Educational: Mathematics and numeracy

Book SynopsisTwo maths coaches who have spearheaded the transition to remote learning in their district have distilled their experience of what works into a guide for teaching maths from a distance. Filled with ready-to-use strategies, this QRG in the new set of Strategies for Distance Learning Guides is organised by 4 priorities: mathematical identitygrowth mindsetreasoning and problem-solvingengaging activities Samantha Bennet and Alaina Barkley show how to incorporate routines into online learning that support these priorities, from connecting with students, to supporting their learning with games and problem-solving tasks, to assessing their work. Each 8.5 x 11 multi-panel guide is laminated for extra durability and 3-hole-punched for binder storage.

Read more less

Book SynopsisThe teaching of numbers in the primary grades is seen in this book as the foundation of the beginnings of mathematical understanding. Mathematics is taken to be a language, and the aim of its teaching is to make the pupil, so to speak, bilingual, or so to increase his understanding that he is able to translate a concrete numerical problem into the symbolic language of calculation. For a child taught along these lines, how much easier, for example, would be the transition from arithmetic to algebra!Miss Churchill is fully conversant with the works of Piaget, Cuisenaire, Cassirer and other leading thinkers in educational philosophy, psychology, and linguistics. She has synthesized their concepts with her own experience and research at Leeds University, and, though written within the contexts of British education, her book should also have a marked influence on the teaching of young children in North America.

Read more less

Book SynopsisTrade Review“...[T]here is a serious dimension to these books that is often not present in standard 'mathematics for teachers' textbooks...This series doesn't bother with the typical chapters on problem solving and elementary set theory that are very much the norm in books for this course, but strikes a blow for serious work by diving right into fractions...We need books for future teachers that take this approach to our subject.” - Mark Bollman, MAA ReviewsTable of Contents Symbolic expressions Translation of verbal information into symbols Linear equations in one variable Linear equations in two variables and their graphs Simultaneous linear equations Functions and their graphs Linear functions and proportional reasoning Linear inequalities and their graphs Exponents Quadratic functions and their graphs Appendix: Facts from [Wu-PreAlg] Bibliography

Read more less

Book SynopsisA playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. The exploration is presented through problems selected from the history of the Mathematical Association of America's American Mathematics Competition.Table of Contents Functions and graphs: What is a function? A swift conceptual overview Sequences as functions on $\mathbb{N}$ Numerical functions on $\mathbb{R}$ Composite functions and inverse functions Graphing Transformations of graphs Average rate of change, constant rate of change Quadratic functions Polynomial functions Rational functions Select special functions and equations Fitting formulas to data points Solutions: Solutions Appendices: Ten problem-solving strategies Connections to the Common Core State Standards: Practice standards and content standards.

Read more less

Book SynopsisIntroduces children to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context that are part of the continuously developing stream of mathematical thought.Table of Contents Numbers as geometric shapes Combinatorics Fibonacci numbers Pascal's triangle Area Selected warmup and challenging problems Handouts Bibliography Index.

Read more less

Book SynopsisPresents a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general maths enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking.Table of Contents Dragons and poison Folding tetrahedra The arbelos Averages via distances Ramsey theory Inner triangles Land or water? Escape Flipping a coin for a year Coinciding digits Inequalities Gauss's shoelace formula Subdividing a square into triangles Equilateral lattice polygons Broken sticks and Viviani's theorem Viviani's converse? Integer right triangles One more question about integer right triangles Intersecting circles Counting triangular and square numbers Balanced sums The Prouhet-Thue-Morse sequence Some partition numbers Ordering colored fractions How round is a cube? Base and exponent switch Associativity and commutativity puzzlers Very triangular and very very triangular numbers Torus circles Trapezoidal numbers Square permutations Tupper's formula Compositional square roots Polynomial permutations.

Read more less

Book SynopsisA bilingual schoolbook of mathematical problems written with the premise that one of the fundamental ways of learning mathematics, in addition to being one of the goals of the subject, is to solve problems. The book is designed for children and young teens and aims to teach mathematics in an entertaining way.Table of Contents Traveling Doing sports Families Short challenges How much? Around the city Caboose Solutions

Read more less

Book SynopsisMaking mathematics concepts understandable is a challenge for any teacher—a challenge that's more complex when a classroom includes students with learning difficulties. With the new edition of this highly practical resource, educators will have just what they need to teach mathematics with confidence: research-based strategies that really work with students who have learning disabilities, ADHD (Attention Deficit Hyperactivity Disorder), or mild cognitive disabilities. With this timely book—updated throughout and filled with invaluable ideas and strategies adaptable for grades K–12—educators will know just what to teach and how to teach it to students with learning difficulties.

Read more less

Book SynopsisMath can’t wait. Children who can count with ease before kindergarten have a better shot at future mathematics success—and with this book, it’s simple and fun to weave counting and other math concepts into everyday activities. Drawn from the authors’ playful and popular LittleCounters® workshops, this guidebook shows early educators, caregivers, and parents how to use purposeful play with children from birth to 5 to promote mathematical thinking and get them ready for formal math instruction. Packed with easy, no-fear strategies any adult can use—even if you’re math-phobic!—this book will help all the teachers in a child’s life foster critical early math knowledge and school readiness. READ THIS BOOK TO Discover amazing facts about the mathematical minds of babies and young children Transform ordinary toys into learning tools that help teach mathematical concepts Organize play environments and activities to encourage math learning Spot teachable moments and add purposeful math talk to daily tasks Teach “meaningful counting”—the skill that underpins children’s potential for future math success Infuse math learning into specific daily routines, such as meals, chores, and bedtime Support children’s readiness for formal math instruction Get started with your own LittleCounters® workshop—or use the principles right away in your program or home PRACTICAL MATERIALS: Examples and vignettes; sample activities and scripts of adult-child dialogue; recommended counting books and songs; and a detailed introduction to interactive LittleCounters® workshops, where parents and kids learn and have fun together.

