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Two and Two Make Zero seeks to decrypt childrens acquisition of numerical concepts by considering this subject from a variety of perspectives, namely, numbers mathematical and conceptual properties, methods of number application in the physical world, the mental processes involved in number perception and cognition, the function, logic, and history of number symbolization, number origin, and childrens cognitive development. Researched and written from a teachers viewpoint, this work aims ultimately to improve elementary mathematics instruction by creating a better understanding of these irreducibly simple, but often misunderstood, concepts.
The purpose of presenting this book to the scholarly world is twofold. In the first place, I wish to provide for the English reader a translation of the earliest extant Arabic work of Hindi arithmetic. It shows this system at its earliest stages and the first steps in its development, a subject not yet well known except for readers of some Arabic publications by the present writer. This book is therefore of particular importance for students of the history of mathematical techniques. The medieval author, AI-UqHdisI, was, it seems, not noticed by bibliographers; neither was his work, which lay hardly noticed by modern scholars until 1960 when I happened to see a microfilm copy of it in the Institute of Arabic Manu scripts in Cairo. A steady labour immediately followed to make a comparative study of the text together with over twenty other texts, some of them not yet known to scholars. This pursuit resulted in (i) a doctoral degree awarded to me in 1966 by the University of Khartoum, (ii) the publication of several texts in Arabic including the text here translated, and (iii) the publication of several articles in Arabic and English on the history of arithmetic in the Middle Ages. The second purpose of this book is to make the main results of my study available to the English reader.
As Zero searches to find his place, he learns of his additive and multiplicative identities, and then he establishes place value.
The activities in this book are designed to teach strategies for mental computation of addition and subtraction. These strategies should be taught after children have learned addition and subtraction, but before they have mastered the facts. Each strategy is introduced using frog counters to teach a way of thinking how to use numbers to find sums and differences quickly and correctly. The strategies utilize numbers with specific properties of addition and subtraction in ways that make sense to a child. Many of the activity pages are purposely designed to be open-ended and may be customized for practice of facts that children find most challenging
Підручник призначений для тренування та контролю знань з практики усного та писемного англійського мовлення студентів старших курсів філологічних факультетів педагогічних та мовних вищих навчальних закладів III та IV рівнів акредитації. Він передбачає максимальне засвоєння студентами теоретичного та практичного матеріалу щляхом цілеспрямованого закріплення й удосконалення мовних навиків вживання синонімічних рядів та фразеологічних одиниць і служить завданню підготувати студентів до введення вказаних навиків у непідготовлене мовлення. У підручнику подаються практичні завдання, спрямовані на формування вмінь у студентів моделювати та відтворювати різні комунікативні ситуації з використанням відповідних синонімів та фразеологічних одиниць. Методика викладу матеріалу, запропоновані вправи та тексти відповідають вимогам, що передбачені програмою вивчення іноземної мови на рівнях Upper-Intermediate та Advanced (бакалавр та магістр).
This Second Edition covers the mathematics needed to teach the Early Learning Goals. It has been up-dated to include new research findings as well as new topics, for example, using number lines with young children. The topics of counting, number (including early addition and subtraction), pattern, measures and shape and space are covered in detail. Each chapter contains suggestions for key questions to ask in order to encourage children to discuss their mathematics and to demonstrate what they know and understand. There are sections on developing problem-solving skills, working with parents and other adults in the nursery setting, as well as detailed charts giving ideas for activities and how to assess learning, and some activities planned in full. The final chapter gives detailed help with planning and assessment of mathematics. The book is intended for anyone working with children in the early years: teachers, nursery nurses, classroom assistants, playgroup leaders and workers, child-minders and day care staff. It is particularly suitable as a course text for those training to be teachers, either through the undergraduate route, or through a PGCE, and for those studying for early childhood degrees or diplomas.
1. The book is prepared for the preparation for the GATE entrance 2. The practice Package deals with Electrical Engineering 3. The practice package is divided into chapters 4. Solved Papers are given from 2021 to 2000 understand the pattern and build concept 5. 3 Mock tests are given for Self-practice 6. Extensive coverage of Physics and General Aptitude are given 7. Questions in the chapters are divided according to marks requirements; 1 marks and 2 marks 8. This book uses well detailed and authentic answers Get the complete assistance with “GATE Chapterwise Solved Paper” Series that has been developed for aspirants who are going to appear for the upcoming GATE Entrances. The Book “Chapterwise Previous Years’ Solved Papers (2021-2000) GATE – Electrical Engineering” has been prepared under the great observation that help aspirants in cracking the GATE Exams. As the name of the book suggests, it covers detailed solutions of every question in a Chapterwise manner. Each chapter provides a detailed analysis of previous years exam pattern. Chapterwise Solutions are given Engineering Mathematics and General Aptitude. 3 Mock tests are given for Self-practice. To get well versed with the exam pattern, Level of questions asked, conceptual clarity and greater focus on the preparation. This book proves to be a must have resource in the solving and practicing previous years’ GATE Papers. TABLE OF CONTENT Solved Paper 2021- 2012, Engineering Mathematics, Electric Circuits and Fields, Signals and Systems, Electrical Machines, Power System, Control Systems, Measuring and Instruments, Analog and Digital Electronics, Power Electronics, General Aptitude, Crack Paper 1-3.
Geometry, Language and Strategy is a way of looking at game theory or strategic decision-making from a scientific perspective, using standard equations from the fields of engineering and physics. To better approximate reality, it extends game theory beyond the two-player set piece. The book begins where former game theory literature ends OCo with multi-person games on a world stage. It encompasses many of the variables encountered in strategic planning, using mathematics borrowed from physics and engineering, rather than the economic models which have not proven to be good in predicting reality. Sample Chapter(s). Chapter 1: Introduction (1,364 KB). Contents: Rules-of-the-Game; Flow of Strategic-Mass; Game Symmetries; Analysis; Graphical Presentation; Applications and Open Problems; Appendices: Thermodynamics; Symmetry in Differential Geometry; Central Strategies; Single Strategy Model; Single Strategy Numerical Solutions; Streamlines; Player Fluid. Readership: Mathematicians and scientists who wish to broaden their understanding of economic possibilities using game theory."
Future Times, Future Tenses examines how the future is expressed by means of tense, aspect, and modality across a wide range of languages, among them French, Polish, Basque, Turkish, and West Greenlandic. From the present point of view, the future is not fixed: while there is arguably only one past, the future is largely open and/or indeterminate. Reference to the future has thus become one of the most hotly-debated topics in contemporary linguistics: the interactions of future tense with future time, and of future tense with the semantics of possible worlds, are crucial to any satisfactory account of temporal linguistics. This book considers and seeks a resolution to outstanding issues in the field by uniting linguistic and philosophical perspectives on future reference in natural language. Scholars from different parts of the world approach these issues from a variety of theoretical perspectives, including those of linguistic typology, formal semantics, pragmatics, and philosophy of language. In the process they question the very validity of the traditional notion of a specific marker for future tense. The book shows the close connections between linguistic, logical, metaphysical, ontological, and epistemological issues concerning the future and reveals the value of linking linguistic considerations of tense and aspect to philosophical approaches to modality and time.