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This paper reviews the research on mathematics teacher education and mathematics education reform to provide a possible foundation for educating mathematics teachers in rural Appalachia. The paper takes the position that teacher change has certain characteristics and impediments that are not limited to any particular circumstance. Research on elementary mathematics teachers in various countries reveals teacher misconceptions and lack of knowledge about mathematics, their difficulty in appreciating its connectedness, and their beliefs about mathematics as a frightening subject. Research on secondary mathematics teachers suggests that secondary teachers' beliefs about mathematics and the intensity of their beliefs impede reform efforts. Commonalities found in research into preservice and inservice teacher education focus on difficulties teachers have in knowing mathematics, knowing about mathematics, and knowing about the teaching of mathematics. From these commonalities, three principles are identified for teaching mathematics to preservice teachers: that preservice teachers should experience mathematics as a pluralistic subject, should explicitly study and reflect on school mathematics, and should experience mathematics in ways that support the development of process-oriented teaching styles. Barriers to school improvement in rural areas are discussed, followed by implications of the rural circumstance for improved teaching/learning of mathematics and improved training of rural mathematics teachers. (Contains 60 references.) (SV)

At the beginning of the new century, education of students faces an ambitious task, namely to realize the vision in which an individuals and institutions, all around the world, appreciate learning, not only as means of accomplishing an aim, but as an aim itself. To pursue the realization of that aim, Department for Educational and Psychological Training at Faculty of Arts in Osijek, has organized an international scientific seminar on Modern Teaching. Teaching is the central topic of the seminar, with emphasis on communication in teaching process, different approaches to the lesson plans, lesson realization and lesson evaluation. All aspects of educational system have been taken into consideration: pre-school education, primary school, secondary school and undergraduate university education. Partly, the works presented here have been directed towards theoretical analysis, and partly towards empirical approach. Collected papers give a survey on a nine-year primary school system in The Republic of Slovenia, as well as a comment on the changes that were brought along by the new educational system in Slovenia. This Collection of papers (further in the text--Collection) also deals with the issues of students' satisfaction with their studies and students' study interests. There is also a mention of the influence of constructivism, a scientific approach in pedagogy, on education of pre-school teachers. Communication in teaching process has been examined, as well as the realistic situation in primary schools. Modern education requires students' active participation in the educational process, and Collection attempts to present the realistic situation in our schools. Theory and practice in teachers' education have also been presented here. Collection points to the necessity of a practical training in the education of future teachers and to the importance of keeping the pace with modern trends in their education. Modern teaching includes all factors of education; therefore Collection examines the importance of cooperation between parents and teachers. What is also stressed here is the irreplaceable role of teachers and parents in the upbringing process. Children's rights are foundation of modern teaching, and they have become one of the everyday-school problems. One of the tasks of the modern education is to develop intercultural awareness, tolerance and prevention of discrimination, stereotypes and prejudices. Modern teaching brings along different changes and challenges, and Collection demonstrates how it influences children's value system. Another important issue mentioned in Collection is the necessity of setting precise evaluation standards for all aspects of educational activities. Teaching mathematics, as well as other natural sciences, particularly requires the modernization of education of its teachers and introduction of the new teaching technologies. Art education is still an important part of education. The influence of gender in development of artistic skills has been also presented here. Papers include: (1) Teaching in a Nine-Year Primary School in the Republic of Slovenia (Milena Ivanus Grmek); (2) Students' Study Interests and Satisfaction with Study (Marko Palekcic and Izabela Soric); (3) Constructivism and Education of Pre-School Teachers (Nada Babic and Stanislava Irovic); (4) Teaching as a (Non-)Mutual Process (Adelka Peko and Marija Sablic); (5) Paradoxes in Teaching and Learning: Synthesis of Theoretical Knowledge, Practical Experience and Personal Reflection (Marija Bratanic); (6) Teachers and Parents as Promoters of Learning and Responsible Behavior in Children (Sofija Vrcelj and Jasminka Zlokovic); (7) Cooperation Between Parents and School (Vesnica Mlinarevic and Edita Boric); (8) Contemporary Teaching and Teaching Values (Emerik Munjiza and Blanka Skender); (9) Contemporary Teaching: Intercultural Paradigms (Neven Hrvatic); (10) Precise Evaluation Standards--Conditions for Successful Teaching (Edita Boric and Andelka Peko); (11) Initial Natural Science and the Use of Contemporary Educational Technology (Samo Fosnaric); (12) Teachers' Contribution to the Modernization of Teaching Mathematics (Margita Pavlekovic and Zdenka Kolar-Begovic); (13) The Role of Gender in the Innovative Approach to the Evaluation of Fine Arts in the Primary School (Matjaz Duh); (14) Art Education: About Students' Spacial Experience in Contemporary Visual Media World (Beatriz Tomsic-Cerke); (15) Didactic Foundations for Visual Art Education (Tonka Tacol); and (16) Effectiveness of Different Methods in Developing the Feeling for Common Meters (Janja Crcinovic Rozman). (Individual papers contain tables, graphs, and references.) [This proceedings was published by the University Josip Juraj Strossmayer in Osijek, Faculty of Philosophy in Osijek. Abstract modified to meet ERIC guidelines.]

