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Exploring Mathematics and Science Teachers' Knowledge: Windows into teacher thinking
by Mike Askew Marissa Rollnick John Loughran Hamsa VenkatGlobally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists are teaching mathematics and science at both primary and secondary levels, and research evidence has revealed how gaps and limitations in teachers’ content understandings can lead to classroom practices that present barriers to students’ learning. This book addresses these issues by investigating how teachers’ content knowledge interacts with their pedagogies across diverse contexts and perspectives. This knowledge-practice nexus is examined across mathematics and science teaching, traversing schooling phases and countries, with an emphasis on contexts of disadvantage. These features push the boundaries of research into teachers’ content knowledge. The book’s combination of mathematics and science enriches each discipline for the reader, and contributes to our understandings of student attainment by examining the nature of specialised content knowledge needed for competent teaching within and across the two domains. Exploring Mathematics and Science Teachers’ Knowledge will be key reading for researchers, doctoral students and postgraduates with a focus on Mathematics, Science and teacher knowledge research.
Exploring Mathematics: An Engaging Introduction to Proof (Cambridge Mathematical Textbooks)
by John Meier Derek SmithExploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
Exploring Modeling with Data and Differential Equations Using R
by John ZobitzExploring Modeling with Data and Differential Equations Using R provides a unique introduction to differential equations with applications to the biological and other natural sciences. Additionally, model parameterization and simulation of stochastic differential equations are explored, providing additional tools for model analysis and evaluation. This unified framework sits "at the intersection" of different mathematical subject areas, data science, statistics, and the natural sciences. The text throughout emphasizes data science workflows using the R statistical software program and the tidyverse constellation of packages. Only knowledge of calculus is needed; the text’s integrated framework is a stepping stone for further advanced study in mathematics or as a comprehensive introduction to modeling for quantitative natural scientists. The text will introduce you to: modeling with systems of differential equations and developing analytical, computational, and visual solution techniques. the R programming language, the tidyverse syntax, and developing data science workflows. qualitative techniques to analyze a system of differential equations. data assimilation techniques (simple linear regression, likelihood or cost functions, and Markov Chain, Monte Carlo Parameter Estimation) to parameterize models from data. simulating and evaluating outputs for stochastic differential equation models. An associated R package provides a framework for computation and visualization of results. It can be found here: https://cran.r-project.org/web/packages/demodelr/index.html.
Exploring Operations Research with R (Chapman & Hall/CRC Series in Operations Research)
by Jim DugganExploring Operations Research with R shows how the R programming language can be a valuable tool – and way of thinking – which can be successfully applied to the field of operations research (OR). This approach is centred on the idea of the future OR professional as someone who can combine knowledge of key OR techniques (e.g., simulation, linear programming, data science, and network science) with an understanding of R, including tools for data representation, manipulation, and analysis. The core aim of the book is to provide a self-contained introduction to R (both Base R and the tidyverse) and show how this knowledge can be applied to a range of OR challenges in the domains of public health, infectious disease, and energy generation, and thus provide a platform to develop actionable insights to support decision making.Features Can serve as a primary textbook for a comprehensive course in R, with applications in OR Suitable for post-graduate students in OR and data science, with a focus on the computational perspective of OR The text will also be of interest to professional OR practitioners as part of their continuing professional development Linked to a Github repository including code, solutions, data sets, and other ancillary material
Exploring Quantum Contextuality with Photons (Springer Theses)
by Zheng-Hao LiuThis thesis highlights research explorations in quantum contextuality with photons.Quantum contextuality is one of the most intriguing and peculiar predictions of quantum mechanics. It is also a cornerstone in modern quantum information science. It is the origin of the famous quantum nonlocality and various nonclassical paradoxes. It is also a resource for many quantum information processing tasks and even universal quantum computing. Therefore, the study of quantum contextuality not only advances the comprehension of the foundations of quantum physics, but also facilitates the practical applications of quantum information technology.In the last fifteen years, the study of quantum contextuality has developed from a purely theoretical level to a stage where direct experimental tests become amenable. However, the experimental research on contextuality at the current stage largely focuses on direct validations of some most famous predictions of contextuality, while other forms of contextuality and its practical applications in quantum information science are rarely involved. The research in this thesis is committed to bridge this gap from two directions: (1) to construct and test stronger forms of contextuality and relieve the requirements of contextuality experiments on experimental platforms, and (2) to explore the connections between contextuality and the other concepts in quantum information science and directly demonstrate the application of contextuality in broader scenarios. Specifically, the thesis have discussed the research topics about the relationship between quantum contextuality and nonlocality, the “all-versus-nothing” paradoxes from quantum contextuality, the ore- and post-selection paradoxes from quantum contextuality, and the topological protection and braiding dynamics of quantum contextuality in quasiparticle systems.
