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This document contains the second 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 43 research reports by presenters with last names beginning between Adl and Fre: (1) Working with Learners' Mathematics: Exploring a Key Element of Mathematical Knowledge for Teaching (Jill Adler, Zain Davis, Mercy Kazima, Diane Parker, and Lyn Webb); (2) A Comparison between Teachers' and Pupils' Tendency to Use a Representativeness Heuristic (Thekla Afantiti-Lamprianou, Julian S. Williams, and Iasonas Lamprianou); (3) Purposeful Task Design and the Emergence of Transparency (Janet G. Ainley, Liz Bills, and Kirsty Wilson); (4) A Developmental Model for Proportional Reasoning in Ratio Comparison Tasks (Silvia Alatorre and Olimpia Figueras); (5) Referential and Syntactic Approaches to Proof: Case Studies from a Transition Course (Lara Alcock and Keith Weber); (6) Teachers' Beliefs about Students' Development of the Pre-Algebraic Concept of Equation (Vassiliki Alexandrou-Leonidou and George N. Philippou); (7) Developing Students' Understanding of the Concept of Fractions as Numbers (Solange Amorim Amato); (8) Multiple Representations in 8th Grade Algebra Lessons: Are Learners Really Getting It? (Miriam Amit and Michael N. Fried); (9) Reform-Oriented Teaching Practices: A Survey of Primary School Teachers (Judy Anderson and Janette Bobis); (10) The Genesis of Signs by Gestures: The Case of Gustavo (Ferdinando Arzarello, Francesca Ferrara, Ornella Robutti, and Domingo Paola); (11) Students' Experience of Equivalence Relations: A Phenomenological Approach (Amir H. Asghari and David Tall); (12) How Series Problems Integrating Geometric and Arithmetic Schemes Influence Prospective Secondary Teachers' Pedagogical Understanding (Leslie Aspinwall, Kenneth L. Shaw, and Hasan Unal); (13) Dealing with Learning in Practice: Tools for Managing the Complexity of Teaching and Learning (Sikunder Ali Baber and Bettina Dahl); (14) Situations of Psychological Cognitive No-Growth (Roberto R. Baldino and Tania C. B. Cabral); (15) Good CAS Written Records: Insight from Teachers (Lynda Ball and Kaye Stacey); (16) Developing Procedure and Structure Sense of Arithmetic Expressions (Rakhi Banerjee and K. Subramaniam); (17) Struggling with Variables, Parameters, and Indeterminate Objects, or How to Go Insane in Mathematics (Caroline Bardini, Luis Radford, and Cristina Sabena); (18) Exploring How Power is Enacted in Small Groups (Mary Barnes); (19) A Framework for the Comparison of PME Research into Multilingual Mathematics Education in Different Sociolinguistic Settings (Richard Barwell); (20) Vygotsky's Theory of Concept Formation and Mathematics Education (Margot Berger); (21) Preservice Teachers' Understandings of Relational and Instrumental Understanding (Kim Beswick); (22) The Transformation of Mathematics in On-Line Courses (Marcelo C. Borba); (23) Using Cognitive and Situated Perspectives to Understand Teacher Interactions with Learner Errors (Karin Brodie); (24) Identification of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (25) The "A4-Project": Statistical World Views Expressed through Pictures (Michael Bulmer and Katrin Rolka); (26) A Whole-School Approach to Developing Mental Computation Strategies (Rosemary Callingham); (27) A Comparison of Perceived Parental Influence on Mathematics Learning among Students in China and Australia (Zhongjun Cao, Helen Forgasz, and Alan Bishop); (28) Using Word Problems in Malaysian Mathematics Education: Looking beneath the Surface (Kah Yein Chan and Judith Mousley); (29) Constructing Pedagogical Knowledge of Problem Solving: Preservice Mathematics Teachers (Olive Chapman); (30) Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research (Charalambos Y. Charalambous and Demetra Pitta-Pantazi); (31) Students' Reflection on Their Sociomathematical Small-Group Interaction: A Case Study (Petros Chaviaris and Sonia Kafoussi); (32) Investigating Teachers' Responses to Student Misconceptions (Helen L. Chick and Monica K. Baker); (33) Studying the Distribution of Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai (David Clarke and Lay Hoon Seah); (34) Indigenous and Non-Indigenous Teaching Relationships in Three Mathematics Classrooms in Remote Queensland (Tom J. Cooper, Annette R. Baturo, and Elizabeth Warren); (35) Exploring the Strategies Used by Grade 1 to 3 Children through Visual Prompts, Symbols and Worded Problems: A Case for a Learning Pathway for Number (Ty Corvell Cranfield, Cally Kuhne, and Gary Powell); (36) Primary Students' Knowledge of the Properties of Spatially-Oriented Diagrams (Carmel Diezmann); (37) A Conceptual Framework for Studying Teacher Preparation: The Pirie-Kieren Model, Collective Understanding, and Metaphor (Maria A. Droujkova, Sarah B. Berenson, Kelli Slaten, and Sue Tombes); (38) Mathematical Modelling with 9-Year-Olds (Lyn English and James Watters); (39) Exploring "Lesson Study" in Teacher Preparation (Maria L. Fernandez); (40) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years (Jillian Fox); (41) The Tacit-Explicit Nature of Students' Knowledge: A Case Study on Area Measurement (Cristina Frade); (42) Teachers as Interns in Informal Mathematics Research (John M. Francisco and Carolyn A. Maher); and (43) Exploring Excellence and Equity within Canadian Mathematics Classrooms (George Frempong). (Individual papers contain references.)

