza Leikin, Bharath Sriraman (eds.)

Advances in Mathematics Education
Roza Leikin
Bharath Sriraman E ditors
Creativity
and
Giftedness
Interdisciplinary perspectives from
mathematics and beyond
Advances in Mathematics Education
Series Editors
Gabriele Kaiser, University of Hamburg, Hamburg, Germany
Bharath Sriraman, The University of Montana, Missoula, MT, USA
International Editorial Board
Ubiratan D’Ambrosio (São Paulo, Brazil)
Jinfa Cai (Newark, NJ, USA)
Helen Forgasz (Melbourne, Victoria, Australia)
Jeremy Kilpatrick (Athens, GA, USA)
Christine Knipping (Bremen, Germany)
Oh Nam Kwon (Seoul, Korea)
More information about this series at w ww.springer.com/series/8392
Roza Leikin • Bharath Sriraman
Editors
Creativity and Giftedness
Interdisciplinary perspectives from
mathematics and beyond
Editors
Roza Leikin Bharath Sriraman
Faculty of Education Department of Mathematical Sciences
RANGE Center, University of Haifa The University of Montana
Haifa , Israel Missoula , Montana , USA
ISSN 1869-4918 ISSN 1869-4926 (electronic)
Advances in Mathematics Education
ISBN 978-3-319-38838-0 ISBN 978-3-319-38840-3 (eBook)
DOI 10.1007/978-3-319-38840-3
Library of Congress Control Number: 2016947794
© Springer International Publishing Switzerland 2017
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Contents
1 Introduction to Interdisciplinary Perspectives to Creativity
and Giftedness ......................................................................................... 1
Roza Leikin and Bharath Sriraman
Part I Perspectives on Creativity
2 Creativity, Imagination, and Early Mathematics Education .............. 7
Maciej Karwowski , Dorota M. Jankowska , and Witold Szwajkowski
3 Formative Assessment of Creativity in Undergraduate
Mathematics: Using a Creativity-in-Progress Rubric (CPR)
on Proving ................................................................................................ 23
Milos Savic , Gulden Karakok , Gail Tang , Houssein El Turkey ,
and Emilie Naccarato
4 Teacher’s Views on Modeling as a Creative
Mathematical Activity ............................................................................ 47
Gudbjorg Palsdottir and Bharath Sriraman
5 The Prominence of Affect in Creativity:
Expanding the Conception of Creativity in Mathematical
Problem Solving ...................................................................................... 57
Eric L. Mann , Scott A. Chamberlin , and Amy K. Graefe
6 When Mathematics Meets Real Objects: How Does
Creativity Interact with Expertise in Problem Solving
and Posing? .............................................................................................. 75
Florence Mihaela Singer and Cristian Voica
7 Constraints, Competency and Creativity in the Classroom ................ 105
Catrinel Haught-Tromp and Patricia D. Stokes
v
vi Contents
8 Convergence in Creativity Development for Mathematical
Capacity ................................................................................................... 117
Ai-Girl Tan and Bharath Sriraman
9 The Origin of Insight in Mathematics ................................................... 135
Reuben Hersh and Vera John-Steiner
10 Creativity in Doubt: Toward Understanding
What Drives Creativity in Learning ...................................................... 147
Ronald A. Beghetto and James B. Schreiber
Part II Perspectives on Giftedness
11 What Is Special About the Brain Activity of Mathematically
Gifted Adolescents? ................................................................................ 165
Roza Leikin , Mark Leikin , and Ilana Waisman
12 Psychological and Neuroscientific Perspectives
on Mathematical Creativity and Giftedness ......................................... 183
