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This timely book provides support for secondary mathematics teachers learning how to enact high-quality, equitable math instruction with dynamic, mathematics-specific technologies. Using practical advice from their own work as well as from interviews with 23 exceptional technology-using math teachers, the authors develop a vision of teaching with technology that positions all students as powerful doers of mathematics using math-specific technologies (e.g., dynamic graphing and geometry applications, data exploration tools, computer algebra systems, virtual manipulatives). Each chapter includes sample tasks, advice from technology-using math teachers, and guiding questions to help teachers with implementation. The book offers a rich space for secondary math teachers to explore important pedagogical practices related to teaching with technology, combined with broader discussions of changing the narratives about students -- emphasizing the mathematics they can do and the mathematics they deserve. Accompanying online support materials include video vignettes of teachers and students interacting around technology-enhanced tasks in the classroom, as well as examples of more than 30 high-quality technology-enhanced tasks.

This book represents a crop of wide-ranging research conducted by renown scholars in sub-Sahara Africa revolving around mathematics teaching and professional development programs for mathematics teachers. The research-based proposals and actual how-to-conduct professional development initiatives that enhance effective mathematics instruction are rooted in teacher input and informed by learners errors and misconceptions. The book provides a comprehensive snapshot on mathematics teaching, learning and effective professional development programmes for mathematics teachers in sub-Sahara Africa. It is the only research output that advances and disseminates issues of mathematics education and research in the region with input from South Africa, Kenya, Rwanda, Uganda, Malawi, Namibia, Lesotho, Ethiopia and Zimbabwe.

This special issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) Proceedings looks at CMESG/GCEDM's collective history, reflects on where the group has been, and who the members have become as an organization. Through a selection of excerpts from past proceedings, the editors have stitched together a partial history of CMESG/GCEDM's time as an organization. This serves not only as a summary of the collective history, but also serves as an introduction to the activities of CMESG/GCEDM through the first 40 years. The pieces selected for inclusion in this special issue stand as signposts along CMESG/GCEDM's history--as exemplifications of what CMESG/GCEDM is as an organization as well as the activities of CMESG/GCEDM at annual meetings. Crafted introductions to each piece articulate the ways in which that piece exemplifies the valued aspects of CMESG/GCEDM. Following an introduction to the special issue (Peter Liljedahl) [Written in English and French], a foreword (Peter Taylor) [Written in English and French], a Preface to the 1977 CMESG Proceedings (Albert Coleman, Bill Higginson, and David Wheeler), and The Origins and Activities of CMESG (David Wheeler), this issue contains the following papers: (1) Mathematics Education Research in Canada: A Prospective View (Tom Kieren); (2) Innovations in Teacher Education Programmes (Claude Gaulin); (3) The Objectives of Mathematics Education (Albert Coleman); (4) Confessions of an Accidental Theorist (Alan Schoenfeld); (5) The Role of Epistemology in the Analysis of Teaching/Learning Relationships In Mathematics Education (Michèle Artigue); (6) Alive Mathematical Reasoning (David Henderson); (7) Toward a Practice-Based Theory of Mathematical Knowledge for Teaching (Deborah Loewenberg Ball and Hyman Bass); (8) Mathematics as Medicine (Edward Doolittle); (9) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (10) The Role of Proof in Post-Secondary Education (William Byers and Harvey Gerber); (11) From Theory To Observational Data (And Back Again) (Carolyn Kieran and Jo Towers); (12) Where Is The Mathematics? (John Mason and Eric Muller); (13) The Arithmetic/Algebra Interface: Implications For Primary And Secondary Mathematics = Articulation Arithmétique/Algèbre: implications pour l'enseignement des mathématiques au primaire et au secondaire (Nadine Bednarz and Lesley) [Written in English and French]; (14) Images Of Undergraduate Mathematics (Miroslav Lovric and David Poole); (15) A Mathematics Curriculum Manifesto (Walter Whiteley and Brent Davis); (16) Learner Generated Examples (Nathalie Sinclair, Anne Watson, and Rina Zazkis); (17) Étude des pratiques d'enseignement (Jamie Pyper, Hassane Squalli, and Laurent Theis) [Written in English and French]; (18) Mathematics of Planet Earth 2013: Education and Communication = Mathématiques de la planète terre 2013: formation et communication (Doug Franks, Kathleen Pineau, and Walter Whiteley); (19) Indigenous Ways of Knowing in Mathematics (Lisa Lunney Borden and Florence Glanfield); (20) The Commonsense of Teaching (David Wheeler); (21) A Historical Perspective on Mathematics Education Research in Canada: The Emergence of a Community (Carolyn Kieran); (22) Lessons from the Past, Questions for the Future: Méditation sur thème impose (Roberta Mura) [Written in French]; (23) Building Thinking Classrooms: Conditions for Problem Solving (Peter Liljedahl); (24) Where Do I Want Students' Attention? And What Can I Do to Affect Their Attention? (David Hewitt); and (25) Measuring the Impact of a Mentor Program (A. J. Dawson). Individual papers contain references.