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.)

This paper explores the value of different paradigms to explain dispositions towards mathematics among primary school students from different social backgrounds. As part of a larger project designed to elicit students' thinking and attitudes towards mathematics, we seek to develop an explanatory model for the socially-differentiated outcomes in students' responses. The three paradigms--psychology, sociology and post-modernism--form the basis of the paper where the data we collected from three geographically close but socially different schools were analysed.

The flipped classroom's pervasiveness in different educational contexts derives from the growing need to focus on student-centered and active learning approaches. The fact that the flipped classroom allocates the lecture delivery to the outside of the classroom endows teachers with the possibility of using the in-class time to develop active learning tasks. At the same time, since students gain insight of the learning material prior to attending the class, they are more prepared to actively engage with the resources and their peers inside the classroom. This paper presents a project developed by the School of Psychology from the University of Queensland in Australia that consisted in flipping a course, PSYC1030, and creating a series of four MOOCs. The students' evaluation of the experience was measured via a survey and showed that, in general, they found the outcomes to be positive, namely at the level of the assessment, collaboration, interaction and their understanding of the material. [For the complete proceedings, see ED579395.]

There is still much to be learnt about best practices in leveraging digital resources for learning in higher education. Research on student interactions with online video indicates such practices are as minimal as setting passive-receptive viewing through to teacher-structured purposeful engagement. This position paper focuses on teacher-set analysis categories to guide student exploration of digital video content and to help novices to scaffold their thinking. Various uses of analysis categories within one Australian university in conjunction with a video annotation tool are reviewed. Then practice examples from other universities are reviewed to demonstrate the use of analysis categories in higher education settings without an annotation tool. The literature indicates that the use of categories to inform the design of digital video analysis needs to ensure that the learning challenge is retained. Analysis guided by teacher-set categories tends to be beneficial for performance evaluation in particular. Further research on university teacher practices with digital video is required. [For full proceedings, see ED571332.]