Exploring Rating Scale Functioning for Survey Research (Quantitative Applications in the Social Sciences)
by Stefanie A. WindItems with ordered response categories are common in survey research, such as when respondents are asked how much they agree with certain statements. But how large are the differences between categories of response, and how well do they distinguish between respondents? This volume is the first to introduce the evaluation of rating scales to an audience of survey researchers. Evaluating Rating Scale Functioning for Survey Research provides researchers with an overview of rating scale analysis along with practical guidance on how to conduct such analyses with their own survey data. Author Stefanie A. Wind presents three categories of methods: Rasch models; non-Rasch Item Response Theory (IRT) models; and non-parametric models, together with practical examples. Tutorials, datasets, and software code (R and Facets) to accompany the book are available on the book’s website.
Exploring Rating Scale Functioning for Survey Research (Quantitative Applications in the Social Sciences)
by Stefanie A. WindItems with ordered response categories are common in survey research, such as when respondents are asked how much they agree with certain statements. But how large are the differences between categories of response, and how well do they distinguish between respondents? This volume is the first to introduce the evaluation of rating scales to an audience of survey researchers. Evaluating Rating Scale Functioning for Survey Research provides researchers with an overview of rating scale analysis along with practical guidance on how to conduct such analyses with their own survey data. Author Stefanie A. Wind presents three categories of methods: Rasch models; non-Rasch Item Response Theory (IRT) models; and non-parametric models, together with practical examples. Tutorials, datasets, and software code (R and Facets) to accompany the book are available on the book’s website.
Exploring Research Frontiers in Contemporary Statistics and Econometrics
by Paul W. Wilson Ingrid Van KeilegomThis book collects contributions written by well-known statisticians and econometricians to acknowledge Léopold Simar's far-reaching scientific impact on Statistics and Econometrics throughout his career. The papers contained herein were presented at a conference in Louvain-la-Neuve in May 2009 in honor of his retirement. The contributions cover a broad variety of issues surrounding frontier estimation, which Léopold Simar has contributed much to over the past two decades, as well as related issues such as semiparametric regression and models for censored data. This book collects contributions written by well-known statisticians and econometricians to acknowledge Léopold Simar's far-reaching scientific impact on Statistics and Econometrics throughout his career. The papers contained herein were presented at a conference in Louvain-la-Neuve in May 2009 in honor of his retirement. The contributions cover a broad variety of issues surrounding frontier estimation, which Léopold Simar has contributed much to over the past two decades, as well as related issues such as semiparametric regression and models for censored data.
Exploring Statistics
by Damaraju RaghavaraoThis book provides an overview of the commonly used statistical methodology. It is intended to enable professionals such as medical doctors, engineers, business executives, laboratory technicians, school teachers, and others to understand the basics of statistical thought through self study.
Exploring Transdisciplinarity in Art and Sciences
by Zoï Kapoula Emmanuelle Volle Julien Renoult Moreno AndreattaThe book is organized around 4 sections. The first deals with the creativity and its neural basis (responsible editor Emmanuelle Volle). The second section concerns the neurophysiology of aesthetics (responsible editor Zoï Kapoula). It covers a large spectrum of different experimental approaches going from architecture, to process of architectural creation and issues of architectural impact on the gesture of the observer. Neurophysiological aspects such as space navigation, gesture, body posture control are involved in the experiments described as well as questions about terminology and valid methodology. The next chapter contains studies on music, mathematics and brain (responsible editor Moreno Andreatta). The final section deals with evolutionary aesthetics (responsible editor Julien Renoult).Chapter "Composing Music from Neuronal Activity: The Spikiss Project" is available open access under a Creative Commons Attribution-NonCommercial 4.0 International License via link.springer.com.
