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Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries
by Ewa Swoboda Paola VighiThis book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula.
Early Mathematical Explorations
by Deborah Butler Nicola Yelland Carmel DiezmannEarly Mathematical Explorations shows readers how to provide young children with rich mathematical learning environments and experiences. This book presents teachers with a sound theoretical framework to encourage children to become numerate in the 21st century. It shows that mathematical learning can occur in a variety of ways, including when children explore ideas through play, problem solving and problem posing; engage in a rich variety of multimodal learning experiences; pursue self-directed activities and cooperate with others; and make connections between ideas and experiences in their everyday worlds. Chapters 2 and 3 explore the ways in which mathematical understandings can be supported from birth to five years. Chapters 4-9 provide an overview of mathematics in the early primary years. The final chapters illustrate the contexts and connections that can be made in early mathematical learning. Early Mathematical Explorations is an essential resource for pre- and in-service teachers alike.
Early Mathematics Learning
by Ulrich Kortenkamp Birgit Brandt Christiane Benz Götz Krummheuer Silke Ladel Rose VogelThis book will gather current research in early childhood mathematics education. A special focus will be the tension between instruction and construction of knowledge. The book includes research on the design of learning opportunities, the development of mathematical thinking, the impact of the social setting and the professionalization of nursery teachers.
Early Numeracy: Assessment for Teaching and Intervention (Math Recovery)
by Ann K Stafford Robert J Wright Mr James Martland'Unlike many books based on research work this book doesn't just let teachers know what is going wrong with children's learning it actually gives some practical advice about what to do next. The whole book is based upon extensive observation and recording of individual children and their difficulties with mathematics. These children are the most difficult to plan for in a busy classroom and the authors appreciate the small steps and the different learning styles approaches needed for these children. This approach fits well with the NNS wave and springboard materials but takes the analysis of the individual's difficulties to a more detailed level. The book brings together research carried out across a range of countries and therefore shows the versatility of the approaches taken. This will be a very useful book for trainee teachers as it exemplifies how to use assessment to feed into teaching. It will be helpful for class teachers and mathematics co-ordinators as well as SENCOs to assist in improving the teaching and learning for specific children in our schools' - Mary Briggs, Primary and Early Years PGCE Co-ordinator, Institute of Education, University of Warwick 'This is a highly practical resource that will be appreciated by classroom and specialist teachers alike. It will provide teachers new to the Math Recovery program with practical help and support to diagnose errors and misconceptions in early numeracy. Practicing Math Recovery Specialists will be thrilled with the addition of four new highly focused assessments and an elaboration of the Learning Framework in Number. Early Numeracy is admirably grounded in international research and well-established theory, characteristics that are much sought after in the current data driven educational environment. Like many others, I was drawn to Math Recovery after reading the first edition of Early Numeracy. This second edition is a treasure - it is exciting to consider the impact it will have on children and teachers, and to the growth of the Math Recovery program' - Audrey Murray, Lead Teacher, Midwest Math Recovery Training Center, Minneapolis This text has been fully updated to include developments and refinements brought about by widespread international application of the assessment tools in the Mathematics Recovery Programme. The book will help practitioners to identify and provide detailed analyses of all children but especially those who are able and those who underachieve in early numeracy. It will enable teachers, learning support personnel, numeracy consultants and educational psychologists to advise colleagues and parents on children's number knowledge and strategies for early numeracy. The Mathematics Recovery Programme has been successfully applied in Australia, the United Kingdom and Ireland, the United States and Canada, both in specialist interventions and classroom settings. The revised version shows how familiarisation with, and understanding of, the diagnostic assessment tools has allowed teachers to become more knowledgeable in understanding children's difficulties and misconceptions, and more skilled and confident in planning programmes of intervention and monitoring the children's progress. This new edition includes: - Integrated frameworks of useful tasks for assessing children's number knowledge and strategies; - Four separate and revised diagnostic assessment interviews; - Assessments for addition and subtraction strategies, Base Ten Arithmetical strategies, Early Grouping strategies, and Advanced Grouping strategies in the four operations; - How the assessment process has impacted significantly on teachers' professional development and contributed to the raising of standards in early numeracy.
Early Software Reliability Prediction: A Fuzzy Logic Approach
by Ajeet Kumar Pandey Neeraj Kumar GoyalThe development of software system with acceptable level of reliability and quality within available time frame and budget becomes a challenging objective. This objective could be achieved to some extent through early prediction of number of faults present in the software, which reduces the cost of development as it provides an opportunity to make early corrections during development process. The book presents an early software reliability prediction model that will help to grow the reliability of the software systems by monitoring it in each development phase, i.e. from requirement phase to testing phase. Different approaches are discussed in this book to tackle this challenging issue. An important approach presented in this book is a model to classify the modules into two categories (a) fault-prone and (b) not fault-prone. The methods presented in this book for assessing expected number of faults present in the software, assessing expected number of faults present at the end of each phase and classification of software modules in fault-prone or no fault-prone category are easy to understand, develop and use for any practitioner. The practitioners are expected to gain more information about their development process and product reliability, which can help to optimize the resources used.