"A Commitment to Teaching: Toward More Efficacious Teacher Preparation" introduces the reader to a collection of thoughtful works by authors that represent current research and thinking about teacher self-efficacy and teacher preparation. It is the intent of the book to provide the reader with current and relevant knowledge concerning preparation of committed and efficacious teachers. Teacher self-efficacy, and the presence of teacher efficacy, in teacher preparation and practice, is fundamental to preparing teachers for the public school classroom. As a construct, teacher self-efficacy beliefs are an integral aspect of the teaching process. While many authors refer to teachers' sense of self-efficacy for teaching, meaning their beliefs about their ability to perform the actions necessary to teach, many others have identified a specific form of self-efficacy pertaining to teaching. These have been called teaching or teacher efficacy. Chapter One opens the book with a focus on the teacher commitment and self-efficacy, providing the reader with an introduction. The authors of Chapters Two-Seven present field-based research that examines the complexities efficacy and commitment in the preparation of teachers. Each chapter offers the reader an examination of teacher self-efficacy and teacher preparation and based on formal research that provides the reader with insight into how the research study was conducted as well as equally important, the findings and conclusions drawn with respect teacher self-efficacy and teacher preparation. Finally, Chapter Nine presents an epilogue that focuses on the for more efficacious teacher preparation. Following the Preface and Acknowledgements, this book contains the following chapters: (1) Ensuring Teachers' Commitment and Sense of Self-efficacy: The Role of Teacher Preparation (Patrick M. Jenlink); (2) The Relationship of Hours of Teacher Preparation Programs' Field Experiences and Pre-Service Teacher Candidates' Sense of Teaching Efficacy (Alison Reddy, Shana Pribesh, Leigh Butler, and Charlene Fleener); (3) How Reflectivity Impacts Teacher Candidates' Self-efficacy (Sherri M. Weber and Julie J. Henry); (4) A Framework for Measuring Algebra Teacher Self-efficacy (Trena L. Wilkerson, M. Alejandra Sorto, William A. Jasper, Sandra Cooper, Winifred Mallam, Colleen M. Eddy, Yolanda A. Parker, Sarah Quebec Fuentes, Judy M. Taylor, and Elizabeth K. Ward); (5) Development of Chinese Teachers' Self-efficacy in Professional Learning Community (Qing Gao and Jian Wang); (6) The Role of Self-efficacy and Other Characteristics of Elementary Mathematics Teachers: A Model to Predict Student Achievement (James A. Telese, Zhidong Zhang, and Maria E. Diaz); (7) Teachers' Knowledge, Perception, Sense of Self-efficacy and Role in Mental Health for Middle School Students (Federico R. Guerra, Jr., Ashwini Tiwari, Nancy Razo, and Lionel Cavazos); and (8) Epilogue: Toward More Efficacious Teacher Preparation (Patrick M. Jenlink).