Read more less

Book SynopsisThe interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematisation or consolidation of the existing literature aimed at undergraduate mathematics education, particularly in the teaching and learning of the history of mathematics and other undergraduate topics. In this monograph, the chapters cover topics such as the development of Calculus through the actuarial sciences and map making, logarithms, the people and practices behind real world mathematics, and fruitful ways in which the history of mathematics informs mathematics education. The book is meant to serve as a source of enrichment for undergraduate mathematics majors and for mathematics education courses aimed at teachers.

Read more less

Book SynopsisThe interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematisation or consolidation of the existing literature aimed at undergraduate mathematics education, particularly in the teaching and learning of the history of mathematics and other undergraduate topics. In this monograph, the chapters cover topics such as the development of Calculus through the actuarial sciences and map making, logarithms, the people and practices behind real world mathematics, and fruitful ways in which the history of mathematics informs mathematics education. The book is meant to serve as a source of enrichment for undergraduate mathematics majors and for mathematics education courses aimed at teachers.

Read more less

Book SynopsisThe official journal of the Organization of Educational Historians VOLUME 39, NUMBER 1, 2012Editor's Introduction, Paul J. Ramsey. ARTICLES. NCLB-The Educational Accountability Paradigm in Historical Perspective, Mark Groen. Using Microbiography to Understand the Occupational Careers of American Teachers, 1900-1950, Robert J. Gough. Flannery O'Conner and Progressive Education: Experiences and Impressions of an American Author, John A. Beineke. The Idea of Infancy and Nineteenth-Century American Education, Joseph Watras. The Great Depression and Elementary School Teachers as Reported in Grade Teacher Magazine, Sherry L. Field and Elizabeth Bellows. Called to Teach: Percy and Anna Pennybacker's Contributions to Education in Texas, 1880-1899, Kelley M. King. A Southern Progressive: M. A. Cassidy and the Lexington Schools, 1886-1928, Richard E. Day and Lindsey N. DeVries. History's Purpose in Antebellum Textbooks, Edward Cromwell McInnis. Texas's Decision to Have Twelve Grades, Kathy Watlington. The Rise and Demise of the SAT: The University of California Generates Change for College Admissions, Susan J. Berger. Imagining Harvard: Changing Visions of Harvard in Fiction, 1890-1940, Christian K. Anderson and Daniel A. Clark. God and Man at Yale and Beyond: The Thoughts of William F. Buckley, Jr. on Higher Education, 1949-1955, James Green. Paul Ricoeur, Memory, and the Historical Gaze: Implications for Education Histories,Sherri Rae Colby. Indefinite Foundings and Awkward Transitions: The Grange's Troubled Formation into an Educational Institution, Glenn P. Lauzon. BOOK REVIEWS. Loss, C. P., Between Citizens and the State: The Politics of American Higher Education in the 20th Century, Princeton, NJ: Princeton University Press, 2011, 344 pp., and Urban, W. J., More Than Science and Sputnik: The National Defense Education Act of 1958. Tuscaloosa, AL: The University of Alabama Press, 2010, 264 pp. Reviewed by T. Gregory Barrett. Hendry, P., Engendering Curriculum History. New York: Routledge. 2011, 258 pp. Reviewed by Daniel M. Ryan. D. E. Mitchell, , R. L. Crowson, and D. Shipps, eds., Shaping Education Policy: Power and Process. New York: Routledge. 2011, 312 pp. Reviewed by Sherri Rae Colby. Gasman, M., The History of U.S. Higher Education: Methods for Understanding the Past. New York: Routledge, 2010, 240 pp. Reviewed by John A. Beineke.VOLUME 39, NUMBER 2, 2012 Editor's Introduction, Paul J. Ramsey. ARTICLES. ""Whosoever Will, Let Him Come"": Evangelical Millennialism and the Development of American Public Education, John Wakefield. ""Good Fences Make Strange Neighbors"": Released Time Programs and the McCollum v. Board of Education Decision of 1948, David P. Setran. Evolution and South Carolina Schools, 1859-2009, Benjamin J. Bindewald and Mindy Spearman. Reverend John Witherspoon's Pedagogy of Leadership, Christie L. Maloyed and J. Kelton Williams.Transatlantic Dialogue: Pestalozzian Influences on Women's Education in the Early Nineteenth Century America,Maria A. Laubach and Joan K. Smith. Is Liberal Arts Education for Women Liberating?: From Cold War Debate to Modern Gender Gaps, Andrea Walton. Coercion, If Coercion Be Necessary: The Educational Function of the New York House of Refuge, 1824-1874, Josie Madison. Shaping Freedom's Course: Charles Hamilton Houston, Howard University, and Legal Instruction on U.S. Civil Rights, Robert K. Poch. Theodore Sizer and the Development of the Mathematics and Science for Minority Students Program at Phillips Academy Andover,Jerrell K. Beckham. Disproportionate Burden: Consolidation and Educational Equity in the City Schools of Warren, Ohio, 1978-2011, Leah J. Daugherty Schmidt and Thomas G. Welsh. The Power of Boarding Schools: A Historiographical Review, Abigail Gundlach Graham. Challenge and Conflict to Educate: The Brazos Agency Indian School, Brandon Moore, Karon N. LeCompte, and Larry J. Kelly. ""Incommensurable Standards"": Academics' Responses to Classical Arrangements of Native American Songs, Jacob Hardesty. A Century of Using Secondary Education to Extend an American Hegemony over Hawaii, Kalani Beyer. BOOK REVIEWS:Titus, J. O., Brown's Battleground: Students, Segregation, & the Struggle for Justice in Prince Edward County, Virginia, Chapel Hill: University of North Carolina Press, 2011, 279 pp. Reviewed by Dionne Danns. Horsford, S. D., Learning in a Burning House: Educational Inequality, Ideology, and (Dis) integration. New York: Teachers College Press. 2011, 129 pp. Reviewed by Melanie Adams. James, R., Jr., Root and Branch: Charles Hamilton Houston, Thurgood Marshall, and the Struggle to End Segregation. New York: Bloomsbury Press. 2010, 276 pp.Reviewed by Robert K. Poch. Burkholder, Z., Color in the Classroom: How American Schools Taught Race, 1900-1954. New York: Oxford University Press, 2011, 264 pp. Reviewed by Amy A. Hunter and Matthew D. Davis. Rury, J. L. and S. A. Hill., The African American Struggle for Secondary Schooling, 1940-1980: Closing the Graduation Gap. New York: Teachers College Press, 2012, 261 pp. Reviewed by Claude Weathersby.Frankenberg E., and E. DeBay, eds., Integrating Schools in a Changing Society: New Policies and Legal Options for a Multiracial Generation. Chapel Hill, NC: University of North Carolina Press. 368 pp. Reviewed by Joseph Watras.

