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Craig Smorynski Chapters in Mathematics. from Pi to Pell


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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Craig Smorynski Chapters in Probability


This book introduces elementary probability through its history, eschewing the usual drill in favour of a discussion of the problems that shaped the field's development. Numerous excerpts from the literature, both from the pioneers in the field and its commentators, some given new English translations, pepper the exposition. First, for the reader without a background in the Calculus, itoffers a brief intuitive explanation of some of the concepts behind the notation occasionally used in the text, and, for those with a stronger background, it gives more detailed presentations of some of the more technical results discussed in the text.Special features include two appendices on the graphing calculator and on mathematical topics. The former begins with a short course on the use of the calculator to raise the reader up from the beginner to a more advanced level, and then finishes with some simulations of probabilistic experimentson the the calculator. The mathematical appendix likewise serves a dual purpose.The book should be accessible to anyone taking or about to take a course in the Calculus, and certainly is accessible to anyone who has already had such acourse. It should be of special interest to teachers, statisticians, or anyone who uses probability or is interested in the history of mathematics or sciencein general.

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Teachers Engaged in Research. Inquiry Mathematics Classrooms, Grades 9-12 (PB)


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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What Mathematics Do Students Know and How is that Knowledge Changing. Evidence from the National Assessment of Educational Progress


This volume is intended for researchers, curriculum developers, policy makers, and classroomteachers who want comprehensive information on what students at grades 4, 8, and 12 (the gradesassessed by NAEP) can and cannot do in mathematics. After two introductory chapters on thedesign of NAEP, the volume contains a chapter on the challenges in analyzing NAEP data at theitem level followed by five chapters that report 2005 through 2013 student performance on specificassessment items. These chapters are organized by content area and then by topic (e.g., understanding of place value, knowledgeof transformations, ability to use metric and U.S. systems of measurement) and thus provide baseline data on the proportion ofstudents who are able to complete the mathematics tasks currently used in the upper elementary, middle, and high‐schoolmathematics curriculum. Additional chapters focus on student reasoning, U.S. performance on international assessments, andusing construct analysis rather than percent correct on clusters of items to understand student knowledge on specific mathematicstopics.Several themes emerge from the volume. One is that while the rate of improvement in mathematics learning in grades 4 and 8 hasslowed in recent years, it has slowed more on some topics than others. Another is that relatively minor changes in wording can havesignificant effects on student performance and thus it is difficult to be specific about what students can do without knowing exactlywhat questio...

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Enacted Mathematics Curriculum. A Conceptual Framework and Research Needs


This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might be used as a text in a university graduate course on curriculum research and design. The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment

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Research on Technology and the Teaching Learning of Mathematics. Vol. 1, Syntheses (PB)


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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Cases in Mathematics Teacher Education. Tools for Developing Knowledge Needed Teaching


The goal of AMTE Monograph 4, "Cases in Mathematics Teacher Education: Tools for Developing Knowledge Needed for Teaching", is to provide detailed accounts of case use that will inform the mathematics teacher education community on the range of ways in which cases can be used to foster teacher learning and the capacity to reflect on and learn from teaching. The chapters in this monograph describe the use of cases with preservice and practicing teachers at all levels K - 12, in content and methods courses as well as professional development settings, and focus on developing various aspects of teachers' knowledge base (i.e., content, pedagogy, and students as learners). Hence, Monograph 4 should prove to be a superb resource for mathematics teacher educators.

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Scholarly Practices and Inquiry in the Preparation of Mathematics Teachers


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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A Decade of Middle School Mathematics Curriculum Implementation. Lessons Learned from the Show-Me Project (PB)


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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Inquiry into Mathematics Teacher Education


The 14 chapters in this monograph provide support for mathematics teacher educators in both their Practical Knowledge and their Professional Knowledge. Individually, these articles provide insights into advancing our thinking about professional development, teacher preparation, and program development. Collectively, they have the potential to help the field of mathematics teacher education move forward in framing effective practices in mathematics teacher education and developing a focused, cohesive research agenda. ATME's Monograph 5, therefore, is a superb resource for mathematics teacher education.

