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These proceedings contain the papers of the 13th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2016), October 28-30, 2016, which has been organized by the International Association for Development of the Information Society (IADIS), co-organized by the University of Mannheim, Germany, and endorsed by the Japanese Society for Information and Systems in Education (JSISE). The CELDA conference aims to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a fast pace and affecting academia and professional practice in many ways. These proceedings contain the following keynote lectures: (1) From Digital to Double Blended Learning (Jeroen J. G. van Merrienboer); and (2) Open Educational Resources: Educational Technology as a Driver for Educational Reform? (Michael Kerres). Full papers in these proceedings include: (1) A Service-Learning Project Using Crowdfunding Strategy: Students' Experience and Reflection (Jessnor Elmy Mat-jizat and Khalizul Khalid); (2) Towards a Theory-Based Design Framework for an Effective E-Learning Computer Programming Course (Ian S. McGowan); (3) An Ontology for Learning Services on the Shop Floor (Carsten Ullrich); (4) The Impact of Technology Integration upon Collegiate Pedagogy from the Lens of Multiple Disciplines (Joan Ann Swanson); (5) A Learning Support System Regarding Motion Trigger for Repetitive Motion Having an Operating Instrument (Hiroshi Toyooka, Kenji Matsuura, and Naka Gotoda); (6) Task-Based Assessment of Students' Computational Thinking Skills Developed through Visual Programming or Tangible Coding Environments (Takam Djambong and Viktor Freiman); (7) Framework for Intelligent Teaching and Training Systems--A Study of the Systems (Nikolaj Troels Graf von Malotky and Alke Martens); (8) Mobile Device Usage in Higher Education (Jan Delcker, Andrea Honal, and Dirk Ifenthaler); (9) Features Students Really Expect from Learning Analytics (Clara Schumacher and Dirk Ifenthaler); (10) Music Technology Competencies for Education: A Proposal for a Pedagogical Architecture for Distance Learning (Fátima Weber Rosas, Leticia Rocha Machado, and Patricia Alejandra Behar); (11) Increasing Students' Science Writing Skills through a PBL Simulation (Scott W. Brown, Kimberly A. Lawless, Christopher Rhoads, Sarah D. Newton, and Lisa Lynn); (12) The Effect of Choosing versus Receiving Feedback on College Students' Performance (Maria Cutumisu and Daniel L. Schwartz); (13) The Impact of Middle-School Students' Feedback Choices and Performance on Their Feedback Memory (Maria Cutumisu and Daniel L. Schwartz); (14) Numerical Acuity Enhancement in Kindergarten: How Much Does Material Presentation Form Mean? (Maria Lidia Mascia, Maria Chiara Fastame, Mirian Agus, Daniela Lucangeli, and Maria Pietronilla Penna); (15) A Video Game for Learning Brain Evolution: A Resource or a Strategy? (Luisa Fernanda Barbosa Gomez, Maria Cristina Bohorquez Sotelo, Naydu Shirley Roja Higuera, and Brigitte Julieth Rodriguez Mendoza); (16) Communication Vulnerability in the Digital Age: A Missed Concern in Constructivism (Fusa Katada); (17) Online Learners' Navigational Patterns Based on Data Mining in Terms of Learning Achievement (Sinan Keskin, Muhittin Sahin, Adem Ozgur, and Halil Yurdugul); (18) Amazed by Making: How Do Teachers Describe Their PBL Experience (Dalit Levy and Olga Dor); (19) Group Work and the Impact, If Any, of the Use of Google Applications for Education (Jannat Maqbool); (20) Fractangi: A Tangible Learning Environment for Learning about Fractions with an Interactive Number Line (Magda Mpiladeri, George Palaigeorgiou, and Charalampos Lemonidis); (21) Evaluation of Learning Unit Design with Use of Page Flip Information Analysis (Izumi Horikoshi, Masato Noguchi, and Yasuhisa Tamura); (22) Einstein's Riddle as a Tool for Profiling Students (Vildan Özeke and Gökhan Akçapinar); (23) Exploring Students' E-Learning Effectiveness through the Use of Line Chat Application (Tassaneenart Limsuthiwanpoom, Penjira Kanthawongs, Penjuree Kanthawongs, and Sasithorn Suwandee); (24) Factors Affecting Perceived Satisfaction with Facebook in Education (Penjuree Kanthawongs, Penjira Kanthawongs, and Chaisak Chitcharoen); (25) Interactive Video, Tablets and Self-Paced Learning in the Classroom: Preservice Teachers' Perceptions (Anthia Papadopoulou and George Palaigeorgiou); (26) Cognitive Design for Learning: Cognition and Emotion in the Design Process (Joachim Hasebrook); (27) Investigating