Educational: Mathematics and numeracy

Book SynopsisThis unique book presents mathematical competition problems primarily aimed at upper elementary school students, but are challenging for students at any age. These problems are drawn from the complete papers of the legendary Leningrad Mathematical Olympiads that were presented to the city’s Grade Five students. The period covered is between 1979 – the earliest year for which relevant records could be retrieved – and 1992, when the former Soviet Union was dissolved.The respective chapters reflect the famous four-step approach to problem solving developed by the great Hungarian mathematics educator Gyorgy Pólya. In Chapter One, the Grade Five Competition problems from the Leningrad Mathematical Olympiads from 1979 to 1992 are presented in chronological order. In Chapter Two, the 83 problems are loosely divided into 26 sets of three or four related problems, and an example is provided for each one. Chapter Three provides full solutions to all problems, while Chapter Four offers generalizations of the problems.This book can be used by any mathematically advanced student at the upper elementary school level. Teachers and organizers of outreach activities such as mathematical circles will also find this book useful. But the primary value of the book lies in the problems themselves, which were crafted by experts; therefore, anyone interested in problem solving will find this book a welcome addition to their library.Table of Contents- Preface.- Understand the Problem.- Make a Plan.- Carry Out the Plan.- Look Back.- Short Answers.- First Problem Index.- Second Problem Index.

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Book SynopsisGetting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book.The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching.This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.Table of ContentsChapter 1: Teaching Principles.- Chapter 2: Equivalent Real Numbers and Infinite Decimals.- Chapter 3: Sequence Convergence and Irrational Decimal Approximations.- Chapter 4: Algebraic Limit Theorem and Error Accumulation.- Chapter 5: Divergence Description and Criteria and Logic in Communication.- Chapter 6: Continuity and Definitions.- Chapter 7: Intermediate Value Theorem and Implicit Assumptions.- Chapter 8: Continuity, Monotonicity, Inverse Functions and Solving Equations.- Chapter 9: Differentiability and the Secant Slope Function.- Chapter 10: Differentiation Rules and Attending to Scope.- Chapter 11: Taylor’s Theorem and Modeling Complex with Simple.- Chapter 12: The Riemann Integral and Area-Preserving Transformations.- Chapter 13: The Fundamental Theorem of Calculus and Conceptual Explanation.

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Book SynopsisCreativity of an Aha! Moment and Mathematics Education introduces bisociation, the theory of Aha! moment creativity into mathematics education. It establishes relationships between Koestler’s bisociation theory and constructivist learning theories. It lays down the basis for a new theory integrating creativity with learning to describe moments of insight at different levels of student development. The collection illuminates the creativity of the eureka experience in mathematics through different lenses of affect, cognition and conation, theory of attention and constructivist theories of learning, neuroscience and computer creativity. Since Aha! is a common human experience, the book proposes bisociation as the basis of creativity for all. It discusses how to facilitate and assess Aha! creativity in mathematics classrooms. Contributors are: William Baker, Stephen Campbell, Bronislaw Czarnocha, Olen Dias, Gerald Goldin, Peter Liljedahl, John Mason, Benjamin Rott, Edme Soho, Hector Soto, Hannes Stoppel, David Tall, Ron Tzur and Laurel Wolf.

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Book SynopsisThe issue of mathematics teaching and its impact on learners' attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers' world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers' education and teachers' knowledge, Teaching and Teachers' personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.Table of ContentsPreface Acknowledgements Notes on Contributors PART 1: Teachers’ Education and Teachers’ Knowledge 1 What Should We Expect from Somebody Who Teaches Mathematics in Elementary School  Shlomo Vinner 2 Pre-Service Mathematics Teachers’ Attitudes Toward Integration of Humor in Mathematics Lessons  Avikam Gazit 3 Geometric Thinking Levels of Pre-Service and In-Service Mathematics Teachers at Various Stages of Their Education  Dorit Patkin and Ruthi Barkai PART 2: Teaching and Teachers’ Personality 4 A Multicultural View of Mathematics Male-Teachers at Israeli Elementary Schools  Eti Gilad and Shosh Millet 5 Do “Those Who Understand” Teach? Mathematics Teachers’ Professional Image  Dorit Patkin and Avikam Gazit 6 Elementary School Mathematics Pre-Service Teachers’ Perception of Their Professional Image  Nili Mendelson Epilog  Dorit Patkin and Avikam Gazit Root Canal  Avikam Gazit