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP). Students will be exposed to the tasks used on assessments, become more confident in solving them, and see how their problem-solving ability stacks up against students nationwide. "Mathematical Thinking" includes chapters on these subjects: Number and Operations; Algebraic Thinking; Geometry and Measurement; and Data Analysis, Statistics, and Probability. Each chapter begins by explaining how its topic has been treated in the NAEP assessment and what skills its lessons are designed to build. Each activity includes the NAEP item that inspired it, sample student responses, and the percentage of students who completed it correctly. All activities include these elements: (1) Learning and performance goals, and a list of relevant Common Core standards and mathematical practices; (2) A list of materials needed--with all activity sheets and templates available for download and printing at NCTM's More4U website; (3) A step-by-step lesson plan in Launch-Explore-Summarize format, with questions and prompts to pose to students and a range of possible responses they might give; and (4) Gearing Up and Gearing Down sections to customize and extend the lessons. With these assessment-based lessons, teachers can not only help students become more adept at reaching a correct answer on tests, but they can also help them do so by becoming better mathematical thinkers and problem solvers. This book contains the following chapters: (1) Number and Operations (Peter Kloosterman, Doris Mohr, Michael Roach, and Gina Borgioli Yoder); (2) Algebraic Thinking (Sheryl Stump, Peter Kloosterman, Doris Mohr, and Shelby P. Morge); (3) Geometry and Measurement (Crystal Walcott, Mark Creager, Paula R. Stickles, and Peter Kloosterman); (4) Data Analysis, Statistics, and Probability (Shelby P. Morge, Michael Daiga, and Peter Kloosterman,).

Research evidence suggests that summer breaks contribute to income-based achievement and opportunity gaps for children and youth. However, summertime can also be used to provide programs that support an array of goals for children and youth, including improved academic achievement, physical health, mental health, social and emotional well-being, the acquisition of skills, and the development of interests. This report is intended to provide practitioners, policymakers, and funders current information about the effectiveness of summer programs designed for children and youth entering grades K-12. Policymakers increasingly expect that the creation of and investment in summer programs will be based on research evidence. Notably, the 2015 Every Student Succeeds Act (ESSA) directs schools and districts to adopt programs that are supported by research evidence if those programs are funded by specific federal streams. Although summer programs can benefit children and youth who attend, not all programs result in improved outcomes. RAND researchers identified 43 summer programs with positive outcomes that met the top three tiers of ESSA's evidence standards. These programs were identified through an initial literature search of 3,671 citations and a full-text review of 1,360 documents and address academic learning, learning at home, social and emotional well-being, and employment and career outcomes. The authors summarize the evidence and provide detailed information on each of the 43 programs, focusing on the evidence linking summer programs with outcomes and classifying the programs according to the top three evidence tiers (strong, moderate, or promising evidence) consistent with ESSA and subsequent federal regulatory guidance.

