This document contains the third volume of the proceedings of the 30th 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 Ead and Kou: (1) Exploring Realistic Mathematics Education in English Schools (Frank Eade and Paul Dickinson); (2) Reasoning about Non-Linearity in 6- to 9-Year-Olds: The Role of Task Presentation (Mirjam Ebersbach and Wilma C. M. Resing); (3) Teachers, Classroom, Students--A Holistic View on Beliefs Concerning the Educational Practice (Andreas Eichler); (4) The Effects of Different Modes of Representation on Problem Solving: Two Experimental Programs (Iliada Elia and Athanasios Gagatsis); (5) Can Moderate Hermeneutics Help Us to Understand Learning and Teaching in the Mathematics Classroom? (Fiona Ell); (6) Sociocultural Approaches to Emotions in Mathematics Education: Initial Comparisons (Jeff Evans and Rosetta Zan); (7) Moral Education in the Teaching of Mathematics (Thomas Falkenberg); (8) The Abductive System (Elisabetta Ferrando); (9) Remembering and Imagining: Moving Back and Forth between Motion and Its Representation (Francesca Ferrara); (10) From Verbal Texts to Symbolic Expressions: A Semiotic Approach to Early Algebra (Pier Luigi Ferrari); (11) Verbal Memory Span Limitations as a Factor in Early Mathematical Learning Difficulties (Maureen Finnane); (12) Connecting Algebraic Development to Mathematical Patterning in Early Childhood (Jillian Fox); (13) Aline's and Julia's Stories: Reconceptualizing Transfer from a Situated Point of View (Cristina Frade, Peter Winbourne, and Selma Moura Braga); (14) Insights into Students' Algebraic Reasoning (John Francisco and Markus Hahkioniemi); (15) Proof, Authority, and Agency: Intimations from an 8th Grade Classroom (Michael N. Fried and Miriam Amit); (16) Students' Thoughts about ICT in School Mathematics (Anne Berit Fuglestad); (17) Primary Trainee Teachers' Understanding of Basic Geometrical Figures in Scotland (Taro Fujita and Keith Jones); (18) An Empirical Four-Dimensional Model for the Understanding of Function (Athanasios Gagatsis, Iliada Elia, Areti Panaoura, Katerina Gravvani, and Panayotis Spyrou); (19) The Hidden Side in Taiwanese Classrooms--Through the Lens of PLS in Geometry (Hagar Gal, Fou-Lai Lin, and Jia-Ming Ying); (20) The Zero and Negativity among Secondary School Students (Aurora Gallardo and Abraham Hernandez); (21) Students' Actions in Open and Multiple-Choice Questions Regarding Understanding of Averages (Juan Antonio Garcia Cruz and Alexandre Joaquim Garrett); (22) Paradoxes: The Interplay of Gender, Social Class and Mathematics in the Caribbean (Patricia George); (23) Insights about the Addition Strategies Used by Grade 1 and Grade 2 Children Who Are Vulnerable in Number Learning (Ann Gervasoni); (24) A Generic Organizer for the Enrichment of the Concept Image of Derivative (Victor Giraldo and Luiz Mariano Carvalho); (25) Pupils' Attitudes to Integrated Learning Systems in Mathematics (Chrysanthi Gkolia and Alan Jervis); (26) The Discourse of Logical Necessity: Rules for Action in Pre-School Mathematics (Geraldo Gomes and Luciano Meira); (27) An Online Community of Practice for Pre-Service and Beginning Teachers of Secondary Mathematics (Merrilyn Goos and Anne Bennison); (28) Development of Abstract Mathematical Thinking through Artistic Patterns (Ivona Grzegorczyk and Despina A. Stylianou); (29) Rational Numbers after Elementary School: Realizing Models for Fractions on the Real Line (Stefan Halverscheid, Melanie Henseleit, and Klaus Lies); (30) Student Beliefs about Mathematics Encoded in Pictures and Words (Stefan Halverscheid and Katrin Rolka); (31) Algebra Teachers' Ways of Thinking