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Book SynopsisThe issue of mathematics teaching and its impact on learners' attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers' world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers' education and teachers' knowledge, Teaching and Teachers' personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.Table of ContentsPreface Acknowledgements Notes on Contributors PART 1: Teachers’ Education and Teachers’ Knowledge 1 What Should We Expect from Somebody Who Teaches Mathematics in Elementary School  Shlomo Vinner 2 Pre-Service Mathematics Teachers’ Attitudes Toward Integration of Humor in Mathematics Lessons  Avikam Gazit 3 Geometric Thinking Levels of Pre-Service and In-Service Mathematics Teachers at Various Stages of Their Education  Dorit Patkin and Ruthi Barkai PART 2: Teaching and Teachers’ Personality 4 A Multicultural View of Mathematics Male-Teachers at Israeli Elementary Schools  Eti Gilad and Shosh Millet 5 Do “Those Who Understand” Teach? Mathematics Teachers’ Professional Image  Dorit Patkin and Avikam Gazit 6 Elementary School Mathematics Pre-Service Teachers’ Perception of Their Professional Image  Nili Mendelson Epilog  Dorit Patkin and Avikam Gazit Root Canal  Avikam Gazit

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Book SynopsisThere is a critical need to prepare diverse teachers with expertise in science, technology, engineering, and mathematics (STEM) with the skills necessary to work effectively with underrepresented K-12 students. Three major goals of funded STEM programs are to attract and prepare students at all educational levels to pursue coursework in the STEM content areas, to prepare graduates to pursue careers in STEM fields, and to improve teacher education programs in the STEM content areas. Drawing upon these goals as the framework for Recruiting, Preparing, and Retaining STEM Teachers for a Global Generation, the 15 chapters contained herein highlight both the challenges and successes of recruiting, preparing, and sustaining novice teachers in the STEM content areas in high-need schools. Recruiting, retaining and sustaining highly-qualified teachers with expertise in STEM content areas to work in hard-to-staff schools and geographic areas are necessary to equalize educational opportunities for rural and urban Title 1 students. High teacher turnover rates, in combination with teachers working out-of-field, leave many students without highly-qualified teachers in STEM fields. Most of the chapters in this volume were prepared by scholars who received NSF funding through Noyce and are engaged in addressing research questions related to these endeavours. Contributors are: Lillie R. Albert, Cynthia Anhalt, Saman A. Aryana, Joy Barnes-Johnson, Lora Bartlett, Brezhnev Batres, Diane Bonilla, Patti Brosnan, Andrea C. Burrows, Alan Buss, Laurie O. Campbell, Phil Cantor, Michelle T. Chamberlin, Scott A. Chamberlin, Marta Civil, Lin Ding, Teresa Dunleavy, Belinda P. Edwards, Jennifer A. Eli, Joshua Ellis, Adrian Epps, Anne Even, Angela Frausto, Samantha Heller, Karen E. Irving, Heather Johnson, Nicole M. Joseph, Richard Kitchen, Karen Kuhel, Marina Lazic, Jacqueline Leonard, Rebecca H. McGraw, Daniel Morales-Doyle, Sultana N. Nahar, Justina Ogodo, Anil K. Pradhan, Carolina Salinas, David Segura, Lynette Gayden Thomas, Alisun Thompson, Maria Varelas, Dorothy Y. White, Desha Williams, and Ryan Ziols.Table of ContentsPreface Acknowledgements List of Figures and Tables Notes on Contributors PART 1: Teacher Recruitment in the stem Content Areas 1 Using stem Internships to Recruit Noyce Scholars into Elementary Education  Jacqueline Leonard, Scott Chamberlin, Saman A. Aryana, Marina Lazic and Anne Even 2 Stronger Together: The Arizona Mathematics Teaching (MaTh) Noyce Program’s Collaborative Model for Secondary Teacher Preparation  Jennifer A. Eli, Rebecca H. McGraw, Cynthia O. Anhalt and Marta Civil 3 Noyce at Vanderbilt: Exploring the Factors That Shape the Recruitment and Retention of Black Teachers   4 Rise, Defy, Teach, and Lead: The enable stem Project  Justina Ogodo, Karen E. Irving, Patti Brosnan and Lin Ding PART 2: Teacher Preparation in stem Education 5 Developing a Culturally and Linguistically Responsive Teacher Identity  Belinda P. Edwards, Desha Williams, Karen Kuhel and Adrian Epps 6 Supporting Noyce Scholars’ Teaching of Mathematics in Rural Elementary Schools  Dorothy Y. White, Jacqueline Leonard, Michelle T. Chamberlin and Alan Buss 7 Building Computational Thinking: Design and Making in Teacher Education  Laurie O. Campbell and Samantha Heller 8 Teacher Preparation Programs, Teacher Diversity, and stem: Considering a “Race-Centered” Political Economy Perspective  Ryan Ziols 9 World Class stem Faculty: An International Dual-Degree Program  Karen E. Irving, Anil K. Pradhan and Sultana N. Nahar PART 3: stem Teacher Mentoring and Retention 10 Negotiating Structures and Agency in Learning to Teach Science for Equity and Social Justice  David Segura, Maria Varelas, Daniel Morales-Doyle, Brezhnev Batres, Phillip Cantor, Diana Bonilla, Angela Frausto, Carolina Salinas and Lynette Gayden Thomas 11 Exemplary Mathematics Teachers for High-Need Schools: A Two-Way Mentoring Model  Lillie R. Albert 12 Becoming Equity-Minded stem Teachers through Mentoring and Internship Experiences  Joy Barnes-Johnson, Saman A. Aryana and Jacqueline Leonard 13 Retention through Community Building: Secondary Science and Math Noyce Scholars’ Use of a Chat Room  Andrea C. Burrows 14 Seeking to Stay: Job Search Process and Teacher Retention  Lora Bartlett and Alisun Thompson 15 The Teacher Induction Network: Findings from over 10 Years of stem Teacher Induction  Joshua A. Ellis Index