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Mathematics Teaching. Putting Research into Practice at All Levels


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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Research on Technology and the Teaching Learning of Mathematics. Vol. 2, Cases Perspectives (PB)


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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Teachers Engaged in Research. Inquiry Mathematics Classrooms, Grades Pre-K-2 (PB)


This volume was written primarily for teachers who have developed (or who are being encouraged to develop) an awareness ofand commitment to teaching mathematics for understanding. The research findings presented in these chapters suggest instructional implicationsworthy of these teachers' consideration. Often, the authors in this volume describe instructional practices or raise issues that have thepotential to broaden views of teaching and learning mathematics. These chapters provide interesting problems and tasks used in the authors'work that readers can use in their own classrooms.The volume can also be used with courses for preservice and inservice teachers, collaborative teacher study groups, and other professionalactivities. A hallmark of good research is its connection to the relevant literature in the field, and the authors of this volume havethemselves drawn from the research literature to inform their work. The reference lists accompanying these chapters can be useful resourcesand should not be overlooked. Most importantly for teacher education, this volume showcases the variety of ways teachers can becomeengaged in research, and we hope that readers will recognize that teacher research can be both accessible and beneficial in the preparationand professional development of teachers.This is not to suggest, however, that this volume is intended only for teachers and teacher educators. It is also intended to be aninteresting, informative resource for other resea...

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Instructional Strategies for Improving Students. Learning. Focus on Early Reading and Mathematics


The twin objectives of the series Psychological Perspectives on Contemporary EducationalIssues are: (1) to identify issues in education that are relevant to professional educators andresearchers; and (2) to address those issues from research and theory in educational psychology,psychology, and related disciplines.The present volume, consisting of two focal chapters, commentaries, and final responses targetsinstructional strategies for improving students' learning in two of the traditional "three R" areas,reading and ′rithmetic (mathematics), in the elementary school grades. The focal chapters in those two skill areas are written by leadingcontributors to the reading and mathematics research literatures, Cathy Collins Block for the reading section and Douglas Clements andJulie Sarama for the mathematics section. Few would dispute the essentiality of these two curricular domains in laying the foundationfor the development of students' competencies in a vast array of academic disciplines in both the in- and out-of-school years that lieahead.The present volume is intended for practitioners and researchers who are seeking the latest instructional research-based strategies forimproving students' early reading and mathematics performance.

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Alexander Karp, Nicholas Wasserman Mathematics in Middle and Secondary School. A Problem Solving Approach


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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International Symposium on Mathematics a Interdisciplinary Educational Research in and Its Connections to the Arts Sciences (PB)


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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Graeme Partington Mathematics. First 100 Lessons


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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Craig Smorynski A Treatise on the Binomial Theorem


"The binomial theorem is usually quite rightly considered as one of the mostimportant theorems in the whole of analysis." Thus wrote Bernard Bolzanoin 1816 in introducing the first correct proof of Newton's generalisation of acentury and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integralexponents, and may also appear incongruous to one familiar with Newton'sseries for rational exponents. Yet his statement was a sound judgment back inthe day. Here the story of the Binomial Theorem is presented in all its glory,from the early days in India, the Moslem world, and China as an essentialtool for root extraction, through Newton's generalisation and its central rolein infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th.The exposition is well-organised and fairly complete with all the necessarydetails, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that.The present book, with its many citations from the literature, will be ofinterest to anyone concerned with the history or foundations of mathematics.

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How Chinese Learn Mathematics. Perspectives from Insiders


“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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Mathematics Teacher Education in the Public Interest. Equity and Social Justice


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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Ranjit Singh Engineering Mathematics for B.Tech Students


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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Selected Writings from the Journal of British Columbia Association Mathematics Teachers. Celebrating 50 years (1962-2012) Vector


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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Interdisciplinarity, Creativity, and Learning. Mathematics with Literature, Paradoxes, History, Technology, Modeling (PB)


A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaInterdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplinesthat rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement ofschools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftednessacross disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists,artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is anattempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that thecultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplineslike theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in otherdisciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japanprovide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technologyand modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

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Richard Wentk Raspberry Pi For Kids Dummies


Getting acquainted with your Raspberry Pi has never been sweeter Raspberry Pi For Kids For Dummies makes it easy for kids to set-up, operate, and troubleshoot like a Pi pro! Introducing you to Pi through a series of entertaining and inspiring projects, this handy, step-by-step guide shows you how to write computer games, build websites, make art and music, create electronic projects, and much more! From downloading the operating system and setting up your Raspberry Pi to creating art in Tux Paint and designing games with Scratch, everything you need to have fun with Pi is inside! Raspberry Pi For Kids For Dummies leaves the confusing tech talk behind and explains in plain English how to unleash all the cool possibilities of Pi, like playing Minecraft in Python, using HTML to make a website, managing and customizing your Raspberry Pi, playing music with Sonic Pi, and understanding and playing with the GPIO. Teaches the basics of Raspberry Pi in a simple and thorough approach Shows you how to zoom around Pi, all while learning valuable programming skills Offers tons of exciting projects to keep you engaged as you learn Includes instruction on everything you need to troubleshoot Raspberry Pi If youre aspiring computer programmer age 8-18 and want to start having fun with Pi, look no further than Raspberry Pi For Kids For Dummies.

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Mathew Akoko Assessment of the Effects Affective Student Characteristics and Educational Background on Mathematics Achievement at Level Higher Education in Cameroon


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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Emerging Perspectives on Gesture and Embodiment in Mathematics


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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Digital Curricula in School Mathematics


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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Robert Stark M. Finite Mathematics. Models and Applications


Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences. In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on probability and statistics, principles and applications of matrices are included as well as topics for enrichment such as the Monte Carlo method, game theory, kinship matrices, and dynamic programming. Supplemented with online instructional support materials, the book features coverage including: Algebra Skills Mathematics of Finance Matrix Algebra Geometric Solutions Simplex Methods Application Models Set and Probability Relationships Random Variables and Probability Distributions Markov Chains Mathematical Statistics Enrichment in Finite Mathematics An ideal textbook, Finite Mathematics: Models and Applications is intended for students in fields from entrepreneurial and economic to environmental and social science, including many in the arts and humanities.

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Critical Issues In Mathematics Education (PB)


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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Graham Shaw Mathematics for Physicists


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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Donald Bindner Mathematics for the Liberal Arts


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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The Role of Mathematics Discourse in Producing Leaders


A Volume in The Montana Mathematics Enthusiast:Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaThe intent of this monograph is to showcase successful implementation ofmathematical discourse in the classroom. Some questions that might beaddressed are:* How does a teacher begin to learn about using discourse purposefully toimprove mathematics teaching and learning?* How is discourse interwoven into professional development content courses toprovide teachers with the tools necessary to begin using discourse in their ownclassrooms?* What does a discourse-rich classroom look like and how is it different from other classrooms, from both theteacher's and the students' perspectives?* How can teachers of pre-service teachers integrate discourse into their content and methods courses?* How can we use discourse research to inform work with teachers, both pre- and in-service, for example, to helpthem know how to respond to elicited knowledge from students in their classrooms?* What are the discourse challenges in on-line mathematics courses offered for professional development? Canon-line classrooms also be discourse-rich? What would that look like?* In what ways does mathematical discourse differ from discourse in general?

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Teachers Engaged in Research. Inquiry Mathematics Classrooms, Grades 6-8 (PB)


Through the chapters in this volume we learn about the research foci and/ or questions that these classroom teachers are interested in examining,the mathematics content through which they engaged their students in these explorations, the data sources they used to make sense oftheir focus and questions, and their roles in the research.An overarching theme through all the chapters in this volume is the learning and professional development that occurs through teacherresearch. What these authors learned about student learning and their own teaching practice far exceeded the focus of their particularresearch questions. For some, the research validated their beliefs and instructional practices; for others, it deepened or extended their understandingof mathematics, or raised their expectations of students' capabilities. For all, it is fair to say, their research increased their awarenessof how students come to know and understand mathematics, and enabled them to gain insight into the complexity of teaching. Lampert(2001) noted, "One reason teaching is a complex practice is that many of the problems a teacher must address to get students to learn occursimultaneously, not one after another" (p. 2). We, as readers, gain a window into these teachers' research within and about the complexity ofclassroom teaching.

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John A. Adam Mathematics in Nature. Modeling Patterns the Natural World


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 Work of Mathematics Teacher Educators. Exchanging Ideas for Effective Practice


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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Selected Writings from the Journal of Mathematics Council Alberta Teachers. Association. Celebrating 50 Years (1962-2012) Delta-K


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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