Cite as: Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.). (2014). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 5). Vancouver, Canada: PME. or Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.). (2014). Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 5). Vancouver, Canada: PME. Website: http://www.pme38.com/ The proceedings are also available via http://www.igpme.org Copyrights © 2014 left to the authors All rights reserved ISSN 0771-100X Vol. 5 ISBN 978-0-86491-365-4 Set ISBN: 978-0-86491-360-9 Cover Design: Kirsty Robbins, University of British Columbia Salmon Design: Haida artist, William (Billy) NC Yovanovich Jr. Ts’aahl Formatting Assistance: Robert Browne, Jacky McGuire Production: Lebonfon, Québec TABLE OF CONTENTS VOLUME 5 RESEARCH REPORTS PR – Z DEMOCRATIZING MATHEMATICAL CREATIVITY THROUGH KOESTLER’S BISOCIATION THEORY ................................................................................................................... 1 Vrunda Prabhu, Bronislaw Czarnocha ASSESSING TEACHERS' PROFOUND UNDERSTANDING OF EMERGENT MATHEMATICS IN A MASTERS COURSE ................................................................................... 9 Armando Paulino Preciado-Babb MENTAL MATHEMATICS AND OPERATIONS ON FUNCTIONS ........................................... 17 Jérôme Proulx USING PRACTICAL WORKSHEET TO RECORD AND EXAMINE METACOGNITVE STRATEGIES IN PROBLEM SOLVING ........................................................................................ 25 Khiok Seng Quek, Tin Lam Toh, Yew Hoong Leong, Foo Him Ho FEATURES OF SUCCESSFUL CALCULUS PROGRAMS AT FIVE DOCTORAL DEGREE GRANTING INSTITUTIONS .......................................................................................... 33 Chris Rasmussen, Jessica Ellis, Dov Zazkis, David Bressoud QUALITATIVE FACETS OF PROSPECTIVE ELEMENTARY TEACHERS’ DIAGNOSTIC COMPETENCE: MICRO-PROCESSES IN ONE-ON-ONE DIAGNOSTIC INTERVIEWS ................................................................................................................................... 41 Simone Reinhold SOFYA KOVALEVSKAYA: MATHEMATICS AS FANTASY ................................................... 49 Veda Roodal Persad GRAPHING CALCULATOR SUPPORTED INSTRUMENTATION SCHEMES FOR THE CONCEPT OF DERIVATIVE: A CASE STUDY............................................................................ 57 Gerrit Roorda, Pauline Vos, Paul Drijvers, Martin Goedhart A FRAMEWORK FOR THE ANALYSIS OF VALUES THROUGH A MATHEMATICAL LITERACY LENS ............................................................................................................................. 65 Sheena Rughubar-Reddy WRITTEN REASONING IN PRIMARY SCHOOL ........................................................................ 73 Silke Ruwisch, Astrid Neumann PME 2014 5 - I LEARNING WITH INTERACTIVE ANIMATED WORKED-OUT EXAMPLES IN GROUPS OF TWO ............................................................................................................................ 81 Alexander Salle IMPACT OF SINGLE STUDENT MATHEMATICAL FIELD EXPERIENCE ON ELEMENTARY TEACHERS OVER TIME .................................................................................... 89 Amanda G. Sawyer, Yi Jung Lee MAKING GENERALIZATIONS EXPLICIT: AN INFERENTIAL PERSPECTIVE ON CONCEPT-FORMATION OF VARIABLES ................................................................................... 97 Florian Schacht, Stephan Hußmann COGNITIVE PROCESSES UNDERLYING MATHEMATICAL CONCEPT CONSTRUCTION: THE MISSING PROCESS OF STRUCTURAL ABSTRACTION ............... 105 Thorsten Scheiner, Márcia M. F. Pinto TYPES OF ARGUMENTS WHEN DEALING WITH CHANCE EXPERIMENTS .................... 113 Susanne Schnell EXPLORING STUDENTS’ MENTAL MODELS IN LINEAR ALGEBRA AND ANALYTIC GEOMETRY: OBSTACLES FOR UNDERSTANDING BASIC CONCEPTS ............................ 121 Sven Schueler, Bettina Roesken-Winter ARE INTEREST AND ENJOYMENT IMPORTANT FOR STUDENTS’ PERFORMANCE? ... 129 Stanislaw Schukajlow, André Krug THE IMPACT OF LEARNING AND TEACHING LINEAR FUNCTIONS PROFESSIONAL DEVELOPMENT ............................................................................................................................ 137 Nanette Seago, Catherine Carroll, Tom Hanson, Steve Schneider MATHEMATICS LEARNING IN MAINLAND CHINA, HONG KONG AND TAIWAN: THE VALUES PERSPECTIVE ...................................................................................................... 145 Wee Tiong Seah, Qiaoping Zhang, Tasos Barkatsas, Huk Yuen Law, Yuh-Chyn Leu IS ELIMINATING THE SIGN CONFUSION OF INTEGRAL POSSIBLE? THE CASE OF CAS SUPPORTED TEACHING..................................................................................................... 