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“A noteworthy feature of the book is that eleven of the chapter authors work in mainland China … The edited collection is a significant contribution to the research literature and provides an important resource in the field.” Research in Mathematics Education “In a context of revolving reforms of the mathematical curricula in the West, the research presented in How Chinese Learn Mathematics certainly gives a lot of food for thought about effectively combining a problem-oriented approach to basic mathematical knowledge and skills with a conceptual and abstract representation of mathematical objects.”EASTM “The book copes with the issue of mathematics education in a culturally attentive way and offer hints to reconsider policies on mathematics education in the Western world. Hence, it should be present in the library of each education department.”EMS Newsletter The book has been written by an international group of very active researchers and scholars who have a passion for the study of Chinese mathematics education. It aims to provide readers with a comprehensive and updated picture of the teaching and learning of mathematics involving Chinese students from various perspectives, including the ways in which Chinese students learn mathematics in classrooms, schools and homes, the influence of the cultural and social environment on Chinese students' mathematics learning, and the strengths and weaknesses of the ways in which Chinese learn mathematics. Furthermore, based on the...
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Growing out of a course in the history of mathematics given to school teachers,the present book covers a number of topics of elementary mathematics from both the mathematical and historical perspectives.Included are topics from geometry (π, Napoleon's Theorem, trigonometry),recreational mathematics (the Pell equation, Fibonacci numbers), and computational mathematics (finding square roots, mathematical tables). Although written with the needs of the mathematics teacher in mind, the book can be read profitably by any high school graduate with a liking for mathematics.
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A volume in the series The Montana Mathematics Enthusiast: Monograph Seriesin Mathematics Education. Series Editor: Bharath Sriraman, The University of MontanaThe teaching and learning of mathematics in Alberta - one of three Canadian provinces sharing aborder 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 AlbertaTeachers' Association. This volume, which presents ten memorable articles from each of the pastfive decades, that is, 50 articles from the past 50 years of the journal, provides an opportunity toshare this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematicseducation. Each decade begins with an introduction, providing a historical context, and concludes with a commentary from a prominentmember of the Alberta mathematics education community. As a result, this monograph provides a historical account as well as acontemporary view of many of the trends and issues in the teaching and learning of mathematics. This volume is meant to serve as aresource for a variety of individuals, including teachers of mathematics, mathematics teacher educators, mathematics educationresearchers, historians, and undergraduate and graduate students. Most importantly, this volume is a celebratory retrospective on thework of the Mathematics Council of the Alberta Teachers' Association.
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A volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationThe teaching and learning of mathematics in British Columbia has a long and storied history. An integral part of the past 50 years (1962-2012) of this history has been Vector: Journal of the British Columbia Association of Mathematics Teachers. 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 British Columbia mathematics education community. As a result, this monograph provides a historical ac-count 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 re-source 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 British Columbia Association of Mathe-matics Teachers.
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Doctoral Thesis / Dissertation from the year 2010 in the subject Sociology - Knowledge and Information, grade: A, Atlantic International University (School of Social and Human Studies), course: Doctorate in Education, language: English, abstract: The primary purpose of this research was to investigate the effects of individual student affective factors and educational background on mathematics achievement among higher education students as measured by semester grades in the core mathematics courses. Student Locus of Control, Self-Efficacy, and Mathematics Anxiety were the specific individual student affective factors that were examined in the study. Educational backgrounds of the students were examined as an attempt to explain the differences in mathematics performance at the higher education level. To achieve this, high school teacher characteristics and instructional practices in influencing students' affective factors were examined. All of the analyses presented were performed on data collected for the study from two institutions of higher education in Cameroon for the student participants and from high school mathematics teachers of the English-Speaking and the French-Speaking subsystems of education. The results of the study show that student internal locus of control, high mathematics self-efficacy, and Mathematics Anxiety were associated with performance in mathematics at the higher education level. The results also revealed a high significant difference in the per...
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A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaThe word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied toa situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments orjudgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authorscontributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics insociety and the implications for education. Traditional reasons for teaching mathematics include: preparing a newgeneration of mathematics researchers and a cadre of technically competent users of mathematics; training students tothink logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remainvalid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing manyaspects of contemporary society, that will connect mathematics education to the lived experiences of students, theircommunities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians andmathematics educators.The book is organized in four sections (1) Mathematics education: For what and why?(2) Globalization and cultural...
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Praise for the Second Edition «An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.» —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.
