Written by Habia, the Hair and Beauty Industry Authority, this write-in workbook is an invaluable resource to help learners improve their Maths and English skills and prepare for Level 1 and Level 2 Functional Skills exams. The workbook format enables learners to practice and improve their maths and English skills and the real-life questions, exercises and scenarios are all written with a beauty therapy context to help students find essential Maths and English theory understandable, engaging and achievable. This workbook is an invaluable resource to support Maths and English learning in the classroom, at work and for personal study at home.

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points.

Developed in cooperation with the International Baccalaureate (R) Enable students to construct, communicate and justify correct mathematical arguments with a range of activities and examples of maths in the real world. - Engage and excite students with examples and photos of maths in the real world, plus inquisitive starter activities to encourage their problem-solving skills - Build mathematical thinking with our new toolkit feature of questions, investigations and activities - Develop understanding with key concepts and applications integrated throughout, along with TOK links for every topic - Prepare your students for assessment with worked examples, and extended essay support - Check understanding with review exercise at the end of the coursebook Follows the new 2019 IB Guide for Mathematics: analysis and approaches Higher Level Available in the series Mathematics for the IB Diploma: Analysis and approaches SL Student Book ISBN: 9781510462359 Student Book Boost eBook ISBN: 9781398334304 Exam Practice Workbook Mathematics for the IB Diploma: Analysis and approaches SL 9781398321182 Exam Practice Workbook Mathematics for the IB Diploma: Analysis and approaches SL Boost eBook 9781398342316 Mathematics for the IB Diploma: Analysis and approaches HL Student Book ISBN: 9781510462366 Student Book Boost eBook ISBN: 9781398334311 Exam Practice Workbook Mathematics for the IB Diploma: Analysis and approaches HL 9781398321878 Exam Practice Workbook Mathematics for the IB Diploma: Analysis and approaches HL Boost eBook 9781398342361 SL & HL Boost Subscription: 9781398341265

• Utilizes case studies from different disciplines and sectors within engineering and other related technical areas to demonstrate how to go from data, to insight, and to decision making • Introduces various approaches to build models that exploits different algorithms • Discusses predictive models that can be built through machine learning and used to mine patterns from large datasets • Explores the augmentation of technical and mathematical materials with explanatory worked examples • Includes a glossary, lecture notes, self-assessments, and worked-out practice exercises

This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its teaching and learning. The book both surveys current research and indicates orientations for fruitful work in the future.

This book is the result of a conference sponsored by the Educational Testing Service and the University of Wisconsin's National Center for Research in Mathematical Sciences Education. The purpose of the conference was to facilitate the work of a group of scholars whose interests included the assessment of higher-order understandings and processes in foundation-level (pre-high school) mathematics. Discussions focused on such issues as the purposes of assessment, guidelines for producing and scoring "real-life" assessment activities, and the meanings of such terms as "deeper and higher-order understanding," "cognitive objectives," and "authentic mathematical activities." Assessment was viewed as a critical component of complex, dynamic, and continually adapting educational systems. During the time that the chapters in this book were being written, sweeping changes in mathematics education were being initiated in response to powerful recent advances in technology, cognitive psychology, and mathematics, as well as to numerous public demands for educational reform. These changes have already resulted in significant reappraisals of what it means to understand mathematics, of the nature of mathematics teaching and learning, and of the real-life situations in which mathematics is useful. The challenge was to pursue assessment-related initiatives that are systematically valid, in the sense that they work to complement and enhance other improvements in the educational system rather than act as an impediment to badly needed curriculum reforms. To address these issues, most chapters in this book focus on clarifying and articulating the goals of assessment and instruction, and they stress the content of assessment above its mode of delivery. Computer- or portfolio-based assessments are interpreted as means to ends, not as ends in themselves. Assessment is conceived as an ongoing documentation process, seamless with instruction, whose quality hinges upon its ability to provide complete and appropriate information as needed to inform priorities in instructional decision making. This book tackles some of the most complicated issues related to assessment, and it offers fresh perspectives from leaders in the field--with the hope that the ultimate consumer in the instruction/assessment enterprise, the individual student, will reclaim his or her potential for self-directed mathematics learning.

Exploring Mathematics with CAS Assistance is designed as a textbook for an innovative mathematics major course in using a computer-algebra system (CAS) to investigate, explore, and apply mathematical ideas and techniques in problem solving. The book is designed modularly with student investigations and projects in number theory, geometry, algebra, single-variable calculus, and probability. The goal is to provoke an inquiry mindset in students and to arm them with the CAS tools to investigate low-entry, open-ended questions in a variety of mathematical arenas. Because of the modular design, the individual chapters could also be used selectively to design student projects in a number of upper-division mathematics courses. These projects could, in fact, lead into undergraduate research projects. The existence of powerful computer-algebra systems has changed the way mathematicians perform research; this book enables instructors to put some of those new methods and approaches into their undergraduate instruction. Prerequisites include a basic working knowledge of discrete mathematics and single-variable calculus. Programming experience and some basic familiarity with elementary probability and statistics are beneficial but not required. The book takes a software-agnostic approach and emphasizes algorithmic structure of solution methods by systematically providing their step-by-step verbal descriptions or suitable pseudocode that can be implemented in any CAS.