Elizabeth City State University (ECSU) serves the 21 counties of rural northeastern North Carolina. In Fall 2000 ECSU administrators met with educators in area school districts to discuss their professional development needs. This paper reports on those expressed needs relevant to mathematics education and discusses ways to help achieve excellence in rural mathematics education. Among the challenges identified were (1) implementing state standards, aligning curricular materials with standards, and aligning preservice and inservice teacher education with the standards and school curricula; (2) connecting mathematics education to students' everyday lives by basing curriculum in local resources, environment, and events; and (3) desire of teachers to increase their mathematics content knowledge and improve their mathematics teaching skills. Mathematicians and mathematics educators can work together to ensure that university programs address mathematics teachers' needs and to develop resource materials. ECSU has increased the exposure of preservice teachers to mathematics courses to deepen teachers' understanding of the mathematics they will teach. In addition, ECSU professors are developing interdisciplinary modules for preservice teachers focused on analysis of research data collected in the nearby Great Dismal Swamp. Other strategies include involvement of mathematicians in mentoring or coaching programs for teachers, college-school collaboration to provide opportunities to discuss research and best practices in mathematics education, and development of university-school-community college partnerships to maximize resources for rural community schooling. (Contains 29 references.) (SV)

Action research, one of the requirements in undergraduate program in education, is a systematic approach that enables teachers to solve problems they face in their classes on a daily basis. Participants in this study are students in their final semester of a three-year teacher preparation program and graduates in their first-year teaching. The study discusses mathematics and science preservice teachers and novice teachers' beliefs and thoughts about their benefits of action research as a means of professional growth and teaching skills. It reports feedback from the two groups about the impact of doing action research on: (a) their learning about action research, (b) their thinking and problem-solving skills, (c) their professional growth, (d) their self-efficacy, (e) their outcome efficacy, (f) their beliefs about whether or not action research is applicable to their future as teachers. Participants views are studied and compared by the mean of a questionnaire that measures the previously mentioned categories. Scores for the six categories were computed by using descriptive statistics for each one of them. [For the full proceedings, see ED652261.]

Over the last two decades, researchers have portrayed quality professional development for mathematics teachers as collaborative and situated in teachers' instructional realities. However, empirical findings also point out various impediments to transforming teacher conversations into consequential learning. These findings illuminate the need to acknowledge additional resources that teachers bring to professional interactions and the need for ever more nuanced theories of teacher learning to inform teacher educators' work. Inspired by ecological models of learning, in this conceptual paper I work towards understanding teachers' collaborative sensemaking as part of broader teacher learning ecologies. I distinguish and name possible scopes and contexts for the study of teacher learning in conversations about instruction, and then identify directions for future research towards stronger connections between immediate and broader contexts. [For the complete proceedings, see ED630060.]

