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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 submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. 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, panel discussions, working group reports, new PhD reports, and summaries of ad hoc and poster sessions. Papers include the following: (1) The Most Unglamorous Job of All: Writing Mathematics Exercises (Yvan Saint-Aubin); (2) 40+ Years of Teaching and Thinking about University Mathematics Students, Proofs, and Proving (Annie Selden); (3) 'Elder Talk'-A Revisionist Version (Joel Hillel); (4) Teaching First Year Mathematics Courses in Transition from Secondary to Tertiary (Ann Arden, Wesley Maciejewski, Nadia Hardy); (5) L'anxiété mathématique chez les futurs enseignants du primaire : à la recherche de nouvelles réponses à des enjeux qui perdurent / Elementary Preservice Teachers and Mathematics Anxiety: Searching for New Responses to Enduring Issues (Manion LeBlanc, Jamie Pyper, Jo Towers) [Written in French and English]; (6) Social Media and Mathematics Education (Judy Larsen, Egan Chernoff, Viktor Freiman); (7) Quantitative Reasoning in the Early Years / Le raisonnement quantitatif dans les premières années du parcours scolaire (Doris Jeannotte, Lynn McGarvey)[Written in English and French ]; (8) Social, Cultural, Historical and Philosophical Perspectives on Tools for Mathematics (Yasmine Abtahi, Susan Gerofsky, Jean Francois); (9) Compréhension approfondie des mathématiques scolaires / Deep Understanding of School Mathematics (Richelle Marynowski, Sarah Dufour, Peter Liljedhal); (10) Modelling Mathematical Modelling / Modéliser la modélisation mathématique (France Caron)[Written in French and English]; (11) Collective Learning: Re-thinking the Environment, Artifacts and Classroom Interactions (Joyce Mgombelo); (12) A Psychological View of Teaching Proof Construction (John Selden); (13) Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions (Yasmine Abtahi); (14) Examining Mathematics Anxiety Among Classroom Teachers (Atinuke Adeyemi); (15) Teaching Teachers: A Look Inside Professional Development (Melania Alvarez); (16) Be Innovative but Don't Be Wrong: Are 21st Century Students Experiencing 21st Century Mathematics? (Jennifer Godfrey Anderson); (17) College Foundational Mathematics: Can the Affordances of ICT Enhance Self-regulation Skill of Students? / Mathématiques fondamentales du collège : est-ce que les apports des « TIC » peuvent améliorer l'autorégulation des compétences des élèves? (Carol Carruthers)[Written in English and French]; (18) Influence of the Learning Environment on Student Test Performance in Undergraduate Mathematics Courses (Amenda Chow); (19) The Role of Oral Communication Strategies in Accessing and Assessing Mathematical Understanding: Case Studies of Primary School Teachers' Perceptions of Teaching Mathematics and Teaching Literacy (Celia Kutas Chisu); (20) Reciprocal Partnership: An Intervention to Enhance Mathematics Self-efficacy and Achievement of First- and Second-semester College Students (Kerry Kwan); (21) Understanding the Interactions within a New Teacher Learning Community Composed of First Time Participants and a Novice Facilitator (Terry Wan Jung Lin); (22) Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis (Gale L. Russell); (23) Opening Space: Complexity Thinking, Classroom Discourse, and Mathematics Learning in the Elementary Classroom / La technologie du forum ouvert: complexité, le discours de classe, et l'apprentissage de mathématiques en école élémentaire (Evan Throop-Robinson)[Written in English and French]; (24) Investigating Mathematics Teachers' Knowledge for Teaching and Their Learning Trajectories (Zhaoyun Wang]; (25) What/How Can We Learn from the Deaf Mathematics Classroom? (Christins M. Krause); (26) The Mathematical Association of Tanzania (MAT) Experience in CMESG Conference (Said A. Sima); (27) Toward a Hybrid Model to Describe Creative Acts in Mathematics Learning Environments (Ayman Aljarrah); (28) Problem Drift: Imaging Emerging Curricular Significance (Nat Banting); (29) Incorporating Writing into the Undergraduate Mathematics Curriculum (Lauren Dedieu); (30) Informing Local Materials Used for Concept-Rich Instruction Practice in Mathematics Class with Pre-service Teachers in Tanzanian Context (Emmanuel, Deogratias); (31) Les jeux technologiques dans les cours de mathématiques au secondaire (Caitlin, Furlong) [Written in French]; (32) De jeunes chercheurs à la rencontre de la philosophie des mathématiques (Sabrina Heroux, Sarah Mathieu-Soucy, Laura Broley) [Provided in French]; (33) Examining Parent Perspectives of Multiple Strategies (Jennifer Holm, Lynn McGarvey, Lixin Luo, Janelle McFeeters, and Iris Yin); (34) La dialectique perfection/imperfection : une nouvelle manière de penser l'activité mathématique (Marie-Line L. LaMarche, Jean-Francois Maheux) [Provided in French]; (35) Understanding School Leaders' Discourse in Regard to Mathematics Achievement (Jhonel Morvan); (36) I SEE What You're Saying: Visualization and the Growth of Mathematical Images (Jennifer Plosz); (37) Students' Relationships With Mathematics Revealed Through Drawings (Jennifer Plosz, Jo Towers, Kori Czuy, Ayman Aljarrah, Andrew Vorhies and Miwa Takeuchi); (38) Teacher Professional Learning in Tanzania: Experiences of Mathematics Teacher Leaders (Calvin Zakaria Swai); (39) "Perimeter is easier to work with than area": Students' Language Use in Group Work (Miwa Akoi Takeuchi); and (40) Toward an Understanding of Mathematics Teachers' Participation in Professional Learning Networks (Xiong Wang). Individual papers provide referenced. [For the 2016 proceedings, see ED581045.]