Read more less

Book SynopsisThe official journal of the Organization of Educational Historians VOLUME 39, NUMBER 1, 2012Editor's Introduction, Paul J. Ramsey. ARTICLES. NCLB-The Educational Accountability Paradigm in Historical Perspective, Mark Groen. Using Microbiography to Understand the Occupational Careers of American Teachers, 1900-1950, Robert J. Gough. Flannery O'Conner and Progressive Education: Experiences and Impressions of an American Author, John A. Beineke. The Idea of Infancy and Nineteenth-Century American Education, Joseph Watras. The Great Depression and Elementary School Teachers as Reported in Grade Teacher Magazine, Sherry L. Field and Elizabeth Bellows. Called to Teach: Percy and Anna Pennybacker's Contributions to Education in Texas, 1880-1899, Kelley M. King. A Southern Progressive: M. A. Cassidy and the Lexington Schools, 1886-1928, Richard E. Day and Lindsey N. DeVries. History's Purpose in Antebellum Textbooks, Edward Cromwell McInnis. Texas's Decision to Have Twelve Grades, Kathy Watlington. The Rise and Demise of the SAT: The University of California Generates Change for College Admissions, Susan J. Berger. Imagining Harvard: Changing Visions of Harvard in Fiction, 1890-1940, Christian K. Anderson and Daniel A. Clark. God and Man at Yale and Beyond: The Thoughts of William F. Buckley, Jr. on Higher Education, 1949-1955, James Green. Paul Ricoeur, Memory, and the Historical Gaze: Implications for Education Histories,Sherri Rae Colby. Indefinite Foundings and Awkward Transitions: The Grange's Troubled Formation into an Educational Institution, Glenn P. Lauzon. BOOK REVIEWS. Loss, C. P., Between Citizens and the State: The Politics of American Higher Education in the 20th Century, Princeton, NJ: Princeton University Press, 2011, 344 pp., and Urban, W. J., More Than Science and Sputnik: The National Defense Education Act of 1958. Tuscaloosa, AL: The University of Alabama Press, 2010, 264 pp. Reviewed by T. Gregory Barrett. Hendry, P., Engendering Curriculum History. New York: Routledge. 2011, 258 pp. Reviewed by Daniel M. Ryan. D. E. Mitchell, , R. L. Crowson, and D. Shipps, eds., Shaping Education Policy: Power and Process. New York: Routledge. 2011, 312 pp. Reviewed by Sherri Rae Colby. Gasman, M., The History of U.S. Higher Education: Methods for Understanding the Past. New York: Routledge, 2010, 240 pp. Reviewed by John A. Beineke.VOLUME 39, NUMBER 2, 2012 Editor's Introduction, Paul J. Ramsey. ARTICLES. ""Whosoever Will, Let Him Come"": Evangelical Millennialism and the Development of American Public Education, John Wakefield. ""Good Fences Make Strange Neighbors"": Released Time Programs and the McCollum v. Board of Education Decision of 1948, David P. Setran. Evolution and South Carolina Schools, 1859-2009, Benjamin J. Bindewald and Mindy Spearman. Reverend John Witherspoon's Pedagogy of Leadership, Christie L. Maloyed and J. Kelton Williams.Transatlantic Dialogue: Pestalozzian Influences on Women's Education in the Early Nineteenth Century America,Maria A. Laubach and Joan K. Smith. Is Liberal Arts Education for Women Liberating?: From Cold War Debate to Modern Gender Gaps, Andrea Walton. Coercion, If Coercion Be Necessary: The Educational Function of the New York House of Refuge, 1824-1874, Josie Madison. Shaping Freedom's Course: Charles Hamilton Houston, Howard University, and Legal Instruction on U.S. Civil Rights, Robert K. Poch. Theodore Sizer and the Development of the Mathematics and Science for Minority Students Program at Phillips Academy Andover,Jerrell K. Beckham. Disproportionate Burden: Consolidation and Educational Equity in the City Schools of Warren, Ohio, 1978-2011, Leah J. Daugherty Schmidt and Thomas G. Welsh. The Power of Boarding Schools: A Historiographical Review, Abigail Gundlach Graham. Challenge and Conflict to Educate: The Brazos Agency Indian School, Brandon Moore, Karon N. LeCompte, and Larry J. Kelly. ""Incommensurable Standards"": Academics' Responses to Classical Arrangements of Native American Songs, Jacob Hardesty. A Century of Using Secondary Education to Extend an American Hegemony over Hawaii, Kalani Beyer. BOOK REVIEWS:Titus, J. O., Brown's Battleground: Students, Segregation, & the Struggle for Justice in Prince Edward County, Virginia, Chapel Hill: University of North Carolina Press, 2011, 279 pp. Reviewed by Dionne Danns. Horsford, S. D., Learning in a Burning House: Educational Inequality, Ideology, and (Dis) integration. New York: Teachers College Press. 2011, 129 pp. Reviewed by Melanie Adams. James, R., Jr., Root and Branch: Charles Hamilton Houston, Thurgood Marshall, and the Struggle to End Segregation. New York: Bloomsbury Press. 2010, 276 pp.Reviewed by Robert K. Poch. Burkholder, Z., Color in the Classroom: How American Schools Taught Race, 1900-1954. New York: Oxford University Press, 2011, 264 pp. Reviewed by Amy A. Hunter and Matthew D. Davis. Rury, J. L. and S. A. Hill., The African American Struggle for Secondary Schooling, 1940-1980: Closing the Graduation Gap. New York: Teachers College Press, 2012, 261 pp. Reviewed by Claude Weathersby.Frankenberg E., and E. DeBay, eds., Integrating Schools in a Changing Society: New Policies and Legal Options for a Multiracial Generation. Chapel Hill, NC: University of North Carolina Press. 368 pp. Reviewed by Joseph Watras.