Exploring What Drives Indian Stock Market During Covid-19: Fads or Fundamentals (SpringerBriefs in Economics)
by Indrani ChakrabortyThis book analyses the dynamics of Indian stock market with a special emphasis during the period following emergence of Covid-19. Coming from the instability in stock market following Covid-19, it delves deeper into the dynamics and unfolds the causal relationship between various economic fundamentals and the stock prices. Observing short-term herding in the stock market following Covid-19, the book's finding suggests that investors in the Indian stock market made investment choices irrationally during Covid-19 crisis periods. It also showcases how the stock market became inefficient following the emergence of pandemic and did not follow the fundamentals. Interestingly, the findings suggest no relationship between stock returns and real economic activities in India. The format of presentation makes the book well suited not only for students, academics, policy makers and investors in the stock markets, but also people engaged or interested in business and finance. The book would thus be of interest to both specialists and the laity. Analysis contained in this book will help different readership groups in different ways. Researchers from economics and finance disciplines will be able to learn about frontiers in the theoretical paradigms discussed in the book; advanced econometric techniques applied in the book will also be useful for their own research. The macroeconomic insights, and insights from behavioural economics, can expand the knowledge of corporate sector, useful in making real life decisions. Finally, it will help policy makers, like SEBI (Securities and Exchange Board of India), to formulate appropriate regulatory policies so as to minimize possibility of speculative bubbles as experienced during the pandemic period in the Indian stock markets.
Exploring the Association Between Military Base Neighborhood Characteristics and Soldiers' and Airmen's Outcomes
by Laura L. Miller Gabriella C. Gonzalez Sarah O. Meadows Jeremy N. V. Miles Brandon T. DuesThis report explores the applicability of neighborhood theory and social indicators research to understanding the quality of life in and around military bases. It also highlights gaps in neighborhood study methodology that need to be addressed in future research. Finally, it outlines how a more in-depth neighborhood analysis of military installations could be conducted.
Exploring the Beauty of Fascinating Numbers (Springer Praxis Books)
by Shyam Sunder GuptaThis book is a great treasure for everyone who enjoys the beauty of the fascinating world of recreational mathematics. It focuses on recreational aspects of numbers to create interest and motivate readers to learn to be creative in improving their problem-solving techniques. The book would help ignite interest in numbers, which will benefit teachers trying to teach math, especially to students who don’t like math, by supplementing their regular curriculum with the module containing material from the book, which provides an opportunity for fun and joy while developing mathematical skills. The ideas for further exploration given in the book offer food for thought to delve into the world of research and fun, in addition to testing computational skills. The book communicates the excitement and fascination of numbers to the students in schools and colleges. The theory behind the subject matter has been kept to a minimum to retain the recreational nature of the book. The book has a delightful coverage of numerical curiosities, coincidences and wonders, revealing many new eye-opening properties of numbers. Organized into 23 chapters, the book contains a large variety of topics: digital root wonders, the elegance of squares, triangular numbers, Smith numbers, amicable numbers, perfect, multiple perfect and sociable numbers, happy numbers, Fibonacci numbers, Lucas numbers, and the Golden ratio, Kaprekar numbers, self-numbers, repunit numbers, equal product of reversible numbers (EPRNs), rare numbers, fascinating factorials, Ulam numbers, mystery of π, cab and vampire numbers, digital invariants and narcissistic numbers, special numbers like autobiographical numbers, Harshad numbers, parasite numbers, polydivisible numbers, Ramanujan numbers, number curiosities such as lucky mistakes, Pascal’s triangle and Pythagorean triplets. Pythagoras attributed mystical qualities to some of the numbers. Even the religious properties of numbers were extensively studied. So, four chapters are exclusively devoted to such numbers, namely, the amazing number 108, the unlucky 13, the beauty of 153, and the number of the beast, with lots of new curiosities and miraculous coincidences.