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Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes work Numerous figures and diagrams as well as hundreds of worked examples and exercises, aiding readers to further visualize the presented concepts Various real-world practical applications of mathematics, including error-correcting codes and the space shuttle program Vignette biographies of renowned mathematicians Appendices with solutions to selected exercises and suggestions for further reading Mathematics for the Liberal Arts is an excellent introduction to the history and concepts of mathematics for undergraduate liberal arts students and readers in non-scientific fields wishing to gain a better understanding of mathematics and mathematical problem-solving skills.
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This monograph marks a major step in the growth of the Association of Mathematics Teacher Educators (AMTE) as the leading organization for mathematics teacher educators. It is an effort by AMTE to provide further support for the work of mathematics teacher educators throughout the United States. It is hoped that readers will find this monograph to be useful in their day-to-day work with mathematics teachers. Learning to be a mathematics teacher is a life-long process, but so is learning to be a mathematics teacher educator. Just as mathematics teachers need opportunities for professional growth, so do mathematics teacher educators. Publications such as this monograph can serve an important role in the professional development of mathematics teacher educators.
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A volume in Research on Technology and the Teaching and Learningof Mathematics: Syntheses, Cases, and PerspectivesAccording to NCTM's Principles and Standards for School Mathematics, "Technology isessential in teaching and learning of mathematics; it influences the mathematics that is taughtand it enhances students' learning." How does research inform this clarion call for technology inmathematics teaching and learning? In response to the need to craft appropriate roles fortechnology in school mathematics new technological approaches have been applied to theteaching and learning of mathematics, and these approaches have been examined by researchersworld-wide.The first volume provides insight into what research suggests about the nature of mathematicslearning in technological environments. Included in this volume are syntheses of research ontechnology in the learning of rational number, algebra, elementary and secondary geometry,mathematical modeling, and calculus. Additional chapters synthesize research on technology in the practice of teaching and on equityissues in the use of technology in mathematics instruction. Instead of simply reporting achievement scores of students who use technologyin their learning, authors provide thoughtful analyses of bodies of research with the goal of understanding the ways in which technologyaffects what and how students learn. Each of the chapters in this volume is written by a team of experts whose own research hasprovided i...
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An easy-to-read presentation of the early history of mathematics Engaging and accessible, An Introduction to the Early Development of Mathematics provides a captivating introduction to the history of ancient mathematics in early civilizations for a nontechnical audience. Written with practical applications in a variety of areas, the book utilizes the historical context of mathematics as a pedagogical tool to assist readers working through mathematical and historical topics. The book is divided into sections on significant early civilizations including Egypt, Babylonia, China, Greece, India, and the Islamic world. Beginning each chapter with a general historical overview of the civilized area, the author highlights the civilization’s mathematical techniques, number representations, accomplishments, challenges, and contributions to the mathematical world. Thoroughly class-tested, An Introduction to the Early Development of Mathematics features: Challenging exercises that lead readers to a deeper understanding of mathematics Numerous relevant examples and problem sets with detailed explanations of the processes and solutions at the end of each chapter Additional references on specific topics and keywords from history, archeology, religion, culture, and mathematics Examples of practical applications with step-by-step explanations of the mathematical concepts and equations through the lens of early mathematical problems A companion website that includes additional exercises An Introduction to the Early Development of Mathematics is an ideal textbook for undergraduate courses on the history of mathematics and a supplement for elementary and secondary education majors. The book is also an appropriate reference for professional and trade audiences interested in the history of mathematics. Michael K. J. Goodman is Adjunct Mathematics Instructor at Westchester Community College, where he teaches courses in the history of mathematics, contemporary mathematics, and algebra. He is also the owner and operator of The Learning Miracle, LLC, which provides academic tutoring and test preparation for both college and high school students.
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The mathematics curriculum - what mathematics is taught, to whom it is taught, and when it is taught - is the bedrock to understanding what mathematics students can, could, and should learn. Today's digital technology influences the mathematics curriculum in two quite different ways. One influence is on the delivery of mathematics through hardware such as desktops, laptops, and tablets. Another influence is on the doing of mathematics using software available on this hardware, but also available on the internet, calculators, or smart phones.These developments, rapidly increasing in their availability and decreasing in their cost, raise fundamental questions regarding a mathematics curriculum that has traditionally been focused on paper-and-pencil work and taught in many places as a set of rules to be practiced and learned.This volume presents the talks given at a conference held in 2014 at the University of Chicago, sponsored by the Center for the Study of Mathematics Curriculum. The speakers - experts from around the world and inside the USA - were asked to discuss one or more of the following topics:• changes in the nature and creation of curricular materials available to students• transformations in how students learn and how they demonstrate their learning• rethinking the role of the teacher and how students and teachers interact within a classroom and across distances from each otherThe result is a set of articles that are interesting and captivating, and challenge u...
