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In this paper the methodological steps taken in the conception of a new mobile application (app) are introduced. This app, called VISP (Videos for Speaking), is easily accessible and manageable, and is aimed at helping students of English as a Foreign Language (EFL) to improve their idiomaticity in their oral production. In order to do so, the app invites the user to make the Audio-Description (AD) of a clip, as part of a communicative task. This paper gives an account of the processes followed after creating and testing VISP, until arriving at the conception of its second version, VISP 2.0. This was accomplished by carrying out several empirical tests to evaluate the app and the learning outcomes it contributes to achieve. The data obtained to date have led to the proposal of some pedagogical guidelines that can be applied to a Mobile-Assisted Language Learning (MALL) app in order to make it enjoyable and, above all, effective. [For full proceedings, see ED564162.]

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided. Plenary lecture papers include: (1) Mathematics, didactical engineering and observation (G. Brousseau); (2) A Semiotic View of the Role of Imagery and Inscriptions in Mathematics Teaching and Learning (N. Presmeg); (3) School Mathematics as a Developmental Activity (S. Stech); and (4) PME 1 to 30--Summing Up And Looking Ahead (P. Tsamir and D. Tirosh). Plenary panel papers include: (1) The Necessity of Collaborations between Mathematicians and Mathematics Educators (Z. Gooya); (2) Generic versus Subject Specific Pedagogy (S. Groves); (3) How Can Schools Put Mathematics in Their Centre? (K. Krainer); and (4) Mathematics in the Centre (T. Rojano). The first research forum (RF01) includes: (1) Seeing More and Differently (L. Brown and A. Coles); (2) Joint Reflection as a Way to Cooperation between Researchers and Teachers (A. Hospesova, J. Machackova, and M. Ticha); (3) Opening the Space of Possibilities (A. Lebethe, N. Eddy, and K. Bennie); (4) Diverse Roles, Shared Responsibility (J. Novotna and A. Pelantova); (5) Research with Teachers (L. Poirier); (6) Developing a Voice (G. Rosen); and (7) Learning about Mathematics and about Mathematics Learning through and in Collaboration (V. Zack and D. Reid). The second research forum (RF02) includes: Exemplification in Mathematics Education (L. Bills, T. Dreyfus, J. Mason, P. Tsamir, A. Watson, and O. Zaslavsky). The third research forum (RF03) includes: (1) Conceptual Change in Mathematics Learning (D. Tirosh and P. Tsamir); (2) Aspects of Students' Understanding of Rational Numbers (X. Vamvakoussi and S. Vosniadou); (3) Conceptual Change in the Number Concept (K. Merenluoto and E. Lehtinen); (4) The Linear Imperative (W. Van Dooren, D. De Bock, and L. Verschaffel); (5) Conceptual Change in Advanced Mathematical Thinking (I. Biza and T. Zachariades); (6) Students' Interpretation of the Use of Literal Symbols in Algebra (K. P. Christou and S. Vosniadou); (7) The Dilemma of Mathematical Intuition in Learning (L. B. Resnick); and (8) Designing for Conceptual Change (B. Greer). Short oral communications papers include: (1) The Mathematics Teachers' Conceptions about the Possible Uses of Learning Objects from RIVED-Brazil Project (C. A. A. P. Abar and L. S. de Assis); (2) On the Way to Understanding Integration (S. Abdul-Rahman); (3) The Impact of Graphic-Calculator Use on Bedouin Students' Learning Functions (M. Abu-Naja and M. Amit); (4) How to Put It All Together? (M. Alagic); (5) Reading Mathematics Textbook as a Storybook (S. E. Anku); (6) Naming and Referring to Quantities When Solving Word Problems in a Spreadsheet Environment (D. Arnau and L. Puig); (7) If It Divides by 4, It Must Divide by 8 (J. Back); (8) Universal and Existential Mathematical Statements (R. Barkai, T. Dreyfus, D. Tirosh, and P. Tsamir); (9) Situtations, Linear Functions and the "Real World" (G. Benke); (10) The Relationship between High School Mathematics and Career Choices among High Achieving Young Women (S. B. Berenson, J. J. Michael, and