Exploring the Effect of Retirement on Health in Japan (SpringerBriefs in Population Studies)
by Masaaki MizuochiThis book examines the relationship between retirement and health of older people in Japan’s super-aging society and provides a key to understanding the remarkable longevity of the population. It also furnishes new evidence in this research field where the findings have been conflicting and the detailed causal mechanism has not been clarified for many years. For that purpose, a large-scale survey was used, “The Longitudinal Survey of Middle-Aged and Elderly Persons,” which was conducted in Japan from 2005 to 2015 with 34,240 respondents aged 50–59 years in the first sample. Using this longitudinal survey, which focused on people just before retirement, and rigorous causal inference including instrumental variable and panel estimation, several research questions were tested.Specifically, existing literature does not provide sufficient findings about the heterogeneity in the effect of retirement on health. Thus, we have questions which should be addressed: does retirement affect health immediately or with delay; does the lifestyle before retirement matter for post-retirement health; and which is better for health retiring early or late? The lack of this viewpoint is believed to have led to the conflicting previous findings. If we know the answers to the questions, we would be able to understand the mechanisms between retirement and health, and prepare more properly for better retirement life.Showing the results of the testing of these questions, this book provides readers, researchers, and policymakers a comprehensive understanding of the retirement–health relationship and a suggestion for an effective labor and health policy in an aging society.
Exploring the Field of Business Model Innovation
by Oliver Gassmann Karolin Frankenberger Roman SauerPresenting a broad literature review of scholarly work in the area of Business Model Innovation, this new book analyses 50 management theories in the context of BMI to yield valuable new insights. Research on BMI is still in its infancy and has so far proved to be more than just a sub-discipline of strategy or innovation research. Exploring the field of Business Innovation demonstrates the importance of the discipline as a more specialized management research field and offers new understandings of this important subject. It presents 'grand theories' that will help researchers approach BMI through a different angle and describes business models as phenomena, enabling readers to understand their patterns and mechanisms. Reviewing the most important academic work on the subject over the last 15 years, the authors aim to open up the debate and inspire researchers to look at this phenomenon from new and different angles.
Exploring the Impact of Extended Reality (Information Systems Engineering and Management #38)
by Dac-Nhuong Le Shashi Kant Gupta Nitu Maurya Toufik MziliThis book offers a groundbreaking exploration of how Extended Reality (XR) technologies can drive environmental sustainability. By integrating virtual, augmented, and mixed realities, it provides innovative solutions to enhance understanding and inspire action on environmental issues. The text is meticulously curated to cover the multifaceted applications of XR, from revolutionizing environmental practices with deep learning to leveraging quantum computing for sustainable solutions. It highlights the synergy between XR and artificial intelligence in optimizing supply chains and enhancing data analytics. Aimed at researchers, practitioners, and policymakers, this resource underscores the critical role of XR in environmental advocacy, emphasizing its potential in effective communication and behavior change. The book also delves into immersive education, fostering a culture of environmental stewardship through experiential learning. Ultimately, it calls for interdisciplinary collaboration to address pressing environmental challenges, envisioning a future where XR technologies are pivotal in safeguarding our planet.
Exploring the Infinite: An Introduction to Proof and Analysis (Textbooks in Mathematics)
by Jennifer BrooksExploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. It guides the reader through the processes of abstraction and log- ical argumentation, to make the transition from student of mathematics to practitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things. The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof" course. Part II constitutes an introduction to the basic concepts of analysis, including limits of sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. Features Two part text for the combined transition and analysis course New approach focuses on exploration and creative thought Emphasizes the limit and sequences Introduces programming skills to explore concepts in analysis Emphasis in on developing mathematical thought Exploration problems expand more traditional exercise sets
Exploring the Integer Addition and Subtraction Landscape: Perspectives on Integer Thinking (Research in Mathematics Education)
by Laura Bofferding Nicole M. Wessman-EnzingerOver the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students’ learning. This book brings together recent work from researchers to illuminate the state of our understanding about issues related to integer addition and subtraction with a goal of highlighting how the variety of perspectives support each other or contribute to the field in unique ways. In particular, this book focuses on three main areas of integer work: students’ thinking, models and metaphors, and teachers’ thinking. Each chapter highlights a theoretically guided study centered on integer addition and subtraction. Internationally known scholars help connect the perspectives and offer additional insights through section commentaries. This book is an invaluable resource to those who are interested in mathematics education and numerical thinking.