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Document from the year 2014 in the subject Mathematics - Applied Mathematics, grade: 13, , course: B.Tech, Semester-II, language: English, abstract: Its applied mathematics notes for B.Tech students of Second Semester of Indian Universities.Strictly according to the syllabus of P.T.U (Jalandhar)
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A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaOur innovative spirit and creativity lies beneath the comforts and security of today's technologicallyevolved society. Scientists, inventors, investors, artists and leaders play a vital role in theadvancement and transmission of knowledge. Mathematics, in particular, plays a central role innumerous professions and has historically served as the gatekeeper to numerous other areas ofstudy, particularly the hard sciences, engineering and business. Mathematics is also a major componentin standardized tests in the U.S., and in university entrance exams in numerous parts ofworld.Creativity and imagination is often evident when young children begin to develop numeric andspatial concepts, and explore mathematical tasks that capture their interest. Creativity is also anessential ingredient in the work of professional mathematicians. Yet, the bulk of mathematical thinking encouraged in the institutionalizedsetting of schools is focused on rote learning, memorization, and the mastery of numerous skills to solve specific problems prescribedby the curricula or aimed at standardized testing. Given the lack of research based perspectives on talent development inmathematics education, this monograph is specifically focused on contributions towards the constructs of creativity and giftedness inmathematics. This monograph presents new perspectives...
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For the first time, all of your first 100 lessons of mathematics are in one book. Come on a journey that takes you from numbers and symbols to branches of mathematics including arithmetic, percentages, geometry, and algebra. Unlock the secrets of the mathematics of money. These first 100 lessons are presented in learning order to maximize your progress.
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Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.
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In this brief treatise, Carus traces the roots of his belief in the philosophical basis for mathematics and analyzes that basis after a historical overview of Euclid and his successors. He then examines his base argument and proceeds to a study of different geometrical systems, all pulled together in his epilogue, which examines matter, mathematics, and, ultimately, the nature of God.
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The seventh monograph of AMTE highlights examples of important scholarship of and for the mathematics teacher education community. This monograph, like others produced by AMTE, serves as a forum for mathematics teacher educators to exchange ideas, experiences, resources, and detailed accounts of work to improve teacher preparation. Chapters in this monograph take up a variety of issues such as using online social networking in the preparation of teachers, examining the impact of textbook-specific professional development, and offering a mathematics-specific reading in the content area course.
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Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested
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A volume in Research on Technology and the Teaching and Learningof Mathematics: Syntheses, Cases, and PerspectivesAccording to NCTM's Principles and Standards for School Mathematics, "Technology isessential in teaching and learning of mathematics; it influences the mathematics that is taughtand it enhances students' learning." How does research inform this clarion call for technology inmathematics teaching and learning? In response to the need to craft appropriate roles fortechnology in school mathematics new technological approaches have been applied to theteaching and learning of mathematics, and these approaches have been examined by researchersworld-wide.The second volume has a dual focus: cases and perspectives. It features descriptive cases thatprovide accounts of the development of technology-intensive curriculum and tools. In thesecases the writers describe and analyze various roles that research played in their developmentwork and ways in which research, curriculum development, and tool development can informeach other. These thoughtful descriptions and analyses provide documentation of how this processcan and does occur. The remaining chapters in the second volume address research-related issues and perspectives on the use oftechnology in the teaching and learning of mathematics. The lessons learned from the research presented in these volumes are lessonsabout teaching and learning that can be applied more broadly than solely in technological setting...
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A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaPaul Ernest's name is synonymous with social constructivism as a philosophy ofmathematics. His contributions to mathematics education have occurred at a veryfundamental level and to an extent shaped theory development in this field. Hisresearch addresses fundamental questions about the nature of mathematics and how itrelates to teaching, learning and society. For the last three decades Paul has been aprolific scholar who has published in a wide array of topics such as the relationshipbetween the philosophy of mathematics and mathematics education, and moregenerally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy ofresearch methodology.The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certaintythat Paul argued for in developing his philosophy, and also a play on words for the fact that absolute "earnestness" mayperhaps be a Platonic construct, and not possible in the realm of language and human discourse! Paul Ernest's scholarlyevolution and life can best be summarized in the words of Walt Whitman "Do I contradict myself? Very well then Icontradict myself" (I am large, I contain multitudes). Indeed his presence has beenlarge and multitudinous and this Festschrift celebrates his 65th Birthday w...