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto--secondly--the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students' engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences, combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become the best starting points to solve current and future problems. This book provides an in-depth coverage of educational innovation developments with an emphasis on educational systems, formal or informal education strategies, learning models, and professional teachers. Indeed, those developments are very important to be explored for obtaining the right way of problem-solving. Providing many ideas from the theoretical foundation into the practice, this book is versatile and well organized for an appropriate audience in the field of education. It is an extremely useful reference for students, teachers, professors, practitioners, and government representatives in many countries. Following a preface, papers in these proceedings are divided into four sections and include the following: Section One, Education System, includes: (1) Integrating Knowledge and Skills-Based Curriculum in TT-TVET through a Blended and Embedded Model: An Innovative Approach at the Faculty of Technical and Vocational Education, (Universiti Tun Hussien Onn Malaysia 3 (A.R.A. Razzaq, M.H.B. Amiruddin, M.A. Rohiat & N.B. Razali); (2) The Effectiveness of Academic Supervision by School Principals 12 (S. Darmawanti & H. Usman); (3) The Performance of State Elementary School Supervisors 18 (R.S. Maulida & H. Usman); (4) Integrated Thematic Learning in the 2013 Curriculum: Implications for the Self-Confidence and Academic Achievement of Primary School Students 24 (U. Tisngati, C.A. Budiningsih & Sugiman); (5) The Effect of Technology Literacy and Learning Environment on Student Motivation in the Educational Revolution 4.0, 32 (A. Saputri Sukirno, H. Kurniawan & H.D. Hermawan); (6) Student Perceptions of Motivational Strategies Used by Junior High School English Teachers in Kota Yogyakarta 37 (G. Ambarini & Ashadi); (7) Study on Graduate Competence in Air-Conditioning Skills at Senior High School with Relation to Job Market Competencies 45 (S. Haryadi); (8) Elementary Students' Performance in Mathematical Reasoning 52 (N. Andrijati, D. Mardapi & H. Retnawati); and (9) Evaluation Model of the Implementation of a Quality Management System of Electrical Skills in Vocational High School 59 (I.G.B. Mahendra & G. Wiyono). Section Two, Formal and Informal Education, contains: (10) Strengthening Character Education through the Local Wisdom: Indonesian Folklore 69 (T.A. Rini & P. Mahanani); (11) Forming Young Citizen Characters through Youth organizations in Indonesia 77 (Wellyana & Marzuki); and (12) Revitalization in Vocational Training Centers for Improving the Quality of Human Resources 82 ( I.A. Manalu & R. Asnawi). Section Three, Learning Models, contains the Following Papers: (13) Theatrical Stage of Technology and Humans in relation to Education 91 (T. Öztürk); (14) Improving Students' Critical Thinking Abilities in Probability Problems through Problem Based Learning 97 (Rauzah & Kusnandi); (15) Cultural Map Media as an Innovation to Overcome Cognitive Learning Difficulties in Social Studies at Elementary School 104 (L. Fatmawati, V.Y. Erviana, D. Hermawati, I. Maryani, M.N. Wangid & A. Mustadi); (16) Learning Innovations in Citizenship Education for Strengthening Digital and Ecological Citizenship 113 (K.E.R. Marsudi & S. Sunarso); (17) Needs Analysis for an Electronic Module (e-module) in Vocational Schools 122 (S. Oksa & S. Soenarto); (18) Analysis of Students' Learning Readiness in Terms of Their Interest and Motivation in Achieving Students' Critical Thinking Skills 129 (R. Putri & A. Ghufron); (19) Study on a Test Scoring System for Vocational Secondary Schools Using Computerized Adaptive Testing (CAT) 135 (F.P. Marsyaly & S. Hadi); and (20) Implementation of Basic Graphic Design Learning Skills Competence of Multimedia in SMK Muhammadiyah Wonosari 141 (L.F.A.N.F. Albana & Sujarwo). Section Four, Professional Teacher, contains the following papers: (21) Developing Video-Based Learning Resources for Music Teachers in Singapore 151 (A. Bautista, S.L. Chua, J. Wong & C. Tan); (22) Teacher-Student Communication Style and Bullying Behavior: Sociometry Evaluation 159 (I. Sholekhah, S. Indartono & D.W. Guntoro); (23) Analysis of Students' Mistakes in solving Algebra Word Problems Using the Newman Procedure 168 (R. Keumalasari & Turmudi); (24) Lesson Study as an Alternative for Teacher Creativity Development in Reflecting and Improving the Quality of Learning of the Indonesian Language 174 (R.W. Eriyanti); (25) Lesson Study to Improve Teacher Creativity in Solving Problems of Mathematics Learning 179 (Y.M. Cholily); (26) Mapping the Innovation of Professional Learning Communities (PLC) in Primary Schools: A Review 184 (P.S. Cholifah & H.I. Oktaviani); (27) Implementation of Snowball Drilling Learning Model on Discrete Mathematics to Improve Student's Independence and Learning Outcomes 190 (L. Novamizanti); (28) What Lecturers Know about Their Role as an Agent of Learning: Levels of Innovativeness in the Learning Process 197 (A. Ghufron); (29) Development and Quality Analysis of a Learning Media Electrical Motor Installation on the Android Platform, for Vocational Students 201 (B.N. Setyanto & H. Jati); (30) The Readiness of Vocational Secondary Schools on Forming Working Characteristics for Industry 4.0 209 (H. Mulyani & I.W. Djatmiko); (31) The Assessment Model for Competency Certification Tests 216 (W. Ramadani & D.L.B. Taruno); (32) Contribution of a Teacher Competency Test to Identifying Teacher Performance in Vocational High Schools 223 (U. Nursusanto & N. Yuniarti); (33) Performance in Innovative Teacher Professional Development (TPD) in Indonesia: Does Gender Matter? 231 (Wuryaningsih, M. Darwin, D.H. Susilastuti & A.C. Pierewan); (34) Needs Identification of Learning Media for People with Disabilities 237 (Rizalulhaq & R. Asnawi); and (35) Implementing Gamification to Improve Students' Financial Skills in Business and Management Vocational Schools 242 (Sukirno, E.M. Sagoro, L.N. Hidayati, Purwanto & D.A.Y Wastari). An author Index is also included.