This book engages with contemporary, and often polarizing, debates surrounding the risks of adolescent use of digital media and internet technologies. By drawing on multiple research studies, the text synthesizes current understandings of the impacts of social network use, online gaming, pornography, and phenomena, including cyberbullying, cyberstalking, and internet addiction, to develop recommendations for the effective identification of at-risk youth, as well as strategies for informed communication about online risks and opportunities. It shows how media discussion of risks to children and teenagers from new technology is highly emotive and often exaggerated, rooted in the “moral panic” surrounding new cultural practices that young people engage in, but which adults do not understand. Online risks are thus conceptualized as centering on three areas, specific to adolescence, which have undergone radical changes due to new internet technology. These include young people’s identity, the types of content that are accessed, and social relationships. The author shows how these matters stem from the potential of new technology to establish new interpersonal connections, emphasizing how it brings opportunities, as much as risks. As such, he provides a uniquely balanced discussion of potential dangers, while also emphasizing the opportunities for social, academic, and personal growth which new technologies afford young people. It will be indispensable for researchers and clinicians interested in assessing levels of online risk, as well as scholars and educators with interests in cyberpsychology, social psychology, cyber culture, social aspects of computing and media, and adolescent development.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

Tessellations: Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. Additionally, it covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Inclusion of special topics like spiral tilings and tessellation metamorphoses allows the reader to explore beautiful and entertaining math and art. The book has a particular focus on 'Escheresque' designs, in which the individual tiles are recognizable real-world motifs. These are extremely popular with students and math hobbyists but are typically very challenging to execute. Techniques demonstrated in the book are aimed at making these designs more achievable. Going beyond planar designs, the book contains numerous nets of polyhedra and templates for applying Escheresque designs to them. Activities and worksheets are spread throughout the book, and examples of real-world tessellations are also provided. Key features Introduces the mathematics of tessellations, including symmetry Covers polygonal, aperiodic, and non-Euclidean tilings Contains tutorial content on designing and drawing Escheresque tessellations Highlights numerous examples of tessellations in the real world Activities for individuals or classes Filled with templates to aid in creating Escheresque tessellations Treats special topics like tiling rosettes, fractal tessellations, and decoration of tiles

An almost obsessional use of numbers characterizes Japanese popular culture. A wide variety of numerical formulas and strategies provide the means for explaining events and solving problems occurring in everyday life. These include such matters as the choice of the name for a child, ranking in almost any game or sport, the diagnosis and cure of illness, or the decision to accept a new job.
"The Japanese Numbers Game" provides a general study of the whole field of Japanese popular numeracy. It introduces, in fascinating detail, a world of numbers in which fortune-telling, the abacus, games involving numbers as well as curious numerical names (of both people and places) illustrate a popular obsession with systems of counting, calculation, and forecasting.
No understanding of Japanese popular culture is complete without some knowledge of the use of numbers by the Japanese. Thomas Crump's meticulous exploration of the cultural roots of these attitudes makes this book essential for students of anthropology and Japanese studies.

'A WITTY BOOK THAT PROVOKES THE IMAGINATION' The Times How many socks make a pair? The answer is not always two. And behind this question lies a world of maths that can be surprising, amusing and even beautiful. Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. If you already like maths you'll discover plenty of new surprises. And if you've never picked up a maths book in your life, this one will change your view of the subject forever.

Make trigonometry as easy as 1-2-3 Believe it or not, trigonometry is easier than it looks! With the right help, you can breeze through your next trig class, test, or exam and be ready for your next math challenge. In Trigonometry For Dummies, you'll learn to understand the basics of sines, cosines, and tangents, graph functions, solve tough formulas, and even discover how to use trig outside the classroom in some cool and interesting ways. Ditch the confusing jargon and take a plain-English tour of one of the most useful disciplines in math. In this lifesaving guide, you'll learn how to: Graph trig functions, including sine, cosine, tangent, and cotangent functions Understand inverse trig functions and solve trig equations Relate triangles to circular functions and get a handle on basic identities So, whether you're looking for an easy-to-use study guide, to boost your math grade, or get a refresher on some basic trig concepts after a long absence from studying, Trigonometry For Dummies is your ticket to understanding the mathematical mysteries of the triangle.

