Reconceptualizing Mathematics

Author: Judith Sowder,Larry Sowder,Susan Nickerson

Publisher: Macmillan

ISBN: 1429281774

Category: Mathematics

Page: N.A

View: 9764

There is today a greater awareness that elementary mathematics is rich in important ideas and that its instruction requires far more than simply knowing the “math facts” and a handful of algorithms. Mathematics courses for teachers must reflect the intellectual depth and challenge of the elementary school curriculum. The Conference Board of Mathematical Sciences (CBMS) recommends that the preparation of mathematics teachers include courses that develop a “deep understanding of the mathematics they teach,” that are designed to “develop careful reasoning and ‘common sense’ in analyzing conceptual relationships, . . . that develop the habits of mind of a mathematical thinker and that demonstrate flexible, interactive styles of teaching” (CBMS, 2000, pp. 7-8). Judy Sowder, Larry Sowder, and Susan Nickerson recognize and accept the challenge of presenting mathematics to teachers in a manner that addresses these recommendations. In doing so they provide instruction that will lead teachers of mathematics to "reconceptualize" the mathematics they often think they already know, thus allowing them to develop a deeper understanding of the mathematics they will teach. The authors believe that teachers must know mathematics differently than most people do. Teachers need to know the mathematics they teach in a way that allows them to hold conversations about mathematical ideas and mathematical thinking with their students. A persistent pursuit of explanation is a hallmark of a classroom in which learning is taking place. A common axiom is that teachers teach the way they were taught. Prospective teachers are unlikely to demonstrate flexible, interactive styles of teaching unless they have experienced mathematics taught this way. Instructors of the "Reconceptualizing Mathematics" courses, however, may not have experienced such instruction themselves. Thus the authors provide many forms of instructional assistance to help instructors better understand the mathematics their prospective teachers need to know, to begin to model teaching strategies that these prospective teachers will be expected to use in their own classrooms, and to assist them in many ways throughout the course.

Building Mathematics Learning Communities

Improving Outcomes in Urban High Schools

Author: Erica N. Walker

Publisher: Teachers College Press

ISBN: 080777104X

Category: Education

Page: 169

View: 8054

“Opportunity to learn (OTL) factors interact and ultimately influence mathematics achievement. Many important OTL interactions take place in school settings. This volume provides insights into the role of peer interactions in the mathematics learning process. The analysis describes with a sense of purpose a topic that is typically overlooked in discussions of mathematics reform. The case study is an important contribution to the urban mathematics education literature.” —William F. Tate, Edward Mallinckrodt Distinguished University Professor in Arts & Sciences, Washington University in St. Louis Drawing on perceptions, behaviors, and experiences of students at an urban high school—both high and low achievers—this timely book demonstrates how urban youth can be meaningfully engaged in learning mathematics. The author presents a “potential” model rather than a “deficit” model, complete with teaching strategies and best practices for teaching mathematics in innovative and relevant ways. This resource offers practical insights for pre- and inservice teachers and administrators on facilitating positive interactions, engagement, and achievement in mathematics, particularly with Black and Latino/a students. It also examines societal perceptions of urban students and how these affect teaching and learning, policies, and mathematics outcomes. Based on extensive research in urban high schools, the author identifies three key principles that must be understood for teachers and students to build strong mathematics communities. They are: Urban students want to be a part of academically challenging environments. Teachers and administrators can inadvertently create obstacles that thwart the mathematics potential of students. Educators can build on existing student networks to create collaborative and non-hierarchical communities that support mathematics achievement. Erica N. Walker is Associate Professor of Mathematics Education at Teachers College, Columbia University.

Theories of Mathematics Education

Seeking New Frontiers

Author: Bharath Sriraman,Lyn English

Publisher: Springer Science & Business Media

ISBN: 3642007422

Category: Education

Page: 668

View: 4194

Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.

Teaching Mathematics Online: Emergent Technologies and Methodologies

Emergent Technologies and Methodologies

Author: Juan, Angel A.

Publisher: IGI Global

ISBN: 1609608763

Category: Education

Page: 414

View: 7786

"This book shares theoretical and applied pedagogical models and systems used in math e-learning including the use of computer supported collaborative learning, which is common to most e-learning practices"--Provided by publisher.

The Teaching and Learning of Mathematics at University Level

An ICMI Study

Author: Derek Holton

Publisher: Springer Science & Business Media

ISBN: 9781402000720

Category: Education

Page: 560

View: 4315

This book arose from the ICMI Study into the teaching and learning of mathematics at university level that began with a conference in Singapore in 1998. The book looks at tertiary mathematics and its teaching from a number of aspects including practice, research, mathematics and other disciplines, technology, assessment, and teacher education. Over 50 authors, all international experts in their field, combined to produce a text that contains the latest in thinking and the best in practice. It therefore provides in one book a state-of-the-art statement on tertiary teaching from a multi-perspective standpoint. No previous book has attempted to take such a wide view of the topic.

Reconceptualizing Early Mathematics Learning

Author: Lyn D. English,Joanne T. Mulligan

Publisher: Springer Science & Business Media

ISBN: 9400764405

Category: Education

Page: 329

View: 7837

This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students’ mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed.

Social Constructivism as a Philosophy of Mathematics

Author: Paul Ernest

Publisher: SUNY Press

ISBN: 9780791435885

Category: Philosophy

Page: 315

View: 1274

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Adolescent Literacy in the Academic Disciplines

General Principles and Practical Strategies

Author: Tamara L. Jetton,Cynthia Shanahan

Publisher: Guilford Press

ISBN: 1462502857

Category: Language Arts & Disciplines

Page: 274

View: 6393

From leading authorities in both adolescent literacy and content-area teaching, this book addresses the particular challenges of literacy learning in each of the major academic disciplines. Chapters focus on how to help students successfully engage with texts and ideas in English/literature, science, math, history, and arts classrooms. The book shows that while general strategies for reading informational texts are essential, they are not enough—students also need to learn processing strategies that are quite specific to each subject and its typical tasks or problems. Vignettes from exemplary classrooms illustrate research-based ways to build content-area knowledge while targeting essential reading and writing skills.

Der lange Weg zur Freiheit


Author: Nelson Mandela

Publisher: S. Fischer Verlag

ISBN: 3104031541

Category: History

Page: 864

View: 8676

»Ich bin einer von ungezählten Millionen, die durch Nelson Mandelas Leben inspiriert wurden.« Barack Obama Eine fast drei Jahrzehnte währende Gefängnishaft ließ Nelson Mandela zum Mythos der schwarzen Befreiungsbewegung werden. Kaum ein anderer Politiker unserer Zeit symbolisiert heute in solchem Maße die Friedenshoffnungen der Menschheit und den Gedanken der Aussöhnung aller Rassen wie der ehemalige südafrikanische Präsident und Friedensnobelpreisträger. Auch nach seinem Tod finden seine ungebrochene Charakterstärke und Menschenfreundlichkeit die Bewunderung aller friedenswilligen Menschen auf der Welt. Mandelas Lebensgeschichte ist über die politische Bedeutung hinaus ein spannend zu lesendes, kenntnis- und faktenreiches Dokument menschlicher Entwicklung unter Bedingungen und Fährnissen, vor denen die meisten Menschen innerlich wie äußerlich kapituliert haben dürften.

Mathematical Difficulties

Psychology and Intervention

Author: N.A

Publisher: Elsevier

ISBN: 9780080559773

Category: Psychology

Page: 272

View: 1537

This book examines the mathematical difficulties in typical and atypical populations. It discusses the behavioural, educational and neuropsychological characteristics of people with mathematical difficulties, and educational interventions to prevent, diagnose, treat or ameliorate such difficulties. The book brings together studies from different disciplines, including developmental psychology, neuroscience and education, and includes perspectives from practicing teachers. The book is divided into three major sections. The first includes chapters about the nature and characteristics of mathematical difficulties in the population as a whole, in relation to both psychology and education. The second deals with mathematical difficulties in children with other problems such as specific language impairment and dyslexia. The third discusses methods of interventions aimed at preventing, treating or ameliorating mathematical difficulties, and will include discussions of assessment and diagnosis.

Reconceptualizing the Nature of Science for Science Education

Scientific Knowledge, Practices and Other Family Categories

Author: Sibel Erduran,Zoubeida R. Dagher

Publisher: Springer

ISBN: 9401790574

Category: Science

Page: 189

View: 887

Prompted by the ongoing debate among science educators over ‘nature of science’, and its importance in school and university curricula, this book is a clarion call for a broad re-conceptualizing of nature of science in science education. The authors draw on the ‘family resemblance’ approach popularized by Wittgenstein, defining science as a cognitive-epistemic and social-institutional system whose heterogeneous characteristics and influences should be more thoroughly reflected in science education. They seek wherever possible to clarify their developing thesis with visual tools that illustrate how their ideas can be practically applied in science education. The volume’s holistic representation of science, which includes the aims and values, knowledge, practices, techniques, and methodological rules (as well as science’s social and institutional contexts), mirrors its core aim to synthesize perspectives from the fields of philosophy of science and science education. The authors believe that this more integrated conception of nature of science in science education is both innovative and beneficial. They discuss in detail the implications for curriculum content, pedagogy, and learning outcomes, deploy numerous real-life examples, and detail the links between their ideas and curriculum policy more generally.

Reconceptualizing the Literacies in Adolescent's Lives

Author: Donna E. Alvermann

Publisher: Psychology Press

ISBN: 0805853855

Category: Language Arts & Disciplines

Page: 322

View: 9105

Reconceptualizing the Literacies in Adolescents' Lives, Second Edition focuses on exploring the impact of young people's identity-making practices in mediating their perceptions of themselves as readers and writers in an era of externally mandated reforms. What is different in the Second Edition is its emphasis on the importance of valuing adolescents' perspectives - in an era of skyrocketing interest in improving literacy instruction at the middle and high school levels driven by externally mandated reforms and accountability measures. A central concern is the degree to which this new interest takes into account adolescents’ personal, social, and cultural experiences in relation to literacy learning. In this new edition of Reconceptualizing the Literacies in Adolescents’ Lives students’ voices and perspectives are featured front and center in every chapter. Particular attention is given throughout to multiple literacies--especially how information and new communication technologies are changing learning from and with text. Nine of the 15 chapters are new; all other chapters are thoroughly updated. The volume is structured around four main themes: * Situating Adolescents’ Literacies–addressing how young people use favorite texts to perform their identities; how they counter school-based constructions of incompetence; and how they re/construct their literate identities in relation to certain kinds of gendered expectations, pedagogies, and cultural resources; * Positioning Youth as Readers and Writers–stressing the importance of classroom discourse, cultural capital, agency, and democratic citizenship in mediating adolescents’ literate identities; * Mediating Practices in Young People’s Literacies–looking at issues of language, social class, race, and culture in shaping how adolescents represent themselves and are represented by others; and * Changing Teachers, Teaching Changes–capturing the productive ambiguities associated with teaching urban adolescents to read and write in changing times, encouraging students to conduct action research on topics that are personally relevant, and using ‘enabling constraints’ as a concept to formulate policies on adolescent literacy instruction. Reconceptualizing the Literacies in Adolescents’ Lives, Second Edition is an essential volume for researchers, faculty, teacher educators, and graduate students in the field of adolescent literacy education.