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume's three major themes--technology, creativity, and affect--represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book's new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. "Broadening the Scope of Research on Mathematical Problem Solving" will prove to be a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

Secondary mathematics teachers are frequently required to take a large number of mathematics courses -- including advanced mathematics courses such as abstract algebra -- as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. "Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers" is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.

The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the generalizations underlying the study of the operations in the elementary and middle grades and teaching strategies that support students' efforts to make sense of the concepts. Reading and discussing the cases under the guidance of the facilitator actively engages participants in their own learning enterprise as they--(1) learn to recognize the key mathematical ideas with which students are grappling; (2) consider the types of classroom settings and teaching strategies that support the development of student understanding; (3) become aware of how core mathematical ideas develop across the grades; (4) work on mathematical concepts and gain better understanding of mathematical content; and (5) discover how to continue learning about children and mathematics. The casebook is composed of eight chapters: the first seven consist of classroom cases from kindergarten through grade 7; chapter 8 is an essay providing an overview of the research related to the situations described in the first seven chapters. The chapters are as follows: (1) Chapter 1: Discovering rules for odds and evens; (2) Chapter 2: Finding relationships in addition and subtraction; (3) Chapter 3: Reordering terms and factors; (4) Chapter 4: Expanding the number system; (5) Chapter 5: Doing and undoing, staying the same; (6) Chapter 6: Multiplying in clumps; (7) Chapter 7: Exploring rules for factors; and (8) Chapter 8: The World of Arithmetic from Different Points of View (Stephen Monk). [For part 1 "Number and Operations, Part 1: Building a System of Tens Casebook," see ED566650. For part 2: Making Meaning for Operations. Casebook," see ED594600.]

When it comes to mathematics, standards aligned is achievement aligned… In the short time since "The Common Core Mathematics Companions" for grades K-2, 3-5 and 6-8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including: (1) The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards; (2) The mathematics embedded in each conceptual category for a deeper understanding of the content; (3) How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate; (4) How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme; and (5) Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning. "The Common Core Mathematics Companion: The Standards Decoded, High School" has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know.

