Ages: 5–7  Level: KS1 Subject: Maths  Power Maths is a leading primary maths mastery scheme, developed in partnership with White Rose Maths.   This edition is fully aligned with the new White Rose Maths schemes of learning (version 3.0) and has been updated in response to current mastery best practice and feedback from teachers.  The Power Maths Teacher Guides provide expert support for day-to-day teaching and continual professional development, including:  How to implement a mastery approach using the Textbooks and Practice Books. Advice and commentary for each Textbook and Practice Book page, including ‘Strengthen’ and ‘Deepen’ ideas for children that need more support or stretch. A guide to the concepts introduced in each unit, including important structures and representations, key language, common misconceptions and intervention strategies. Support with key strategies such as modelling a growth mindset, assessing mastery, speedy same-day intervention, and using the Concrete-Pictorial-Abstract approach to embed deep understanding. Templates for teacher reflection, lesson study, and tracking pupil progress.

Ernst Specker has made decisive contributions towards shaping direc tions in topology, algebra, mathematical logic, combinatorics and algorith mic over the last 40 years. We have derived great pleasure from marking his seventieth birthday by editing the majority of his scientific publications, and thus making his work available in a unified form to the mathematical community. In order to convey an idea of the richness of his personality, we have also included one of his sermons. Of course, the publication of these Selecta can pay tribute only to the writings of Ernst Specker. It cannot adequately express his originality and wisdom as a person nor the fascination he exercises over his students, colleagues and friends. We can do no better than to quote from Hao Wang in the 'Festschrift' Logic and Algorithmic I: Specker was ill for an extended period before completing his formal education. He had the leisure to think over many things. This experi ence may have helped cultivating his superiority as a person. In terms of traditional Chinese categories, I would say there is a taoist trait in him in the sense of being more detached, less competitive, and more under standing. I believe he has a better sense of what is important in life and arranges his life better than most logicians. We are grateful to Birkhauser Verlag for the production of this Selecta volume. Our special thanks go to Jonas Meon for sharing with us his intimate knowledge of his friend Ernst Specker."

Don't let your students miss out on easy marks, prepare them for those Maths questions with this essential guide. Written specifically to build students' confidence in maths and to prepare them for the more challenging mathematical requirements which make up 15% of the new DT specifications. - Improve confidence with structured progression of worked examples, guided and non-guided questions, and worked solutions for every question - Strengthen students' maths skills and subject understanding with worked examples and practice questions all embedded in the subject context - Develop exam confidence with exam-style maths questions - An essential tool throughout the AS and A Level course with every maths skill mapped to subject topics, and applicable to every major exam board - Reviewed by subject and maths expert Glyn Granger (former D&T chief examiner)

Features A broad and accessible overview of non-homogeneous Markov chains and systems Fills a significant gap in the current literature A good balance of theory and applications, with advanced mathematical details separated from the main results Many illustrative examples of potential applications from a variety of fields Suitable for use as a course text for postgraduate students of applied probability, or for self-study Potential applications included could open it up to other quantitative areas

Explore the fundamentals of Multi-Criteria Decision Analysis with help from Excel® and R In Smart Decisions: A Structured Approach to Decision Analysis using MCDA, a distinguished team of decision-making specialists delivers a comprehensive and insightful exploration of the fundamentals of Multi-Criteria Decision Analysis methods. The book offers guidance on modeling decision problems using some of the most powerful methods in operations research. Each chapter introduces a core MCDA method and guides the reader through a step-by-step approach to the implementation of the method using Microsoft® Excel® and then using R, a popular analytical language. The book also includes: A thorough, step-by-step guide to Multi-Criteria Decision Analysis methods and the application of these methods in Microsoft Excel and R Extensive illustrations, R code, and software screenshots to aid the reader’s understanding of the concepts discussed within A starter’s guide to Excel and R programming Perfect for graduate students in MBA programs and business schools, Smart Decisions: A Structured Approach to Decision Analysis Using MCDA is also an ideal resource for practitioners who apply MCDA in business, finance, applied mathematics, and engineering.

This tract gives a fairly elementary account of the theory of quadratic forms with integral coefficients and variables. It assumes a knowledge of the rudiments of matrix algebra and of elementary number theory, but scarcely any analysis. It is therefore intelligible to beginners and helps to prepare them for the study of the advanced work on quadratic forms over general rings. Dr Watson works step by step from wider (and easier) to narrower relations between forms, the final goal being the study of equivalence. The important problem of representation of integers is fully discussed in the course of the main development. There is an early chapter on reduction. Existing work on the theory of integral quadratic forms is obscure (partly for historical reasons). But the straightforward approach adopted by Dr Watson leads to a consideration of most of the main problems; there are proofs of many recent results, including some discovered by Dr Watson but hitherto unpublished.