the Potential of the Flipped Classroom Model in K-12 Mathematics Teaching and Learning (Maria Katsa, Stylianos Sergis, and Demetrios G. Sampson; (28) Learning Analytics to Understand Cultural Impacts on Technology Enhanced Learning (Jenna Mittelmeier, Dirk Tempelaar, Bart Rienties, and Quan Nguyen); (29) Widening and Deepening Questions in Web-Based Investigative Learning (Akihiro Kashihara and Naoto Akiyama); (30) Year 9 Student Voices Negotiating Digital Tools and Self-Regulated Learning Strategies in a Bilingual Managed Learning Environment (Ulla Freihofner, Simone Smala, and Chris Campbell); (31) Purposeful Exploratory Learning with Video Using Analysis Categories (Meg Colasante); (32) Building a Learning Experience: What Do Learners' Online Interaction Data Imply (Mehmet Kokoç and Arif Altun); (33) Rules for Adaptive Learning and Assistance on the Shop Floor (Carsten Ullrich); and (34) Participation and Achievement in Enterprise MOOCs for Professional Learning (Florian Schwerer and Marc Egloffstein). Short papers included in these proceedings include: (1) Connectivist Communication Networks (Ingolf Waßmann, Robin Nicolay, and Alke Martens); (2) Learning and Skills Development in a Virtual Class of Educommunications Based on Educational Proposals and Interactions (Maria Cristina Bohorquez Sotelo, Brigitte Julieth Rodriguez Mendoza, Sandra Milena Vega, Naydu Shirley Roja Higuera, and Luisa Fernanda Barbosa Gomez); (3) The Relationship among ICT Skills, Traditional Reading Skills and Online Reading Ability (I-Fang Liu and Hwa-Wei Ko); (4) Towards Concept Understanding Relying on Conceptualisation in Constructivist Learning (Farshad Badie); (5) E-Learning in Chemistry Education: Self-Regulated Learning in a Virtual Classroom (Rachel Rosanne Eidelman and Yael Shwartz); (6) Relationship of Mobile Learning Readiness to Teacher Proficiency in Classroom Technology Integration (Rhonda Christensen and Gerald Knezek); (7) Human Computer Interaction (HCI) and Internet Residency: Implications for Both Personal Life and Teaching/Learning (Linda Crearie); (8) A Portfolio for Optimal Collaboration of Human and Cyber Physical Production Systems in Problem-Solving (Fazel Ansari and Ulrich Seidenberg); (9) Innovative Collaborative Learning Strategies for Integrated Interactive E-Learning in the 21st Century (Barbara Son); (10) Educational Criteria for Evaluating Simple Class Diagrams Made by Novices for Conceptual Modeling (Mizue Kayama, Shinpei Ogata, David K. Asano, and Masami Hashimoto); (11) Digital Natives and Digital Divide: Analysing Perspective for Emerging Pedagogy (Uriel U. Onye and Yunfei Du); (12) E-Learning System Using Segmentation-Based MR Technique for Learning Circuit Construction (Atsushi Takemura); (13) Students' Google Drive Intended Usage: A Case Study of Mathematics Courses in Bangkok University (Krisawan Prasertsith, Penjira Kanthawongs, and Tan Limpachote); (14) An Empirical Study on the Impact of Self-Regulation and Compulsivity towards Smartphone Addition of University Students (Penjira Kanthawongs, Felicito Angeles Jabutay, Ruangrit Upalanala, and Penjuree Kanthawongs); (15) Adaptive Game Based Learning Using Brain Measures for Attention--Some Explorations (Jelke van der Pal, Christopher Roos, Ghanshaam Sewnath, and Christian Rosheuvel); (16) Evaluation of the Course of the Flight Simulators from the Perspective of Students and University Teachers (Feyzi Kaysi, Bünyamin Bavli and Aysun Gürol); (17) Development of Critical Thinking with Metacognitive Regulation (Yasushi Gotoh); (18) Enacting STEM Education for Digital Age Learners: The "Maker" Movement Goes to School (Dale S. Niederhauser and Lynne Schrum); (19) New Scenarios for Audience Response Systems in University Lectures (Daniel Schön, Stephan Kopf, Melanie Klinger, and Benjamin Guthier); (20) Academic Retention: Results from a Study in an Italian University College (Maria Lidia Mascia, Mirian Agus, Maria Assunta Zanetti, Eliano Pessa, and Maria Pietronilla Penna); and (21) Learning How to Write an Academic Text: The Effect of Instructional Method and Reflection on Text Quality. Reflection papers in these proceedings include: (1) Teachers' Attitude towards ICT Use in Secondary Schools: A Scale Development Study (Mehmet Kemal Aydin, Ali Semerci, and Mehmet Gürol); and (2) Inventing the Invented for STEM Understanding (Alicia Stansell, Tandra Tyler-Wood, and Christina Stansell). An author index is included. Individual papers contain references.