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Book SynopsisThere is a critical need to prepare diverse teachers with expertise in science, technology, engineering, and mathematics (STEM) with the skills necessary to work effectively with underrepresented K-12 students. Three major goals of funded STEM programs are to attract and prepare students at all educational levels to pursue coursework in the STEM content areas, to prepare graduates to pursue careers in STEM fields, and to improve teacher education programs in the STEM content areas. Drawing upon these goals as the framework for Recruiting, Preparing, and Retaining STEM Teachers for a Global Generation, the 15 chapters contained herein highlight both the challenges and successes of recruiting, preparing, and sustaining novice teachers in the STEM content areas in high-need schools. Recruiting, retaining and sustaining highly-qualified teachers with expertise in STEM content areas to work in hard-to-staff schools and geographic areas are necessary to equalize educational opportunities for rural and urban Title 1 students. High teacher turnover rates, in combination with teachers working out-of-field, leave many students without highly-qualified teachers in STEM fields. Most of the chapters in this volume were prepared by scholars who received NSF funding through Noyce and are engaged in addressing research questions related to these endeavours. Contributors are: Lillie R. Albert, Cynthia Anhalt, Saman A. Aryana, Joy Barnes-Johnson, Lora Bartlett, Brezhnev Batres, Diane Bonilla, Patti Brosnan, Andrea C. Burrows, Alan Buss, Laurie O. Campbell, Phil Cantor, Michelle T. Chamberlin, Scott A. Chamberlin, Marta Civil, Lin Ding, Teresa Dunleavy, Belinda P. Edwards, Jennifer A. Eli, Joshua Ellis, Adrian Epps, Anne Even, Angela Frausto, Samantha Heller, Karen E. Irving, Heather Johnson, Nicole M. Joseph, Richard Kitchen, Karen Kuhel, Marina Lazic, Jacqueline Leonard, Rebecca H. McGraw, Daniel Morales-Doyle, Sultana N. Nahar, Justina Ogodo, Anil K. Pradhan, Carolina Salinas, David Segura, Lynette Gayden Thomas, Alisun Thompson, Maria Varelas, Dorothy Y. White, Desha Williams, and Ryan Ziols.Table of ContentsPreface Acknowledgements List of Figures and Tables Notes on Contributors PART 1: Teacher Recruitment in the stem Content Areas 1 Using stem Internships to Recruit Noyce Scholars into Elementary Education  Jacqueline Leonard, Scott Chamberlin, Saman A. Aryana, Marina Lazic and Anne Even 2 Stronger Together: The Arizona Mathematics Teaching (MaTh) Noyce Program’s Collaborative Model for Secondary Teacher Preparation  Jennifer A. Eli, Rebecca H. McGraw, Cynthia O. Anhalt and Marta Civil 3 Noyce at Vanderbilt: Exploring the Factors That Shape the Recruitment and Retention of Black Teachers   4 Rise, Defy, Teach, and Lead: The enable stem Project  Justina Ogodo, Karen E. Irving, Patti Brosnan and Lin Ding PART 2: Teacher Preparation in stem Education 5 Developing a Culturally and Linguistically Responsive Teacher Identity  Belinda P. Edwards, Desha Williams, Karen Kuhel and Adrian Epps 6 Supporting Noyce Scholars’ Teaching of Mathematics in Rural Elementary Schools  Dorothy Y. White, Jacqueline Leonard, Michelle T. Chamberlin and Alan Buss 7 Building Computational Thinking: Design and Making in Teacher Education  Laurie O. Campbell and Samantha Heller 8 Teacher Preparation Programs, Teacher Diversity, and stem: Considering a “Race-Centered” Political Economy Perspective  Ryan Ziols 9 World Class stem Faculty: An International Dual-Degree Program  Karen E. Irving, Anil K. Pradhan and Sultana N. Nahar PART 3: stem Teacher Mentoring and Retention 10 Negotiating Structures and Agency in Learning to Teach Science for Equity and Social Justice  David Segura, Maria Varelas, Daniel Morales-Doyle, Brezhnev Batres, Phillip Cantor, Diana Bonilla, Angela Frausto, Carolina Salinas and Lynette Gayden Thomas 11 Exemplary Mathematics Teachers for High-Need Schools: A Two-Way Mentoring Model  Lillie R. Albert 12 Becoming Equity-Minded stem Teachers through Mentoring and Internship Experiences  Joy Barnes-Johnson, Saman A. Aryana and Jacqueline Leonard 13 Retention through Community Building: Secondary Science and Math Noyce Scholars’ Use of a Chat Room  Andrea C. Burrows 14 Seeking to Stay: Job Search Process and Teacher Retention  Lora Bartlett and Alisun Thompson 15 The Teacher Induction Network: Findings from over 10 Years of stem Teacher Induction  Joshua A. Ellis Index

