The 9th MATHEMATICAL CREATIVITY AND GIFTEDNESS International 2015, June, 25 - 28 Conference PROCEEDINGS Editors: F l o r e n c e Mihaela Singer Florentina Toader Cristian Voica ISBN: 978-606-727-100-3 The 9th MATHEMATICAL CREATIVITY AND GIFTEDNESS International Conference PROCEEDINGS The International Group for Mathematical Creativity and Giftedness Sinaia, ROMANIA 2015 Table of contents WELLCOMING THE MCG-9 CONFERENCE................................................................................................................ 5 Florence Mihaela Singer, Roza Leikin MATHEMATICAL PATHOLOGIES AS PATHWAYS INTO CREATIVITY ......................................................................... 9 Bharath Sriraman PROFESSIONAL COMPETENCES OF TEACHERS AND ITS RELATION TO CREATIVITY ............................................... 10 Gabriele Kaiser MATHEMATICAL GIFTEDNESS GOES ONLINE: WHAT ARE THE NEW WAYS, TOOLS, RESOURCES TO DEVELOP TALENTS AND CREATIVITY IN STUDENTS? ............................................................................................................ 11 Viktor Freiman VIRTUAL CONVERSATIONS ON MATHEMATICAL TASKS ....................................................................................... 12 Rina Zazkis CONNECTION BETWEEN THEORY AND PRACTICE IN GIFTED EDUCATION ............................................................. 14 Roza Leikin, Florence Mihaela Singer, Linda Sheffield, Jong Sool Choi NURTURING STUDENTS’ CREATIVITY THROUGH TELLING MATHEMATICAL STORIES ............................................ 16 Anna Prusak SOLVING A MATHEMATICAL CREATIVITY TASK .................................................................................................... 22 Maria Kattou, Constantinos Christou, & Demetra Pitta-Pantazi THE PERCEPTION OF THE CONCEPT OF A “CHALLENGING TASK” BY MATHEMATICALLY PROMISING ELEMENTARY SCHOOL STUDENTS .............................................................................................................................................. 28 Mark Applebaum, Elena Gofman USING OPEN-ENDED PROBLEMS AND PROBLEM POSING ACTIVITIES IN ELEMENTARY MATHEMATICS CLASSROOM ........................................................................................................................................................ 34 Aleksandra Mihajlović, Mirko Dejić TH THE ANALYSIS OF 6 GRADE STUDENTS’ WORKS AT THE OPEN MATHEMATICAL OLYMPIAD ............................. 42 Ingrida Veilande, Sandra Krauze LEARNING MATH THROUGH RESEARCH AND COOPERATION ............................................................................... 48 Ariana-Stanca Văcărețu NOVELTIES IN MATH OLYMPIADS IN LATVIA ........................................................................................................ 54 Dace Kūma LE-MATH: LEARNING MATHEMATICS THROUGH NEW COMMUNICATION FACTORS ........................................... 60 Gregory Makrides and project Le-MATH partners PROBLEM SOLVING AND CHOICE-BASED PEDAGOGIES ........................................................................................ 68 Boris Koichu PROBLEM POSING COGNITIVE STYLE - CAN IT BE USED TO ASSESS MATHEMATICAL CREATIVITY? ...................... 74 Florence Mihaela Singer, Ildikó Pelczer, Cristian Voica The 9th International MCG Conference 2 Sinaia, Romania, 2015 CREATIVITY AND BISOCIATION ............................................................................................................................ 80 Bronislaw Czarnocha, William Baker SELF-CONTROL AND SELF-MONITORING PROCESSES OF GIFTED STUDENTS IN MATHEMATICAL PROBLEM SOLVING SITUATIONS .......................................................................................................................................... 86 Gönül Yazgan-Sağ, Ziya Argün COMBINATIONAL PLAY BETWEEN MATHEMATICAL DOMAINS AS ONE DIMENSION OF MATHEMATICAL CREATIVITY IN THE EARLY YEARS ......................................................................................................................... 94 Melanie Beck LOOKING FOR THE WAY TO SUPPORT CHILDREN’S MATHEMATICAL CREATIVITY .............................................. 100 Jana Slezakova, Ewa Swoboda IDENTIFYING MATHEMATICALLY GIFTED PRESCHOOLERS .................................................................................. 100 Panayiota Irakleous, Demetra Pitta-Pantazi MYTHS ABOUT “GIFTED” MATHEMATICS STUDENTS: HOW WIDESPREAD ARE THEY? ....................................... 114 Linda Jensen Sheffield MATHEMATICAL GIFTEDNESS AS DEVELOPING EXPERTISE................................................................................. 120 Torsten Fritzlar BAYBURT’S GOT GIFTED ..................................................................................................................................... 