M. Vouk); (11) Students' Understanding of Ambiguity in Symbols (K. P. Blair); (12) Reform-Oriented Teaching Practices and the Influence of School Context (J. Bobis and J. Anderson); (13) Approaching Linear (In)Dependence with Example-Generation (M. Bogomolny); (14) Metaphors in Teacher's Discourse (J. Bolite Frant, V. Font, and J. Acevedo); (15) Designing Instructional Programs that Facilitate Increased Reflection (J. Bowers and S. Nickerson); (16) Conformism in Teaching Mathematics (A. Braverman, P. Samovol, and M. Applebaum); (17) Constructing Multiplication (J. Brocardo, L. Serrazina, and I. Rocha); (18) The Trigonometric Connection (S. A. Brown); (19) Student Beliefs and Attitudes from Poetry Writing in Statistics (M. Bulmer, B. Lea, and K. Rolka); (20) The Teaching of Proof in Textbooks (R. Cabassut); (21) Classroom: A Learning Context for Teachers (A. P. Canavarro); (22) An Investigation of Differences in Performance in Mathematics between Parallel Students and Normal Entry Students at the Polytechnic--University of Malawi (P. C. Chamdimba); (23) A Study on Eliciting the Formula for the Area of Triangle from Students' Structuring of Tile Arrays and Figure Reconstructions (J.-H. Chen and S.-K. S. Leung); (24) Decision Making at Uncertainty (E. Chernoff and R. Zazkis); (25) A Study on Implementating Inquiry-Based Teaching to Facilitate Secondary School Students' Learning in the Retaking Mathematics Course (E.-T. Chin, C.-Y. Chen, C.-Y. Liu, and C.-P. Lin); (26) Girls Excelled Boys in Learning Geometric Transformation Using Tessellations (S. Choi-Koh and H. Ko); (27) A National Survey of Young Children's Understanding of Basic Time Concepts (J. Chung and C.-C. Yang); (28) An Exploration of the Mathematical Literacy of Irish Student Primary School Teachers (D. Corcoran); (29) Mathematics Teachers' Knowledge and Practice (J. P. da Ponte and O. Chapman); (30) Psychological Aspects of Students Thinking at the Stage of Graphical Representation in the Process of Investigation of Functions (M. Dagan); (31) Formative Feedback and Mindful Teaching of Undergraduate Mathematics (G. E. Davis and M. A. McGowen); (32) Mathematics Education in the South and Western Pacific (A. J. Dawson); (33) Teacher Meditation of Technology-Supported Graphing Activity (R. Deaney, S. Hennessy, and K. Ruthven); (34) A Categorization of Difficulties Encountered by 13-to-15-Year-Olds while Selecting Inverse Algebraic Operation (A. Demby); (35) "It's Infinity" (T. Dooley); (36) What Is to Be Known? (J.-P. Drouhard); (37) "The Most Normal Path" (M. Droujkova, S. Berenson, G. Mojica, K. Slaten, and H. Wilson); (38) Exploratory Mathematics Talk in Friendship Groups (J.-A. Edwards); (39) Conceptual Basis of Proof (L. D. Edwards); (40) In-Service Education under Market Conditions (L. R. Ejersbo); (41) Statements of Problems and Students' Choices between Linear or Non-Linear Models (C. Esteley, M. Villarreal, and H. Alagia); (42) Equity and Quality Mathematics Education (G. Frempong); (43) Is Sensitivity for the Complexity of Mathematics Teaching Measurable? (T. Fritzlar); (44) By Using the Outcome-Based Approach to Strengthen Students' Learning Capabilities (A. T.-F. Fung and K.-M. Leung); (45) Patterns of Students' Interactions while Doing Geometric Proofs in Groups (F. L. Gallos); (46) Dialogue: A Tool for Creating Mathematical Proof (S. Gholamazad); (47) Beginning Teachers in Mathematical Inquiry (B. Graves and C. Suurtamm); (48) Learning Trajectory of Fraction in Elementary Education Mathematics (S. Hadi); (49) Elementary Education Students' Affect towards and Advancement in Mathematics (M. S. Hannula, R. Kaasila, E. Pehkonen, and A. Laine); (50) Pre-Service Mathematics Teachers (B. Hartter and J. Olson); (51) Effectiveness of Video-Case Based Elementary Mathematics Teacher Training (R. Huang and J. Bao); (52) Improving Students' Level of Geometrical Thinking through Teacher's Regulating Roles (M. Imprasitha); (53) What's the Connection between Ears and Dice (I. Jan and M. Amit); (54) Tactile Perception in 3D Geometry (D. Jirotkova and G. Littler); (55) High