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis 2013, Chania 2012, Eindhoven 2011, Pittsburgh 2010, Cordoba 2009 and Montreal 2008). The EDM conference is the leading international forum for high-quality research that leverages educational data, learning analytics, and machine learning to answer research questions that shed light on the learning processes. This year's conference features three invited talks by: Rakesh Agrawal, President and Founder of Data Insights Laboratories; Marcia C. Linn, Professor of the University of California at Berkeley; and Judy Kay, Professor of the University of Sydney. Judy Kay's invited paper entitled "Enabling people to harness and control EDM for lifelong, life-wide learning" is also presented in the proceedings. Together with the "Journal of Educational Data Mining" ("JEDM"), the EDM 2016 conference supports a "JEDM" Track that provides researchers a venue to deliver more substantial mature work than is possible in a conference proceedings and to present their work to a live audience. The papers submitted to this track followed the "JEDM" peer review process; three papers have been accepted to the track and were presented at the conference. The abstracts of the invited talks, panels and accepted "JEDM" Track papers can be found in these proceedings. [For the 2015 proceedings, see ED560503.]

Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical generalizations. We address these challenges by introducing a comprehensive framework characterizing students' generalizing, the Relating-Forming-Extending framework. Based on individual interviews with 90 students, we identify three major forms of generalizing and address relationships between forms of abstraction and forms of generalization. This paper presents the generalization framework and discusses the ways in which different forms of generalizing can play out in activity. [For complete proceedings, see ED581294.]

This document contains the fourth volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 64 research report papers: (1) Situated or Abstract: The Effect of Combining Context and Structure on Constructing an Additive (Part-Part-Whole) Schema (Irit Peled and Ruth Meron); (2) Using Graphical Profiles to Study the Learning and Teaching of Mathematics (Dvora Peretz); (3) The Role of Number in Proportional Reasoning: A Prospective Teacher's Understanding (Axelle C. Person, Sarah B. Berenson, and Paula J. Greenspon); (4) Learning to Use CAS: Voices from a Classroom (Robyn Pierce and Kaye Stacey); (5) Technical School Students' Conceptions of Tangent Lines (Marcia Maria Fusaro Pinto and Valeria Guimaraes Moreira); (6) Elementary School Students' Mental Representations of Fractions (Demetra Pitta-Pantazi, Eddie M. Gray, and Constantinos Christou); (7) A Structural Model for Problem Posing (M. Pittalis, C. Christou, N. Mousoulides, and D. Pitta-Pantazi); (8) Some Undergraduates' Experiences of Learning Mathematics (Hilary Povey and Corinne Angier); (9) Normalising Geometrical Constructions: A Context for the Generation of Meanings for Ratio and Proportion (Georgos Psycharis and Chronis Kynigos); (10) The Sensual and the Conceptual: Artefact-Mediated Kinesthetic Actions and Semiotic Activity (Luis Radford, Serge Demers, Jose Guzman, and Michele Cerulli); (11) A Sociocultural Account of Students' Collective Mathematical Understanding of Polynomial Inequalities in Instrumented Activity (Ferdinand Rivera and Joanne Rossi Becker); (12) Infinity as a Multi-Faceted Concept in History and in the Mathematics Classroom (Ornella Robutti, Ferdinando Arzarello, and Maria G. Bartolini Bussi); (13) Successful Undergraduate Mathematicians: A Study of Students in Two Universities (Melissa Rodd and Margaret Brown); (14) Bilingual Lessons and Mathematical World Views--A German Perspective (Katrin Rolka); (15) The Use of Models in Teaching Proof by Mathematical Induction (Gila Ron and Tommy Dreyfus); (16) Reflecting on Prospective Elementary Teachers' Mathematics Content Knowledge: The Case of Laura (Tim Rowland, Peter Huckstep, and Anne