David H. Cropley , Martin Westwell , and Florence Gabriel
13 What Have We Learned About Giftedness and Creativity?
An Overview of a Five Years Journey ................................................... 201
Demetra Pitta-Pantazi
14 The Interplay Between Excellence in School
Mathematics and General Giftedness: Focusing
on Mathematical Creativity ................................................................... 225
Miriam Lev and Roza Leikin
15 Mathematically Gifted Education: Some Political Questions ............. 239
Alexander Karp
Part III Commentary
16 Commentary on Interdisciplinary Perspectives
to Creativity and Giftedness ................................................................... 259
Bharath Sriraman and Roza Leikin
Index ................................................................................................................. 265
Chapter 1
Introduction to Interdisciplinary Perspectives
to Creativity and Giftedness
Roza Leikin and Bharath Sriraman
Invention, innovation, originality, insight, illumination and imagination are core
elements of the individual and societal progress along human history from ancient
times till the modern society. While these phenomena are often considered as indi-
cators of creativity and talent in science, technology, business, arts, and music; they
are also basic mechanisms of learning. Till the past decade mathematical creativity
and giftedness were overlooked in the educational research. Luckily lately more
attention is paid to their nature and nature. For example, in 2010 International Group
of Mathematical Creativity and Giftedness ( i gmcg.org) was established following
fi ve international conferences of the community of research mathematicians, math-
ematics educators and educational researchers. During the last decade several books
and edited volumes were devoted to the constructs of mathematical creativity and
mathematical talent, their identifi cation and development (see commentary for ref-
erences). Still there are many open questions remain and researches debate the
question of inborn character of creative talents vs. possibility of developing creativ-
ity and ability in all students. The current volume presents international panorama
of the research of creativity and giftedness, refl ects the state of the art in the fi eld
and provides a broad range of views on the phenomena of creativity and giftedness
with special attention to creativity and giftedness in mathematical.
P art I of the volume focuses on different aspect of creativity in mathematics and
beyond. A group of studies presents possible ways of defi ning and evaluation math-
ematical creativity applied in empirical studies conducted in primary school (Pitta-
Pantazi), in secondary school (Lev and Leikin), in undergraduate mathematics
(Savic et al.), and in courses for mathematics teachers (Palsdottir and Sriraman;
R. Leikin (*)
Faculty of Education, RANGE Center , University of Haifa , Haifa 31905 , Israel
e-mail: [email protected]
B. Sriraman
Department of Mathematical Sciences , T he University of Montana ,
Missoula , Montana , USA
© Springer International Publishing Switzerland 2017 1
R. Leikin, B. Sriraman (eds.), Creativity and Giftedness,
Advances in Mathematics Education, DOI 10.1007/978-3-319-38840-3_1
2 R. Leikin and B. Sriraman
Voica and Singer). Some researchers describe types of mathematical tasks
appropriate for the evaluation and development of mathematical creativity. Palsdottir
and Sriraman argue that mathematical modeling may be viewed as a creative math-
ematical activity, while Voica and Singer analyze problem-posing and constructive
activities as facilitators of the development of creativity in mathematics. Palsdottir
and Sriraman examine the views of a group of Icelandic high school teachers about
modeling activities, and characterize ways in which they implement them in the
classroom. Voica and Singer analyze participants’ creativity through focus on stu-
dents’ cognitive variety and novelty and demonstrate that creative interactions of
the participants increase their problem-solving and problem-posing expertise. Pitta-
Pantazi and Lev and Leikin examined relationship between creativity and gifted-
ness. Lev and Leikin introduce a model for the evaluation of mathematical creativity
using multiple solution tasks and Savic et al. introduces an assessment tool for
evaluation of mathematical creativity that can be implemented in an introductory
proof course.
Several chapters in the book present theoretical perspectives on mathematical
creativity, on general creativity and the relationship between them. Karwowski and
Dziedziewicz present a typological model of creativity made up of creative abilities,
openness to experiences, and independence and suggest its consequences for early
mathematics education. The authors pay special attention to the role of visual and
creative imagination and on new ways of enhancing mathematical creativity using
heuristic rhymes. Tan and Sriraman highlight the role of convergence in developing
creativity and mathematical capacity, distinguish between convergence i n diver-
gence f or emergence as three creativity mechanisms and argue that continuity, inter-
action and complementarity are three principles of experience that lead to the
development of creativity. Hersh and John-Steiner address some psychological
sources that motivate creative mathematicians, analyze their cognitive and mathe-
matical strategies that lead to mathematical insight, and provide examples of cre-
ative breakthroughs in the teaching of mathematics. The authors argue that the
pursuit of novelty, unrestricted by any other prescribed goal or objective, radically
speeds up evolutionary adaptation. Mann and Chamberlin stress importance of
affect in the production of creative outcomes in mathematical problem solving. In
their view anxiety, aspiration(s), attitude, interest, and locus of control, self-effi cacy,
self-esteem, and value are major factors that affect creative problem solving.