Achieving Students' Conceptions of Limits (K. Juter); (56) Reading Visual Representations of Data with Kindergarten Children (S. Kafoussi); (57) Students' Use of Gestures to Support Mathematical Understandings in Geometry (L. H. Kahn); (58) Mathematical Abilities for Developing Understanding of Formal Proof (E. Kapetanas and T. Zachariades); (59) An Analysis of Connections between Errors and Prior Knowledge in Decimal Calculation (J. Kim, J. Pang, and K. Song); (60) Insights into Primary Teachers' Interpretations of Students' Written Answers in Mathematics (A. Klothou and H. Sakonidis); (61) The Role of Proof (S. Kmetic); (62) A Comparison of Mathematically Gifted and Non-Gifted Students in Intuitively Based, Probabilistic Misconception (E. S. Ko, B. H. Choi, and E. H. Lee); (63) Exploring Teaching and Learning of Letters in Algebra (A. Kullberg and U. Runesson); (64) Teaching Mathematics to Indigenous Students and Pupils from Multicultural Backgrounds (E. K. Lam); (65) Limitations of a Partitive Fraction Scheme in Developing Multiplicative Reasoning about Fractions (H. S. Lee); (66) Teachers' Reflection and Self-Assessment through the Use of a Videotape of Their Own Mathematics Instruction (S. Lee and J. Pang); (67) A Case Study on the Introducing Methods of the Irrational Numbers Based on the Freudenthal's Mathematising Instruction (Y. R. Lee); (68) A Case Study of an Elementary School Teacher's Professional Development on Mathematics Teaching in Context (Y.-C. Leu, C.-H. Hsu, and W.-L. Huang); (69) "But after All, We'll Need This for School" (N. Leufer and S. Prediger); (70) Developing Primary Students' Cognitive Skills through Interactive Mathematics Lessons (K.-M. Leung); (71) A Study on the Effects of Multiple Representation Curriculum on Fraction Number Learning Schemes for Fourth Grade Children (S.-K. S. Leung and I.-J. Wang); (72) Teachers' Knowledge about Definitions (E. Levenson and T. Dreyfus); (73) Supporting Teachers on Maintaining High-Level Instructional Tasks in Classroom by Using Research-Based Cases (P.-J. Lin); (74) Towards an Anti-Essentialist View of Technology in Mathematics Education (B. Lins and C. H. de Jesus Costa); (75) Comparing Teaching of Common Mathematical Tasks in Different Countries (G. Littler and M. Tzekaki); (76) New Approach of Neurocognition in Mathematical Education Research and further Implications (C. Liu, F.-L. Lin, and C.-N. Dai); (77) Reasoning and Generalizing about Functional Relationship in a Grade 2 Classroom (S. London McNab); (78) The MathematicalPerformances in Solving the Norming Problem (H.-L. Ma); (79) The Education of Reasoning (E. Macmillan); (80) The Effect of Rephrasing Word Problems on the Achievements of Arab Students in Mathematics (A. Mahajne and M. Amit); (81) An Approach to Eary Algebra Using Technology as an Enhancement (C. A. Maher and G. Gjone); (82) Teachers' Beliefs and Competencies of Creative Mathematical Activities (B. Maj); (83) Manipulative Representation (N. Mark-Zigdon and D. Tirosh); (84) Language, Power and Mathematics Learning (M. Mathye and M. Setati); (85) Children Learning as Participation in Web-Based Communities of Practice (J. F. Matos and M. Santos); (86) Recognizing Mathematical Competences (J. F. Matos, M. Santos, and M. Mesquita); (87) Mathematics Teachers' Preparation Program (A. S. Md. Yunus, R. Hamzah, H. Ismail, S. K. S. Hussain, and M. R. Ismail); (88) Mathematics Register Acquisition (T. Meaney); (89) Development of Spatial Abilities (H. Meissner); (90) An Encounter between Queer Theory and Mathematics Education (H. Mendick); (91) Establishing a Mathematics Learning Community in the Study of Mathematics for Teaching (J. Mgombelo and C. Buteau); (92) Talking Mathematics in a Second Language (H. Miranda); (93) Objects in Motion (I. Miranda, L. Radford, and J. G. Hernandez); (94) Researching the Appearance of Mathematical Argumentation (C. Misailidou); (95) Teachers' Pedagogical Content Knowledge in the Teaching of Quadrilaterals (I. A. C. Mok and M. Y. H. Park); (96) Out-of-School Experts in Mathematics Classes (J. Monaghan); (97) A