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A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.
This textbook covers in one volume all topics required in the pure mathematics section of single subject A-Level Mathematics syllabuses in the UK, as well as a significant part of the work required by those studying for Further Mathematics and for A-Level
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow style, the book clearly explains the workings of basic financial calculations, captures the concepts behind loans and interest in a step-by-step manner, and details how these steps can be implemented for practical purposes. Rather than simply providing investment and borrowing strategies, the author successfully equips readers with the skills needed to make accurate and effective decisions in all aspects of personal finance ventures, including mortgages, annuities, life insurance, and credit card debt. The book begins with a primer on mathematics, covering the basics of arithmetic operations and notations, and proceeds to explore the concepts of interest, simple interest, and compound interest. Subsequent chapters illustrate the application of these concepts to common types of personal finance exchanges, including: Loan amortization and savings Mortgages, reverse mortgages, and viatical settlements Prepayment penalties Credit cards The book provides readers with the tools needed to calculate real costs and profits using various financial instruments. Mathematically inclined readers will enjoy the inclusion of mathematical derivations, but these sections are visually distinct from the text and can be skipped without the loss of content or complete understanding of the material. In addition, references to online calculators and instructions for building the calculations involved in a spreadsheet are provided. Furthermore, a related Web site features additional problem sets, the spreadsheet calculators that are referenced and used throughout the book, and links to various other financial calculators. Understanding the Mathematics of Personal Finance is an excellent book for finance courses at the undergraduate level. It is also an essential reference for individuals who are interested in learning how to make effective financial decisions in their everyday lives.
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Understanding Mathematics is a carefully written series of mathematics to help students encourage the study of mathematics in the best interactive form. It contains ample practice material, attractive illustrations and real-life examples for the students to relate the topics with their everyday life. Special care has been taken while teaching topics like geometry and probability to the students. Keeping in mind the development status and comprehension level of students, the text has been presented in a well graded manner.
How would you teach the concept of odd and even numbers to a child? What is the probability of throwing a three on a six-sided die? How could you help a child who is confusing ratio and proportion? By seamlessly combining subject knowledge and pedagogy, the second edition of Understanding and Teaching Primary Mathematics will not only build your own confidence in mathematics, but also equip you with the curriculum understanding and pedagogical know-how to excel at teaching maths to children of any age. Written in a clear and accessible way, the book guides you through the fundamental ideas which are at the heart of teaching and learning maths, with special focus on observation and assessment of primary and early years children. Hallmark features Links to the classroom and research are provided throughout to help you relate educational theory to your own teaching practice. Portfolio and audit tasks allow you to assess your own subject knowledge and build up a portfolio of evidence to gain Qualified Teacher Status. The accompanying extra resources offers topic-specific self-audits for you to monitor your progress, exemplar lesson plans, a range of Portfolio Tasks mapped directly to current teacher standards and web-links to up-to-date online resources. New to this edition Resource Inspiration boxes give inviting examples of different activities to do with your class to provide inspiration for your own teaching. High quality videos with corresponding discussion, have been expertly selected from Teachers TV help to widen your skills and develop your practice, offering tips, lesson ideas and classroom resources.
The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.
This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7. Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.
"Simple, clear explanations of twenty ways in which mathematics helps us to understand practical issues of everyday life. Suitable for teenagers and adults, and beautifully produced. Highly recommended!" - Professor Ian Stewart, bestselling author of The Cabinet of Mathematical Curiosities Mathematics is an indispensable tool for life. From the systems that underpin our newsfeeds, through to the data analysis that informs our health and financial decisions, to the algorithms that power how we search online – mathematics is at the heart of how our modern world functions. In 20 dip-in lessons, Understanding Numbers explains how and why mathematics fuels your world and arms you with the knowledge to make wiser choices in all areas of your life. • Make sense of health statistics • Understand the mathematics behind political voting systems • Get to grips with how online search tools work • Discover how mathematics can create the perfect city