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Primary Mathematics Pedagogy at the Intersection of Education Reform, Policy, and Culture: Comparative Insights from Ghana, Singapore, and the US (Routledge Research in International and Comparative Education)
by Sarah Murray Princess AlloteyThis volume provides an in-depth, comparative examination of how primary mathematics education is influenced by national education reform, policy, local resources, and culture in three different countries. By drawing on first-hand observations and interviews, as well as analysis of policy documents and learning resources, the book considers the viability of transferring best practices in primary mathematics education across global contexts. Three diverse countries – Ghana, the US, and Singapore – are explored. Similarities and differences are highlighted, and the influence of national and regional initiatives related to pedagogical strategies, teacher education, and cultural expectations are considered, to offer an insightful examination of how best practices might be shared across borders. This book will benefit researchers, academics, and postgraduate scholars with an interest in international and comparative education, mathematics, and educational policy. Those with a specialization in primary mathematics education, including pedagogy and teacher preparation, will also benefit from this book.
Primary Mathematics: Teaching Theory and Practice (Achieving QTS Series)
by Claire Mooney Alice Hansen Mary Briggs Mike Fletcher Judith McCullouchAn extensive knowledge of the primary Mathematics curriculum is not enough for you as a trainee teacher, you need to know how to teach Mathematics in the primary classroom. This is the essential teaching theory and practice text for primary Mathematics that takes a focused look at the practical aspects of teaching. It covers the important skills of classroom management, planning, monitoring and assessment and relates these specifically to primary Maths. Practical guidance, features and resources help you translate your learning to the classroom and understand the wider context of teaching: - Online practical lesson ideas for the classroom - The Primary National Curriculum for Mathematics in Key Stages one and two - Tips for planning primary Maths - Useful weblinks for primary Mathematics teaching The ninth edition of this popular book includes a new chapter on ′Mathematics in the primary classroom′ exploring primary mathematics teaching today. It is also updated to include the new ′Ready to progress′ criteria.
Primary Mathematics: Teaching Theory and Practice (Achieving QTS Series)
by Claire Mooney Alice Hansen Mary Briggs Mike Fletcher Judith McCullouchAn extensive knowledge of the primary Mathematics curriculum is not enough for you as a trainee teacher, you need to know how to teach Mathematics in the primary classroom. This is the essential teaching theory and practice text for primary Mathematics that takes a focused look at the practical aspects of teaching. It covers the important skills of classroom management, planning, monitoring and assessment and relates these specifically to primary Maths. Practical guidance, features and resources help you translate your learning to the classroom and understand the wider context of teaching: - Online practical lesson ideas for the classroom - The Primary National Curriculum for Mathematics in Key Stages one and two - Tips for planning primary Maths - Useful weblinks for primary Mathematics teaching The ninth edition of this popular book includes a new chapter on ′Mathematics in the primary classroom′ exploring primary mathematics teaching today. It is also updated to include the new ′Ready to progress′ criteria.
Primary Mathematics, Textbook, 1A, Standards Edition
by Marshall Cavendish International (Singapore) Private LimitedTextbook.
Primary Mathematics, Textbook, 1B, Standards Edition
by Marshall Cavendish International (Singapore) Private LimitedTextbook.
Primary Mathematics, Textbook, 2A, Standards Edition
by Kho Tek HongThe Primary Mathematics U.S. Edition series of elementary math textbooks and workbooks is meant to be part of a system of learning in which adult supervision and independent practice go hand in hand. The main feature of this series is the use of the Concrete-- gt Pictorial-- gt Abstract approach. The students are provided with the necessary learning experiences beginning with the concrete and pictorial stages, followed by the abstract stage to enable them to learn mathematics meaningfully. This approach encourages active thinking, communication of mathematical ideas and problem solving. This helps develop the foundation students will need for more advanced mathematics. Practice exercises are designed to provide the students with further practice after they have done the relevant workbook exercises. Review exercises are provided for cumulative reviews of concepts and skills. All the practice exercises and review exercises are optional exercises.Level 2A covers Numbers to 1000, Addition and Subtraction, Multiplication and Division, Length, and Weight.Format: Paperback, 112 pages Pubisher: Singapore
Primary Mathematics, Textbook, 2B, Standards Edition
by Jennifer HoerstThe Primary Mathematics Standards Edition is a series of elementary math textbooks and workbooks from the publishers of Singapore's successful Primary Mathematics series. Newly adapted to align with the Mathematics Framework for California Public Schools, the program aims to equip students with sound concept development, critical thinking and efficient problem-solving skills. Features of the series: Mathematical concepts are introduced in the opening pages and taught to mastery through specific learning tasks that allow for immediate assessment and consolidation. The modeling method enables students to visualize and solve mathematical problems quickly and efficiently. The Concrete > Pictorial > Abstract approach enables students to encounter math in a meaningful way and translate mathematical skills from the concrete to the abstract. The pencil icon provides quick and easy reference from the Textbook to the relevant Workbook pages. The direct correlation of the Workbook to the Textbook facilitates focused review and evaluation. New mathematical concepts are introduced throughout a spiral progression that builds on concepts already taught and mastered. Metacognition is employed as a strategy for learners to monitor their thinking processes in problem solving. Speech and thought bubbles provide guidance through the thought processes, making even the most challenging problems accessible to students. Color patch is used to invite active student participation and to facilitate lively discussion about the mathematical concepts taught. Reviews in the Workbooks for 1A-1B and regular reviews in the Textbooks and Workbooks for 2A-5B provide consolidation of concepts learned. The glossary effectively combines pictorial representation with simple mathematical definitions to provide a comprehensive reference guide for students. Answer keys booklets are not included, but are available - one for Primary 1A-3B and one for Primary 4A-6B.