Thwaites); (17) The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems. A Didactical Model Based on a Numerical Approach with Junior High Students (Guillermo Rubio and Rafael Del Valle); (18) Language and Concept Development in Geometry (Frode Ronning); (19) The Role of Gestures in Conceptualisation: An Exploratory Study on the Integral Function (Cristina Sabena); (20) Psychological Aspects of Genetic Approach to Teaching Mathematics (Ildar S. Safuanov); (21) Routines in Non-Routine Problem Solving Processes (Wolfgang Schloeglmann); (22) Teacher Guidance of Knowledge Construction (Baruch Schwarz, Tommy Dreyfus, Nurit Hadas, and Rina Hershkowitz); (23) Types of Student Reasoning on Sampling Tasks (J. Michael Shaughnessy, Matt Ciancetta, and Dan Canada); (24) Didactic Model--Bridging a Concept with Phenomena (Beba Shternberg and Michal Yerushalmy); (25) Elaborating the Teacher's Role--Towards a Professional Language (Dianne Siemon, Jo Virgona, Maria Lasso, Vanessa Parsons, and Juli Cathcart); (26) Making the Connection: Procedural and Conceptual Students' Use of Linking Words in Solving Problems (Adrian Simpson and Nora Zakaria); (27) Children's Conceptual Understanding of Counting (Hannah Slovin and Barbara J. Dougherty); (28) Adding Fractions Using "Half" as an Anchor for Reasoning (Alina Galvao Spinillo and Maria Soraia Silva Cruz); (29) Persistence of Decimal Misconceptions and Readiness to Move to Expertise (Vicki Steinle and Kaye Stacey); (30) Molly and Equations in A2: A Case Study of Apprehending Structure (Nada Stehlikova and Adrian Simpson); (31) Image--Metaphor--Diagram: Visualisation in Learning Mathematics (Rudolf Straber and Gert Kadunz); (32) Images of Fractions "as" Processes and Images of Fractions "in" Processes (Marek Sulista, Jan Herman, Lucia Ilucova, Veronika Kremsova, Jiri Pribyl, Janka Ruppeldtova, Adrian Simpson, Nada Stehlikova, and Michaela Ulrychova); (33) Describing Elements of Mathematics Lessons that Accommodate Diversity in Student Background (Peter Sullivan, Judy Mousley, and Robyn Zevenbergen); (34) Orchestrating Mathematical Proof through the Use of Digital Tools (Rosamund Sutherland, Federica Olivero, and Marnie Weeden); (35) School-Based Community of Teachers and Outcomes for Students (Paola Sztajn, Martha Alexsaht-Snider, Dorothy Y. White, and Amy Hackenberg); (36) Thinking through Three Worlds of Mathematics (David Tall); (37) The Effect of Students' Roles on the Establishment of Shared Meanings During Problem Solving (Konstantinos Tatsis and Eugenia Koleza); (38) Integrating CAS Calculators into Mathematics Learning: Partnership Issues (Michael O. J. Thomas and Ye Yoon Hong); (39) The Development of Structure in the Number System (Noel Thomas); (40) Orientations to Numeracy: Teachers' Confidence and Disposition to Use Mathematics Across the Curriculum (Steve Thornton and John Hogan); (41) Efficiency and Adaptiveness of Multiple School-Taught Strategies in the Domain of Simple Addition (Joke Torbeyns, Lieven Verschaffel, and Pol Ghesquiere); (42) Supporting Teachers on Developing Teaching Norms Based on Children's Learning Mathematics (Wen-Huan Tsai); (43) Prospective Teachers' Images and Definitions: The Case of Inflection Points (Pessia Tsamir and Regina Ovodenko); (44) Fostering Mathematical Meaning via Scientific Inquiry: A Case Study (Ron Tzur, Rita A. Hagevik, and Mary E. Watson); (45) Students Building Isomorphisms (Elizabeth B. Uptegrove and Carolyn A. Maher); (46) How Do High School Students Interpret Parameters in Algebra? (Sonia Ursini and Maria Trigueros); (47) Causes Underlying Pre-Service Teachers' Negative Beliefs and Anxieties about Mathematics (Liisa Uusimaki and Rod Nason); (48) Fractions in Adult's Elementary School: The Lucina (Marta Elena Valdemoros-Alvarez); (49) Students' Overreliance on Proportionality: Evidence from Primary School Pupils Solving Arithmetic Word Problems (Wim Van Dooren, Dirk De Bock, An Hessels; Dirk Janssens, and Lieven Verschaffel); (50) From Functions to Equations: Introduction of Algebraic Thinking to 13 Year-Old Students (Petros Verikios, Vasiliki Farmaki, and Nikos Nikoudatos); (51) Critical Awareness of