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The Mathematics That Every Secondary Math Teacher Needs To Know

Author: Alan Sultan
Publisher: Routledge
ISBN: 1135157839
Size: 77.96 MB
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What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.

Mathematics For Secondary School Teachers

Author: Elizabeth G. Bremigan
Publisher: MAA
ISBN: 0883857731
Size: 63.28 MB
Format: PDF, ePub, Mobi
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Mathematics for Secondary School Teachers discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement.Acknowledging diversity in the mathematical backgrounds of pre-service teachers and in the goals of teacher preparation programs, the authors have written a flexible text, through which instructors can emphasize any of the following: Basics: exploration of key pre-college topics from intuitive and rigorous points of view; Connections: exploration of relationships among topics, using tools from college-level mathematics; Extensions: exploration of college-level mathematical topics that have a compelling relationship to pre-college mathematics.Mathematics for Secondary School Teachers provides a balance of discovery learning and direct instruction. Activities and exercises address the range of learning objectives appropriate for future teachers. Beyond the obvious goals of conceptual understanding and computational fluency, readers are invited to devise mathematical explanations and arguments, create examples and visual representations, remediate typical student errors and misconceptions, and analyze student work. Introductory discussion questions encourage prospective teachers to take stock of their knowledge of pre-college topics. A rich collection of exercises of widely varying degrees of difficulty is integrated with the text. Activities and exercises are easily adapted to the settings of individual assignments, group projects, and classroom discussions.Mathematics for Secondary School Teachers is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers. It can also be used in alternative licensure programs, as a supplement to a mathematics methods course, as the text for a graduate course for in-service teachers, and as a resource and reference for in-service faculty development.

Knowing And Teaching Elementary Mathematics

Author: Liping Ma
Publisher: Routledge
ISBN: 1135149496
Size: 80.52 MB
Format: PDF, Mobi
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Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Teaching Secondary School Mathematics

Author: Merrilyn Goos
Publisher: Allen & Unwin
ISBN: 1741156130
Size: 43.23 MB
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Excellent mathematics teachers make a major difference to the learning outcomes of the students they teach. What are the professional skills and knowledge that really matter? Teaching Secondary School Mathematics is a research based introduction to the professional knowledge, attributes and practices needed to teach mathematics well at secondary level. The authors explain the challenges that secondary mathematics teachers face today, and how they can build on the experiences students bring from primary school and from outside the classroom to ensure students develop concepts and skills in mathematical thinking and a positive attitude to mathematics. They outline the secondary mathematical curriculum and methods of assessment, and examine the pedagogical strategies teachers can use to engage student interest in mathematical concepts. They emphasise the importance of working with mathematical reasoning and problem solving, real world applications, and mathematical communication skills. The core mathematical topics covered at secondary level are reviewed, and the authors also explore the issues teachers need to consider with students of diverse backgrounds. 'I highly recommend this book to practising mathematics teachers as well as pre-service teachers. The combination of research and practical teaching ideas ensures current and worthwhile advice for teaching secondary or middle school students.' Dr Judy Anderson, The University of Sydney 'An excellent book - very readable, interspersed with useful tasks which are grounded in attending to effective classroom practices. A much overdue resource for initial teacher preparation courses.' Associate Professor Glenda Anthony, Massey University

Engaging Young Children In Mathematics

Author: Douglas H. Clements
Publisher: Routledge
ISBN: 0805842101
Size: 64.86 MB
Format: PDF, Mobi
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Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Conference of Teachers of Mathematics and the National Association for the Education of Young Children. The main goal of the Conference was to work collectively to help those responsible for framing and implementing early childhood mathematics standards. Although it has its roots in the Conference, the expanded scope of the standards and recommendations covered in this book includes the full range of kindergarten to grade 2. The volume is organized into two main parts and an online appendix (http://www.gse.buffalo.edu/org/conference/). Part One, Major Themes and Recommendations, offers a framework for thinking about pre-kindergarten - grade 2 mathematics education and specific recommendations. Part Two, Elaboration of Major Themes and Recommendations, provides substantive detail regarding young students' understandings of mathematical ideas. Each Part includes five parallel subsections: "Standards in Early Childhood Education"; "Math Standards and Guidelines"; "Curriculum, Learning, Teaching, and Assessment"; "Professional Development"; and "Toward the Future: Implementation and Policy." As a whole the book: * presents comprehensive summaries of research that provide specific guidelines for standards, curriculum, and teaching; * takes the recent reports and recommendations for early childhood mathematics education to the next level; * integrates practical details and research throughout; and * provides a succinct, but thorough review of research on the topics, sequences, and learning trajectories that children can and should learn at each of their first years of life, with specific developmental guidelines that suggest appropriate content for each topic for each year from 2-year-olds to 7-year-olds. This is an indispensable volume for mathematics educators, researchers, curriculum developers, teachers and policymakers, including those who create standards, scope and sequences, and curricula for young children and professional teacher development materials, and students in mathematics education, early childhood trainers, teacher educators, and faculty in mathematics education.

Becoming A Reflective Mathematics Teacher

Author: Alice F. Artzt
Publisher: Routledge
ISBN: 1317691997
Size: 67.74 MB
Format: PDF, ePub, Mobi
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Ideal for preservice mathematics teachers who are taking methods courses or are student teaching, this research-based, activity-oriented guide offers a highly effective framework for teacher reflection and self-assessment. Highlighting inquiry-based, learner-centered teaching and grounded in a cognitive perspective, Becoming a Reflective Teacher of Mathematics, Third Edition features: Detailed observation instruments for observing other teachers Reflective activities that provide a structure for beginning teachers to think about their teaching Guidelines and instruments for supervisors to use when observing, conferencing with, and assessing beginning or student teachers The Third Edition of Becoming a Reflective Teacher of Mathematics is aligned with the latest standards for teaching mathematics including the Common Core State Standards-Mathematics, and the latest assessments for mathematics teacher certification which place a high priority on reflective practice. Thoroughly revised and updated throughout, the Third Edition continues to provide preservice and in-service mathematics teachers with practical ideas for developing and honing reflective and self-analytical skills needed to advance and improve instruction.

A Focus On Multiplication And Division

Author: Elizabeth T. Hulbert
Publisher: Routledge
ISBN: 1351671693
Size: 52.64 MB
Format: PDF, Mobi
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A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K–6 mathematics educators. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers.

Understanding Emotions In Mathematical Thinking And Learning

Author: Ulises Xolocotzin
Publisher: Academic Press
ISBN: 0128024895
Size: 51.32 MB
Format: PDF, ePub, Docs
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Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. Covers methodologies in studying emotion in mathematical knowledge Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches Explores the role of anxiety in mathematical learning Synthesizes unifies the work of multiple sub-disciplines in one place

Aimssec Maths Teacher Support Series Mathematical Thinking In The Lower Secondary Classroom

Author: AIMSSEC
Publisher: Cambridge University Press
ISBN: 1316503623
Size: 23.29 MB
Format: PDF, Kindle
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This series is for maths teachers who want to develop their maths teaching skills. This book is for teachers and educators who want to develop their maths teaching skills where English is the language of instruction. It has been written by the international group of educators based at AIMSSEC, The African Institute for Mathematical Sciences Schools Enrichment Centre. The book provides practical classroom activities underpinned by sound pedagogy and recent research findings. The activities are designed for teachers working alone or in 'self-help' teachers' workshops. They are designed to develop mathematical thinking and offer immediate practical tools to help deliver this approach.

Early Childhood Mathematics Education Research

Author: Julie Sarama
Publisher: Routledge
ISBN: 1135592497
Size: 73.53 MB
Format: PDF
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This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.