Sequel to Trends in International Mathematics and Science Study (TIMSS), 2003, in Botswana (S. M. Montsho); (98) The Pattern and Structure Mathematics Awareness Project (PASMAP) (J. Mulligan and M. Mitchelmore); (99) Primary Pupils' Mathematics Achievement (C. Opolot-Okurut); (100) Images of Functions Defined in Pieces (R. Ovodenko and P. Tsamir); (101) A Comparative Analysis of Elementary Mathematics Textbooks of Korea and Singapore (J. Pang and H. Hwang); (102) Substitutions on Algebraic Statements, Based on Associations in Natural Reasoning (M. Panizza); (103) Virtual Learning Environments and Primary Teachers' Professional Development (M. C. Penalva-Martinez and C. Rey-Mas); (104) Cypriot Preservice Primary School Teachers' Subject-Matter Knowledge of Mathematics (M. Petrou); (105) Phenomenological Mathematics Teaching (P. Portaankorva-Koivisto); (106) Using the Debate to Educate Future Teachers of Mathematics (J. Proulx); (107) Surprise on the Way from Change of Length to Change of Area (N. Prusak, N. Hada, and R. Hershkowitz); (108) Discovering of Regularity (by 11-Years-Old Children) (M. Pytlak); (109) Using Manipulatives to Teach Students in College Developmental Math Classes about Fractions (S. L. Reynolds and E. B. Uptegrove); (110) Sixth Graders' Ability to Generalize Patterns in Algebra (F. Rivera and J. Rossi Becker); (111) Variety of Representational Environments in Early Geometry (F. Roubicek); (112) From Research on Using Problems Related to Functional Equations as Multifunctional Tools for Revealing Subject Mater Knowledge of Functions in Future Mathematics Teachers (M. Sajka); (113) Expert and Novice Primary Teachers' Intervening in Students' Mathematical Activity (H. Sakonidis, M. Kaldrimidou, and M. Tzekaki); (114) Examining Teachers' Reflections about Mathematics Teaching, Learning, and Assessment (V. M. Santos-Wagner); (115) Analyzing Students' Thought Process in Revealing Correspondence between Formulas and Geometrical Objects (P. Satianov and M. Dagan); (116) "No Need to Explain, We Had the Same" (K. Schreiber); (117) Characteristics of Malaysian Students' Understanding about Functions (S. A. Sh. Abdullah); (118) Mathematical Induction via Conceptual Representation (A. Sharif-Rasslan); (119) Exploring the Meanings of Events in Mathematics Classroom from Learners' Perspective (Y. Shimizu); (120) A Study on the Law of Large Numbers Instruction through Computer Simulation (B.-M. Shin and K.-H. Lee); (121) Mathematics Learning Quality for Gifted Junior High School Students in Taiwan (H.-Y. Shy, C.-H. Liang, and W.-M. Liang); (122) A Preservice Teacher's Growth in Subject Matter Knowledge while Planning a Trigonometry Lesson (K. M. Slaten); (123) Comparing Numbers: Counting-Based and Unit-Based Approaches (H. Slovin); (124) Mathematically Gifted 6th Grade Korean Students' Proof Level for a Geometric Problem (S Song, Y. Chong, J. Yim, and H. Chang); (125) Probability Reasoning Level of Gifted Students in Mathematics (S. Song, K. Lee, G. Na, and D. Han); (126) Analysis of Mathematically Gifted 5th and 6th Grade Students' Process of Solving "Straight Line Peg Puzzle" (S. Song, J. Yim, Y. Chong, and J. Kim); (127) Standard Mathematics Discourses of Developmental Algebra Undergraduates (S. K. Staats); (128) Novice Students, Experienced Mathematicians, and Advanced Mathematical Thinking Processes (E. Stadler); (129) The "Soil" of Extended Problems: The Cultural Background of the Chinese Mathematics Teaching Practice (X. Sun and N.