Mathematical Creativity and Mathematical Giftedness: Enhancing Creative Capacities in Mathematically Promising Students

423 Pages·2018·9.266 MB·English

by  Florence Mihaela Singer (eds.)

ICME-13 Monographs
Florence Mihaela Singer Editor
Mathematical
Creativity and
Mathematical
Giftedness
Enhancing Creative Capacities in
Mathematically Promising Students
ICME-13 Monographs
Series editor
Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität
Hamburg, Hamburg, Germany
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
volumeisbasedonthediscussionsandpresentationsduringtheICME-13Congress
and includes the best papers from one of the ICME-13 Topical Study Groups or
Discussion Groups.
More information about this series at http://www.springer.com/series/15585
Florence Mihaela Singer
Editor
Mathematical Creativity
and Mathematical Giftedness
Enhancing Creative Capacities
in Mathematically Promising Students
123
Editor
Florence Mihaela Singer
Faculty of Letters andScience
Oil & GasUniversity of Ploiești
Ploiești
Romania
ISSN 2520-8322 ISSN 2520-8330 (electronic)
ICME-13 Monographs
ISBN978-3-319-73155-1 ISBN978-3-319-73156-8 (eBook)
https://doi.org/10.1007/978-3-319-73156-8
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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 . . . . 27
Demetra Pitta-Pantazi, Maria Kattou and Constantinos Christou
3 Mathematical Giftedness and Creativity in Primary Grades. . . . . . 55
Daniela Assmus and Torsten Fritzlar
4 Cognitive Variety in Rich-Challenging Tasks . . . . . . . . . . . . . . . . . 83
Cristian Voica and Florence Mihaela Singer
5 Mathematical Creativity and Its Subdomain-Specificity.
Investigating the Appropriateness of Solutions in Multiple
Solution Tasks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Daniela Assmus
7 The Cognitive Demand of a Gifted Student’s Answers to
Geometric Pattern Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Angel Gutierrez, Clara Benedicto, Adela Jaime and Eva Arbona
v
vi Contents
8 Twice-Exceptional Students: Students with Special Needs
and a High Mathematical Potential. . . . . . . . . . . . . . . . . . . . . . . . . 199
Marianne Nolte
Part III Teaching Strategies to Foster Creative Learning
9 Flexibility of Pre-services Teachers in Problem Posing in
Different Environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Wajeeh Daher and Ahlam Anabousy
10 Ornaments and Tessellations: Encouraging Creativity in the
Mathematics Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Hana Moraová, Jarmila Novotná and Franco Favilli
11 Instances of Promoting Creativity with Procedural Tasks . . . . . . . 285
Michal Tabach and Alex Friedlander
Part IV Tasks and Techniques to Enhance Creative Capacities
12 Gifted Students Approaches When Solving Challenging
Mathematical Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Andreas Poulos and Joanna Mamona-Downs
13 Repeated Participation at the Mathematical Olympiads:
A Comparative Study of the Solutions of Selected Problems. . . . . . 343
Ingrida Veilande, Liga Ramana and Sandra Krauze
14 Complex and Open-Ended Tasks to Enrich Mathematical
Experiences of Kindergarten Students . . . . . . . . . . . . . . . . . . . . . . 373
Viktor Freiman
Commentary Paper: A Reflection on Mathematical Creativity and
Giftedness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Linda Jensen Sheffield
Author Index.. .... .... .... ..... .... .... .... .... .... ..... .... 425
Subject Index.. .... .... .... ..... .... .... .... .... .... ..... .... 427
Introduction
What are the relationships between mathematical creativity and mathematical
giftedness? How could mathematical creativity contribute to a balanced develop-
ment of the child? What are the characteristics of mathematical giftedness in early
ages?Whataboutthesecharacteristicsatuniversitylevel?Whatteachingstrategies
mightenhancecreativelearning?Howmathematicalpromiseofyoungchildrencan
bemaintainedandextendedtowardsavarietyofprofessions?Thesearesomeofthe
questions addressed by this book. The book offers, among others: analyses of
substantial learning environmentsfor supportingcreativity inmathematics lessons,
discussions ofa varietyof strategiesin problem-solvingand posing, investigations
of students’ progress along years of training, and examinations of technological
toolsandvirtualresourcesmeanttoenhancelearningwithunderstanding.Multiple
perspectivesintheinterdisciplinaryfieldsofmathematicalcreativityandgiftedness
are developed to offer a springboard for further research. The theoretical and
empiricalstudiesincludedinthebookofferconsistentdatausefulforresearchers,as
well as for the teachers of the gifted in specialized or inclusive settings, at various
levels of education.
vii
Chapter 1
Enhancing Creative Capacities
in Mathematically-Promising Students.
Challenges and Limits
Florence Mihaela Singer
Abstract The links between research in mathematics education, psychology of
creativity and research in gifted education started to gain more attention in the last