Read more less

Book SynopsisMathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem.The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education.The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. Thepurpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners andstudents both in and outside Asia, and complement the Nordic and NCTM perspectives.

Read more less

Book SynopsisMathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem.The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education.The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. Thepurpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners andstudents both in and outside Asia, and complement the Nordic and NCTM perspectives.

Read more less

Book SynopsisThe driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics—how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings—and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories.A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.)This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children’s mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories’ evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

Read more less

Book SynopsisThe driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics—how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings—and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories.A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.)This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children’s mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories’ evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

Read more less

Book SynopsisThe teaching and learning of mathematics in Alberta - one of three Canadian provinces sharing a border with Montana - has a long and storied history. An integral part of the past 50 years (1962-2012) of this history has been delta-K: Journal of the Mathematics Council of the Alberta Teachers' Association. This volume, which presents ten memorable articles from each of the past five decades, that is, 50 articles from the past 50 years of the journal, provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a commentary from a prominent member of the Alberta mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues in the teaching and learning of mathematics. This volume is meant to serve as a resource for a variety of individuals, including teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students. Most importantly, this volume is a celebratory retrospective on the work of the Mathematics Council of the Alberta Teachers' Association.

Read more less

Book SynopsisThe teaching and learning of mathematics in Alberta - one of three Canadian provinces sharing a border with Montana - has a long and storied history. An integral part of the past 50 years (1962-2012) of this history has been delta-K: Journal of the Mathematics Council of the Alberta Teachers' Association. This volume, which presents ten memorable articles from each of the past five decades, that is, 50 articles from the past 50 years of the journal, provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a commentary from a prominent member of the Alberta mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues in the teaching and learning of mathematics. This volume is meant to serve as a resource for a variety of individuals, including teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students. Most importantly, this volume is a celebratory retrospective on the work of the Mathematics Council of the Alberta Teachers' Association.

Read more less

Book SynopsisThe book is a collection of problems in school mathematics specifically written for the teachers. It is an attempt to enrich prospective and current teachers with the deep knowledge of school mathematics and to develop their reasoning and proving skills. Also, it is supposed to help them to anticipate and analyze their students’ errors and use them as teachable moments.The book is intended to be used in mathematics education courses (or professional development) for pre-service or in-service secondary school teachers. It can be used in graduate and undergraduate courses, in accordance with the orientations of different teacher preparation programs. Additionally, it can be used for the independent studies. One can also imagine situations in which teachers might use certain problems from this problem book directly in working with students, but this would constitute a supplementary use of the book.Table of Contents Foreword Part I: Problems Chapter 1: Numbers and Algebraic Expressions Chapter 2: Linear and Piecewise Linear Functions. Linear Equations Chapter 3: Quadratic functions. Quadratic equations Chapter 4: Inequalities Chapter 5: Functions and Graphs Chapter 6: Some More Complicated Equations Chapter 7: Math Contest Problems Part II: Answer Key And Solutions Answer Key and Solutions Chapter 1 Answer Key and Solutions Chapter 2 Answer Key and Solutions Chapter 3 Answer Key and Solutions Chapter 4 Answer Key and Solutions Chapter 5 Answer Key and Solutions Chapter 6 Answer Key and Solutions Chapter 7 About the Authors