Voice in Mathematics Classroom Discourse: Learning the Steps in the "Dance of Agency" (David Wagner); (52) Metaphors and Cultural Models Afford Communication Repairs of Breakdowns between Mathematical Discourses (G. D. Wake and J. S. Williams); (53) Generalising Arithmetic: Supporting the Process in the Early Years (Elizabeth Warren); (54) A Framework for Describing the Processes that Undergraduates Use to Construct Proofs (Keith Weber); (55) The Nature of Spontaneity in High Quality Mathematics Learning Experiences (Gaye Williams); (56) Spreadsheet Generalising and Paper and Pencil Generalising (Kirsty Wilson, Janet Ainley, and Liz Bills); (57) A Comparison of a Visual-Spatial Approach and a Verbal Approach to Teaching Mathematics (Pamela Woolner); (58) Differentiation of Students' Reasoning on Linear and Quadratic Geometric Number Patterns (Kai-Lin Yang and Fou-Lai Lin); (59) Map Construction as a Context for Studying the Notion of Variable Scale (Nikoleta Yiannoutsou and Chronis Kynigos); (60) Understanding How the Concept of Fractions Develops: A Vygotskian Perspective (Kaori Yoshida); (61) Secondary Mathematics Teachers' Knowledge Concerning the Concept of Limit and Continuity (T. Zachariades and E. Mastorides); (62) Characteristics of Mathematical Problem Solving Tutoring in an Informal Setting (Orit Zaslavsky and Iris Zodik); (63) Making Sense of Irrational Numbers: Focusing on Representation (Rina Zazkis and Natasa Sirotic); and (64) Numeracy Practices of Young Workers (Robyn Zevenbergen and Kelly Zevenbergen). (Individual papers contain references.)

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one year. This paper focuses on two aspects of the study related to developing students' functional thinking by visualising the structure of a growing pattern in different ways. An appendix presents the assessment task used at the beginning of the lesson sequence.

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces that students leave when they interact, either individually or collaboratively, with learning management systems, interactive learning environments, intelligent tutoring systems, educational games or when they participate in a data-rich learning context. The types of data therefore range from raw log files to eyetracking devices and other sensor data. Being hosted in London, UK the theme of the conference is "Big Data--Big Ben--Education Data Mining for Big Impact in Teaching and Learning". In this seventh year of EDM conferences, it is clear that the field is continuing to grow at a rapid pace. With renewed focus on education driven by big data learning analytics has put the EDM field in the center of growing interest. Traditional educational technologies, intelligent tutoring systems, educational games, and learning management systems all continue to generate growing amounts of data that are becoming available for analysis. The new interest in MOOCs and their promise to reach thousands or even hundreds of thousands of students per class requires techniques for feedback and grading that are being researched in the EDM domain. The conference submissions this year also continue to grow. A tremendous amount of work has gone into bringing this conference together, and the following are presented: (1) The Field of EDM: Where We Came from and Where We're Going (Joseph Beck); (2) Generative Adaptivity for Optimization of the Learning Ecosystem (Zoran Popovic; (3) 150K+ Online Students at a Time: How to Understand What's Happening in Online 4 Learning (Daniel Russell); (4) Adaptive Practice of Facts in Domains with Varied Prior Knowledge (Jan Papoušek, Radek Pelánek and Vít Stanislav); (5) Alternating Recursive Method for Q-Matrix Learning (Yuan Sun, Shiwei Ye, Shunya Inoue and Yi Sun); (6) Application of Time Decay Functions and the Elo System in Student Modeling (Radek Pelánek); (7) Causal Discovery with Models: Behavior, Affect, and Learning in Cognitive Tutor Algebra (Stephen Fancsali); (8) Choice-Based Assessment: Can Choices Made in Digital Games Predict 6th-Grade Students' Math Test Scores? (Min Chi, Daniel Schwartz, Kristen Pilner