This book examines the beliefs, attitudes, values and emotions of students in Years 5 to 8 (aged 10 to 14 years) about mathematics and mathematics education. Fundamentally, this book focuses on the development of affective views and responses towards mathematics and mathematics learning. Furthermore, it seems that students develop their more negative views of mathematics during the middle school years (Years 5 to 8), and so here we concentrate on students in this critical period. The book is based on a number of empirical studies, including an enquiry undertaken with 45 children in Years 5 and 6 in one school; a large-scale quantitative study undertaken with students from a range of schools across diverse communities in New Zealand; and two related small-scale studies with junior secondary students in Australia. This book brings substantial, empirically-based evidence to the widely held perception that many students have negative views of mathematics, and these affective responses develop during the middle years of school. The data for this book were collected with school students, and students who were actually engaged in learning mathematics in their crucial middle school years. The findings reported and discussed here are relevant for researchers and mathematics educators, policy makers and curriculum developers, and teachers and school principals engaged in the teaching of mathematics.

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. The new Must Know series is like a lightning bolt to the brain Every school subject has must know ideas, or essential concepts, that lie behind it. This book uses that fact to help students learn in a unique way. Most self-study guides begin a chapter with a set of goals, often leaving the starting point unclear. In Must Know Math Grade 8, however, each chapter immediately introduces students to the must know idea, or ideas, that lie behind each new math topic. As students learn these must know ideas, they are shown how to apply that knowledge to solving math problems. Focused on the essential concepts of sixth-grade math, this accessible guide helps students develop a solid understanding of the subject quickly and painlessly. Clear explanations are accompanied by numerous examples and followed with more challenging aspects of the math. Practical exercises close each chapter and instill learners with confidence in their growing math skills. * Each chapter begins with the must know ideas behind the new topic * Extensive examples illustrate these must know ideas * Students learn how to apply this new knowledge to problem solving * 250 practical review questions instill confidence * IRL (In Real Life) sidebars present real-life examples of the subject at work in culture, science, and history * Special BTW (By the Way) sidebars provide study tips, exceptions to the rule, and issues students should pay extra attention to * Bonus app includes 100 flashcards to reinforce what students have learned

How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making decisions where the outcome may be uncertain or the interests of others have to taken into consideration. Professor Koerner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with pithy observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Intended for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.

Martin Gardner continues to delight readers in Origami, Eleusis, and the Soma Cube, which is the second volume in the new Cambridge series, The New Martin Gardner Mathematical Library, based off his enormously popular Scientific American columns. He introduces young and old readers alike to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.

Written by expert teachers, X-kit Achieve Study Guides are a reliable resource for learning and revising, preparing learners for tests and exams. The content is organised into units according to CAPS, and clear, step-by-step explanations help learners understand concepts. Worked examples, summary tables, highlighted keywords and definitions, and annotated diagrams enhance learners’ understanding. Learners can practice, assess and improve their skills with graded exercises and answers.

This contributed volume is devoted to the recent history and evolution of mathematics education in Eastern Europe, exploring how it was influenced by social and political changes in this part of the world. Despite the broad recognition of the importance of these changes, little scholarship exists that examines the ways in which they were followed by changes in the teaching of mathematics in the post-socialist countries. Indeed, the analyzed processes are complex and vary across the states. Accordingly, this book touches on many factors--including differences in cultures and traditions - that find expression in the teaching of mathematics. Specifically, this volume seeks to explore what changes there were in education in general and in the position of mathematics in school education in these years, and how these changes may be explained and documented; what changes there were in the content of mathematics education and its assessment, and how were they motivated and adopted; what new textbooks appeared and what new methodological ideas were offered in them; how and why mathematics teacher education and/or professional development changed; what was the role (if any) of foreign influences on mathematics education, etc.The book will be of interest to both researchers in mathematics education and practitioners-teachers, as well as a broader audience of historians and educators exploring the political aspects of education.

Examine the basic concepts behind today's power systems as well as the tools you need to apply your newly acquired skills to real-world situations with POWER SYSTEM ANALYSIS AND DESIGN, SI, 7th Edition. The latest updates throughout this new edition reflect the most recent trends in the field as the authors highlight key physical concepts with clear explanations of important mathematical techniques. New co-author Adam Birchfield joins this prominent author team with fresh insights into the latest technological advancements. The authors develop theory and modeling from simple beginnings, clearly demonstrating how you can apply the principles you learn to new, more complex situations. New learning objectives and helpful case study summaries help focus your learning, while the updated PowerWorld (R) Simulation works seamlessly with this edition's content to provide hands-on design experience. WebAssign for Glover/Overbye/Sarma's Power System Analysis and Design, SI, 7th Edition, helps you prepare for class with confidence. Its online learning platform for your math, statistics, science and engineering courses helps you practice and absorb what you learn.