Earlybird Kindergarten Mathematics, Textbook, A, Standards Edition
by Winnie Tan Yeap Ban HarNIMAC-sourced textbook
Earn It! (A Moneybunny Book)
by Cinders McLeodIn this delightful introduction to the simple concept of earning money, an exuberant little bunny learns that fame and fortune must be earned. Bun wants to be rich and famous. She loves to sing and knows she&’s meant for a career on stage. It should all be pretty easy—her mom can just drive her to the concert hall to perform! But her mom reminds her that most good things, like the garden they are growing, take time and work. At first, Bun isn&’t terribly excited by the idea of singing lessons and practice, but as she does the math and daydreams about her future singing career, the more she starts to like the idea of earning her way to stardom—a feeling just as good as being rich and famous!
Earth Science Reference Tables Workbook 4th Edition
by Topical Review Book CompanyThis workbook correlates with the current New York State Physical Setting Earth Science Reference Tables. Each table has its own section. Each section contains a detailed overview of the material, additional information, and a series of related practice questions.
Earthquake Data in Engineering Seismology
by Polat Gülkan Sinan Akkar Torild Van EckThis book addresses current activities in strong-motion networks around the globe, covering issues related to designing, maintaining and disseminating information from these arrays. The book is divided into three principal sections. The first section includes recent developments in regional and global ground-motion predictive models. It presents discussions on the similarities and differences of ground motion estimations from these models and their application to design spectra as well as other novel procedures for predicting engineering parameters in seismic regions with sparse data. The second section introduces topics about the particular methodologies being implemented in the recently established global and regional strong-motion databanks in Europe to maintain and disseminate the archived accelerometric data. The final section describes major strong-motion arrays around the world and their historical developments. The last three chapters of this section introduce projects carried out within the context of arrays deployed for seismic risk studies in metropolitan areas. Audience: This timely book will be of particular interest for researchers who use accelerometric data extensively to conduct studies in earthquake engineering and engineering seismology.
Earthquake Occurrence: Short- and Long-term Models and their Validation
by Giuseppe Falcone Maura Murru Rodolfo ConsoleEarthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models. In short-term models, known by the term ETAS, the occurrence space and time rate density of earthquakes is modeled as the sum of two terms, one representing the independent or spontaneous events, and the other representing the activity triggered by previous earthquakes. Examples of the application of such algorithms in real cases are also reported. Dealing with long-term recurrence models, renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what has occurred in the past. The book also introduces a number of computer codes developed by the authors over decades of seismological research.
Earthquake Statistical Analysis through Multi-state Modeling
by Nikolaos Limnios Irene Votsi Eleftheria Papadimitriou Georgios TsaklidisEarthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.
East Asian Societies
by W. Lawrence NeumanSo very many teach introductions to East Asia under different disciplines, including the Humanities, Sociology, Economics, History, and Religious Studies, but what makes this work so promising is its transferability across these lines of demarcation for the student engaged in her first serious study of the region. Neuman’s fine overview addresses the recurring cultural tasks across East Asia from family, to school and work, and socio-economic stratifications. Neuman has written an ideal introductory text with a sociologist’s clarity, a humanist’s learning, a researcher’s sharp eye, and a teacher’s fine sense of proportion. This is the only intellectual guidebook you will need to take with you for your voyage to East Asia.
East Indians in a West Indian Town: San Fernando, Trinidad, 1930-70 (Routledge Revivals)
by Colin G ClarkeFirst published in 1986, East Indians in a West Indian Town explores the complex geographical, sociological and anthropological dimensions of Trinidad society before and after its political independence, by employing three sets of materials – census data, questionnaires and participant-observation records. Cartographic, humanistic and statistical approaches are combined in a historical perspective to deal with the significance of race, cultural distinctions and class in San Fernando. A major concern of the book is to examine the social complexity that lies behind geographical patterns, and to compare aggregate data with group behaviour. This book will be of interest to students of geography, sociology and anthropology.
Eastern Asian Population History and Contemporary Population Issues (SpringerBriefs in Population Studies)
by Toru SuzukiThis book interprets and explains contemporary population issues from historical and cultural perspectives. These include lowest-low fertility in the Republic of Korea and Taiwan, early population aging in China relative to the developmental level, and various modes of domestic and international migration in the region. The book shows that divergent fertility decline can be attributed to the family patterns established in the pre-modern era in each country. It also examines the diversity of international migration in Eastern Asian countries today is also understood from the long-term historical view.