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Book SynopsisThe Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field. The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.Table of ContentsForeword  Barbara J. Reis Preface and Introduction Abstract Thinking Action Research Active Mathematics Teaching and Learning Additive Reasoning Algebraic Reasoning Algorithm Assessment in Mathematics  Formative Assessment  Summative Assessment  Progressive Assessment Basic (Number) Facts Beliefs/Attitudes Cognitive Demand Cognitive Science Cognitively Guided Instruction (CGI) Common Core State Standards for Mathematics (CCSSM) Computer Algebra Systems (CAS) Concept Image Conceptual Knowledge Conjecture Constructivist Theory of Learning Cooperative Learning Council for the Accreditation of Educator Preparation (CAEP) Counting Covariational Reasoning Curricular Reasoning Curriculum Curriculum Alignment Curriculum Coherence Curriculum Knowledge Decentering Deductive Reasoning Design Research in Education Didactic Differentiated Instruction Direct Modeling Discourse Discovery Learning Dynamic Geometry Software (DGS) Educational Technology Epistemology Equity Error Patterns Ethnomathematics Fidelity of Implementation Flipped Classroom Functions-Based Approach to Teaching Algebra Geometric Reasoning High-Stakes Testing Inductive Reasoning Instructional Strategies and Techniques  Direct Instruction/Lecture Method  Inquiry Based Instruction/Active Learning  Three-Act Tasks  Launch-Explore-Summarize  5 Practices  Flipped Classroom Approach Learning Trajectory Lesson Study Longitudinal Study Manipulatives Math Anxiety Math Wars Mathematical Identity Mathematical Knowledge for Teaching (MKT) Mathematical Literacy Mathematical Modeling Mathematics Skills Meaningful Learning Mental Discipline Mental Math Metacognition Misconceptions Model-Eliciting Activities (MEA’s) Multiple Embodiment Multiplicative Reasoning National Assessment of Educational Progress (NAEP) NCTM Standards New Math Non-Anticipatory Number Sense/Numeracy Numerical Estimation Pedagogical Content Knowledge (PCK) Performance Based Assessments Prior Knowledge Problem Based Learning (PrBL) Problem Solving Heuristics Problem Structure Procedural Knowledge Productive Struggle Professional Development (PD) Professional Organizations in Mathematics Education  National Council of Teachers of Mathematics (NCTM)  National Council of Supervisors of Mathematics (NCSM)  Association of Mathematics Teacher Educators (AMTE)  Psychology of Mathematics Education (PME)  American Educational Research Association (AERA)  International Commission on Mathematical Instruction (ICMI)  Research Council on Mathematics Learning (RCML)  Mathematical Association of America (MAA)  American Mathematical Society (AMS) Program for International Student Assessment (PISA) Project Based Learning (PBL) Proportional Reasoning Quantitative Literacy (QL) Quantitative Reasoning (QR) Radical Constructivism Reification Relational Thinking Representational Fluency Representations Response to Intervention (RtI) Responsive Teaching Rigor Rote Learning Scaffolding Sense-Making Situated Learning (Cognition) Social Constructivism Socio-Cultural Learning Theory (SCLT) Sociomathematical Norms Spatial Thinking Strands of Mathematical Proficiency Subitizing Task Analysis Teacher Noticing Technological and Pedagogical Content Knowledge (TPACK) Trends in Mathematics and Science Study (TIMMS) Van Hiele Levels of Geometric Thinking Zone of Proximal Development (ZPD)

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