This document is the fourth volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 42 research reports by presenters with last names beginning between Mul and Wu: (1) Case Studies of Children's Development of Structure in Early Mathematics: A Two-Year Longitudinal Study (Joanne Mulligan, Michael Mitchelmore, and Anne Prescott); (2) A Case Study of How Kinesthetic Experiences Can Participate in and Transfer to Work with Equations (Ricardo Nemirovsky and Chris Rasmussen); (3) The Construction of Proportional Reasoning (Stephen Norton); (4) The Transition of a Secondary Mathematics Teacher: From a Reform Listener into a Believer (Jo Clay Olson and Karmen Kirtley); (5) Substantive Communication of Space Mathematics in Upper Primary School (Kay Owens); (6) Transforming Korean Elementary Mathematics Classrooms to Student-Centered Instruction (JeongSuk Pang); (7) The Effect of Improved Automaticity and Retrieval of Basic Number Skills on Persistently Low-Achieving Students (John Pegg, Lorraine Graham, and Anne Bellert); (8) Degrees of Freedom in Modeling: Taking Certainty out of Proportion (Irit Peled and Ronit Bassan-Cincinatus); (9) "I Know That You Don't Have to Work Hard": Mathematics Learning in the First Year of Primary School (Bob Perry and Sue Dockett); (10) Disentangling Mentors' Role in the Development of Prospective Teachers' Efficacy Beliefs in Teaching Mathematics (George Philippou and Charalambos Y. Charalambous); (11) Linear Functions and a Triple Influence of Teaching on the Development of Students' Algebraic Expectation (Robyn Pierce); (12) Engaging the Learner's Voice? Catechetics and Oral Involvement in Reform Strategy Lessons (Adrian J. Pinel); (13) Teaching Projectile Motion to Eliminate Misconceptions (Anne Prescott and Michael Mitchelmore); (14) An Investigation of a Preservice Teacher's Use of Representations in Solving Algebraic Problems Involving Exponential Relationships (Norma Presmeg and Rajeev Nenduradu); (15) On Embodiment, Artifacts, and Signs: A Semiotic-Cultural Perspective on Mathematical Thinking (Luis Radford, Caroline Bardini, Cristina Sabena, Pounthioun Diallo, and Athanase Simbagoye); (16) Generalization Strategies of Beginning High School Algebra Students (Joanne Rossi Becker and Ferdinand Rivera); (17) Synchronizing Gestures, Words and Actions in Pattern Generalizations (Cristina Sabena, Luis Radford, and Caroline Bardini); (18) Analyzing Student Modeling Cycles in the Context of a "Real World" Problem (Roberta Y. Schorr and Miriam Amit); (19) Negotiating about Perceived Value Differences in Mathematics Teaching: The Case of Immigrant Teachers in Australia (Wee Tiong Seah); (20) Development of Mathematical Norms in an Eighth-Grade Japanese Classroom (Yasuhiro Sekiguchi); (21) Solving Additive Problems at Pre-Elementary School Level with the Support of Graphical Representation (Ana Coelho Vieira Selva, Jorge Tarcisio da Rocha Falcao, and Terezinha Nunes); (22) From the Everyday, through the Authentic, to Mathematics: Reflecting on the Process of Teaching Mathematics through the Everyday (Godfrey Sethole); (23) Personal Experiences and Beliefs in Early Probabilistic Reasoning: Implications for Research (Sashi Sharma); (24) Assimilating Innovative Learning/Teaching Approaches into Teacher Education: Why Is It so Difficult? (Atara Shriki and Ilana Lavy); (25) Student Thinking Strategies in Reconstructing Theorems (Tatag Yuli Eko Siswono); (26) A Comparison of How Textbooks Teach Multiplication of Fractions and Division of Fractions in Korea and in U.S. (Ji-Won Son); (27) Mathematical Knowledge of Pre-Service Primary Teachers (Beth Southwell and Marina Penglase); (28) Analysing Longitudinal Data on Students' Decimal Understanding Using Relative Risk and Odds Ratios (Vicki Steinle and Kaye Stacey); (29) Girls Journey toward Proportional Reasoning (Olof Bjorg Steinthorsdottir); (30) University Student Perceptions of CAS Use in Mathematics Learning (Sepideh Stewart and Michael O. J. Thomas); (31) Prospective Teachers' Understanding of Proof: What if the Truth Set of an Open Sentence Is Broader than that Covered by the Proof? (Andreas J. Stylianides, Gabriel J. Stylianides, and George Philippou); (32) Planning and Teaching Mathematics Lessons as a Dynamic, Interactive Process (Peter Sullivan, Robyn Zevenbergen, and Judy Mousley); (33) Teacher Factors in Integration of Graphic Calculators into Mathematics Learning (Michael O. J. Thomas and Ye Yoon Hong); (34) Students' Overreliance on Linearity: An Effect of School-Like Word Problems (Wim Van Dooren, Dirk De Bock, Dirk Janssens, and Lieven Verschaffel); (35) A Process of Abstraction by Representations of Concepts (N. C. Verhoef and H. G. B. Broekman); (36) Argumentation Profile Charts as Tools for Analysing Students' Argumentations (Jill Vincent, Helen Chick, and Barry McCrae); (37) Characterizing Middle School Students' Thinking in Estimation (Tanya N. Volkova); (38) Reviewing and Thinking the Affect/Cognition Relation (Margaret Walshaw and Tania Cabral); (39) Young Children's Ability to Generalise the Pattern Rule for Growing Patterns (Elizabeth Warren); (40) Consolidating One Novel Structure whilst Constructing Two More (Gaye Williams); (41) Spreadsheets, Pedagogic Strategies and the Evolution of Meaning for Variable (Kirsty Wilson, Janet Ainley, and Liz Bills); and (42) A Study of the Geometric Concepts of the Elementary School Students Who Are Assigned to the van Hiele Level One (Der-bang Wu and Hsiu-Lan Ma). (Individual papers contain references.)