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic. Section 1, Foundations, contains: (1) Research: To Inform, Deform, or Reform? (Jere Confrey); (2) Linking Research and Practice in Mathematics Education: Perspectives and Pathways (Edward A. Silver and Crystal Lunsford); (3) Education Reform, Research, and Policy: Interwoven Influences on Mathematics Education in the United States (Joan Ferrini-Mundy); (4) A Taxonomy of Approaches to Learning Trajectories and Progressions (Joanne Lobato and C. David Walters); (5) The Role of Theory Development in Increasing the Subject Specificity of Research on Mathematics Teaching.(Patricio Herbst and Daniel Chazan); and (6) Exploring Different Theoretical Frontiers for Different (and Uncertain) Possibilities in Mathematics Education Research (David W. Stinson and Margaret Walshaw). Section 2, Methods, contains: (7) Qualitative Methods (Elizabeth de Freitas, Stephen Lerman, and Amy Noelle Parks); (8) Aligning Statistical Modeling With Theories of Learning in Mathematics Education Research (Finbarr C. Sloane and Jesse L. M. Wilkins); and (9) Conducting Design Studies to Investigate and Support Mathematics Students' and Teachers' Learning (Paul Cobb, Kara Jackson, and Charlotte Dunlap Sharpe). Section 3, Mathematical Processes and Content, contains: (10) Research on the Teaching and Learning of Proof: Taking Stock and Moving Forward (Gabriel J. Stylianides, Andreas J. Stylianides, and Keith Weber); (11) The Teaching and Learning of Mathematical Modeling (Gabriele Kaiser); (12) Providing Support for Student Learning: Recommendations from Cognitive Science for the Teaching of Mathematics (Jon R. Star and Lieven Verschaffel); (13) Early Number and Operations: Whole Numbers (Arthur J. Baroody with David J. Purpura); (14) Learning and Teaching Measurement: Coordinating Quantity and Number (John P. Smith III and Jeffrey E. Barrett); (15) Algebraic Thinking in the Elementary and Middle Grades (Ana C. Stephens, Amy B. Ellis, Maria Blanton, and Bárbara M. Brizuela); (16) Variation, Covariation, and Functions: Foundational Ways of Thinking Mathematically (Patrick W. Thompson and Marilyn P. Carlson); (17) The Learning and Teaching of Geometry (Nathalie Sinclair, Michelle Cirillo, and Michael de Villiers; (18) Teaching and Learning Probability and Statistics: An Integrated Perspective (Cynthia W. Langrall, Katie Makar, Per Nilsson, and J. Michael Shaughnessy); (19) Understanding the Concepts of Calculus: Frameworks and Roadmaps Emerging From Educational Research (Sean Larsen, Karen Marrongelle, David Bressoud, and Karen Graham); and (20) Post-Calculus Research in Undergraduate Mathematics Education (Chris Rasmussen and Megan Wawro). Section 4, Students, Teachers, and Learning Environments, contains: (21) Language Diversity and Mathematics: Second Language, Bilingual, and Multilingual Learners (Richard Barwell, Judit N. Moschkovich, and Mamokgethi Setati Phakeng); (22) Race and Mathematics Education (Danny Bernard Martin, Celia Rousseau Anderson, and Niral Shah); (23) Identity in Research on Mathematics Education (Jennifer M. Langer-Osuna and Indigo Esmonde); (24) Research on Gender and Mathematics (Sarah Theule Lubienski and Colleen M. Ganley); (25) The Complexities of Mathematical Engagement: Motivation, Affect, and Social Interactions (James Middleton, Amanda Jansen, and Gerald A. Goldin); (26) The Multimodal Material Mind: Embodiment in Mathematics Education (Luis Radford, Ferdinando Arzarello, Laurie Edwards, and Cristina Sabena); (27) Highlighting Heritages and Building Tasks: A Critical Analysis of Mathematics Classroom Discourse Literature (Beth Herbel-Eisenmann, Tamsin Meaney, Jessica Pierson Bishop, and Einat Heyd-Metzuyanim); (28) Research on Core Practices in K--12 Mathematics Teaching (Victoria R. Jacobs and Denise A. Spangler); (29) Research on Mathematics Professional Development (Paola Sztajn, Hilda Borko, and Thomas M. Smith); (30) Issues in Curriculum Studies: Evidence-Based Insights and Future Directions (Gwendolyn M. Lloyd, Jinfa Cai, and James E. Tarr); and (31) Technology for Learning Mathematics (Jeremy Roschelle, Richard Noss, Paulo Blikstein, and Nicholas Jackiw). Section 5, Futuristic Issues, contains: (32) Mathematics Educational Neuroscience: Promises and Challenges (Anderson Norton and Martha Ann Bell); (33) Instruction That Meets the Needs of Students With Mathematics Disabilities and Difficulties (Anne Foegen and Barbara Dougherty); (34) Creativity and Giftedness in Mathematics Education: A Pragmatic View (Bharath Sriraman and Per Haavold); (35) Assessment in the Era of Teacher Accountability (Peter Kloosterman and Hugh Burkhardt); (36) Doctorates in Mathematics Education: How They Have Evolved, What Constitutes a High-Quality Program, and What Might Lie Ahead (Robert E. Reys); (37) Mathematics Education at U.S. Public Two-Year Colleges (Vilma Mesa); and (38) Toward a Vibrant and Socially Significant Informal Mathematics Education (Ricardo Nemirovsky, Molly L. Kelton, and Marta Civil).

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students' strategic competence in modeling mathematical ideas.