This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc sessions and a panel discussion. Papers include: (1) Understanding Abstraction in Mathematics Education: Meaning, Language, Gesture, and the Human Brain (Rafael Nunez); (2) Mathematics Departments, New Faculty, and the Future of Collegiate Mathematics (T. Christine Stevens); (3) Outreach in Mathematics--Activities, Engagement, & Reflection (Veronique Hussin and Eric Muller); (4) Geometry, Space, and Technology: Challenges for Teachers and Students (Shelley Hunter, Donna Kotsopoulos, and Walter Whiteley); (5) The Design and Implementation of Learning Situations (Anna McQuillan, Fernando Hitt, and Luis Radford); (6) The Multifaceted Role of Feedback in the Teaching and Learning of Mathematics (Jerome Proulx and Florence Glanfield); (7) Mathematics Educational Neuroscience: Origins, Activities, and New Opportunities (Stephen R. Campbell); (8) Communicating the Excitement and Beauty of Mathematics (Malgorzata Dubiel); (9) Conception et experimentation de situations didactiques au prescolaire/primaire / Design and Experimentation of Didactical Situations in Kindergarten and Elementary School (Jacinthe Giroux) [Written in French]; (10) Cabri 3D: An Environment for Purposeful Mathematical Activity? (Kate Mackrell); (11) Equity and Opportunities to Learn in Cooperative Mathematical Work (Indigo Esmond); (12) (Elargir les) Connaissances mathematiques des enseignants de mathematiques du secondaire: une etude sur la formation continue / (Enlarging) Secondary-Level Mathematics Teachers' Mathematical Knowledge: An Investigation of Professional Development (Jerome Proulx) [Presented in both French and English]; (13) Un paradigme d'experimentation au laboratoire de sciences pour l'identification et l'optimisation statistique d'un modele algebrique par interaction visuo-graphique (Georges Touma) [Written in French]; (14) What Factors Influence Understanding of Written Arithmetic Problems? (Dominic Voyer); (15) Probabilities / Probabilites (Egan Chernoff and Annie Savard); (16) First Steps toward an Archeology of Gesture in Graphing (Susan Gerofsky); (17) Function Modelling Using Secondary Data from Statistics Canada's E-STAT Database (Jennifer Hall); (18) Explanation and Proof in Mathematics and Mathematics Education (Gilla Hanna, Ella Kaye, and Riaz Saloojee); (19) Exploring Our Embodied Knowing of the Gauss-Bonnet Theorem: Barn-Raising and Endo-Pentakis-Icosi-Dodecahedron (Eva Knoll); (20) Mathematical Biography (John Grant McLoughlin); (21) This Is Mathematics; This Isn't Mathematics; But That... I'm Not So Certain About: The Possible "Emancipation" of Secondary School Mathematics from the Bonds of "Real" Mathematics (Craig Newell); and (22) What Courses Could or Should Mathematics Departments Offer to Graduate Programs in Mathematics Education? (France Caron, Morris Orzech, and Elaine Simmt). Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lecture at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2006 proceedings, see ED529562.]