Read more less

Book SynopsisThe book is a collection of problems in school mathematics specifically written for the teachers. It is an attempt to enrich prospective and current teachers with the deep knowledge of school mathematics and to develop their reasoning and proving skills. Also, it is supposed to help them to anticipate and analyze their students’ errors and use them as teachable moments.The book is intended to be used in mathematics education courses (or professional development) for pre-service or in-service secondary school teachers. It can be used in graduate and undergraduate courses, in accordance with the orientations of different teacher preparation programs. Additionally, it can be used for the independent studies. One can also imagine situations in which teachers might use certain problems from this problem book directly in working with students, but this would constitute a supplementary use of the book.Table of Contents Foreword Part I: Problems Chapter 1: Numbers and Algebraic Expressions Chapter 2: Linear and Piecewise Linear Functions. Linear Equations Chapter 3: Quadratic functions. Quadratic equations Chapter 4: Inequalities Chapter 5: Functions and Graphs Chapter 6: Some More Complicated Equations Chapter 7: Math Contest Problems Part II: Answer Key And Solutions Answer Key and Solutions Chapter 1 Answer Key and Solutions Chapter 2 Answer Key and Solutions Chapter 3 Answer Key and Solutions Chapter 4 Answer Key and Solutions Chapter 5 Answer Key and Solutions Chapter 6 Answer Key and Solutions Chapter 7 About the Authors

Read more less

Book SynopsisAMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K–12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students’ mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated.SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles.Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

Read more less

Book SynopsisAMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K–12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students’ mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated.SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles.Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisVol. II: Short-Term Programs features eight OST STEM programs for females from across the United States that run oneto three days in length, in most cases, a single day. In this book, the chapter authors describe their programs, the effectiveness of those programs, and practical implications of their program evaluation data. This book series is the first of its kind to offer researchers, educators, school administrators, policy makers, and others detailed insight intothe promise and practice of out-of-school-time STEM programs for females.Science, technology, engineering, and mathematics (STEM) disciplines play a pivotal role in societal progress and economic prosperity, in addition to enhancing individual lives. However, U.S. students lack strong STEM performance in an international context. The pool of STEM-proficient workers is thus insufficient to fuel the nation, with females being one group that is noticeably absent.Out-of-school-time (OST) programs, which are on the rise, are increasingly suggested as a way to support andencourage underrepresented groups in STEM. Participants in OST programs have shown improved achievement, interest, and confidence in STEM, as well as greater awareness of STEM role models and careers.Table of Contents Introduction: OST Programs as STEM Support for Females, Lynda R.Wiest, Heather Glynn Crawford-Ferre, and Jafeth E. Sanchez. FEMMES STEM Program for Girls, Kathy Ziyue Dai, Nina Kuprasertkul, and Deborah Liu. Expanding Your Horizons: An Out-of-School-Time STEM Conference for Girls, Judith Iriarte-Gross, Myra Norman, and Monika Whitfield. STEM for Girls: A One-Day Event to Improve Girls’ Attitudes Toward STEM, Julia S. Ribeiro, Michelle E. Kossack, and Tina Jeoh. Girls in Engineering, Math, and Science (GEMS): A Successful Program for Middle School Girls and College Women in Southwest Florida, Zanna Beharry, Katie Johnson, and Laura Frost. Science Technology Engineering Preview Summer (STEPS) at the University of St. Thomas, Deborah Besser and AnnMarie Thomas. The Girls in STEM Program, Sean Hill and Jafeth E. Sanchez. Tech Savvy: The Difference a Day Makes to Facilitate STEM Interest in Girls and the Adults in Their Lives, Tamara E. Brown. Exploring the Impact of Out-of-School STEM Experiences for Girls, Jacqueline D. Spears, Chardie L. Baird, and Beth A. Montelone. Conclusion: Short-Term OST STEM Programs for Females, Lynda R. Wiest, Heather Glynn Crawford-Ferre, and Jafeth E. Sanchez. About the Editors. About the Contributors.