Iconoclasm is discussed by the authors as instrumental construct to the production
of creative outcomes. In the chapter by Haught and Stokes creativity follows com-
petency and the product called creative must be both novel and appropriate to its
domain. they argue that paired constraints can make very young children competent
in mathematics and college students more creative in composition. Beghetto and
Schreiber ask “What propels creativity in learning?” They discuss abductive reason-
ing as a special form of creative reasoning that is triggered by states of genuine
doubt that represent opportunities for creative learning.
P art II of the book devoted to research on mathematical giftedness and the educa-
tion of mathematically gifted students. Clearly when discussing giftedness the
authors also touch upon creativity while using different research paradigms and
1 Introduction to Interdisciplinary Perspectives to Creativity and Giftedness 3
research methodologies. Leikin, Leikin & Waissman and Cropley, Westwell &
Gabriel provide Neuro-scientifi c analysis of mathematical creativity and giftedness.
Leikin et al. present an empirical study that uses event related potentials methodol-
ogy to analyze brain activity related to solving mathematical problems by students
of different levels of mathematical abilities. To analyze relationships between math-
ematical creativity and giftedness they employ distinctions between insigh-based
(i.e. creative) and learning-based (routine) problem solving. Cropley et al. provide
meta-analysis of studies on psychological and neuro-scientifi c perspectives on
mathematical creativity and giftedness. They discuss how these approaches can
inform our understanding of creativity as a component of giftedness in general and
how giftedness manifests in mathematics in the creative-productive sense. As men-
tioned above Lev and Leikin and Pitta-Pantazi describe empirical studies that ana-
lyze relationship between mathematical creativity and giftedness. Pitta-Pantazi
summarizes series of studies regarding identifi cation of mathematically gifted stu-
dents and the relation between mathematical creativity, intelligence and cognitive
styles. Chapters by Leikin et al. and Lev and Leikin introduce distinctions between
high achievements in mathematics, general giftedness and superior performance in
mathematics. They stress that excellence in school mathematics and general gifted-
ness are interrelated but different in nature personal characteristics related to math-
ematical giftedness.
A s described above, while Palsdottir and Sriraman and Voica and Singer suggest
approaches to teaching mathematics that develops creativity in all students, Tan and
Sriraman and Hersh and John-Steiner provide theoretical perspectives on mathe-
matics teaching that leads to creative production in mathematics and beyond. The
last but not least important, Karp provides theoretical analysis of mathematically
gifted education from political perspective. He stresses that “practice of recognizing
certain children as more gifted than others and selecting them accordingly becomes
inevitably a focus of public attention, frequently giving rise to disagreements, fi nd-
ing itself at the heart of political discussions, sometimes instigating such discus-
sions, and sometimes refl ecting already existing confl icts” (p. 239).
T he analysis performed by Karp refl ects hidden (political and educational)
debate between the different authors that contributed their chapters to this volume.
As one can see, some authors believe creativity is a characteristic of gifted individu-
als while others think it can be developed in all students; some believe that creativity
is an outcome of the learning process whereas other believe creativity leads to
development of mathematical profi ciency. We trust that the readers will enjoy and
be intrigued when reading this book. We hope that readers will hear authors’ voices,
will understand their positions and will be encouraged to perform further research
that will shed more light on the nature and nurture of giftedness and creativity, the
relationship between them, the approaches to education of gifted as well as teaching
with and for creativity.