This submission contains the Proceedings of the 2012 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Laval University in Québec City, Québec. 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, a panel discussion, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) Towards an Understanding of Ethical Practical Action in Mathematics Education: Insights from Contemporary Inquiries (Margaret Walshaw); (2) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (3) Cooda, Wooda, Didda, Shooda: Time Series Reflections on CMESG/GCEDM (William Higginson); (4) Panel: What is Fundamental Mathematics for Learners? (Elaine Simmt, Darien Allan, Ralph Mason, Ruth Beatty, Peter Taylor, and Hélène Paradis); (5) Numeracy: Goals, Affordances, and Challenges (France Caron and Peter Liljedahl); (6) Diversities in Mathematics and their Relation to Equity (Beverly Caswell and David Wagner); (7) Technology and Mathematics Teachers (K-16) / La technologie et l'enseignant mathématique (K-16) (Chantal Buteau and Nathalie Sinclair); (8) La preuve en mathématiques et en classe / Proof in Mathematics and in Schools (David Reid and Denis Tanguay); (9) The Role of Text/books in the Mathematics Classroom / Le rôle des manuels scolaires dans la classe de mathématiques (Peter Appelbaum and Susan Gerofsky); (10) Preparing Teachers to Develop Algebraic Thinking in Primary and Secondary School / Préparer les enseignants au développement de la pensée algébrique au primaire et au secondaire (Hassane Squalli, Chris Suurtamm, and Viktor Freiman); (11) Collaboration Between Research in Mathematics Education and Teaching Mathematics: Case Study of Teaching Infinity in Calculus (Miroslav Lovric); (12) Dialogue sur la lecture de textes historiques dans la classe de mathématiques / Dialogue on Reading Original Texts in the Mathematics Classroom (Louis Charbonneau and David Guillemette) [Written in French]; (13) Teaching Toward Equity in Mathematics (Beverly Caswell); (14) Inequalities in the History of Mathematics: From Peculiarities to a Hard Discipline (Elena Halmaghi); (15) The Study of On-line Situations of Validation Experienced by 13- and 14-year-old Students With and Without the Aid of an Electronic Forum (Manon Leblanc); (16) Institutional Acculturation of the Researcher, Teacher, and Secondary 1 Students with Learning Difficulties in Problem Situations Involving Rational Numbers / Les effets d'une démarche d'acculturation sur l'action didactique conjointe de l'enseignant, des élèves et du chercheur, dans l'enseignement/apprentissage des nombres rationnels auprès d'élèves en difficultés d'apprentissage (Geneviève Lessard) [Written in French]; (17) Mathematics Education: An Aporetic of Epistemology, Language and Ethics (Jean-François Maheux); (18) Diverse Perspectives on Teaching "Math for Teachers": Living the Tensions (Susan Oesterle); (19) Conversations Held and Roles Played During Mathematics Teachers' Collaborative Design: Two Dimensions of Interaction (Armando Paulino Preciado Babb); (20) The Ordinary Yet Extraordinary Emotions and Motives of Preservice Mathematics Teachers (Oana Radu); (21) Élaboration et analyse d'une intervention didactique, co-construite entre chercheur et enseignant, visant le développement d'un contrôle sur l'activité mathématique chez les élèves du secondaire / Development and Analysis of a Didactic Intervention, Co-constructed Between Researcher and Teacher For the Development of a Control of the Mathematical Activity Among High School Students (Mireille Saboya) [Written in French]; (22) Publishing in the Journal of Mathematics Teacher Education (Olive Chapman and Margaret Walshaw); (23) Is It Possible to Measure the Effectiveness of a Specific Approach to Teaching Foundations Mathematics in a Post-Secondary Setting? / Est-il possible de mesurer l'efficacité d'une approche spécifique à l'enseignement mathématiques fondations dans un cadre de post-secondaire? (Taras Gula); (24) Challenges in Supporting Mathematics Teachers to Develop Their Teaching Practices (Lionel Lacroix); (25) Rapport sur le ad hoc éthique et éducation mathématique / Report on the Ethics and Mathematics Education Ad Hoc (Jean-François Maheux); (26) Reading Biographies and Autobiographies of Mathematicians: What Do They Tell Us About the Subject of Mathematics? (Veda Roodal Persad); (27) Online Environments for Mathematics Sharing and Collaboration (Geoffrey Roulet); (28) Ad Hoc Session on Planning for the Next Canadian Math Education Forum (CMEF) to be Held in May 2014 (Peter Taylor); (29) Preservice Elementary Teachers' Beliefs Toward Mathematics and Mathematics Teaching (Sean Beaudette, Alexandra Penn, and Geoffrey Roulet); (30) Gearing Up For Grade 9: A Learning Object (Laura Broley); (31) Students' Perceptions of the Role of Theory and Examples in College Level Mathematics (Dalia Challita and Nadia Hardy); (32) Une expérimentation de pratiques gagnantes en enseignement des mathématiques / An Experiment with Successful Practices in Mathematics Teaching (Lucie Deblois); (33) Blended Mathematical Collaboration Using a Wiki, Geogebra and Jing (Jill Lazarus and Geoffrey Roulet); (34) Some Things Technologies Can Tell Us About Technologies: An Instrumented Analysis of Two Successive Mathematics Curricula (Jean-François Maheux and Fabienne Venant); (35) Investigating the Teaching Practices of a Group of Mathematics Graduate Students (Tod L. Shockey and Sibylle Weck-Schwarz); (36) Mathematics For Young Children: Exploring What is Possible in Early Mathematics Education? (Diane Tepylo, Joan Moss, Catherine Bruce, Tara Flynn, Diana Chang, and Zachary Hawes); and (37) Mise à l'essai d'une situation d'enseignement-apprentissage en lien avec le métier du scénographe pour favoriser l'engagement mathématique des élèves du 1er cycle du secondaire (Josianne Trudel) [Written in French]. Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, tables, and figures. [For the 2011 proceedings, see ED547245.]