Read more less

Book SynopsisVol. II: Short-Term Programs features eight OST STEM programs for females from across the United States that run oneto three days in length, in most cases, a single day. In this book, the chapter authors describe their programs, the effectiveness of those programs, and practical implications of their program evaluation data. This book series is the first of its kind to offer researchers, educators, school administrators, policy makers, and others detailed insight intothe promise and practice of out-of-school-time STEM programs for females.Science, technology, engineering, and mathematics (STEM) disciplines play a pivotal role in societal progress and economic prosperity, in addition to enhancing individual lives. However, U.S. students lack strong STEM performance in an international context. The pool of STEM-proficient workers is thus insufficient to fuel the nation, with females being one group that is noticeably absent.Out-of-school-time (OST) programs, which are on the rise, are increasingly suggested as a way to support andencourage underrepresented groups in STEM. Participants in OST programs have shown improved achievement, interest, and confidence in STEM, as well as greater awareness of STEM role models and careers.Table of Contents Introduction: OST Programs as STEM Support for Females, Lynda R.Wiest, Heather Glynn Crawford-Ferre, and Jafeth E. Sanchez. FEMMES STEM Program for Girls, Kathy Ziyue Dai, Nina Kuprasertkul, and Deborah Liu. Expanding Your Horizons: An Out-of-School-Time STEM Conference for Girls, Judith Iriarte-Gross, Myra Norman, and Monika Whitfield. STEM for Girls: A One-Day Event to Improve Girls’ Attitudes Toward STEM, Julia S. Ribeiro, Michelle E. Kossack, and Tina Jeoh. Girls in Engineering, Math, and Science (GEMS): A Successful Program for Middle School Girls and College Women in Southwest Florida, Zanna Beharry, Katie Johnson, and Laura Frost. Science Technology Engineering Preview Summer (STEPS) at the University of St. Thomas, Deborah Besser and AnnMarie Thomas. The Girls in STEM Program, Sean Hill and Jafeth E. Sanchez. Tech Savvy: The Difference a Day Makes to Facilitate STEM Interest in Girls and the Adults in Their Lives, Tamara E. Brown. Exploring the Impact of Out-of-School STEM Experiences for Girls, Jacqueline D. Spears, Chardie L. Baird, and Beth A. Montelone. Conclusion: Short-Term OST STEM Programs for Females, Lynda R. Wiest, Heather Glynn Crawford-Ferre, and Jafeth E. Sanchez. About the Editors. About the Contributors.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisThe value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond.Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep -seated cognitive patterns that both teachers and students bring to the classroom require change.Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Read more less

Book SynopsisThe value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond.Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep -seated cognitive patterns that both teachers and students bring to the classroom require change.Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Read more less

Book SynopsisMuch of the content that students study in a high school geometry course is totally new to them. The middle school mathematics curriculum does not contain preparatory work for many of these topics as it does in preparing students for the study of Algebra. The proposed text would be a landmark book giving students the ability to gain some understanding of the content before it is formally addressed in the lesson in the course.While many teachers use initial classroom activities called 'DoNows,' there are no structured materials available to teachers of Geometry for this purpose. When teachers do use them, these activities are constructed by the teachers. The text provides the teachers with such materials and is structured to address what the teachers are about to present to the students. The Labs can also be used for exploration of topics at the middle school level enhancing the program there and giving students a better preparation for their high school Geometry program.Table of Contents SECTION I: Angles SECTION II: Area and Surface Area SECTION III: Circles SECTION IV: Congruence SECTION V: Geometry in Space SECTION VI: Midpoint SECTION VII: Parallel Lines SECTION VIII: Perimeter SECTION IX: Perpendicular Lines SECTION X: Properties of Polygons SECTION XI: Pythagorean Theorem and Distance Formula SECTION XII: Similarity SECTION XIII: Triangles SECTION XIV: Volume

Read more less

Book SynopsisMuch of the content that students study in a high school geometry course is totally new to them. The middle school mathematics curriculum does not contain preparatory work for many of these topics as it does in preparing students for the study of Algebra. The proposed text would be a landmark book giving students the ability to gain some understanding of the content before it is formally addressed in the lesson in the course.While many teachers use initial classroom activities called 'DoNows,' there are no structured materials available to teachers of Geometry for this purpose. When teachers do use them, these activities are constructed by the teachers. The text provides the teachers with such materials and is structured to address what the teachers are about to present to the students. The Labs can also be used for exploration of topics at the middle school level enhancing the program there and giving students a better preparation for their high school Geometry program.Table of Contents SECTION I: Angles SECTION II: Area and Surface Area SECTION III: Circles SECTION IV: Congruence SECTION V: Geometry in Space SECTION VI: Midpoint SECTION VII: Parallel Lines SECTION VIII: Perimeter SECTION IX: Perpendicular Lines SECTION X: Properties of Polygons SECTION XI: Pythagorean Theorem and Distance Formula SECTION XII: Similarity SECTION XIII: Triangles SECTION XIV: Volume

Read more less

Book SynopsisA perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level.The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice.Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.

Read more less

Book SynopsisA perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level.The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice.Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisThe aim of this book is to offer some help to teachers who are not very confident of their own understanding of mathematics, but want to give some basic help to dyslexics and others in the particular areas needed by them. To that end the chapters give separate topics with clear explanations for the teacher of the content to be taught, suggestions about how to teach it, exercises with answers, and in the Appendix a list of helpful materials and software. Teachers can pick out a topic without necessarily following the order in the book.Table of Contents1 - General Advice on Teaching. 2 - Estimation. 3 - Understanding number. 4 - The Four Operational Rules. 5 - Addition, Magic Squares. 6 - subtraction. 7 - Multiplication, Multiplication Tables. 8 - Division. 9 - The 'equals' Concept and Sign. 10 - Summary of Four Operational Rules. 11 - Calculators. 12 - Money. 13 - Time. 14 - Fractions. 15 - Decimals. 16 - Correction to Significant Figures and Changing Fractions to Decimals and Vice Versa. 17 - Percentages. 18 - Probability. 19 - Ratio and Proportion. 20 - A Useful Procedure for Tackling Maths Problems. Appendix. The National Numeracy Strategy. 100 number Square and Number Grids. Tables Practice Sheets-find The Right Answer. East Court Table Sums-graded Card Lists for Pupils' Individual Learning. Coinage. Clock Faces. Fraction Diagrams. Answers to Practice Sheets at Ends of Sections. More General Practice Sums Together With Answers. List of materials. Books and Computer Software, Together With Addresses.