-Y. Wong); (130) Immersion in Mathematical Inquiry: The Experiences of Beginning Teachers (C. Suurtamm and B. Graves); (131) The Whole Idea (S. Tobias); (132) The Teaching Modes (R. A. Tomas Ferreira); (133) Didactic Decisions (J. Trgalova and I. Lima); (134) Evaluating a Large-Scale National Program for Incorporating Computational Technologies to Mathematics Classrooms (M. Trigueros and A. I. Sacristan); (135) Symmetry: Equality or a Dynamic Transformation? (K. Tselepidis and C. Markopoulos); (136) Teaching Children to Count (F. Turner); (137) Student Conceptions and Textbook Messages (B. Ubuz); (138) Students' Errors in Transforming Terms and Equations (A. Ulovec and A. Tollay); (139) Mathematics with Technology (S. Ursini, G. Sanchez, and D. Santos); (140) Francisca Uses Decimal Numbers (M. E. Valedmoros Alvarez and E. F. Ledesma Ruiz); (141) Development of Numerical Estimation in Grade 1 to 3 (M. van Galen and P. Reitsma); (142) Mathematics Education and Neurosciences (MENS) (F. van Nex and T. Gebuis); (143) Symbolizing and Modeling to Promote a Flexible Use of the Minus Sign in Algebraic Operations (J. Vlassis); (144) An Analysis of Preservice Teachers' Estimation Strategies within the Context of Whole Numbers, Fractions, Decimals, and Percents (T. N. Volkova); (145) What Does It Mean to Interpret Students' Talk and Actions? (T. Wallach and R. Even); (146) The Research of Co-Teaching Math between Experienced and Preservice Teachers in Elementary School (J.-H. Wang); (147) The Influence of Teaching on Transforming Math Thinking (T.-Y. Wang and F.-J. Hsieh); (148) Searching for Common Ground (J. Watson, L. Webb, L. King, and P. Webb); (149) Are Beliefs and Practices Congruent or Disjoint? (L. Webb and P. Webb); (150) Working Memory and Children's Mathematics (M. Witt and S. Pickering); (151) Mathematics Education Reform in the United States (T. Wood); (152) A Modeling Perspective on Problem Solving in Students' Mathematics Project (F.-M. Yen and C.-K. Chang); and (153) Development of a Questionnaire to Measure Teachers' Mathematics-Related Beliefs (S.-Y. Yu and C.-K. Chang). Poster presentations include: (1) A Comparative Analysis of Mathematics Achievement and Attitudes of Male and Female Students in Botswana Secondary Schools (A. A. Adeyinka); (2) Logical-Mathematical Learning for Student with Down's Syndrome (R. M. Aguilar, A. Bruno, C. S. Gonzalez, V. Munoz, A. Noda, and L. Moreno); (3) The Math Fair as a Bridge between Mathematics and Mathematics Education, the University and Elementary or Junior High School (M. Beisiegel); (4) One Teaching Episode from a Learner's, an Observer's and a Teacher's Point of View (H. Binterova and J. Novotna); (5) A Framework for Studying Curricular Effects on Students' Learning (J. Cai and J. C. Moyer); (6) Preservice Elementary Teachers' Conceptual Understanding of Word Problems (O. Chapman); (7) Mathematics Education and School Failure (P.Chaviaris and S. Kafoussi); (8) Enhancing the Seventh Graders' Learning on Equality Axiom and Linear Equation through Inquiry-Oriented Teaching and Integrated Mathematics and Science Curriculum (K.-J. Chen, S.-Y. Yu, E.-T. Chin, and H.-L. Tuan); (9) To Conjecture the Staff Development Model of Mathematical Teacher According to Spark's Theory (Y.-T. Chen and S. Leou); (10) Discovery of Implementing Teaching by Discussion in Mathematics Classrooms (J. Chung); (11) Modeling Teachers' Questions in High School Mathematics Classes (S. Dalton, G. Davis, and S. Hegedus); (12) My Assistant, a Didactic Tool of Mathematics for Primary School Teachers (N. de Bengoechea-Olguin); (13) A Model to Interpret Teacher's Practices in Technology-Based Environment (N. C. Dedeoglu); (14) The Gnomon (P. Delikanlis); (15) The Teacher's Proactive Role in the Context of Word Problem Solving by Young Beginners in Algebra (I. Demonty); (16) Students' Geometrical Thinking Development at Grade 8 in Shanghai (L. Ding and K. Jones); (17) An Interdisciplinary Perspective on Learning to Teach Mathematical Writing (H. M. Doerr, K. Chandler-Olcott, and J. O. Masingila); (18) Multiplication Models (D. Droujkov and M. Droujkova); (19) Quantitative Grids and Cyclic Patterns (D. Droujkov and M. Droujkova); (20) Learners' Influence in Computer Environments (M. Droujkova nd D. Droujkov); (21) Alleviating Obstructions to Learning (D. Easdown); (22) Knowledge and Interpretation of Teachers to the School Content of Proportionality (H. Enriquez Ramirez and E. Jimenez de la Rosa Barrios); (23) Mathematical Flexibility in the Domain of School Trigonometry (C. Fi); (24) "Moving Fluidly among Worlds" (S. Gerofsky); (25) Making Practice Studyable (H. Ghousseini and L. Sleep); (26) Cognitive Roots for the Concept of Asymptote (V. Giraldo, M. Chaves, and E. Belfort); (27) Flemish and Spanish High School Students' Mathematics-Related Beliefs Systems (I. M. Gomez-Chacon, P. Op't Eynde, and E. De Corte); (28) Cube Nets (M.Hejny and D. Jirotkova); (29) From Word Notation of Relations between Constants and Unknown to Algebraic Notation (Pretest) (J. Herman); (30) Mathematics and Community Capacity Building (P. Howard and B. Perry); (31) A Study on the Mathematical Thinking in Learning Process (C.J.