As high school students make more and more important decisions, their need for financial literacy increases significantly. To succeed in life, they need both an understanding of financial issues and the math skills to make financially sound choices. With all the requirements and standards to be met in high schools today, how can teachers find room to include financial literacy? The key is to integrate financial topics into mathematics instruction, using everyday topics to bring math concepts to life. This book's ten chapters provide lessons and activities on important financial skills to handle such experiences as making investments, buying insurance, understanding a credit score, leasing or buying a car, and choosing and paying for education after high school. The related mathematical skills include analyzing and representing data, evaluating probabilities, modeling real-life situations, creating functions, and more. Each chapter includes: (1) a "Balance Sheet" summing up the mathematical and financial literacy knowledge that students will take from the lesson; (2) relevant Common Core mathematics standards and practices and Jump$tart financial literacy standards; (3) a full lesson plan, complete with sections on the "Sales Pitch," the "Fine Print," and "Closing the Deal"; (4) activity sheets and other classroom material, which are also available for download at NCTM's More4U website; and (5) suggestions for extended learning, including references and resources. The book begins with a Foreword by Neale Godfrey, an Introduction, and ten chapters divided into three parts. Part 1: Algebra and Functions, contains-- Chapter 1: Your Best Interest: Finding the Right Place to Save Money; Chapter 2: Grow Me the Money! Evaluating Investment Options; and Chapter 3: Fast Cash: Pawnshops and Payday Loans. Part 2: Modeling, contains-- Chapter 4: Know the Score: Measuring and Reporting Creditworthiness; Chapter 5: Unraveling the Mystery of Credit Card Payments; and Chapter 6: Learning to Appreciate Depreciation. Part 3: Data Analysis and Statistics, contains: Chapter 7: Investigating Investments: Which Is Better?; Chapter 8: Wall Street Apples: Following Stock Values over Time; Chapter 9: To Educate or Not to Educate: Is Postsecondary Education Worth It?; and Chapter 10: Risky Business: Insurance and Probability. Appended is Financial Literacy Resources. [For "On the Money: Math Activities to Build Financial Literacy Grades 6-8," see ED566539.]

Despite increased interest in mobile devices as learning tools, the amount of available primary research studies on their integration into mathematics teaching and learning is still relatively small due to the novelty of these technologies. "Integrating Touch-Enabled and Mobile Devices into Contemporary Mathematics Education" presents the best practices in mathematics education research and teaching practice by providing an account of current and future trends and issues in mobile mathematics learning and associated technologies and educational methodologies. This edited volume approaches a broad audience including researchers and practitioners interested in the exploitation of mobile technologies in mathematics teaching and learning, as well as mathematics teachers at all levels. This premier reference source compiles the best practices and recommended processes for effectively utilizing the vast capabilities of mobile technologies in the mathematics classroom through a collection of chapters covering topics including, but not limited to, touch-enabled virtual mapping, perceptual learning technologies, mobile teaching, statistics apps for mobile devices, smartphones for the visually impaired, pedagogical and instructional design, and touch screen interfaces in algebraic instruction. Follwing a foreword (Celia Hoyles, Richard Noss, Tim Erickson) and a preface (Maria Meletiou-Mavrotheris, Katerina Mavrou, Efi Paparistodemou), the following chapters are presented: (1) Students' Kinaesthetic Interactions with a Touch-Enabled Virtual Mapping Tool (Theodosia Prodromou, Maria Meletiou-Mavrotheris, Andreas O. Kyriakides); (2) Graspable Mathematics: Using Perceptual Learning Technology to Discover Algebraic Notation (Erin Ottmar, David Landy, Erik Weitnauer, Rob Goldstone); (3) Whatever Be Their Number: Counting on the Visible, the Audible, and the Tangible (Nathalie Sinclair, David Pimm); (4) Learning Maths with Mobiles: Cross-Cultural Design of Technology with Experiences in South-Africa and Finland (Teija Vainio, Tanja Walsh); (5) Investigating the Mathematics of Inaccessible Objects: Algebra Videos with iPads (Susan Staats, David Ernst, Shelley Berken, Douglas Robertson); (6) Changing Children's Stance towards Mathematics through Mobile Teaching: The Case of Robot A.L.E.X. (Andreas O. Kyriakides, Maria Meletiou-Mavrotheris, Theodosia Prodromou); (7) Off-Line Communication in Mathematics Using Mobile Devices (Pierre Clanché, Antonín Jancarík, Jarmila Novotná); (8) An Exploration of Developing Mathematics Content for Mobile Learning (Vani Kalloo, Permanand Mohan); (9) Introducing iPads into Primary Mathematics Classrooms: Teachers' Experiences and Pedagogies (Catherine Attard); (10) A Multimodal Discourse on the Use of Touch Enabled Mobile Devices for Mathematics Education (Jenny Lane); (11) Probability and Statistics Apps for Mobile Devices: A Review (Howard P. Edwards); (12) Microworlds: Influencing Children's Approaches to Linear Equations (Stuart Cork); and (13) Using Smartphones for Orientation Training for the Visually Impaired (Georgios Stylianou, Katerina Mavrou). A section about the contributors and an index are also included.