This document contains the fifth 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 59 research reports by presenters with last names beginning between Sac and Zaz: (1) Bryan's Story: Classroom Miscommunication about General Symbolic Notation and the Emergence of a Conjecture during a CAS-Based Algebra Activity (Ana Isabel Sacristan and Carolyn Kieran); (2) A Teacher's Method to Introduce Story-Problems: Student-Generated Problems (Adalira Saenz-Ludlow); (3) "There's More than Meets the Eye": Analysing Verbal Protocols, Gazes and Sketches on External Mathematical Representations (Jonathan P. San Diego, James Aczel, Barbara Hodgson, and Eileen Scanlon); (4) Notions of Variability in Chance Settings (Ernesto Sanchez and Miguel Mercado Martinez); (5) Elementary Preservice Teacher Learning Levels (Victoria Sanchez and Miguel Mercado Martinez); (6) Mathematics Achievement: Sex Differences vs. Gender Differences (Dora Santos, Sonia Ursini, Martha Patricia Ramirez, and Gabriel Sanchez); (7) Self Assessment and Appropriation of Assessment Criteria (Leonor Santos and Anabela Gomes); (8) Drawing as Problem-Solving: Young Children's Mathematical Reasoning through Pictures (Carole Saundry and Cynthia Nicol); (9) The Role of the Teacher in Turning Claims to Arguments (Baruch Schwarz, Rina Hershkowitz, and Shirly Azmon); (10) Learning Mathematics for Teaching (Nanette Seago and Lynn Goldsmith); (11) Coherence of Mathematics Lessons in Japanese Eighth-Grade Classrooms (Yasuhiro Sekiguchi); (12) Triangle Property Relationships: Making the Connections (Penelope Serow); (13) Access to Mathematics versus Access to the Language of Power (Mamokgethi Setati); (14) Compartmentalization of Representation in Tasks Related to Addition and Subtraction Using the Number Line (Myria Shiakalli and Athanasios Gagatsis); (15)The Derivation of a Learning Assessment Framework for Multiplicative Thinking (Dianne Siemon, John Izard, Margarita Breed, and Jo Virgona); (16) Sources of Students' Frustration in Bridging Mathematics Courses (Anna Sierpinska); (17) What Makes a Good Problem? An Aesthetic Lens (Nathalie Sinclair and Sandra Crespo); (18) Discovering a Rule and Its Mathematical Justification in Modeling Activities Using Spreadsheet (Hong-chan Son and Hee-chan Lew); (19) Investigating Preservice Teachers' Understanding and Strategies on a Student's Errors of Reflective Symmetry (Ji-Won Son); (20) Exploring the Role Played by the Remainder in the Solution of Division Problems (Alina Galvao Spinillo and Sintria Labres Lautert); (21) Incomplete or Incorrect Understanding of Decimals: An Important Deficit for Student Nurses (Vicki Steinle and Robyn Pierce); (22) Proportional Reasoning: Variable Influencing the Problems Difficulty Level and One's Use of Problem Solving Strategies (Olof Bjorg Steinthorsdottir); (23) The Impact of the Intuitive Rule "If A Then B, If Not A Then Not B" in Perimeter and Area Tasks (Lambros Stephanou and Demetra Pitta-Pantazi); (24) Process-Object Difficulties in Linear Algebra: Eigenvalues and Eigenvectors (Sepideh Stewart and Michael O. J. Thomas); (25) Conceptual Changes as Dialectical Transformation (Nadia Stoyanova Kennedy); (26) Content Knowledge for Mathematics Teaching: The Case of Reasoning and Proving (Andreas J. Stylianides and Gabriel J. Stylianides); (27) "Making Proof Central to Pre-High School Mathematics Is an Appropriate Instructional Goal": Provable, Refutable, or Undecidable Proposition? (Gabriel J. Stylianides and Andreas J. Stylianides); (28) Power and Poverty--Whose, Where, and Why?: School Mathematics, Context and the Social Construction of "Disadvantage" (Dalene M. Swanson); (29) Documenting Learning in School-Based Mathematics Communities of Teachers (Paola Sztajn); (30) Research and Teaching--Can One Person Do Both? A Case Study (MichalTabach); (31) Computer "Knowledge" and Student's Images of Figures: The Case of Dragging (Varda Talmon and Michal Yerushalmy); (32) Graphics Calculators for Mathematics Learning in Singapore and Victoria (Australia): Teachers' Views (Hazel Tan and Helen J. Forgasz); (33) Vague Language in Greek and English Mathematical Talk: A Variation Study in Face-Work (Konstantinos Tatsis and Tim Rowland); (34) Teachers Using Computers in Mathematics: A Longitudinal Study (Michael O. J. Thomas); (35) Analysing Classroom Interactions Using Critical Discourse Analysis (Steve Thornton and Noemi Reynolds); (36) Pre-Service and In-Service Mathematics Teachers' Concept Images of Radian (Tahsin Topcu, Mahmut Kertil, Hatice Akkoc, Kamil Yilmaz, and