Eastern European Mathematics Education in the Decades of Change (International Studies in the History of Mathematics and its Teaching)
by Alexander KarpThis 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.
Easy 4-Step Method to Drug Calculations
by S. D. FoustThis unique work-text has been class-tested by hundreds of students. It makes the difficult concept of drug dosage calculations easy to understand and master by using a simple four-step method that focuses only on the information necessary for learning this skill. The readers are guided through every step of the calculation process with easy-to-understand and follow explanations. This is the perfect resource for paramedics, nurses, students and any other health care professionals who administer medication. Features Include: *Straightforward and easy to read *Hundreds of practice problems that incorporate realistic patient scenarios, protocols, and the latest trends in treatment management. *Final review section *Worked out-answer section clearly shows students every step of the problem-solving process.
Easy Algebra Step-by-Step: Master High-Frequency Concepts and Skills for Algebra Proficiency--FAST!
by Sandra Luna McCune William D. ClarkEasy Algebra Step-by-Step is an interactive approach to learning basic algebra. It contains completely worked-out sample solutions that are explained in detailed, step-by-step instructions. Moreover, it features guiding principles, cautions against common errors, and offers other helpful advice as "pop-ups" in the margins. The book takes you from number concepts to skills in algebraic manipulation and ends with word problems. Concepts are broken into basic components to provide ample practice of fundamental skills. The anxiety you may feel while trying to succeed in algebra is a real-life phenomenon. Many people experience such a high level of tension when faced with an algebra problem that they simply cannot perform to the best of their abilities. It is possible to overcome this difficulty by building your confidence in your ability to do algebra and by minimizing your fear of making mistakes.
Easy Mathematics for Biologists
by Peter C. FosterBecause elementary mathematics is vital to be able to properly design biological experiments and interpret their results. As a student of the life sciences you will only make your life harder by ignoring mathematics entirely. Equally, you do not want to spend your time struggling with complex mathematics that you will never use. This book is the pe
Easy R: Access, Prepare, Visualize, Explore Data, and Write Papers
by Elizabeth A. Gohmert Quan L. Li Douglas R. WiseDo you want to learn R? This book is built on the premise that anyone with a bit of free time and a healthy curiosity can learn to use R in their studies or at work. The authors focus on using R to do useful things like writing reports, creating data and graphs, accessing datasets collected by others, preparing data, and conducting simple data analysis. In this book you’ll learn how to: install R and RStudio®, and set up an RStudio® project and folders; write an essay with graphs based on simple real-world data using R Markdown; create variables from everyday numeric information and visualize data through five types of charts—bar plot, histogram, pie chart, scatter plot, and time series line plot—to identify patterns in the data; write and run R programs, and prepare your data following the tidyverse approach; import external datasets into R, install R data packages, and carry out initial data validity checks; conduct exploratory data analysis through three exercises involving data on voting outcomes, natural resource consumption, and gross domestic product (GDP) via data visualization, correlation coefficient, and simple regression; and write a research paper on the impact of GDP per capita on life expectancy using R Markdown. Student-friendly language and examples (such as binge-watched shows on Netflix, and the top 5 songs on Spotify), cumulative learning, and practice exercises make this a must-have guide for a variety of courses where data are used and reports need to be written. Code and datasets used to carry out the examples in the book are available on an accompanying website.
Easy R: Access, Prepare, Visualize, Explore Data, and Write Papers
by Elizabeth A. Gohmert Quan L. Li Douglas R. WiseDo you want to learn R? This book is built on the premise that anyone with a bit of free time and a healthy curiosity can learn to use R in their studies or at work. The authors focus on using R to do useful things like writing reports, creating data and graphs, accessing datasets collected by others, preparing data, and conducting simple data analysis. In this book you’ll learn how to: install R and RStudio®, and set up an RStudio® project and folders; write an essay with graphs based on simple real-world data using R Markdown; create variables from everyday numeric information and visualize data through five types of charts—bar plot, histogram, pie chart, scatter plot, and time series line plot—to identify patterns in the data; write and run R programs, and prepare your data following the tidyverse approach; import external datasets into R, install R data packages, and carry out initial data validity checks; conduct exploratory data analysis through three exercises involving data on voting outcomes, natural resource consumption, and gross domestic product (GDP) via data visualization, correlation coefficient, and simple regression; and write a research paper on the impact of GDP per capita on life expectancy using R Markdown. Student-friendly language and examples (such as binge-watched shows on Netflix, and the top 5 songs on Spotify), cumulative learning, and practice exercises make this a must-have guide for a variety of courses where data are used and reports need to be written. Code and datasets used to carry out the examples in the book are available on an accompanying website.