Primary Mathematics, Textbook, 4A, Standards Edition
by Marshall Cavendish International (Singapore) Private LimitedTextbook.
Primary Mathematics, Textbook, 4B, Standards Edition
by Marshall Cavendish International (Singapore) Private LimitedTextbook.
Primary Mathematics, Textbook, 5A, Standards Edition
by Marshall Cavendish CorporationNIMAC-sourced textbook
Primary Mathematics, Textbook, 5B, Standards Edition
by Marshall Cavendish CorporationNIMAC-sourced textbook
Primary Mathematics, Workbook, 2B, Standards Edition
by Jennifer HoerstThe Primary Mathematics Standards Edition is a series of elementary math textbooks and workbooks from the publishers of Singapore's successful Primary Mathematics series. Newly adapted to align with the Mathematics Framework for California Public Schools, the program aims to equip students with sound concept development, critical thinking and efficient problem-solving skills. Features of the series: Mathematical concepts are introduced in the opening pages and taught to mastery through specific learning tasks that allow for immediate assessment and consolidation. The modeling method enables students to visualize and solve mathematical problems quickly and efficiently. The Concrete > Pictorial > Abstract approach enables students to encounter math in a meaningful way and translate mathematical skills from the concrete to the abstract. The pencil icon provides quick and easy reference from the Textbook to the relevant Workbook pages. The direct correlation of the Workbook to the Textbook facilitates focused review and evaluation. New mathematical concepts are introduced throughout a spiral progression that builds on concepts already taught and mastered. Metacognition is employed as a strategy for learners to monitor their thinking processes in problem solving. Speech and thought bubbles provide guidance through the thought processes, making even the most challenging problems accessible to students. Color patch is used to invite active student participation and to facilitate lively discussion about the mathematical concepts taught. Reviews in the Workbooks for 1A-1B and regular reviews in the Textbooks and Workbooks for 2A-5B provide consolidation of concepts learned. The glossary effectively combines pictorial representation with simple mathematical definitions to provide a comprehensive reference guide for students. Answer keys booklets are not included, but are available - one for Primary 1A-3B and one for Primary 4A-6B.
Primary Mathematics Workbook 2A Standards Edition
by Kho Tek HongThe Primary Mathematics U.S. Edition series of elementary math textbooks and workbooks is meant to be part of a system of learning in which adult supervision and independent practice go hand in hand. The main feature of this series is the use of the Concrete-- gt Pictorial-- gt Abstract approach. The students are provided with the necessary learning experiences beginning with the concrete and pictorial stages, followed by the abstract stage to enable them to learn mathematics meaningfully. This approach encourages active thinking, communication of mathematical ideas and problem solving. This helps develop the foundation students will need for more advanced mathematics. Practice exercises are designed to provide the students with further practice after they have done the relevant workbook exercises. Review exercises are provided for cumulative reviews of concepts and skills. All the practice exercises and review exercises are optional exercises.Level 2A covers Numbers to 1000, Addition and Subtraction, Multiplication and Division, Length, and Weight.Format: Paperback, 112 pages Pubisher: Singapore
Primary Mathematics, Workbook, 4A, Standards Edition
by Marshall Cavendish International (Singapore) Private LimitedTextbook.
Primary Mathematics, Workbook, 5A, Standards Edition
by Marshall Cavendish CorporationNIMAC-sourced textbook
Prime Divisors and Noncommutative Valuation Theory
by Fred Van Oystaeyen Hidetoshi MarubayashiClassical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions.
The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta (The\mit Press Ser.)
by Thomas LinQuanta Magazine's stories of mathematical explorations show that “inspiration strikes willy-nilly,” revealing surprising solutions and exciting discoveries.If you're a science and data nerd like me, you may be interested in "Alice and Bob Meet the Wall of Fire" and "The Prime Number Conspiracy" from Quanta Magazine and Thomas Lin. - Bill GatesThese stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.” Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good for you?”ContributorsAriel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie WolchoverCopublished with Quanta Magazine
Prime Numbers and Computer Methods for Factorization
by Hans RieselFrom the original hard cover edition: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. Hans Riesel's highly successful first edition of this book has now been enlarged and updated with the goal of satisfying the needs of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination. It includes important advances in computational prime number theory and in factorization as well as re-computed and enlarged tables, accompanied by new tables reflecting current research by both the author and his coworkers and by independent researchers. The book treats four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes and the factorization of large numbers. The author provides explicit algorithms and computer programs, and has attempted to discuss as many of the classically important results as possible, as well as the most recent discoveries. The programs include are written in PASCAL to allow readers to translate the programs into the language of their own computers. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.
Prime Numbers and the Riemann Hypothesis
by Barry Mazur William SteinPrime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
by John DerbyshireIn August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic -- defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows -- subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.--It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof -- and those who have been consumed by it.
Prime Time: Factors and Multiples
by Glenda Lappan Elizabeth Difanis Phillips James T. Fey Susan N. FrielThink about some of the ways you use numbers. You use them to count and to measure. You use number to make comparisons and to describe where places are located. Numbers help you communicate and find information. You use numbers to use technology and to make purchases. Numbers can help you think about situations such as those on the previous page.