Blair and Doris B. Chin); (9) Comparing Expert and Metric-Based Assessments of Association Rule Interestingness (Diego Luna Bazaldua, Ryan Baker and Maria Ofelia San Pedro); (10) Different Parameters - Same Prediction: An Analysis of Learning Curves (Tanja Käser, Kenneth Koedinger and Markus Gross); (11) Discovering Gender-Specific Knowledge from Finnish Basic Education Using PISA Scale Indices (Mirka Saarela and Tommi Kärkkäinen); (12) EduRank: A Collaborative Filtering Approach to Personalization in E-Learning (Avi Segal, Ziv Katzir, Kobi Gal, Guy Shani and Bracha Shapira); (13) Exploring Differences in Problem Solving with Data-Driven Approach Maps (Michael Eagle and Tiffany Barnes); (14) General Features in Knowledge Tracing: Applications to Model Multiple Subskills, Temporal Item Response Theory, and Expert Knowledge (José González-Brenes, Yun Huang and Peter Brusilovsky); (15) Generating Hints for Programming Problems Using Intermediate Output ( Barry Peddycord III, Andrew Hicks and Tiffany Barnes); (16) Integrating Latent-Factor and Knowledge-Tracing Models to Predict Individual Differences in Learning (Mohammad Khajah, Rowan Wing, Robert Lindsey and Michael Mozer); (17) Interpreting Model Discovery and Testing Generalization to a New Dataset (Ran Liu, Elizabeth A. McLaughlin and Kenneth R. Koedinger); (18) Learning Individual Behavior in an Educational Game: A Data-Driven Approach (Seong Jae Lee, Yun-En Liu and Zoran Popovic); (19) Predicting Learning and Affect from Multimodal Data Streams in Task-Oriented Tutorial Dialogue (Joseph Grafsgaard, Joseph Wiggins, Kristy Elizabeth Boyer, Eric Wiebe and James Lester); (20) Sentiment Analysis in MOOC Discussion Forums: What does It Tell Us? (Miaomiao Wen, Diyi Yang and Carolyn Rose); (21) The Effect of Mutual Gaze Perception on Students' Verbal Coordination (Bertrand Schneider and Roy Pea); (22) The Opportunities and Limitations of Scaling Up Sensor-Free Affect Detection (Michael Wixon, Ivon Arroyo, Kasia Muldner, Winslow Burleson, Cecil Lozano and Beverly Woolf); (23) The Problem Solving Genome: Analyzing Sequential Patterns of Student Work with Parameterized Exercises (Julio Guerra, Shaghayegh Sahebi, Peter Brusilovsky and Yu-Ru Lin); (24) Trading Off Scientific Knowledge and User Learning with Multi-Armed Bandits (Yun-En Liu, Travis Mandel, Emma Brunskill and Zoran Popovic); (25) Vertical and Stationary Scales for Progress Maps (Russell Almond, Ilya Goldin, Yuhua Guo and Nan Wang); (26) Visualization and Confirmatory Clustering of Sequence Data from a Simulation- Based Assessment Task (Yoav Bergner, Zhan Shu and Alina von Davier); (27) Who's in Control?: Categorizing Nuanced Patterns of Behaviors within a Game- Based Intelligent Tutoring System (Erica Snow, Laura Allen, Devin Russell and Danielle McNamara); (28) Acquisition of Triples of Knowledge from Lecture Notes: A Natural Language Processing Approach (Thushari Atapattu, Katrina Falkner and Nickolas Falkner); (29) Towards Assessing Students' Prior Knowledge from Tutorial Dialogues (Dan Stefanescu, Vasile Rus and Art Graesser); (30) Assigning Educational Videos at Appropriate Locations in Textbooks (Marios Kokkodis, Anitha Kannan and Krishnaram Kenthapadi) (31) Better Data Beats Big Data (Michael Yudelson, Stephen Fancsali, Steven Ritter, Susan Berman, Tristan Nixon and Ambarish Joshi); (32) Building a Student At-Risk Model: An End-to-End Perspective (Lalitha Agnihotri and Alexander Ott); (33) Can Engagement be Compared? Measuring Academic Engagement for Comparison (Ling Tan, Xiaoxun Sun and Siek Toon Khoo); (34) Comparison of Algorithms for Automatically Building Example-Tracing Tutor Models (Rohit Kumar, Matthew Roy, Bruce Roberts and John Makhoul); (35) Computer-Based Adaptive Speed Tests (Daniel Bengs and Ulf Brefeld); (36) Discovering Students' Complex Problem Solving Strategies in Educational Assessment (Krisztina Tóth, Heiko Rölke, Samuel Greiff and Sascha Wüstenberg); (37) Discovering Theoretically Grounded Predictors of Shallow vs. Deep-Level Learning (Carol Forsyth, Arthur Graesser, Philip I. Pavlik Jr., Keith Millis and Borhan