Common Core education standards establish a clear set of specific ideas and skills that all students should be able to comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. "Cases on Technology Integration in Mathematics Education" provides a compilation of cases and vignettes about the application of technology in the classroom in order to enhance student understanding of math concepts. This book is a timely reference source for mathematics educators, educational technologists, and school district leaders employed in the mathematics education or educational technology fields. Following a foreword by Chandra Hawley Orrill and preface by Drew Polly, this book is organized into the following sections and chapters: Section 1: Leveraging Technology to Teach Specific Content: (1) Leveraging Dynamic and Dependable Spreadsheets Focusing on Algebraic Thinking and Reasoning; (Margaret L. Niess); (2) A Case Study of Primary School Students' Use of a Dynamic Statistics Software Package for Analyzing and Interpreting Data (Irene Kleanthous and Maria Meletiou-Mavrotheris); (3) Local Lotto: Mathematics and Mobile Technology to Study the Lottery (Vivian Lim, Erica Deahl, Laurie Rubel, and Sarah Williams); (4) Bringing Dynamic Geometry to Three Dimensions: The Use of SketchUp in Mathematics Education (Nicholas H. Wasserman); (5) Playing with Perpendicular Lines: The Case of Laura (Douglas A. Lapp and Dennis St. John); and (6) Students' Experiences Composing and Decomposing Two-Dimensional Shapes in First and Second Grade Mathematics Classrooms (Drew Polly, Trisha Hill, and Tabitha Vuljanic). Section 2: Leveraging Technology to Support Mathematical Practices: (7) Using New Technologies to Engage and Support English Language Learners in Mathematics Classrooms (Robert Pritchard, Susan O'Hara, and Jeff Zwiers); (8) The Port Lesson: Grade 5 Mathematics Modeling for a Local Context (Charles B. Hodges, Edie R. Hipchen, and Traci Newton); (9) What Does Technology Bring to the Common Core Mathematical Practices? (Marshall Lassak); (10) Utilizing Technology to Engage in Statistical Inquiry in Light of the Standards for Mathematical Practice (Christine Browning and Dustin Owen Smith); and (11) Using Dynamic Geometry Software to Engage Students in the Standards for Mathematical Practice: The Case of Ms. Lowe (Milan Sherman, Carolyn McCaffrey James, Amy Hillen, and Charity Cayton). Section 3: Examples of Technological Tools to Support Teaching and Learning: (12) Integrating Multimedia Animations to Support Common Core State Standards in Mathematics Classrooms (Jesus Trespalacios, Karen Trujillo, and Lida J. Uribe-Flórez); (13) Teaching Fundamental Math Concepts: There's an App for That ... Or is There? (Jennifer Wall and Michael P. Rogers); (14) Interactive Whiteboards: Preparing Secondary Mathematics Teachers to Avoid Catch-22 (Tracy Goodson-Espy and Lisa Poling); (15) Young Children, Mathematics, and Coding: A Low Floor, High Ceiling, Wide Walls Environment (George Gadanidis); (16) Leveraging Interactive Clickers as a Tool for Formative Assessment (Drew Polly, Elizabeth Rodgers, and Melissa Little); (17) Mathematics Gaming in Early Childhood: Describing Teacher Moves for Effective and Appropriate Implementation (Alejandra Salinas and Chu Ly); and (18) Using the AMC Anywhere Web-Based Assessment System to Examine Primary Students' Understanding of Number Sense (Christie Sullivan Martin and Drew Polly). Section 4: Leveraging Technology to Support Mathematics Education Courses and Programs: (19) Teaching and Learning the Common Core State Standards in Mathematics with Web 2.0 Tools (Jeffrey Hall, Lucy Bush, and William Lacefield); (20) Contextualizing Algebraic Word Problems through Story Using Technology (Terri L. Kurz, Barbara Bartholomew, Amanda Sibley, and Scott Fraser); (21) The Synergism of Mathematical Thinking and Computational Thinking (Gerard Rambally); and (22) Application of Information and Communication Technology to Create E-Learning Environments for Mathematics Knowledge Learning to Prepare for Engineering Education (Tianxing Cai). A compilation of references, an about the contributors section, and an index are also included.

"Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned."--BCcampus website