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Curriculum materials are among the most pervasive and powerful influences on schoolmathematics. In many mathematics classes, student assignments, the questions theteacher asks, the ways students are grouped, the forms of assessment, and much moreoriginate in curriculum materials. At the same time, teachers have considerable latitude inhow they use their curriculum materials. Two classes making use of the same materialsmay differ markedly in what mathematics content is emphasized and how students are engaged in learning that content.This volume considers a variety of research tools for investigating the enactment of mathematics curriculum materials,describing the conceptualization, development, and uses of seven sets of tools. Mathematics education researchers,curriculum developers, teacher educators, district supervisors, teacher leaders, and math coaches will find insights that canimprove their work, and guidance for selecting, adapting, and using tools for understanding the complex relationshipbetween curriculum materials and their enactment in classroom instruction.
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This book provides examples of the ways in which 9-12 grade mathematics teachers from across North America are engaging inresearch. It offers a glimpse of the questions that capture the attention of teachers, the methodologies that they use to gather data, and theways in which they make sense of what they find. The focus of these teachers' investigations into mathematics classrooms ranges from students'understanding of content to pedagogical changes to social issues. Underlying the chapters is the common goal of enabling students todevelop a deep understanding of the mathematics they learn in their classrooms.By opening their analysis of their classroom practice to our inspection, these courageous teachers have invited us to think alongwith them and to learn more about our own teaching as a result. By sharing their work, they have given the mathematics education communityan important opportunity. Everyone who reads this book-teachers, researchers, teacher-researchers, policy makers, administrators, andothers interested in mathematics education-can learn from the findings and the light that they shed on issues important to mathematics education.This book, and the series of which it is a part, also provides the opportunity to step back and reflect on what can be learned aboutresearch from teachers who have engaged in the process. Areas of insight include: (a) the importance of collaboration and participation incommunities that value research, (b) the potential of teache...
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This book presents examples of the scholarship of Brazilian mathematics educators. The authors who contributed to this collection situate their work within the construct of creative insubordination. With this collection we hope to increase the participation of Brazilian scholars in the international conversations of research on mathematics teaching and learning.
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A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaInternational Perspectives and Research on Social Justice in Mathematics Education is the highly acclaimedinaugural monograph of The Montana Mathematics Enthusiast now available through IAP. The book coversprescient social, political and ethical issues for the domain of education in general and mathematics educationin particular from the perspectives of critical theory, feminist theory and social justice research. The majorthemes in the book are (1) relevant mathematics, teaching and learning practices for minority andmarginalized students in Australia, Brazil, South Africa, Israel, Palestine, and the United States., (2) closingthe achievement gap in the U.K, U.S and Iceland across classes, ethnicities and gender, and (3) the politicaldimensions of mathematics. The fourteen chapters are written by leading researchers in the internationalcommunity interested and active in research issues of equity and social justice.
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Mathematics teacher education has a critical role to play in preparing teachers to put at center stage goals tosupport equity in mathematics education and to diversify student interest and participation in mathematics.These goals must also resonate with broader public interest goals to improve educational and socialconditions both in the U.S. and abroad. The Mathematics Teacher Education in the Public Interest book aimsto support mathematics teacher educators to prepare teachers with new knowledge and skills to support allstudents to learn mathematics and to become informed, engaged, and critical citizens within theircommunity, nation, and world. While internationally there is considerable interest among mathematicseducators in issues of equity and social justice, the literature on mathematics teacher education for equity andsocial justice thus far has been very limited.The book provides theoretical discussions on the need for equity and social justice emphases inmathematics teacher education, as well as practical examples from mathematics teacher educators, documenting their own professional efforts tocenter practices on equity and social justice. Section emphases include critical perspectives on mathematics teacher education, the use of equity andsocial justice-themed activities in mathematics teacher preparation courses, and issues of identity and community and cultural contexts in mathematicsteacher education. In addition syntheses of major ideas of the book are offered b...
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A Volume in International Perspectives on Mathematics Education- Cognition, Equity & SocietySeries Editor Bharath Sriraman, The University of Montana and Lyn English, QueenslandUniversity of TechnologyThe purpose of the book is to consider embodiment as it applies to mathematical thinking, and tolink mathematics education research to recent work in gesture studies, cognitive linguistics andthe theory of embodied cognition. Just as in past decades, mathematics education experienced a"turn to the social" in which socio-cultural factors were explored, in recent years there has been anascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in thefact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in,and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biologicaland cognitive capabilities, as well as certain common physical experiences that come with being humans living in a materialworld. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range ofbodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume willpresent recent research on gesture and mathematics, within a framework that addresses several level...