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr and Dri: (1) The Odds of Understanding the Law of Large Numbers: A Design for Grounding Intuitive Probability in Combinatorial Analysis (Dor Abrahamson and Rose M. Cendak); (2) Imaginary-Symbolic Relations, Pedagogic Resources and the Constitution of Mathematics for Teaching in In-Service Mathematics Teacher Education (Jill Adler and Zain Davis); (3) Relationship between Pre-Service Mathematics Teachers' Teaching and Learning Beliefs and Their Practices (Hatice Akkoc and Feral Ogan-Bekiroglu); (4) Teachers' Awareness of Dimensions of Variation: A Mathematics Intervention Project (Thabit Al-Murani); (5) The Student Teacher and the Others: Multimembership on the Process of Introducing Technology in the Classroom (Nelia Amado and Susana Carreira); (6) Improving Student Teachers' Understanding of Fractions (Solange Amorim Amato); (7) Autodidactic Learning of Probabilistic Concepts through Games (Miriam Amit and Irma Jan); (8) Graduate Students' Processes in Generating Examples of Mathematical Objects (Samuele Antonini); (9) Reasoning in an Absurd World: Difficulties with Proof by Contradiction (Samuele Antonini and Maria Alessandra Mariotti); (10) Will Penelope Choose Another Bridegroom? Looking for an Answer through Signs (Ferdinando Arzarello, Luciana Bazzini, Francesca Ferrara, Ornella Robutti, Cristina Sabena, and Bruna Villa); (11) Motivation and Perceptions of Classroom Culture in Mathematics of Students across Grades 5 to 7 (Chryso Athanasiou and George N. Philippou); (12) Deductive Reasoning: Different Conceptions and Approaches (Michal Ayalon and Ruhama Even); (13) The Tendency to Use Intuitive Rules among Students with Different Piagetian Cognitive Levels (Reuven Babai); (14) Coming to Appreciate the Pedagogical Uses of CAS (Lynda Ball and Kaye Stacey); (15) Students' Conceptions of "m" and "c": How to Tune a Linear Function (Caroline Bardini and Kaye Stacey); (16) A Contradiction between Pedagogical Content Knowledge and Teaching Indications (Ibrahim Bayazit and Eddie Gray); (17) Identifying and Supporting Mathematical Conjectures through the Use of Dynamic Software (David Benitez Mojica and Manuel Santos Trigo); (18) Students Constructing Representations for Outcomes of Experiments (Palma Benko and Carolyn A. Maher); (19) Logarithms: Snapshots from Two Tasks (Tanya Berezovski and Rina Zazkis); (20) Trying to Reach the Limit--The Role of Algebra in Mathematical Reasoning (Christer Bergsten); (21) Semiotic Sequence Analysis--Constructing Epistemic Types Empirically (Angelika Bikner-Ahsbahs); (22) Service Teaching: Mathematical Education of Students of Client Departments (Erhan Bingolbali, John Monaghan, and Tom Roper); (23) Students' Thinking about the Tangent Line (Irene Biza, Constantinos Christou, and Theodossios Zachariades); (24) Habermas' Theory of Rationality as a Comprehensive Frame for Conjecturing and Proving in School (Paulo Boero); (25) Extending Students' Understanding of Decimal Numbers via Realistic Mathematical Modeling and Problem Posing (Cinzia Bonotto); (26) Different Media, Different Types of Collective Work in Online Continuing Teacher Education: Would You Pass the Pen, Please? (Marcelo C. Borba and Rubia B. A. Zulatto); (27) Reformulating "Mathematical Modelling" in the Framework of the Anthropological Theory of Didactics (Marianna Bosch, Fco. Javier Garcia, Josep Gascon, and Luisa Ruiz Higueras); (28) Students' Impressions of the Value of Games for the Learning of Mathematics (Leicha A. Bragg); (29) The Transition from Arithmetic to Algebra: To Reason, Explain, Argue, Generalize and Justify (Trygve Breiteig and Barbro Grevholm); (30) Resisting Reform Pedagogy: Teacher and Learner Contributions (Karin Brodie); (31) Manifestations of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (32) Types of Representations of the Number Line in Textbooks (Alicia