Read more less

Book SynopsisWritten by a teacher with many years' experience of teaching mathematics to primary school dyslexic and dyspraxic children with a wide range of abilities, this book is designed to be a practical teaching guide. It offers detailed guidance and specific teaching suggestions to all specialist teachers, support teachers, classroom teachers and parents who either directly teach mathematics to dyslexic and dyspraxic children or who support the mathematics teaching programmes of dyslexic or dyspraxic children. Although the book has grown out of teaching experience it is also informed by widely acknowledged contemporary and international research, which explores the cognitive aspects of learning mathematics and tries to understand why it is that some children fail to learn mathematics. Many of the teaching principles described in the text have specific and quite far-reaching implications. The theoretical arguments should therefore also be of interest to special needs co-ordinators, heads of maths departments, head teachers or other professionals who are responsible for designing or modifying the maths learning programmes of children with special learning and maths difficulties. In more general terms, the book hopes to contribute to the broad discussion of the cognitive features and educational needs of dyslexic and dyspraxic children.Table of ContentsForeword by Steve Chinn Preface Part 1 - Definitions and Premises Part 2 - Basic Counting and The Early Stages of Addition and Subtraction Part 3 - The Number System Part 4 - More Addition and Subtraction, Working With Larger numbers Part 5 - Multiplication and Division. Appendix. References. Index

Read more less

Book SynopsisFrom an early age, deaf children excel in thinking about and remembering what they learn through visual spatial instruction. This strength in information processing can be used in the mathematics classroom to achieve better learning outcomes. This book discusses ways to teach deaf children about the four arithmetic operations through spatial representation in problem solving. Examples for the teaching of fractions and graphs are also included. These visual representations are useful to support the children's understanding of mathematical concepts and to promote peer collaboration. The teaching programme was tested with deaf children in six schools with excellent results: the children in the project made significantly more progress in one school year than expected for either deaf and hearing children over the same time. This work was made possible through the generous support of The Nuffield Foundation.Trade Review"...this book gives a comprehensive account of the mathematical tests and assessments used with both deaf and hearing children..." (British Association of Community Doctors in Audiology Newsletter, April 2005)Table of ContentsPreface. Acknowledgements. Conventions used for descriptions of interviews. Chapter 1 Introduction. Chapter 2 Counting and its creative uses. Chapter 3 Additive reasoning: connecting addition and subtraction. Chapter 4 Reading and writing numbers. Chapter 5 Multiplicative reasoning: connecting multiplication, division and many other mathematical ideas. Chapter 6 Teaching mathematics to deaf children: how the story began and the happy ending. References. Index.

Read more less

Book SynopsisSubtraction Facts That Stick will guide you, step-by- step, as you teach your child to understand and memorize the subtraction facts, from 1 - 1 through 9 - 9. Hands-on activities, fun games your child will love, and simple practice pages help young students remember the subtraction facts for good. In 15 minutes per day (perfect for after school, or as a supplement to a homeschool math curriculum) your child will master the subtraction facts, gain a greater understanding of how math works, and develop greater confidence, in just six weeks! Mastery of the math facts is the foundation for all future math learning. Lay that foundation now, and make it solid, with Subtraction Facts That Stick!

Read more less

Book Synopsis

Read more less

Book SynopsisSimple and straightforward workbook pages give children practice with new concepts and provide daily review of previously-learned skills. Short, simple pages give children written practice without tiring small hands Daily review helps children retain what they have learned All answers provided in the Instructor’s Guide for easy correcting Colorful, whimsical illustrations Age Range: 7-8 Grade Range: Second Grade

Read more less

Book Synopsis Der Band stellt mathematikdidaktisches Basiswissen bereit, das für den Unterricht in der Sekundarstufe relevant ist. Im Fokus steht dabei ein schülerorientierter und kognitiv aktivierender Mathematikunterricht, der inhaltlich und konzeptionell auf den aktuell gültigen Bildungsstandards aufbaut. Einerseits werden theoretische Ideen und empirische Evidenz rund um das Lehren und Lernen beschrieben, andererseits steht die Auseinandersetzung mit dem Fach Mathematik im Vordergrund, die an exemplarischen Inhalten illustriert und mit geeigneten Aufgaben unterstützt wird. Die behandelten Themen umfassen beispielsweise Begründungen für die Bedeutung des Mathematikunterrichts, nationale Bildungsstandards und mathematische Kompetenz, Grundmuster des Fachs, die Rolle von Aufgaben und Fehlern im Unterricht oder die Entwicklung mathematischen Denkens. In der zweiten Auflage wurden die Beispiele noch einmal erweitert, um so den Bezug zur schulischen Praxis zu stärken. Adressaten sind Studentinnen und Studenten des Lehramts, aber auch Lehrkräfte an Schulen. Der Band kann ihnen sowohl als zusammenfassende Darstellung als auch als Handbuch zu einzelnen Fragen des Mathematikunterrichts dienen.Table of Contents1 Ziele des Mathematikunterrichts.- 2 Mathematik unterrichten.- 3 Die Entwicklung mathematischen Denkens.- 4 Individuelle Voraussetzungen des Lernens im schulischen Kontext.- 5 Grundmuster des Arbeitens in der Mathematik.- 6 Didaktische Prinzipien.- 7 Bildungsstandards und Kompetenzen.- 8 Aufgaben im Mathematikunterricht.- 9 Fehler und Fehlerdiagnose.- 10 Planung von Mathematikunterricht.- Literaturverzeichnis.- Namen- und Stichwortverzeichnis.