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This is a book about zero. This is not a book about the zero you learnt about in school. This is a book about three different types of zeros, a misunderstanding and the impact it has had on Western mathematics and physics. It is one of the strangest tales in the history of mathematics and science. It is no coincidence that the most controversial areas of mathematics are also involved in many of the unexplained problems in physics. After thousands of years of research, you would think that we would know all there is to know about basic algebra. However, as our understanding of mathematics and physics has advanced, it has exposed deficiencies in our theories about numbers and basic mathematics.
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A perennial discussion about teacher development is the optimal content background for teachers. Inrecent years, that discussion has taken center stage in the work of mathematics education researchers,mathematicians, mathematics professional developers, and mathematics education policymakers. Muchof the existing and prior work in this area has been directed toward mathematical knowledge forteaching at the elementary level. The work described in this volume takes a sometimes-neglectedapproach, focusing on the dynamic nature of mathematical understanding rather than on a stabledescription of mathematical knowledge, and on mathematics for secondary teaching rather thanmathematics for teaching at the elementary level.The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-basedresponse to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics thatteachers could use-each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. Wedeveloped our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. Wecall the work practice-based because the MUST framework is based on actu...
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A volume in Cognition, Equity, & Society: International PerspectivesSeries Editors: Bharath Sriraman, University of Montanaand Lyn English, Queensland University of TechnologyMathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the argumentsand controversy of politics and social life. However, critical mathematics challenges these assumptions andactively attacks the idea that mathematics is pure, objective, and value‐neutral. It argues that history, society,and politics have shaped mathematics-not only through its applications and uses but also through molding its concepts, methods, and evenmathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching andlearning of mathematics, showing how these are value‐laden activities indissolubly linked to social and political life. Instead, it argues that the valuesof openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship arenecessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice.This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field.Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, thehegemony o...
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A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, Iowa State UniversityThis volume contains papers from the Second International Curriculum Conference sponsored by the Centerfor the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculumdevelopers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.
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A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, University of MississippiThe purpose of this book is to document the work of the Show-Me Project (1997-2007) and to highlight lessonslearned about curriculum implementation. Although the Show-Me Project was charged with promotingthe dissemination and implementation of four distinct comprehensive curriculum programs (Connected Mathematics,Mathematics in Context, MathScape, and MathThematics), most of the lessons learned from this workare not curriculum specific. Rather, they cut across the four programs and share commonalities with standards-based curriculum reform at any level.We believe that documenting these lessons learned will be one of the legacies of the Show-Me ProjectWe anticipate that the comprehensive nature of this work will attract readers from multiple audiences that include state and district mathematics supervisors,middle grades mathematics teachers and administrators involved in curriculum reform, as well as mathematics teacher educators. Those aboutto embark on the review of curriculum materials will appreciate reading about the processes employed by other districts. Readers with interests in aparticular curriculum program will be able to trace the curriculum-specific chapters to gain insights into how the design of the curricula relate to professionaldevelopment, adoption and implementation issues, and teachers' personal experience using the curriculum materials. Individuals...
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From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.
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The realism/anti-realism debate is one of the traditional central themes in the philosophy of mathematics. The controversies about the existence of the irrational numbers, the complex numbers, the infintesimals, etc. will be familiar to all who are acquainted with the history of mathematics.This book aims mainly at presenting and defending a non-Platonist form of mathematical structural realism which, in the respect of the history of mathematics, harmonizes with a plausible epistemology that naturally arises from it."Gianluigi Oliveri's book embodies a masterly survey of salient questions in the philosophy of mathematics, and propounds a challenging, if controversial, theory of the subject." Michael Dummett
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Discrete Mathematics for Teachers is a text designed to fill this void. The topic is right. Discrete mathematics provides a rich and varied source of problems for exploration and communication, expands knowledge of mathematics in directions related to elementary and middle school curricula, and is easily presented using our best understanding of the ways that mathematics is learned and taught. The presentation is right. In the spirit of NCTM's Principles and Standards for School Mathematics, topics are presented with careful attention to the best traditions of problem solving, reasoning and proof, communication, connections with other disciplines and other areas of mathematics, and varied modes of representation.
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A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, University of MississippiThis volume contains the proceedings of the First International Curriculum Conference sponsored by theCenter for the Study of Mathematics Curriculum (CSMC). The CSMC is one of the National Science FoundationCenters for Learning and Teaching (Award No. ESI-0333879).The countries-China, Japan, Korea, and Singapore (in alphabetical order, which also happens to be theorder of their populations)-have each been in the news because of their performance on international testsand/or their economic performance and potential. They also have centralized education ministries that createa single mathematics curriculum framework followed in the entire country.