The second edition of Mark Wolfmeyer's award-winning primer offers future and current math teachers an introduction to the connections that exist between mathematics and a critical orientation to education, one that accounts for race, social class, gender, sexuality, language diversity, and ability. Expanded and updated from the first edition, this book demonstrates how elements of human diversity and intersectionality have real effects in the mathematics classroom, and prepares teachers with a more critical math education that increases accessibility and equity for all students. By refocusing math learning toward the goals of democracy and social and environmental crises, the book also introduces readers to broader contemporary school policy and reform debates and struggles, especially in light of Covid-19 and the ongoing struggle for racial equity. Featuring concrete strategies and examples in both formal and informal educational settings, as well as discussion questions for teachers and students, text boxes with examples of critical education in practice, a glossary, and suggestions for further reading, Mark Wolfmeyer shows how critical mathematics education can be put into practice, relevant for undergraduate and graduate students in education, current teachers, and teacher educators.

First published in 1991. D. W. Winnicott-one of this century's most important theorists-is the focus of the new edition of this extraordinary volume. Drawing extensively upon Winnicott' s own papers and lectures, the main themes of his theory and personal development are revealed. His vast contributions to the understanding of the profound significance of infancy in the total life of human beings is brought to the foreground. And throughout, D. W. Winnicott-noted pediatrician and child analyst, revered teacher and theorist-shines through. Part I, The Background, discusses Winnicott's personal beliefs and the evolution of his theory of emotional development. In Part II, The Theory of Emotional Development, his main themes are introduced: Basic Assumptions, Early Psychic Functioning, Adapting to Shared Reality, and The Environmental Provision. Part III, Boundary and Space. considers some of the implications of Winnicott' s theory of development for the individual, and for society. Boundary and Space provides the first systematic presentation of D. W. Winnicott' s developmental and clinical methodology. This up dated edition also includes a comprehensive bibliography of the works from which the book draws, in addition to an enlightening article that links Winnicott' s evolving ideas to various stages of his life. For all pro fessionals and students interested in human development, this volume is an essential invitation into the world of D. W. Winnicott. his words and work.

This book provides an introduction to the computer language A Programming Language (APL), providing quick access to the powerful computational capabilities of the language for the newcomer to APL. It focuses on the mathematical nature of the language, and complements standard curricula.

Exam board: OCR Level: A-level Subject: Mathematics First teaching: September 2017 First exams: Summer 2019 Benefit from the expert input of experienced examiners and subject specialists including Heather Davis in this assessment-led Practice Book; tailored to the new 2017 specifications and packed with exam-style questions. - Thoroughly prepare your students for the exam with over 200 exam-style questions that are matched to the new specifications. - Provide structured support and extra practice with questions focused on problem-solving, modelling and technology. - Create opportunities for self-directed learning and assessment with answers at the back of the book, plus full step-by-step worked solutions and mark schemes supplied online. - Enhance learning with extra practice designed to supplement the textbooks and the My Revision Notes series.

Exam Board: SQA Level: Higher Subject: Maths Two books in one! Combining a revision guide and a full set of practice test papers, this fantastic resource is all you need to revise for the exam. The revision guide * Covers all of the topics in the CfE Higher Maths curriculum, broken down into manageable chunks for easy revision * Clearly explains key concepts, research evidence and real-life applications * Contains Quick Tests to let students check their knowledge and understanding as they go along The practice test papers * Are in the format and the style of the SQA exam, giving students an opportunity to practice taking the Higher Maths exam Marking instructions and sample answers are provided online, so students can check their progress.

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

The book gives an up-to-date account of various approaches availablefor the analysis of infectious disease data. Most of the methods havebeen developed only recently, and for those based on particularlymodern mathematics, details of the computation are carefullyillustrated. Interpretation is discussed at some length and the emphasisthroughout is on making statistical inferences about epidemiologicallyimportant parameters.Niels G. Becker is Reader in Statistics at La Trobe University,Australia.

This timely book addresses the increasing need for collaboration, innovation and solution-focussed skills by looking at examples of cutting-edge pedagogy that can inform future directions. Integrating STEM in Higher Education shows how applying digital innovations that can be generated through the implementation of deliberately designed STEM education can change the world for the better. References to over 45 higher education institutions from around the world are included, where integrated approaches are already occurring. A wide range of teaching strategies and assessment methods are discussed, promoting a transformative method in which students can generate new knowledge within coursework and simultaneously develop skills and attributes for their future careers, lives and the world's needs. This book is essential reading for STEM educators, administrators and academic leaders, as well as learning designers in higher education.

Rely on the TeeJay method that students have known and loved throughout their school years to deliver the results they want in Higher Maths. This book provides hundreds of practice questions, with progression and consolidation - the core TeeJay philosophy - underpinning every exercise and chapter. - Covers the updated SQA Higher specification, for first assessment in 2019 - Starts with a Chapter Zero that revises all necessary algebraic and numeric skills from National 5 - Every chapter ends with Exam Practice Exercises that mirror the question types in the SQA exams - Every third chapter ends with a cumulative Home Exercise for revision and recall of the topics covered across all chapters up to that point - Includes Specimen Exam Papers 1 and 2 at the end of the book - Answers for all questions are in the back of the book; answers for the Home Exercises and Specimen Exam Papers are available on the TeeJay Maths website

Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.

The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.