Osman Onder); (37) Adaptive Expertise in the Number Domain 20-100 (Joke Torbeyns, Lien Vanderveken, Lieven Verschaffel, and Pol Ghesquiere); (38) Mathematical Activity in a Technological Workplace: Results from an Ethnographic Study (Chrissavgi Triantafillou and Despina Potari); (39) Pupils' Over-Use of Proportionality on Missing-Value Problems: How Numbers May Change Solutions (Wim Van Dooren, Dirk De Bock, Marleen Evers, and Lieven Verschaffel); (40) Arithmetical Procedures in the Solution of a Problem Involving Velocity (Veronica Vargas and Jose Guzman); (41) Introducing Algebraic Thinking to 13 Year-Old Students: The Case of the Inequality (Petros Verikios and Vassiliki Farmaki); (42) Why Is a Discontinuous Function Differentiable? (Antti Viholainen); (43) Overgeneralization of Linear Models: Presence and Characteristics among University Students (Monica Villareal, Cristina Esteley, and Humberto Alagia); (44) Educational Design Research in Mozambique: Starting Mathematics from Authentic Resources (Pauline Vos, Tiago G. Devesse, and Assane Rassul); (45) "The Big Test": A School Community Experiences Standardized Mathematics Assessment (Fiona Walls); (46) Numeracy Reform in New Zealand: Factors that Influence Classroom Enactment (Margaret Walshaw and Glenda Anthony); (47) An Investigation of Factors Influencing Teachers' Scoring Student Responses to Mathematics Constructed-Response Assessment Tasks (Ning Wang and Jinfa Cai); (48) Teacher Actions that Assist Young Students to Write Generalizations in Words and in Symbols (Elizabeth Warren); (49) Promoting Pre-Service Teachers' Understanding of Decimal Notation and Its Teaching (Wanty Widjaja and Kaye Stacey); (50) Impetus to Explore: Approaching Operational Deficiency Optimistically (Gaye Williams); (51) Generating and Evaluating Geometry Conjectures with Self-Directed Experiments (Chao-Jung Wu, Wing-Kwong Wong, Ying-Hao Cheng, and Yunn-Wen Lien); (52) The Distributions of van Hiele Levels of Geometric Thinking among 1st and 6th Graders (Der-bang Wu and Hsiu-Ian Ma); (53) Elementary Teacher Education and Teacher Efficacy toward Mathematics and Science (Su-Chiao Wu and Yu Liang Chang); (54) Spatial Rotation and Perspective Taking Abilities in Relation to Performance in Reflective Symmetry Tasks (Xenia Xistouri and Demetra Pitta-Pantazi); (55) Elementary Teachers' Mathematics Beliefs and Teaching Practices after a Curriculum Reform (Shirley M. Yates); (56) Inquiry Activities in a Classroom: Extra-Logical Processes of Illumination vs. Logical Process of Deductive and Inductive Reasoning. A Case Study (Oleksiy Yevdokimov); (57) Developments of a Child's Fraction Concepts with the Help of Psychological Tools: A Vygotsky's Cultural-Historical Perspective (Kaori Yoshida); (58) A Teacher's Treatment of Examples as Reflection of Her Knowledge-Base (Orit Zaslavsky, Guershon Harel, and Alfred Manaster); and (59) Cognitive Conflict and its Resolution via Pivotal/Bridging Example (Rina Zazkis and Egan Chernoff). (Individual papers contain references.)

Third in a series of seven volumes containing the proceedings of the 1983 Australian Family Research Conference, this publication deals with marital adjustment and breakdown. Papers are organized into four major sections: education for family tasks, marital satisfaction, adjustment to separation, and construction of family image. Papers and authors included are: "Education for Family Life: What Kind of Knowledge Do Families Need?" (Moira Eastman), "From Courtship to Divorce: Unrealised or Unrealistic Expectations" (Ilene Wolcott), "Stepparenting Special Skills" (Joy Conolly), "Spouse Selection and Satisfaction with the Quality of Family Life" (Wolfgang L. Grichting and E. Ruth Bradshaw), "Marital Synchrony Inventory: A Measure of Interpersonal Perception" (Daniel Kahans, Nigel Reece, and Naomi Crafti), "Correlates of Marital Adjustment in Australia" (Christopher F. Sharpley), "Family Cohesion: A Delphi Investigation" (James Nixon), "Marital Breakdown: Reactions to Separation and Post-Separation Experiences of Adults" (Freya Headlam), "On Being Single Again: A Mutual Aid Response" (Eva Learner, Bill Healy, and June Polglaze), "Kin and Non-Kin Support in the Separation Process" (Myra Browne), "Three Generations of the Single Parent Family" (Penny Jools and Margaret Kennedy), "The Princess: Machiavellian Maxims for Single Mothers" (Helen J. Baxter), and "Social and Psychological Factors Affecting a Family over Six Generations: Study of the Nathan-Maclaurin-Mackerras Family" (Mary R. Power).