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Every Cloud Has Its Own Name is a collection of poems and essays of Cai Tianxin, a renowned Chinese poet, traveler, photographer and mathematics professor. "Travelers are those trying to gain inspirations and enlightment through spacial movements". Inspired by both his outer and inner journeys, Cai Tianxin wonders in his world of emotional geometry, fascinated by the changs of perspective, builds a small universe of space, feeling and sensuality. "Mathematics is like a true language, which not only records and expresses ideas and the process of thinking, but also creats itself through poets and writers. It could be said that mathematics and poetry are the freest intellectual activistes of human beings. " ----Cai Tianxin
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The book is based on the recently held Symposium on mathematics and its connections to the artsand sciences, namely the second Mathematics and its Connections to the Arts and Sciences(MACAS2)Symposium in Odense, Denmark (May 29-31, 2007). The chapters are an eclectic collectionof interdisciplinary research initiatives undertaken by mathematics educators with implicationsfor practitioners concerned with teaching and learning processes. The papers cover a widegenre of research domains within mathematics education (cognition, modelling, problem solving,teacher education, ethnomathematics, mathematical/statistical literacy, curricular and technologicalinitiatives and research related to science education). The major interdisciplinary themes of thepapers in this book are:1. How can modelling activities be used to foster interdisciplinary projects in the school and university setting?2. How can the intricate connections between mathematics and physics be used to design and researchinterdisciplinary activities in schools and the university?3. How can research within the ethnomathematics domain of mathematics education be linked to criticalmathematics education and interdisciplinary projects involving mathematics, art and culture?4. How can the push for mathematical and statistical literacy be connected to other subjects in the schoolcurricula and emphasized via interdisciplinary activities?5. What are concrete examples of classroom experiments with empirical data that demonstrate ne...
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A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the third-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person – anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.
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Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
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The performance of Mathematics at Kenya Certificate of Primary Education has remained low compared to other subjects at this level (KNEC, 2006,2007,2008). This study investigated the factors affecting the teaching and learning of Mathematics in selected public primary schools in Usian Gishu between the period of May and July 2010. The study was guided by the following objectives: to establish the teacher, learner, syllabus and school-related factors affecting the teaching and learning of Mathematics and to determine challenges faced in Mathematics teaching and learning in primary schools. The study employed a descriptive survey study design and was guided by the education production function theory. The study population comprised of head teachers, teachers and pupils in public primary schools in Usian Gishu of Rift-Valley province. Stratified random sampling was used in selecting 15 schools for participation in this study. Purposive sampling was used to select fifteen head teachers and 45 teachers of Mathematics for inclusion in this study.
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A Volume in International Perspectives on Mathematics Education- Cognition, Equity & SocietySeries Editor Bharath Sriraman, The University of Montana and Lyn English, QueenslandUniversity of TechnologyThis volume represents a serious attempt to understand what it is that structures the pedagogicalexperience. In that attempt there are two main objectives. One is a theoreticalinterest that involves examining the issue of the subjectivity of the teacher and exploringhow intersubjective negotiations shape the production of classroom practice. A secondobjective is to apply these understandings to the production of mathematical knowledgeand to the construction of identities in actual mathematics classrooms. To that end thebook will contain substantial essays that draw on postmodern philosophies of the socialto explore theory's relationship with the practice of mathematics pedagogy.Unpacking Pedagogy takes new ideas seriously and engages readers in theory development. Groundbreaking in content, thebook investigates how our thinking about classroom practice in general, and mathematics teaching (and learning), in particular,might be transformed. As a key resource for interrogating and understanding classroom life, the book's sophisticatedanalyses allow readers to build new knowledge about mathematics pedagogy. In turn, that new knowledge will providethem with the tools to engage more actively in educational criticism and to play a role in educational change.
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A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
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Mathematics and Science education have both grown in fertile directions indifferent geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice todevelopments in cognition, curriculum, teacher development, assessment, policy and implementation ofmathematics and science in many countries. Paradoxically, in spite of advances in information technology andthe "flat earth" syndrome, old distinctions and biases between different groups of researcher's persist. In additionlimited accessibility to conferences and journals also contribute to this problem.The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of theworld and provides a platform for researchers to showcase their research anddevelopment 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 synthesizedtreatment of mathematics education that has both developed and is nowprominently emerging in the Asian and South Asian world. The book isorganized in sections coordinated by leaders in mathematics education inthese countries and editorial teams for each country affiliated with them. Thepurpose of unique sourcebook is to both consolidate and survey theestablished body of research in these countries with findings that haveinfluenced ongoing research agendas and informed practices in Europe,North America (...