Easy as Pi: Maths Made Simple
by Liz StrachanIf you're brilliant at everything else, but lack confidence when it comes to maths, join Liz Strachan, a maths teacher with many, many years of experience, on this magical tour through the seeming mysteries of numbers, algebra and geometry.In the same inimitable, entertaining way she did in her previous bestselling books, A Slice of Pi and Numbers Are Forever, Liz will take readers from number-phobics to mathematical know-it-alls in no time at all. Peppered with absolutely terrible maths jokes and quirkily illustrated by Steven Appleby, this light-hearted but informative book will appeal to anyone with an enquiring mind.
Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
by Joachim Hilgert Max Hoffmann Tobias WeichIn diesem Lehrbuch stellen die Autoren einen axiomatischen Zugang zur ebenen Geometrie dar, der im Vergleich zu den Hilbertaxiomen und anderen oft gewählten Zugängen strukturelle und didaktische Vorteile bietet. Dieser auf metrischen Räumen basierende Zugang wird ausführlich motiviert und didaktisch aufbereitet. Ein besonderes Augenmerk liegt auf der besseren Verzahnung der Mathematikausbildung der Lehramtsstudierenden mit dem Schulstoff. In Ergänzung des axiomatischen Zugangs erklären die Autoren auch, wie man sich der ebenen Geometrie mit Mitteln der linearen Algebra nähern kann und stellen so den Bezug zur analytischen Geometrie der Oberstufe her. Als weitere Schnittstellen zwischen Schulmathematik und axiomatischer Geometrie werden die Begriffe Kongruenz und Symmetrie vertieft und so wichtigen Zusammenhänge zwischen den Begriffen Isometrie, Kongruenz und Symmetrie transparent gemacht und in schultypische Kontexte eingebettet.
Eco-Environmental Informatics
by TianXiang Yue Na Zhao WenJiao Shi ZeMeng FanThis book describes the basic contents of eco-environmental informatics (EEI) systematically. It consists of ten chapters: development history of the groundworks of knowledge, data and models for the EEI emergence since the early 1850s, the core principles of EEI including methods for high-accuracy surface modelling and the fundamental theorem for eco-environmental surface modelling, spatial interpolations, scale-transformations, data fusion, and model-data assimilation, as well as their applications connecting ecology, environmental science, and geographical science. It is used as a textbook for advanced undergraduate and graduate students in the field of EEI. It also serves as a reference book for researchers involved in geographical information science, ecological informatics, environmental informatics, computer-aided design, and planetary surface modelling.
Eco-Stats: From t-tests to Multivariate Abundances (Methods in Statistical Ecology)
by David I WartonThis book introduces ecologists to the wonderful world of modern tools for data analysis, especially multivariate analysis. For biologists with relatively little prior knowledge of statistics, it introduces a modern, advanced approach to data analysis in an intuitive and accessible way. The book begins by reviewing some core principles in statistics, and relates common methods to the linear model, a general framework for modeling data where the response is continuous. This is then extended to discrete data using generalized linear models, to designs with multiple sampling levels via mixed models, and to situations where there are multiple response variables via model-based approaches to multivariate analysis. Along the way there is an introduction to: important principles in model selection; adaptations of the model to handle non-linearity and cyclical variables; dependence due to structured correlation in time, space or phylogeny; and design-based techniques for inference that can relax some of the modelling assumptions. It concludes with a range of advanced topics in model-based multivariate analysis relevant to the modern ecologist, including fourth corner, latent variable and copula models. Examples span a variety of applications including environmental monitoring, species distribution modeling, global-scale surveys of plant traits, and small field experiments on biological controls. Math Boxes throughout the book explain some of the core ideas mathematically for readers who want to delve deeper, and R code is used throughout. Accompanying code, data, and solutions to exercises can be found in the ecostats R package on CRAN.
Ecological Models and Data in R
by Benjamin M. BolkerEcological Models and Data in R is the first truly practical introduction to modern statistical methods for ecology. In step-by-step detail, the book teaches ecology graduate students and researchers everything they need to know in order to use maximum likelihood, information-theoretic, and Bayesian techniques to analyze their own data using the programming language R. Drawing on extensive experience teaching these techniques to graduate students in ecology, Benjamin Bolker shows how to choose among and construct statistical models for data, estimate their parameters and confidence limits, and interpret the results. The book also covers statistical frameworks, the philosophy of statistical modeling, and critical mathematical functions and probability distributions. It requires no programming background--only basic calculus and statistics. Practical, beginner-friendly introduction to modern statistical techniques for ecology using the programming language R Step-by-step instructions for fitting models to messy, real-world data Balanced view of different statistical approaches Wide coverage of techniques--from simple (distribution fitting) to complex (state-space modeling) Techniques for data manipulation and graphical display Companion Web site with data and R code for all examples