Exploring the Mathematical Education of Teachers Using TEDS-M Data
by Maria Teresa Tatto Michael C. Rodriguez Wendy M. Smith Mark D. Reckase Kiril BankovThis book uses the publicly available TEDS-M data to answer such questions as: How does teacher education contribute to the learning outcomes of future teachers? Are there programs that are more successful than others in helping teachers learn to teach mathematics? How does the local and national policy environment contribute to teacher education outcomes? It invites readers to explore these questions across a large number of international settings. The importance of preparing future mathematics teachers has become a priority across many nations. Across the globe nations have allocated resources and expertise to this endeavour. Yet in spite of the importance accorded to teacher education not much is known about different approaches to preparing knowledgeable teachers and whether these approaches do in fact achieve their purpose. The Mathematics Teacher Education and Development Study (TEDS-M) is the first, and to date the only, cross-national study using scientific and representative samples to provide empirical data on the knowledge that future mathematics teachers of primary and secondary school acquire in their teacher education programs. The study addresses the central importance of teacher knowledge in learning to teach mathematics by examining variation in the nature and influence of teacher education programs within and across countries. The study collected data on teacher education programs structure, curriculum and opportunities to learn, on teacher educators’ characteristics and beliefs, and on future mathematics teachers’ individual characteristics, beliefs, and mathematics and pedagogical knowledge across 17 countries providing a unique opportunity to explore enduring questions in the field.
Exploring the Size of the Proton
by Philipp JörgThis book is a rare jewel, describing fundamental research in a highly dynamic field of subatomic physics. It presents an overview of cross section measurements of deeply virtual Compton scattering. Understanding the structure of the proton is one of the most important challenges that physics faces today. A typical tool for experimentally accessing the internal structure of the proton is lepton–nucleon scattering. In particular, deeply virtual Compton scattering at large photon virtuality and small four-momentum transfer to the proton provides a tool for deriving a three-dimensional tomographic image of the proton. Using clear language, this book presents the highly complex procedure used to derive the momentum-dissected transverse size of the proton from a pioneering measurement taken at CERN. It describes in detail the foundations of the measurement and the data analysis, and includes exhaustive studies of potential systematic uncertainties, which could bias the result.
Exploring the World of Mathematics
by John Hudson TinerNumbers surround us. Just try to make it through a day without using any. It's impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. For instance: What timely invention was tampered with by the Caesars and almost perfected by a pope? Why did ten days vanish in September of 1752? How did Queen Victoria shorten the Sunday sermons at chapel? What important invention caused the world to be divided into time zones? What simple math problem caused the Mars Climate Orbiter to burn up in the Martian atmosphere? What common unit of measurement was originally based on the distance from the equator to the North Pole? Does water always boil at 212? Fahrenheit? What do Da Vinci's Last Supper and the Parthenon have in common? Why is a computer glitch called a "bug"? It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.
Explosions in Underground Coal Mines: Risk Assessment And Control
by Jianwei ChengThis book addresses the hazard of gas explosions in sealed underground coal mines, and how the risk of explosion can be assessed, modeled, and mitigated. With this text, coal mine operators and managers will be able to identify the risks that lead to underground mine gas explosions, and implement practical strategies to optimize mining safety for workers. In six chapters, the book offers a framework for understanding the sealed coal mine atmosphere, the safety characteristics that are currently in place, and the guidelines to be followed by engineers to improve upon these characteristics. The first part of the book describes the importance and characteristics of underground gas mine explosions in a historical context with data showing the high number of fatalities from explosion incidents, and how risk has been mitigated in the past. Chapters also detail mathematical models and explosibility diagrams for determining and understanding the risk factors involved in mine explosions. Readers will also learn about safety operations, and assessments for the sealed mine atmosphere. With descriptions of chapter case studies, mining engineers and researchers will learn how to apply safety measures in underground coal mines to improve mining atmospheres and save lives.
Exponential Distribution: Theory, Methods and Applications
by K. BalakrishnanThe exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Exponentiated Distributions
by Essam K. AL-Hussaini Mohammad AhsanullahThis book contains entirely new results, not to be found elsewhere. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions such as Weibull distributions, exponentiated Burr type XII distributions and exponentiated exponential distributions and their properties are demonstrated. Analysis of real as well as well-simulated data are analyzed. A number of inferences based on a finite mixture of distributions are also presented.
Export Diversification and Economic Growth
by Juan Felipe MejíaThe main research problem addressed in the book is the one regarding the role that export diversification could play for enhancing economic growth in Colombia, both in terms of new products and new geographic markets. The underlying motivation for centering the analysis on the European Union's market are manifold, reaching from the evident concentration of exports - both in terms of composition and markets- that Colombia still shows, to the small amount of empirical studies analyzing the current status and potentialities of the commercial relations between Colombia and the European Union.