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person – anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person – anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.
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The sixth monograph of AMTE highlights examples of the important scholarship of the mathematics teacher education community. This monograph, like others produced by AMTE, serves as a forum for mathematics teacher educators to exchange ideas, experiences, resources, and detailed acounts of work to improve preservice and inservice teacher preparation. Chapters address important issues such as: designing tasks to emphasize mathematics knowledge for teaching; capitalizing on opportunities for student teaching mentor learning; and learning to lead classroom mathematics discussions.
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Proficiency in algebra is critical to success in today's competitive world. Algebra is the foundation for any form of higher mathematics in high school and beyond. Research indicates that completion of Algebra II correlates significantly with success in college and earnings from employment; students who complete Algebra II are more than twice as likely to graduate from college as students less prepared in mathematics (NMAP, 2008). The results on the standardized tests in California are startling: our eighth graders ranked 44th in the nation in 2007 in mathematics and nationwide there are no signs of growth in mathematical proficiency. The National Mathematics Advisory Panel, the National Council of Teachers of Mathematics, and other organizations are actively engaged in an effort to streamline the K-8 mathematics curriculum and find the best research based practices which will guarantee success in Algebra for all students. Many "quick fixes" have been proposed, one of which is discussed in the present study.
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Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: Interfaces with modern school mathematics syllabuses All topics usually taught in the first two years of a physics degree Worked examples throughout Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will be an excellent resource for undergraduate students in physics and a quick reference guide for more advanced students, as well as being appropriate for students in other physical sciences, such as astronomy, chemistry and earth sciences.
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The experience and knowledge acquired in teacher education courses should build important fundamentalsfor the future teaching of mathematics. In particular, experience in mathematical problem solving, and inplanning lessons devoted to problem solving, is an essential component of teacher preparation. This bookdevelops a problem solving approach and is intended to be a text used in mathematics education courses (orprofessional development) for pre-service or in-service middle and secondary school teachers. It can be usedboth in graduate and undergraduate courses, in accordance with the focus of teacher preparation programs.The content of the book is suited especially for those students who are further along in their mathematicseducation preparation, as the text is more involved with mathematical ideas and problem solving, anddiscusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as anintroduction to mathematics education (a first course), but rather as a second, or probably, third course. Thebook deals both with general methodology issues in mathematics education incorporating a problem solvingapproach (Chapters 1-6) and with more concrete applications within the context of specific topics - algebra, geometry, and discrete mathematics(Chapters 7-13).The book provides opportunities for teachers to engage in authentic mathematical thinking. The mathematical ideas under consideration build onspecific middle and secondary school ...
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Document from the year 2012 in the subject Education - Educational Tests & Measurements, , language: English, abstract: Mathematics is an important discipline of learning at the secondary stage. It predominantly contributes to the development of precision, rational and analytical thinking, reasoning and scientific temper. One of the basic aims of teaching Mathematics at secondary stage is to inculcate the skill of quantification of experience gathered by the learner. But still some of the students find Mathematics as very difficult subject. Among different branches of Mathematics, Algebra is used to enable the learner to apply its knowledge to other branches of Mathematics. The pre-requisite test can help the students to know their weaknesses in the basic concepts and it also helps the teachers to know the level of their students. The authors had constructed a pre-requisite test covering all units of Algebra of standard X and implemented on the randomly selected standard X students of the twelve non-granted Gujarati medium schools of Vadodara, Gujarat, India. Based on the findings of the study, the authors discussed and suggested some ways for the teachers teaching Mathematics at secondary school level.
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Bachelor Thesis from the year 2018 in the subject Mathematics - Didactics, grade: 6, Mountains of the Moon University, language: English, abstract: This study aimed at establishing teachers' quality factors that affect pupils' achievement in mathematics. The study was based on two objectives; to establish the relative effect of teacher's qualification and experience on pupils' achievement levels, to establish the relationship between teachers' commitment and pupils' achievement in mathematics. The study tested the hypotheses; there is no correlation between teacher's qualification and pupils' achievement levels, there is no relationship between teachers experience and pupils' achievement levels, there is no correlation between teachers' commitment and pupils' achievement in mathematics. The study used teachers, pupils and head teachers to obtain data, a total of 70 respondents were randomly and purposively selected from five primary schools of Kyondo sub-county, Kasese district. Basing on the findings and discussions, it was revealed that first, the teachers' qualification and experience have nothing to do with pupils' level of achievement in mathematics. Secondly, the teachers' low level of commitment is responsible for the low levels of pupils' achievement in Kyondo sub-county.