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.)

Collected in this document are papers presented at a conference on designing a mathematics methods course for secondary school teachers. Papers are organized under the following categories: (1) Realistic goals for a methods course, (2) Minimal content for a methods course, and (3) Teaching strategies used in methods courses. The seven short papers included under teaching strategies cover mathematical ideas which determine strategies, micro-teaching, modular organization, laboratory approach, student-centered strategy, discovery, and tutoring skills. The document concludes with a paper discussing creativity in teaching. Methods course syllabi are collected in Appendix I, while Appendix II gives a list of conference participants. (DT)

The professional development of teachers is a task recognized by the European parliament and pursued by many institutions, both national and international ones. The support to teachers in STEM disciplines was one of the aims of the Erasmus+ SMART (Science and Mathematics Advanced Research for good Teaching) project, born in a European context, which developed as its main intellectual output two open online courses called Mathematical Modelling and Observing, Measuring and Modelling in Science, in order to help teachers in their continuous professional development. Both courses contain interactive problem-based materials ready to be downloaded, modified, used in the classroom and redistributed to the community. This paper gives an overview of the structure of the course Mathematical Modelling and analyzes its instructional quality, taking into account some measurables obtained in two years of operativity. [For the full proceedings, see ED621557.]

A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. We are studying the knowledge construction of mathematics teachers utilising multi-camera research techniques during lesson planning, classroom interactions and reflection. This paper reports on the learning of two Year 7 teachers, one in Melbourne and one in Chicago, teaching the same initial lesson focusing on division, remainders and context. Both teachers claimed to have learned about their students' mathematical thinking after teaching the initial lesson, but found planning a second lesson to accommodate this learning challenging.

Mathematics teacher educators face a challenge of preparing teachers to use technology that is rapidly changing and easily available. Teachers have access to thousands of digital tools to use with students and need guidance about how to critically choose and use tools to support students' mathematics learning. Research provides guidance to teachers about what features to look for in a technology tool and suggestions are offered about how mathematics teacher educators and researchers can support teachers in using technology to teach mathematics. [For complete proceedings, see ED581294.]

Mathematics teacher education has been criticized, both internally and externally, for failing to identify shared practices and goals within teacher preparation programs. Work has begun to address this criticism at the elementary level but less exists at the secondary level. This paper reports on a national survey with responses from 116 secondary mathematics methods course instructors from colleges and universities. The purpose of the survey was to identify those topics, or "touchstones," in secondary methods courses that are widely valued. The survey asked participants to rank 41 potential "touchstones" of secondary mathematics methods courses on a scale from one to five according to those touchstones they value most in their methods courses. The results were quantitatively and qualitatively analyzed looking for important characteristics that would spur discussion about shared goals in secondary teacher preparation. [For the complete proceedings, see ED583989.]

The research presented in this paper focuses on the cognitive diagnostic strategies that prospective elementary mathematics teachers (PTs) use in their reflections of one-on-one diagnostic interviews with children in grade one. Thereby, it responds to the detected lack of knowledge regarding qualitative facets of diagnostic proceeding in interview assessments. Results include facets of collecting data and facets of interpreting within a diagnostic micro-process. The discussion takes up the relevance of these findings for teacher education.

Effective lesson planning is a real challenge for many beginning teachers. This paper presents a case study of one such teacher, and the author's efforts to support her in the planning process. Results show supporting the beginning teacher's planning by (a) providing access to resources such as web-sites and teaching handbooks, (b) modelling, and (c) providing an explication of planning were insufficient to create substantive and necessary changes in the teacher's planning during the period of research. Implications for supporting beginning teachers are considered.