-Hsieh and F.-J. Hsieh); (32) A Case Study on Pre-Service Teachers Making Mathematical Model of Voronoi-Diagram (C.-T. Hu and T.-Y. Tso); (33) A Fast-Track Approach to Algebra for Adults (R. Hubbard); (34) The Validity of On-Screen Assessment of Mathematics (S. Hughes); (35) After Using Computer Algebra System, Change of Students' Rationales and Writing (I. K. Kim); (36) Using a Socrates' Method in a Course of Mathematics Education for Future Mathematics Teachers (N. H. Kim); (37) Beyond Visual Level (G. Kospentaris and T. Spirou); (38) Videopapers and Professional Development (T. Lima Costa and H. Nascentes Coelho); (39) Concurrent Calibration Design for Mathematics Learning Progress Investigation (C.-J. Lin, P.-H. Hung, and S. Lin); (40) Further Insights into the Proportion Reasoning and the Ratio Concept (C. Liu, F.-L. Lin, W. Kuo, and I.-L. Hou); (41) Coursework Patterns between Mathematics and Science among Secondary Students (X. Ma); (42) Beginning the Lesson (C. Mesiti and D. Clarke); (43) Development of Web Environment for Lower Secondary School Mathematics Teachers with 3D Dynamic Geometry Software (M. Miyazaki, H. Arai, K. Chino, F. Ogihara, Y. Oguchi, and T. Morozumi); (44) The Effect of the Teacher's Mode of Instruction inside Math Classrooms with a Computer (S. Mochon and M. E. F. Olvera); (45) Mathematics Education in Rural Schools (J. Mousley and G. Marks); (46) Mathematically Gifted Students' Conception of Infinity (G. Na and E. Lee); (47) A Good Moment in Time to Stop "Shying Away from the Nature of Our Subject"? (E. Nardi); (48) Toward Real Change through Virtual Communities (K. T. Nolan); (49) Powerful Ideas, Learning Stories and Early Childhood Mathematics (B. Perry, E.Harley, and S. Dockett); (50) Tracing the Development of Knowledge about Mathematics Teaching (C. Rey-Mas and C. Penalva-Martinez); (51) Preschool Children's Number Sense (L. de C. Ribeiro and A. G. Spinillo); (52) A First Approach to Students' Learning of Mathematical Contents (G. Sanchez-Matamoros and I. Escudero); (53) Young Children's Mathematics Education within a Philosophical Community of Inquiry (A. Sawyer); (54) Learning Mathematics in Austria (H. Schwetz and G. Benke); (55) The Influence of a Mathematician on His Students' Perceptions (A. Sharif-Rasslan); (56) Analysis on the Algebraic Generalization of Some Korean Mathematically Promising Elementary Students (S. Song, J. Yim, Y. Chong, and E. Park); (57) Students' Linguistic Strategies for Shared Authority in Undergraduate Algebra Discussions (S. Staats); (58) Contrasting Decimal Conceptions of Adult and School Students (K. Stacey and V. Steinle); (59) Mathematical Writing and the Development of Understanding (N. Stehlikova); (60) Enhancing Teachers' Professional Development through Developing Teaching Norms Based on Developing Classroom Learning Norms (W.-H. Tsai); (61) The Features in the Process of Mathematical Modeling with Dynamic Geometric Software (T.-Y. Tso); (62) Finding Instructive Characteristics of Picture Books that Support the Learning of Mathematics (S. van den Boogaard and M. van den Heuvel-Panhuizen); (63) High School Course Pathways of High Achieving Girls (P. H. Wilson, G. F. Mojica, K. M. Slaten, and S. B. Berenson); (64) The Developmental Stages of Representations of Simple Regular Space Figures of Elementary School Students (D.-B. Wu, J.-L. Ma, and D.-C. Chen); (65) How to Assess Mathematical Thinking? (S. Yesildere and E. B. Turnuklu); and (66) Lasting Effects of a Professional Development Initiative (S. Zehetmeier). (Individual papers contain references.)