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At the age of twenty, George Boole taught himself mathematics, then worked his way through the mathematics of his day, published papers in a wide range of mathematical fields, until, in this remarkably accessible seminal work, he laid down postulates and axioms for logic for the first time - just as Euclid had done for geometry. Boolean algebra has become the basis for practical digital circuit design; thus Boole has provided the theoretical grounding for the Information Age."A classic of pure mathematics and symbolic logic"- Scientific American."Pure mathematics was discovered by George Boole in his work published in 1854."-Bertrand Russell.
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The driving forces behind mathematics learning trajectories is the need to understand how children actuallylearn and make sense of mathematics-how they progress from prior knowledge, through intermediateunderstandings, to the mathematics target understandings-and how to use these insights to improveinstruction 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 potentialapplications of learning trajectories.A synthesis and research outcome in their own right, learning trajectories provide detailed description ofinstructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building ondecades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks thatcontribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely onconceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as anorganizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that arenow consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Stand...
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Книга "Remarks on the Foundation of Mathematics [Bemerkungen Uber Die Grundlagen Der Mathematik]".2014 Reprint of 1956 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Published in English and German with each text presented on opposing pages. "Remarks on the Foundations of Mathematics" are Wittgenstein's notes on the philosophy of mathematics. It has been translated from German to English by G.E.M. Anscombe, edited by G.H. von Wright and Rush Rhees, and published first in 1956. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937-1944 and a few passages are incorporated in the "Philosophical Investigations" which were composed later. Wittgenstein's philosophy of mathematics is exposed chiefly by simple examples on which further skeptical comments are made. The text offers an extended analysis of the concept of mathematical proof and an exploration of Wittgenstein's contention that philosophical considerations introduce false problems in mathematics. Wittgenstein in the "Remarks" adopts an attitude of doubt in opposition to much orthodoxy in the philosophy of mathematics. Wittgenstein's influence has been felt in nearly every field of the humanities and the social sciences, though many of his views remain controversial. Wittgenstein's work remains, undeniably, now, that of one of those few phil...
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The Englishman Dudeney has indeed never studied mathematics, but is now regarded as one of the mathematical genius of his time. This newly edited work from 1917 made it into the contemporary bestseller lists and is still very popular. It uniquely combines fun with mathematics and must therefore be considered as one of the great classics of popular nonfiction books.
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An unabridged, unaltered edition to include: The Abstract Nature Of Mathematics - Variables - Methods Of Application - Dynamics - The Symbolism Of Mathematics - Generalizations Of Number - Imaginary Numbers - Coordinate Geometry - Conic Sections - Functions - Periodicity In Nature - Trigonometry Series - The Differential Calculus - Geometry - Quantity - Note On Books (Bibliography) - Comprehensive Index
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In Somaliland mathematics is performed poorly in secondary schools. In 2010-2014, the mean score of mathematics was 53.95% against 73.72% in Languages, 68.68% in Sciences, and 83.16% in S/Studies. But the influence of personal characteristics of the teacher had not been investigated. Guided by Trait Theory of Personality, the study used a cross sectional research design, on a stratified sample of 350 students and 16 teachers in 10 secondary schools in Borama District, in February of 2014. The study found teacher gender (t [14] = -.276, p = .785), and teacher qualification (F [1, 14] = .578, p = .568) had no significant influence on students' performance. But teacher experience (F [1, 14] = 4.375, p = .022), and self-efficacy (F [1, 14] = 10.790, p = .000) had a significant influence on students' performance. The study concluded that teacher's personal characteristics influence performance of students in mathematics. The study recommends that MoEHS conduct awareness education to change the attitude that mathematics is a male friendly subject; and that an experimental study be done to determine the actual effect of teachers' personal characteristics on the performance of students.
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A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, University of MississippiThis monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given toquadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by thosewho create curriculum, but it is not usually done systematically and it is rarely published.Many terms in mathematics education can be found to have different definitions in mathematics books.Among these are "natural number," "parallel lines" and "congruent triangles," "trapezoid" and "isoscelestrapezoid," the formal definitions of the trigonometric functions and absolute value, and implicit definitions ofthe arithmetic operations addition, subtraction, multiplication, and division.Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. Andeven those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria.Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand therole of definition in mathematics.We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is somedisagreement in the definitions and, consequently, in the ways in which quadrilate... Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.