Characterizing the Mental Act of Problem Posing (Guershon Harel, Boris Koichu, and Alfred Manaster); (32) Mathematical Impairment among Epileptic Children (Izabel Hazin, Jorge T. da Rocha Falcao, and Selma Leitao); (33) Patterns of Participation in Networked Classrooms (Stephen Hegedus, Sara Dalton, Laura Cambridge, and Gary Davis); (34) Teacher Training Students' Probabilistic Reasoning about Compound Stochastic Events in an ICT Environment (Tore Heggem and Kjaerand Iversen); (35) Learning to Prove with Heuristic Worked-out Examples (Aiso Heinze, Kristina Reiss, and Christian GroB); (36) Teacher Actions: Enhancing the Learning of Mental Computation in Year 2 (Ann Heirdsfield and Janeen Lamb); (37) Early Conceptual Thinking (Milan Hejny, Darina Jirotkova, and Jana Kratochvilova); (38) Diversity in the Construction of a Group's Shared Knowledge (Rina Hershkowitz, Nurit Hadas, and Tommy Dreyfus); (39) Structure Sense versus Manipulation Skills: An Unexpected Result (Maureen Hoch and Tommy Dreyfus); (40) Young Children Developing Place Value Understandings (Marj Horne and Sharyn Livy); (41) New Insights into Learning Processes from Some Neuroscience Issues (Donatella Iannece, Maria Mellone, and Roberto Tortora); (42) Fostering Conceptual Mathematical Thinking in the Early Years: A Case Study (Paola Iannone and Anne D. Cockburn); (43) The Role of Mathematical Context in Evaluating Conditional Statements (Matthew Inglis and Adrian Simpson); (44) Knowledge for Teaching Fraction Arithmetic: Partitioning Drawn Representations (Andrew Izsak); (45) Inquiry Community in an Activity Theory Frame (Barbara Jaworski and Simon Goodchild); (46) Gender Differences in Patterns of Strategy Use amongst Secondary School Mathematics Students (Tim Jay); (47) Positioning of a Subject Based and Investigative Dialogue in Practice Teaching (Marit Johnsen Hoines and Beate Lode); (48) Everyday Computer-Based Maths Teaching: The Predominance of Practical Activities (Helga Jungwirth); (49) Facilitators for Change of Elementary Teacher Student's View of Mathematics (Raimo Kaasila, Markku S. Hannula, Anu Laine, and Erkki Pehkonen); (50) The Mathematical Beliefs of Teachers about Applications and Modelling--Results of an Empirical Study (Gabriele Kaiser); (51) An Analysis of Solving Groups of Problems (toward the Study of Problem Solving Instruction) (Alexander Karp); (52) Advancing Low Achievers in Secondary Schools by Using Non-Professional Mathematics Tutoring (Ronnie Karsenty); (53) Mathematical Knowledge for Teaching: Adding to the Description through a Study of Probability in Practice (Mercy Kazima and Jill Adler); (54) Measurements with a Physical and a Virtual Quadrant: Students' Understanding of Trigonometric Tangent (Stefanos Keisoglou and Chronis Kynigos); (55) Language and Mathematics: Towards Social Justice for Linguistically Diverse Students (Lena Licon Khisty); (56) Concept Definition, Concept Image and the Discrete-Continuous Interplay (Ivy Kidron and Thierry Dana Picard); (57) Reconceiving Strategic Knowledge in Proving from the Student's Perspective (Jessica Knapp and Keith Weber); (58) Patterns of Middle School Students' Heuristic Behaviors in Solving Seemingly Familiar Problems (Boris Koichu, Abraham Berman, and Michael Moore); (59) Improper Proportional Reasoning: A Comparative Study in High School (Katerina Kontoyianni, Modestina Modestou, Maria Erodotou, Polina Ioannou, Athinos Constantinides, Marinos Parisinos, and Athanasios Gagatsis); and (60) Integer Instruction: A Semiotic Analysis of the "Compensation Strategy" (Andreas Koukkoufis and Julian Williams). (Individual papers contain references.)