This article reports on initial findings, including the mathematics components, of a multi-institutional Science, Technology, Engineering, and Mathematics (STEM) project, "It's part of my life: Engaging university and community to enhance science and mathematics education." This project is focussed on improving the scientific and mathematical thinking of pre-service teachers (PSTs) by aligning their pedagogy with the scientific and mathematical thinking that occurs in authentic, real-world contexts. This article discusses emotional literacy and emotional regulation as aspects of self-reflective professional development and how these measures are conceptually related to improving competence and confidence for pre-service STEM teachers. This report details how emotional feedback was used in trials of a pilot program to enable PSTs to analyse, understand, and make use of emotional information to improve their teaching confidence, particularly in mathematics. [This paper reports on research associated with the project: "It's part of my life: Engaging university and community to enhance science and mathematics education," a project supported by a three-year $1 million grant awarded to the Regional Universities Network (RUN) by the Australian Government Office for Learning and Teaching (OLT).]

There has been limited attention to early career teachers' (ECTs) understandings and practices related to language in teaching and learning mathematics. In this qualitative case study, we drew upon frameworks for teacher noticing to study the language practices of six early career elementary and middle school mathematics teachers. We describe multiple themes that cut across teachers' noticing related to language and language learners, and discuss one theme (i.e., Perspectives on multiple languages) in more detail, including evidence of specific forms of noticing. Implications for teacher education and professional development are discussed. [For the complete proceedings, see ED583608.]

This paper investigates the relationship between teachers' professional vision and their classroom practices. In particular, the study finds that teachers with similar professional vision can have different classroom practices related to noticing and responding to student thinking. Data is drawn from a study in which teachers reflected on video online as well as collected video from their own classrooms. Analysis revealed two teachers with similar attention to student mathematical thinking when watching classroom videos. However, these teachers recalled noticing interesting moments of student thinking, made space for student thinking to emerge, and probed students' underlying understandings with different frequency in their classrooms. [For the complete proceedings, see ED584443.]

This paper explains the investigative attempts of The New York City Math Exchange Group (MEG) on elementary mathematics teachers' content knowledge in Adult Basic Education (ABE). The study is comparative in nature and took place in a workshop at the Adults Learning Maths Conference in Boston. The new members of the MEG professional development group were compared to the veteran members. It is observed that among the experienced MEG members, the ability to compute a division problem, create story problems, and reason mathematically and abstractly were higher than in other studies of U.S. teachers and the sample of new MEG members. It is concluded that it is only through comprehensive and ongoing staff development that all teachers can better understand, apply, and teach mathematics to their students. (SOE)

A pervasive theme running throughout a conference on mathematical education was the transformation of the learning and teaching of mathematics using technology. This publication is a collection of papers representing an American view of the events of the international conference. The papers share the views of collegiate mathematicians, elementary school teachers, teacher educators, researchers in mathematics education, middle and secondary school teachers, two-year-college faculty members, and others. The first three authors focus on the special aspects of the relationship between prior ICME meetings and higher education (S. Hill), technology and mathematics education (J. T. Fey), and assessment around the world (N. Webb). The remaining 35 papers report the activities, insights, and growth of many of the 40 individuals who received support awards for attending the Congress through a National Science Foundation grant to the National Council of Teachers of Mathematics. (MDH)

The learning and teaching of mathematics are key elements for primary school teachers, and various approaches for teaching mathematics to pre-service teachers are evident in mathematics education. This paper reports on a project to develop a critical approach to using mathematical subject knowledge in choosing learning examples and examines data from United Kingdom pre-service teachers' lessons. The data suggests pre-service teachers have no structured method for choosing examples, which impacts on the quality of the learning experiences of students.

A current concern is student learning outcomes and these are largely a function of teachers' knowledge and their practice. This position paper is premised on the notion that certain knowledge is required for the teaching of mathematics. An exploration of literature demonstrates that such professional knowledge development can be supported by Learning Trajectories (LT). We propose to use LT as theoretical lens to examine pre-service teachers' Content and Pedagogical Content knowledge and advance a research design.

Using rehearsals and in-the-moment coaching is being explored in mathematics teacher education courses at two New Zealand universities. This paper describes the perceptions of students, gathered using questionnaires, from two classes at our institution using different approaches for incorporating rehearsals and coaching. Students believed rehearsals and coaching enabled their development as teachers and mathematical understanding by providing relevant practice, discussions, and feedback. Implications include that realistic teaching opportunities with empowering coaching interruptions are useful components of teacher education.