Read more less

Book SynopsisNach einer stürmischen Bewegung in den sechzigerund Anfang der siebziger Jahre befindet sich der Mathematikunterricht in der Grundschule seit etwa zwei Jahren zweifellos in einer Phase der Konsolidierung, mit der eine kritische Revision der bisherigen didaktischen Ent­ wicklungen und eine Trennung von Spreu und Weizen einhergehen. Es mag mancher.1 Kollegen im gegenwärtigen Zeitpunkt als zu früh erscheinen, wenn wir mit dem vorliegenden Buch eine "Didaktik" des Mathematikunterrichts in der Grund­ schule vorlegen. Auch wir selbst sind uns sehr bewußt, daß unsere Konzeption nicht in dem Umfang erprobt und überarbeitet ist, wie man es wünschen möchte und wie es z. B. bei den traditionellen Rechendidaktiken in der Regel der Fall war. Wir haben uns aber trotzdem aus drei Gründen zu einer Publikation entschlossen. Erstens halten wir es für notwendig, daß die Lehrerschaft am Prozeß der weiteren Konsoli­ dierung mitarbeiten kann, und glauben, daß dazu Orientierungsrahmen angeboten werden müssen, innerhalb deren experimentiert und diskutiert werden kann. Das vorliegende Buch entwickelt einen solchen Rahmen.Table of Contents1. Unterrichtsbeispiele.- 2. Die Situation des Mathematikunterrichts in der Grundschule — Kritische Bilanz der Reformbewegung und ein Ansatz zu einer Konsolidierung.- 3. Didaktische Analyse zentraler Themen des Mathematikunterrichts in der Primarstufe.- 4. Didaktische Fragmente.- Hinweise zur Lösung der nicht mit * versehenen Aufgaben.- Sachwortverzeichnis.

Read more less

Book SynopsisWie lernen Kinder Mathematik? Wie können Lernende und Lehrende Mathematik so darstellen, dass intensive Kommunikationsprozesse beim Mathematiklernen angeregt werden? Deuten SchülerInnen bestimmte mathematische Darstellungen während des Lernprozesses anders als Lehrende? Wie können Lehrende Kinder dabei unterstützen, Mathematik zu verstehen? Lehramtsstudierende und Lehrende setzen sich fast täglich mit diesen und ähnlichen Fragen auseinander. Die BeitragsautorInnen beschäftigen sich mit diesen Fragestellungen und zeigen unterschiedliche Sichtweisen und Perspektiven auf. Der Bogen der Beiträge spannt sich von einem Überblick über mathematische Begriffsbildung und Darstellungen als notwendiges Ausdrucksmittel mathematischer Ideen über das frühe mathematische Lernen in Kindertagesstätten bzw. Kindergärten, Sichtweisen zur Primar- und Sekundarstufe bis hin zu Beiträgen zur mathematischen Hochschullehre.Table of Contents​Lehrerausbildung.- Mathematikdidaktik.- Frühkindliche Bildung.- Primarstufe.- Sekundarstufe.- Hochschule.​

Read more less

Book Synopsis​Die Fähigkeit, verschiedene Darstellungsformen zu nutzen und zwischen ihnen zu wechseln, ist in den Bildungsstandards und Lehrplänen der Grundschule fest verankert. Katharina Kuhnke untersucht mithilfe von 15 Einzelfallstudien den Prozess des Darstellungswechsels, indem sie das Vorgehen von Kindern beim Wechsel zwischen verschiedenen multiplikativen Darstellungen betrachtet. Sie analysiert diesen Prozess aus epistemologischer Perspektive, rekonstruiert ihn als komplexes Gefüge und arbeitet verschiedene Kriterien heraus, auf die Kinder beim dieser Tätigkeit fokussieren.​Table of Contents​Darstellungswechsel als Übersetzungsprozess.- Darstellungswechsel als Lernprozess.- Vorgehensweisen.- Epistemologisches Dreieck.- Fokussierungen.- Variation​.

Read more less

Book SynopsisDer Tagungsband gibt einen breiten Überblick über Ziele, Kursszenarien und Lehr-Lernkonzepte, Unterstützungsmaßnahmen in der Studieneingangsphase, Möglichkeiten des Assessments und der Diagnostik sowie einen Ausblick zur Zukunft von mathematischen Vor- und Brückenkursen. Zudem werden aktuelle Vor- und Brückenkursprojekte vorgestellt und der aktuelle empirische und theoretisch-konzeptionelle didaktische Forschungsstand in diesem Bereich abgebildet. ​Table of ContentsZiele, Inhalte und Adressaten von Vorkursen.- Kursszenarien und Lehr-Lernkonzepte, inkl. Rolle von E-Learning-Elementen.- Assessment und Diagnostik vor/in/nach einem Kurs.- Unterstützungsmaßnahmen in der Studieneingangsphase.

Read more less