153 Eyup Sevimli, Ali Delice THE IMPACT OF A TEACHER DEVELOPMENT PROGRAM ON 7TH GRADERS’ LEARNING OF ALGEBRA ........................................................................................................... 161 Sheree Sharpe, Analúcia D. Schliemann EXPLORING ‘WHAT JAPANESE STUDENTS FIND IMPORTANT IN MATHEMATICS LEARNING’ BASED ON THE THIRD WAVE PROJECT .......................................................... 169 Yusuke Shinno, Chikara Kinone, Takuya Baba 5 - II PME 2014 STUDENTS’ SELF-ASSESSMENT OF CREATIVITY: BENEFITS AND LIMITATIONS ...... 177 Atara Shriki, Ilana Lavy PROSPECTIVE TEACHERS’ CONCEPTIONS ABOUT A PLANE ANGLE AND THE CONTEXT DEPENDENCY OF THE CONCEPTIONS ................................................................ 185 Harry Silfverberg, Jorma Joutsenlahti AN EMERGING THEORY FOR DESIGN OF MATHEMATICAL TASK SEQUENCES: PROMOTING REFLECTIVE ABSTRACTION OF MATHEMATICAL CONCEPTS ............... 193 Martin A. Simon TWO STAGES OF MATHEMATICS CONCEPT LEARNING: ADDITIONAL APPLICATIONS IN ANALYSIS OF STUDENT LEARNING .................................................... 201 Martin A. Simon, Nicora Placa, Arnon Avitzur NUMBER’S SUBTLE TOUCH: EXPANDING FINGER GNOSIS IN THE ERA OF MULTI-TOUCH TECHNOLOGIES .............................................................................................. 209 Nathalie Sinclair, David Pimm WHY ANNA LEFT ACADEMIA .................................................................................................. 217 Lovisa Sumpter TONY’S STORY: READING MATHEMATICS THROUGH PROBLEM SOLVING ............... 225 Eng Guan Tay, Pee Choon Toh, Jaguthsing Dindyal, Feng Deng MOTIVATING PROSPECTIVE ELEMENTARY TEACHERS TO LEARN MATHEMATICS VIA AUTHENTIC TASKS ............................................................................... 233 Eva Thanheiser, Randolph A. Philipp, Jodi Fasteen THE ROLE OF TEACHING DECISIONS IN CURRICULUM ALIGNMENT ........................... 241 Mike Thomas, Caroline Yoon WHEN UNDERSTANDING EVOKES APPRECIATION: THE EFFECT OF MATHEMATICS CONTENT KNOWLEDGE ON AESTHETIC PREDISPOSITION ................ 249 Hartono Tjoe DESIGNING TASKS FOR CONJECTURING AND PROVING IN NUMBER THEORY ......... 257 Pee Choon Toh, Yew Hoong Leong, Tin Lam Toh, Foo Him Ho USING AN EXPERIMENTAL FRAMEWORK OF KEY ELEMENTS TO PARSE ONE-TO-ONE, TARGETED INTERVENTION TEACHING IN WHOLE-NUMBER ARITHMETIC ................................................................................................................................. 265 Thi L. Tran, Robert J. Wright PME 2014 5 - III HOW UNDERGRADUATE STUDENTS MAKE SENSE OUT OF GRAPHS: THE CASE OF PERIODIC MOTIONS .................................................................................................................... 273 Chrissavgi Triantafillou, Vasiliki Spiliotopoulou, Despina Potari EXAMINING MATHEMATICS-RELATED AFFECT AND ITS DEVELOPMENT DURING COMPREHENSIVE SCHOOL YEARS IN FINLAND ................................................. 281 Laura Tuohilampi, Markku S. Hannula, Anu Laine, Jari Metsämuuronen MATHEMATICAL ACTIVITY IN EARLY CHILDHOOD: IS IT SO SIMPLE? ....................... 289 Marianna Tzekaki CONCEPTUAL AND BRAIN PROCESSING OF UNIT FRACTION COMPARISONS: A COGNEURO-MATHED STUDY ................................................................................................... 297 Ron Tzur, Brendan E. Depue ARGUMENTATION IN UNDERGRADUATE MATH COURSES: A STUDY ON PROBLEM SOLVING .................................................................................................................... 305 Behiye Ubuz, Saygın Dinçer, Ali Bülbül LEARNING MATHEMATICS WITH PICTURE BOOKS ........................................................... 313 Marja van den Heuvel-Panhuizen, Iliada Elia, Alexander Robitzsch IMPROVING REFLECTIVE ANALYSIS OF A SECONDARY SCHOOL MATHEMATICS TEACHERS PROGRAM ................................................................................................................ 321 Yuly Marsela Vanegas, Joaquin Gimenez, Vicenç Font, Javier Díez-Palomar EXPLORING THE FEASIBILITY AND EFFECTIVENESS OF ASSESSMENT TECHNIQUES TO IMPROVE STUDENT LEARNING IN PRIMARY MATHEMATICS EDUCATION .................................................................................................................................. 329 Michiel Veldhuis, Marja van den Heuvel-Panhuizen CONNECTIONS AND SIMULTANEITY: ANALYSING SOUTH AFRICAN G3 PART-PART-WHOLE TEACHING ............................................................................................... 337 Hamsa Venkat, Anna-Lena Ekdahl, Ulla Runesson PREDICTORS OF FUTURE MATHEMATICS TEACHERS’ READINESS TO TEACH: A COMPARISON OF TAIWAN,