This book covers all the content needed for Year 2 of the Edexcel Statistics and Mechanics A-Level course and is fully up to date for the latest specifications. It has the clearest notes on all the theory for every topic, including annotated worked examples and explanations; hundreds of challenging questions for every chapter, including problem-solving and modelling; a realistic Practice Paper with a complete mark scheme; and a free Online Edition to read on PC, Mac or tablet (use the unique code printed inside the cover to gain full access). For full A-Level Maths coverage don't miss the Year 2 Pure Maths Student Textbook (9781789088410), and our Year 1 Student Textbooks for Pure Maths (9781789088397) and Statistics and Mechanics (9781789088403).

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This book is written by practitioners whose primary teaching subject is not math but who use math extensively in their courses in STEM disciplines, social science statistics, and their own research. Moreover, in the writing of this book, the authors have used the teaching principles of anchoring, overlearning, pruning the course to its essentials, and using simple and familiar language in word problems.

The present work is an introductory text in statistics, addressed to researchers and students in the field of material science. It aims to give the readers basic knowledge on how statistical reasoning is exploitable in this field, improving their knowledge of statistical tools and helping them to carry out statistical analyses and to interpret the results. It also focuses on establishing a consistent multivariate workflow starting from a correct design of experiment followed by a multivariate analysis process.

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches - Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student's experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students' backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms

Why on earth do cars have the same symmetry as dragonflies? Is there really a beautiful swirling pattern lurking in every dripping tap? What do insect eggs have in common with planets, and why? In this exquisite book, the smallest and most concise ever produced, designer David Wade introduces the main principles of symmetry, and shows how, despite opinions over exactly what it is, symmetry can be found in almost every corner of science, nature and human culture. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

The Mathematical Brain Across the Lifespan is the latest volume in the Progress in Brain Research series that focuses on new trends and developments. This established international series examines major areas of basic and clinical research within the neurosciences, as well as popular and emerging subfields.

This book is of interest to mathematics educators, researchers in mathematics education, gender, social justice, equity and democracy in education; and practitioners/teachers interested in the use of project work in mathematics teaching and learning. The book builds theoretical ideas from a careful substantial description of practice, in the attempt to improve both theory and practice in mathematics education. It thus interrogates and develops theoretical research tools for mathematics education and provides ideas for practice in mathematics classrooms.

Dit stel ouers in staat om van vroeg af en te midde van 'n druk lewe alledaagse geleenthede om hulle te gebruik om hul kleingoed gemaklik in die wereld van wiskunde in te lei. En dit verg geen spesiale kennis of opleiding van ouers nie; net 'n positiewe instelling en 'n opskerping van hulle interaksie met hul kleingoed om hulle al spelenderwys vertroud te maak met wiskundebegrippe.

This book provides the key technologies involved in an organization's digital transformation. It offers a deep understanding of the key technologies (Blockchain, AI, Big Data, IoT, etc.) involved and details the impact, the decision-making process, and the interplay between technologies, business models, and operations. Managing the Digital Transformation: Aligning Technologies, Business Models, and Operations provides frameworks and models to support digital transformation projects. The book presents the importance of digital transformation as a resilience approach to the operations processes and business models. It covers the essential elements integrating the technology, the organizations, the operations, and supply chain management used to move toward digital transformation. Concepts and mini-case studies are included to provide a deeper understanding of digital transformation projects with a holistic view. The book also examines the role that digital transformation plays with consideration of inter-organizational and intra-organizational capabilities, along with the role of digital culture, the worker's skills, business models, reconfiguration, as well as an operations optimization angle. Practitioners, consultants, governments, managers, scholars, and anyone interested in digital transformation will find the contents of this book very useful.

This new edition of Luke Robinson's popular textbook 'Pure Mathematics for CCEA AS Level' has been comprehensively updated to meet the requirements of the CCEA specification and fully covers unit AS1: Pure Mathematics. Following teacher feedback, it has been re-designed with a new two-colour style for ease of use. Each section of the book contains theory and examples with key words and definitions throughout. It also provides a large number of exercises, with answers included at the back of the book. Contents: Indices and Surds Quadratics Simultaneous Equations and Inequalities Algebraic Manipulation Graph Manipulation Graphs and Transformations Straight Lines Circles Binomial Expansion Trigonometry Exponentials and Logs Differentiation Integration Vectors Problem Solving