Samei); (38) Domain Independent Assessment of Dialogic Properties of Classroom Discourse (Borhan Samei, Andrew Olney, Sean Kelly, Martin Nystrand, Sidney D'Mello, Nathan Blanchard, Xiaoyi Sun, Marci Glaus and Art Graesser); (39) Empirically Valid Rules for Ill-Defined Domains (Collin Lynch and Kevin Ashley); (40) Entropy: A Stealth Measure of Agency in Learning Environments (Erica Snow, Matthew Jacovina, Laura Allen, Jianmin Dai and Danielle McNamara); (41) Error Analysis as a Validation of Learning Progressions (Brent Morgan, William Baggett and Vasile Rus); (42) Exploration of Student's Use of Rule Application References in a Propositional Logic Tutor (Michael Eagle, Vinaya Polamreddi, Behrooz Mostafavi and Tiffany Barnes); (43) Exploring Real-Time Student Models Based on Natural-Language Tutoring Sessions (Benjamin Nye, Mustafa Hajeer, Carolyn Forsyth, Borhan Samei, Xiangen Hu and Keith Millis); (44) Forum Thread Recommendation for Massive Open Online Courses (Diyi Yang, Mario Piergallini, Iris Howley and Carolyn Rose); (45) Investigating Automated Student Modeling in a Java MOOC (Michael Yudelson, Roya Hosseini, Arto Vihavainen and Peter Brusilovsky); (46) Mining Gap-Fill Questions from Tutorial Dialogues (Nobal B. Niraula, Vasile Rus, Dan Stefanescu and Arthur C. Graesser); (47) Online Optimization of Teaching Sequences with Multi-Armed Bandits (Benjamin Clement, Pierre-Yves Oudeyer, Didier Roy and Manuel Lopes); (48) Predicting MOOC Performance with Week 1 Behavior (Suhang Jiang, Adrienne Williams, Katerina Schenke, Mark Warschauer and Diane O'Dowd); (49) Predicting STEM and Non-STEM College Major Enrollment from Middle School Interaction with Mathematics Educational Software (Maria Ofelia San Pedro, Jaclyn Ocumpaugh, Ryan Baker and Neil Heffernan); (50) Quantized Matrix Completion for Personalized Learning (Andrew Lan, Christoph Studer and Richard Baraniuk); (51) Reengineering the Feature Distillation Process: A Case Study in Detection of Gaming the System (Luc Paquette, Adriana de Carvahlo, Ryan Baker and Jaclyn Ocumpaugh); (52) SKETCHMINER: Mining Learner-Generated Science Drawings with Topological Abstraction (Andy Smith, Eric N. Wiebe, Bradford W. Mott and James C. Lester); (53) Teachers and Students Learn Cyber Security: Comparing Software Quality, Security (Shlomi Boutnaru and Arnon Hershkovitz); (54) Testing the Multimedia Principle in the Real World: A Comparison of Video vs. Text Feedback in Authentic Middle School Math Assignments (Korinn Ostrow and Neil Heffernan); (55) The Importance of Grammar and Mechanics in Writing Assessment and Instruction: Evidence from Data Mining (Scott Crossley, Kris Kyle, Laura Allen and Danielle McNamara); (56) The Long and Winding Road: Investigating the Differential Writing Patterns of High and Low Skilled Writers (Laura Allen, Erica Snow and Danielle McNamara); (57) The Refinement of a Q-Matrix: Assessing Methods to Validate Tasks to Skills Mapping (Michel Desmarais, Behzad Beheshti and Peng Xu); (58) Tracing Knowledge and Engagement in Parallel in an Intelligent Tutoring System (Sarah Schultz and Ivon Arroyo); (59) Tracking Choices: Computational Analysis of Learning Trajectories (Erica Snow, Laura Allen, G.Tanner Jackson and Danielle McNamara); (60) Unraveling Students' Interaction Around a Tangible Interface Using Gesture Recognition (Bertrand Schneider and Paulo Blikstein); (61) A Predictive Model for Video Lectures Classification (Priscylla Silva, Roberth Pinheiro and Evandro Costa); (62) Accepting or Rejecting Students' Self-Grading in their Final Marks by using Data Mining (Javier Fuentes, Cristobal Romero, Carlos García-Martínez and Sebastián Ventura); (63) Analysis and extraction of behaviors by students in lectures 329 Eiji Watanabe, Takashi Ozeki and Takeshi Kohama (64) Analysis of Student Retention and Drop-Out Using Visual Analytics (Jan Géryk and Lubomír Popelínský); (65) Automatic Assessment of Student Reading Comprehension from Short Summaries (Lisa Mintz, Dan Stefanescu, Shi Feng, Sidney D'Mello and Arthur Graesser); (66) Building an Intelligent PAL from the Tutor.com Session Database Phase 1: Data Mining (Donald Morrison, Benjamin Nye, Borhan Samei, Vivek Varma Datla, Craig Kelly and Vasile Rus); (67) Building Automated Detectors of Gameplay Strategies to Measure Implicit Science Learning (Elizabeth Rowe, Ryan Baker, Jodi Asbell-Clarke, Emily Kasman and William Hawkins); (68) Challenges on Applying BKT to Model Student Knowledge in Multi-Context Online Learning Environment (Wolney Mello Neto and Eduardo Barbosa); (69) Combination of Statistical and Semantic Data Sources for the Improvement of Software Engineering Courses (Michael Koch, Markus Ring, Florian Otto and Dieter Landes); (70) Comparing Learning in a MOOC and a Blended On-Campus Course (Kimberly Colvin, John Champaign, Alwina Liu, Colin Fredericks and David Pritchard); (71) Cost-Effective, Actionable Engagement Detection at Scale (Ryan Baker and Jaclyn Ocumpaugh); (72) Data Mining of Undergraduate Course Evaluations (Sohail Javaad Syed, Yuheng Helen Jiang and Lukasz Golab); (73) Data Sharing: Low-Cost Sensors for Affect and Cognition (Keith Brawner) (74) Diagnosing Algebra Understanding via Inverse Planning (Anna Rafferty and Thomas Griffiths); (75) Discovering and Describing Types of Mathematical Errors (Thomas McTavish and Johann Larusson); (76) Discovering Prerequisite Relationships Among Knowledge Components (Richard Scheines, Elizabeth Silver and Ilya Goldin); (77) Dynamic Re-Composition of Learning Groups Using PSO-Based Algorithms (Zhilin Zheng and Niels Pinkwart); (78) Educational Data Mining and Analyzing of Student Learning Outcomes from the Perspective of Learning Experience (Zhongmei Shu, Qiong-Fei Qu and Lu-Qi Feng); (79) Using EEG in Knowledge Tracing (Yanbo Xu, Kai-Min Chang, Yueran Yuan and Jack Mostow); (80) Exploring Engaging Dialogues in Video Discussions (I-Han Hsiao, Hui Soo Chae, Manav Malhotra, Ryan Baker and Gary Natriello); (81) Exploring Indicators from Keyboard and Mouse Interactions to Predict the User Affective State (Sergio Salmeron-Majadas, Olga C. Santos and Jesus G. Boticario); (82) Extracting Latent Skills from Time Series of Asynchronous and Incomplete Examinations (Shinichi Oeda, Yu Ito and Kenji Yamanishi); (83) Generalizing and Extending a Predictive Model for Standardized Test Scores Based On Cognitive Tutor Interactions (Ambarish Joshi, Stephen Fancsali, Steven Ritter, Tristan Nixon and Susan Berman); (84) How Patterns in Source Codes of Students Can Help in Detection of Their Programming Skills? (Štefan Pero and Tomáš Horváth); (85) A Preliminary Investigation of Learner Characteristics for Unsupervised Dialogue Act Classification (Aysu Ezen-Can and Kristy Elizabeth Boyer); (86) Improving Retention Performance Prediction with Prerequisite Skill Features (Xiaolu Xiong, Seth Adjei and Neil Heffernan); (87) Indicator Visualization for Adaptive Exploratory Learning Environments (Sergio Gutierrez Santos, Manolis Mavrikis, Alex Poulovassilis and Zheng Zhu); (88) Learning Aid Use Patterns and Their Impact on Exam Performance in Online Developmental Mathematics (Nicole Forsgren Velasquez, Ilya Goldin, Taylor Martin and Jason Maughan); (89) Learning to Teach like a Bandit (Mykola Pechenizkiy and Pedro A. Toledo); (90) Matching Hypothesis Text in Diagrams and Essays (Collin Lynch, Mohammad Falakmasir and Kevin Ashley); (91) Matrix Factorization Feasibility for Sequencing and Adaptive Support in Intelligent Tutoring Systems (Carlotta Schatten, Ruth Janning, Manolis Mavrikis and Lars Schmidt-Thieme); (92) Microgenetic Designs for Educational Data Mining Research (Taylor Martin, Nicole Forsgren Velasquez, Ani Aghababyan, Jason Maughan and Philip Janisiewicz); (93) Mining and Identifying Relationships among Sequential Patterns in Multi-Feature, Hierarchical Learning Activity Data (Cheng Ye, John Kinnebrew and Gautam Biswas); (94) Mining Coherent Evolution Patterns in Education through Biclustering (André Vale, Sara C. Madeira and Claudia Antunes); (95) Mining Multi-Dimensional Patterns for Student Modelling (Andreia Silva and Claudia Antunes); (96) Mining Reading Comprehension Within Educational Objective Frameworks (Terry Peckham and Gordon McCalla); (97) Mining