126 Zekeriya Karadag, Yasemin Devecioglu-Kaymakci CREATIVITY DEVELOPED WITHIN AN ACTIVITY THAT AFFORDS MULTIPLE SOLUTION AND MULTYMODAL ARGUMENTATION ............................................................................................................................................. 134 Naomi Prusak, Rina Hershkowitz “MATHE FÜR KLEINE ASSE” – AN ENRICHMENT PROJECT AT THE UNIVERSITY OF MÜNSTER ............................. 140 Ralf Benölken XCOLONY EDUCATIONAL ACTIVITIES ENHANCE SPATIAL REASONING IN MIDDLE SCHOOL STUDENTS .............. 146 Sorin Alexe, Gabriela Alexe, Consuela Voica, Cristian Voica ANALOGICAL-REASONING ABILITIES OF MATHEMATICALLY GIFTED CHILDREN - FIRST RESULTS OF THE VIDEO STUDY VISTAD ................................................................................................................................................... 154 Daniela Assmus, Frank Förster HIGHER ORDER THINKING IN MATHEMATICS .................................................................................................... 160 Paraskevi Sophocleous, Demetra Pitta-Pantazi EXAMINING COVERT IMPEDIMENTS TO INCLUSIVE EDUCATION FOR THE MATHEMATICALLY GIFTED LEARNERS IN SOUTH AFRICA ............................................................................................................................. 166 Michael Kainose Mhlolo “THE WEEK OF MATHEMATICS” – A PROJECT WITH CREATIVE APPROACHES .................................................... 172 Nicolae Popa A METHOD OF TEACHING MATHEMATICS IN KOREA SCIENCE ACADEMY ........................................................... 176 Choi Jong Sool PROSPECTIVE TEACHERS’ VIEWS OF CREATIVITY IN SCHOOL MATHEMATICS .................................................... 182 Elçin Emre-Akdoğan, Gönül Yazgan-Sağ The 9th International MCG Conference 3 Sinaia, Romania, 2015 ABILITY GROUPING FOR MATHEMATICALLY PROMISING STUDENTS ................................................................. 188 Sinan Kanbir SUPERMATH: A CREATIVE WAY TO ENGAGE TALENTED MATH STUDENTS ......................................................... 194 Edel M. Reilly DO TEACHER'S WAYS OF ENHANCING DISCOURSE IN HER CLASS LEAVE TRACES ON HER STUDENTS' POST-TEST RESPONSES? ...................................................................................................................................................... 206 Rina Hershkowitz, Michal Tabach, Shirly Azmon, Chris Rasmussen, Tommy Dreyfus ALGEBRAIC SYMBOLS AND CREATIVE THINKING ................................................................................................ 212 Michal Tabach, Alex Friedlander A STUDY ON THE RELATIONSHIP BETWEEN CREATIVE SCHOOL ENVIRONMENT AND CREATIVE STUDENTS` PERSONALITY, PROCESS AND PRODUCT ............................................................................................................ 212 Emilia Velikova MATHEMATICAL CREATIVITY AND THE AFFORDANCES OF DYNAMIC AND INTERACTIVE MATHEMATICS LEARNING ENVIRONMENTS ............................................................................................................................... 224 Zekeriya Karadag, Dragana Martinovic, Seyda Birni RATIONAL CREATIVITY: ALGORITHMS OR INNOVATION? TEACHING OPERATIONS WITH FRACTIONS ............... 231 Linda Jensen Sheffield EFFECTIVE FEEDBACK FOR EFFICIENT LEARNING: A COMPUTER-BASED SYSTEM OF ASSESSMENT ..................... 233 Florence Mihaela Singer, Cristian Voica VISUALIZING GEOMETRIC CONCEPTS USING A NOVEL TYPE OF 3D PUZZLES ...................................................... 235 Consuela Luiza Voica, Aurelia Grigorescu ACTIVITIES THAT ENGAGE GIFTED AND TALENTED STUDENTS IN PRODUCTIVE STRUGGLES WITH DESIRABLE DIFFICULTIES: A MODEL ENCOURAGING INTENSE DISCOURSE AND DEEP REASONING .................................... 237 William R. Speer USE OF ALGEBRAIC REASONING FOR EARLY IDENTIFICATION OF MATHEMATICAL TALENT ............................... 239 Sinan Kanbir THE NATURE OF CREATIVITY .............................................................................................................................. 242 Bronislaw Czarnocha, William Baker FOSTERING MATHEMATICAL GIFTEDNESS IN REGULAR CLASSROOM SETTING AND IN SPECIAL PROGRAMS ..... 244 Marianne Nolte The 9th International MCG Conference 4 Sinaia, Romania, 2015 WELLCOMING THE MCG-9 CONFERENCE Florence Mihaela Singer Roza Leikin Univ. of Ploiesti, Romania University of Haifa., Israel Chair - MCG-9 Conference President MCG Mathematical creativity and giftedness is a topic of increasing interest around the world. The International Group for Mathematical Creativity and Giftedness (MCG) brings together mathematics educators, mathematicians, researchers, and others who support the development of mathematical creativity and mathematical giftedness. The