decade, from researchers and the large public as well. The paper is intended to
provide a concise survey of these links, with a focus on: frameworks for studying
students’creativityandgiftedness inmathematics;domainspecificityofcreativity;
some characteristics of mathematical creativity resulting from its specificity; rela-
tionships between mathematical giftedness and creativity from a mind-and-brain
perspective; relationships between creativity, giftedness and social inclusion;
underlying connections between mathematical creativity and innovation, creativity
and metacognition, creativity, giftedness and expertise; and the teaching of
mathematically-promising students with a focus on structuring their mathematical
competencies. The paper offers also brief reviews of the chapters included in the
book,stressingonthebenefitsofanintegratedapproachofcreativityandgiftedness
in mathematics education.
(cid:1)
Keywords Mathematical creativity Mathematical giftedness
(cid:1) (cid:1)
Mathematically-promising students Problem solving Problem posing
(cid:1) (cid:1)
Domain-specific creativity Expertise Metacognition
1.1 Introduction: Setting the Context
A few years ago, in a comprehensive review study, Leikin (2011) identified a gap
between research in mathematics education and research in gifted education. She
noticed that in the first ten years of the twenty-first century, seven key journals in
the fields of intelligence and giftedness (American Psychologist, Creativity
Research Journal, Gifted Child Quarterly, High Ability Studies, Journal for the
F.M.Singer(&)
FacultyofLettersandScience,UniversityofPloiesti,
39BucharestBoulevard,100680Ploiesti,Romania
e-mail:[email protected]
©SpringerInternationalPublishingAG2018 1
F.M.Singer(ed.),MathematicalCreativityandMathematicalGiftedness,
ICME-13Monographs,https://doi.org/10.1007/978-3-319-73156-8_1
2 F.M.Singer
EducationoftheGifted,TheJournalofSecondaryGiftedEducation,andReviewof
General Psychology) published very few articles devoted directly to mathematical
giftedness or creativity. In addition, a search of seven leading research journals in
mathematics education (Educational Studies in Mathematics, Focus on Learning
ProblemsinMathematics,FortheLearningofMathematics,JournalforResearch
in Mathematics Education, Journal of Mathematical Behavior, Mathematical
Thinking and Learning, and ZDM Mathematics Education) revealed that in that
same decade again only few articles were explicitly devoted to mathematical
giftedness. A small number of publications in other journals (such as Journal of
Educational Psychology, Psychological Science Journal, and Journal of Applied
Psychology) have been focused on specific issues related to problem solving and
mathematical reasoning in the gifted population, usually with a focus on creativity
(Leikin 2011). In addition, a few edited volumes had in focus these aspects (e.g.
Sriraman 2008; Leikin et al. 2009).
Things seem to have changed, however, in the last years. Thus, recently, two
new special issues of ZDM Mathematics education address the topics of mathe-
matical giftedness (Singer et al. 2017a) and psychology of mathematical creativity
(Sriraman 2017), completing the series initiated by the special issue devoted to
mathematical creativity (Leikin and Pitta-Pantazi 2013). The change is not only in
thefocus,butitgoesdeeplyintotherelationshipbetweenpsychologyofcreativity
and the applied domain-specific study of creativity and giftedness in mathematics.
Moreover,communitiesofpracticecontributetodevelopingthesefieldsonamore
systematic base, and their activities were reflected in 2016, during the 13th
International Congress on Mathematical Education (ICME-13), through the Topic
StudyGroup4(TSG4)focusedonActivitiesfor,andResearchon,Mathematically
Gifted Students and TSG 29, which addressed Mathematics and Creativity. TSG 4
published a topical survey before the congress, and this current monograph builds
on the work presented in both of those TSGs during the congress.
What looked like to be a far-off goal, i.e. situating mathematics education
research within an existing canon of work in mainstream psychology (Sriraman
et al. 2013) seems to be today more tangible than ever. Moreover, the call for
interdisciplinaryviewsappearstohavebecometheruleratherthanapproachesthat
request narrow (frequently ill-defined) conceptualizations. For example, the recent
developed model of the Active Concerned Citizenship and Ethical Leadership
(ACCEL)forunderstandinggiftedness(Sternberg2017a)coversaspectsrelatedto:
teaching for creativity; the role of science, technology, engineering, and mathe-
matics (STEM) in teaching for wisdom; the developmental nature of giftedness;
teacher education (Sternberg 2017a, b), and many other integrative perspectives.
Thepresentbookputstogetherviewsunderlying,beyondthevarietyofapproaches,
strong connections between the psychology of creativity, mathematics education,
and the study of giftedness as an interdisciplinary field.