Students' Strategies to enable Collaborative Learning (Sergio Gutierrez-Santos, Manolis Mavrikis and Alexandra Poulovassilis); (98) Modeling Student Socioaffective Responses to Group Interactions in a Collaborative Online Chat Environment (Whitney Cade, Nia Dowell, Art Graesser, Yla Tausczik and James Pennebaker); (99) Now We're Talkin': Leveraging the Power of Natural Language Processing to Inform ITS Development (Laura Allen, Erica Snow and Danielle McNamara); (100) Peer Assessment in the First French MOOC: Analyzing Assessors' Behavior (Matthieu Cisel, Rémi Bachelet and Eric Bruillard); (101) Peer Influence on Attrition in Massively Open Online Courses (Diyi Yang, Miaomiao Wen and Carolyn Rose); (102) Predicting Students' Learning Achievement by Using Online Learning Patterns in Blended Learning Environments: Comparison of Two Cases on Linear and Non-Linear Model (Jeong Hyun Kim, Yeonjeong Park, Jongwoo Song and Il-Hyun Jo); (103) Predictive Performance of Prevailing Approaches to Skills Assessment Techniques: Insights from Real vs. Synthetic Data Sets (Behzad Beheshti and Michel Desmarais); (104) Recent-Performance Factors Analysis (April Galyardt and Ilya Goldin); (105) Refining Learning Maps with Data Fitting Techniques: Searching for Better Fitting Learning Maps (Seth Adjei, Douglas Selent, Neil Heffernan, Zach Pardos, Angela Broaddus and Neal Kingston); (106) Relevancy Prediction of Micro-Blog Questions in an Educational Setting (Mariheida Cordova-Sanchez, Parameswaran Raman, Luo Si and Jason Fish); (107) Singular Value Decomposition in Education: A Case Study on Recommending Courses (Fábio Carballo and Claudia Antunes); (108) The Predictive Power of SNA Metrics in Education (Diego García-Saiz, Camilo Palazuelos and Marta Zorrilla); (109) Data-Driven Curriculum Design: Mining the Web to Make Better Teaching Decisions (Antonio Moretti, Jose Gonzalez-Brenes and Katherine McKnight); (110) Towards IRT-Based Student Modeling from Problem Solving Steps (Manuel Hernando, Eduardo Guzmán, Sergey Sosnovsky, Eric Andres and Susanne Narciss); (111) Towards Uncovering the Mysterious World of Math Homework (Mingyu Feng); (112) Towards Using Similarity Measure for Automatic Detection of Significant Behaviors from Continuous Data (Ben-Manson Toussaint, Vanda Luengo and Jérôme Tonetti); (113) Using Data Mining to Automate ADDIE (Fritz Ray, Keith Brawner and Robby Robson); (114) Using Multimodal Learning Analytics to Study Learning Mechanisms in Hands-on Environments (Marcelo Worsley and Paulo Blikstein); (115) Using Problem Solving Times and Expert Opinion to Detect Skills (Juraj Nižnan, Radek Pelánek and Jirí Rihák); (116) Toward Collaboration Sensing: Multimodal Detection of the Chameleon Effect in Collaborative Learning Settings (Bertrand Schneider); (117) The Use of Student Confidence for Prediction & Resolving Individual Student Knowledge Structure (Charles Lang); (118) Nonverbal Communication and Teaching Performance (Roghayeh Barmaki); (119) Data-Driven Feedback Beyond Next-Step Hints (Michael Eagle and Tiffany Barnes); (120) E3: Emotions, Engagement and Educational Games (Ani Aghababyan); (121) MOOC Leaner Motivation and Learning Pattern Discovery--A Research Prospectus Paper (Yuan Wang); and (122) Personalization and Incentive Design in E-learning Systems (Avi Segal). Workshops presented include: (1) Graph-based Educational Data Mining (G-EDM) (Collin F. Lynch, Tiffany Barnes); (2) Non-Cognitive Factors & Personalization for Adaptive Learning (NCFPAL@EDM) (Steven Ritter, Stephen E. Fancsali); (3) Approaching Twenty Years of Knowledge Tracing: Lessons Learned, Open Challenges, and Promising Developments (Michael Yudelson, José P. González-Brenes, Michael Mozer); and (4) Feedback from Multimodal Interaction in Learning Management Systems (Lars Schmidt-Thieme, Arvid Kappas, Carles Sierra, Emanuele Ruffaldi). References are included in each presentation.

This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students' understandings of growing patterns. Indigenous students in Year 2 and 3 (n = 16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced.