Seeing Solids And Silhouettes

There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.

This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies. Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks. This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.

This state-of-the-art Handbook brings together important mathematics education research that makes a difference in both theory and practice--research that: anticipates problems and needed knowledge before they become impediments to progress; interprets future-oriented problems into researchable issues; presents the implications of research and theory development in forms that are useful to practitioners and policymakers; and facilitates the development of research communities to focus on neglected priorities or strategic opportunities. The volume represents a genuine attempt by contributors from around the world to advance the discipline, rather than simply review what has been done and what exists. The Handbook was developed in response to a number of major global catalysts for change, including the impact of national and international mathematics comparative assessment studies; the social, cultural, economic, and political influences on mathematics education and research; the influence of progressively sophisticated and available technology; and the increasing globalization of mathematics education and research. From these catalysts have emerged specific priority themes and issues for mathematics education research in the 21st century. Three key themes were identified for attention in this volume: life-long democratic access to powerful mathematical ideas; advances in research methodologies; and influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development as an important component of all these aspects. Dynamic and forward looking, the Handbook of International Research in Mathematics Education is distinguished by its focus on new and emerging theoretical models, perspectives, and research methodologies; its uniformly high standard of scholarship; and its emphasis on the international nature of mathematics education research. It is an essential volume for all researchers, professionals, and students interested in mathematics education research in particular and, more generally, in international developments and future directions in the broad field of educational research.

"This book is the third in an important trilogy of edited collections on the teaching and learning of primary mathematics. To each book the editor, Ian Thompson, has attracted a team of expert contributors, and himself set the characteristically high standard of writing and clarity... When, in 10 or 20 years' time, people want to know about the state of English primary mathematics at the turn of the 21st century, they will turn to this volume. You would do well to read it now." Mathematics in Schools "This is the third book in the popular series edited by Ian Thompson that brings together an impressive array of contributing authors. Current issues are discussed in an informed but concise way that makes research accessible to the wider community of mathematics educators." Julia Anghileri, University of Cambridge This book explores the effect that the National Numeracy Strategy and its successor, the Primary Strategy, have had on the way in which mathematics is taught in primary schools. Prominent contributors examine the Strategies' recommendations from the perspective of their own research areas or interests, and discuss the issues involved, including: Ideas for extending current practice Suggestions of important aspects of mathematics teaching that are being given little or no emphasis Alternative approaches that could be integrated into current practice Aspects of current practice that need to take account of recent research findings or emerging issues. Each chapter discusses implications for teaching and learning primary mathematics. The book will be particularly useful for trainees, practising teachers, mathematics coordinators and numeracy consultants. Contributors: Mundher Adhami, Mike Askew, Carol Aubrey, Margaret Brown, Ann Dowker, Rosemary Hafeez, Steve Higgins, Keith Jones, Lesley Jones, Valsa Koshy, Alison Millett, Claire Mooney, Laurie Rousham, Malcolm Swan, Ian Thompson, Helen J Williams.

Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.

The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics. Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding. The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers. Contents:PrefaceAcknowledgmentsAbout the AuthorsFostering the Learning of MathematicsConstruction of Concepts and Mathematical InterpretationsNumberingAddition and SubtractionMultiplication and DivisionFractions, Decimals, and PercentagesMeasurementExploring SpaceProbability and StatisticsPatterns, Relations, and FunctionsThe Joy of PuzzlesTechnology: A Tool for Analysis and InterpretationAssessmentConcluding Remarks Readership: Teachers, trainee teachers, researchers interested in mathematics education, homeschool parents, and parents with children in primary/ elementary school. Key Features:This book is grounded on solid mathematics learning research, as well as on the authors' own observations in the classroom, and so combines theoretical knowledge with practiceWritten in an accessible mannerGives educators ideas which they can easily implement in the classroom