Bruno and Noemi Cabrera); (33) Educational Neuroscience: New Horizons for Research in Mathematics Education (Stephen R. Campbell); (34) Variability in a Probability Context: Developing Pre-Service Teachers' Understanding (Daniel L. Canada); (35) Implementing a Reform-Oriented Mathematics Syllabus: A Survey of Secondary Teachers (Michael Cavanagh); (36) Student's Modelling with a Lattice of Conceptions in the Domain of Linear Equations and Inequations (Hamid Chaachoua, Marilena Bittar, and Jean-Francois Nicaud); (37) Using Reading and Coloring to Enhance Incomplete Prover's Performance in Geometry Proof (Ying-Hao Cheng and Fou-Lai Lin); (38) Aspects of Teachers' Pedagogical Content Knowledge for Decimals (Helen Chick, Monica Baker, Thuy Pham, and Hui Cheng); (39) Collaborative Action Research on Implementing Inquiry-Based Instruction in an Eighth Grade Mathematics Class: An Alternative Mode for Mathematics Teacher Professional Development (Erh-Tsung Chin, Yung-Chi Lin, Yann-Tyng Ko, Chi-Tung Chien, and Hsiao-Lin Tuan); (40) Routine and Novel Mathematical Solutions: Central-Cognitive or Peripheral-Affective Participation in Mathematics Learning (Mei-Shiu Chiu); (41) The Role of Self-Generated Problem Posing in Mathematics Exploration (Victor V. Cifarelli and Jinfa Cai); (42) A Longitudinal Study of Children's Mental Computation Strategies (Barbara Clarke, Doug M. Clarke, and Marj Horne); (43) Assessing Fraction Understanding Using Task-Based Interviews (Doug M. Clarke, Michal Sukenik, Anne Roche, and Annie Mitchell); (44) Evaluation of a Teaching Concept for the Development of Problem Solving Competences in Connection with Self-Regulation (Christina Collet and Regina Bruder); (45) Developing Probability Thinking in Primary School: A Case Study on the Constructive Role of Natural Language in Classroom Discussions (Valeria Consogno, Teresa Gazzolo, and Paulo Boero); (46) Collaboration with Teachers to Improve Mathematics Learning: Pedagogy at Three Levels (Tom J. Cooper, Annette R. Baturo, and Edlyn J. Grant); (47) "Aim High--Beat Yourself": Effective Mathematics Teaching in a Remote Indigenous Community (Tom J. Cooper, Annette R. Baturo, Elizabeth Warren, and Edlyn J. Grant); (48) Development of Children's Understanding of Length, Area, and Volume Measurement Principles (Margaret Curry, Michael Mitchelmore, and Lynne Outhred; (49) Mathematics-for-Teaching: The Cases of Multiplication and Division (Brent Davis, Elaine Simmt, and Dennis Sumara); (50) Generative Concept Images (Gary E. Davis and Catherine A. Pearn); (51) Developmental Assessment of Data Handling Performance Age 7-14 (Pauline Davis, Maria Pampaka, Julian Williams, and Lawrence Wo); (52) The Effect of Different Teaching Tools in Overcoming the Impact of the Intuitive Rules (Eleni Deliyianni, Eleni Michael, and Demetra Pitta-Pantazi); (53) Investigating Social and Individual Aspects in Teacher's Approaches to Problem Solving (Fien Depaepe, Erik De Corte, and Lieven Verschaffel); (54) Maths Avoidance and the Choice of University (Pietro Di Martino and Francesca Morselli); (55) Primary Students' Reasoning about Diagrams: The Building Blocks of Matrix Knowledge (Carmel M. Diezmann); (56) Integrating Errors into Developmental Assessment: "Time" for Ages 8-13 (Brian Doig, Julian Williams, Lawrence Wo, and Maria Pampaka); (57) Vygotsky's Everyday Concepts/Scientific Concepts Dialectics in School Context: A Case Study (Nadia Douek); (58) Creating Mathematical Models with Structures (Katherine Doyle); (59) Mechanisms for Consolidating Knowledge Constructs (Tommy Dreyfus, Nurit Hadas, Rina Hershkowitz, and Baruch Schwarz); and (60) Reconciling Factorizations Made with CAS and with Paper-and-Pencil: The Power of Confronting Two Media (Paul Drijvers, Carolyn Kieran, Andre Boileau, Fernando Hitt, Denis Tanguay, Luis Saldanha, and Jose Guzman). (Individual papers contain references.)