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  • Teaching, Tutoring and Training in the Lifelong Learning Sector
    Teaching, Tutoring and Training in the Lifelong Learning Sector

    This core text provides comprehensive support for pre-service and in-service trainee teachers in the Lifelong Learning Sector covering all they need to know to achieve QTLS status. Supporting trainees through all stages of their professional development, the text takes the reader through the theoretical background underpinning teaching and learning and offers practical guidance on day-to-day challenges. This fourth edition has been fully revised and updated and includes a new chapter on teaching practice with notes on observation and lesson planning.New information on behaviour management has been added to support trainees in an aspect of teaching that many find challenging.

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  • Computer Science Education : Perspectives on Teaching and Learning in School
    Computer Science Education : Perspectives on Teaching and Learning in School

    Drawing together the most up-to-date research from experts all across the world, the second edition of Computer Science Education offers the most up-to-date coverage available on this developing subject, ideal for building confidence of new pre-service and in-service educators teaching a new discipline.It provides an international overview of key concepts, pedagogical approaches and assessment practices. Highlights of the second edition include:- New sections on machine learning and data-driven (epistemic) programming- A new focus on equity and inclusion in computer science education- Chapters updated throughout, including a revised chapter on relating ethical and societal aspects to knowledge-rich aspects of computer science education- A new set of chapters on the learning of programming, including design, pedagogy and misconceptions- A chapter on the way we use language in the computer science classroom. The book is structured to support the reader with chapter outlines, synopses and key points.Explanations of key concepts, real-life examples and reflective points keep the theory grounded in classroom practice. The book is accompanied by a companion website, including online summaries for each chapter, 3-minute video summaries by each author and an archived chapter on taxonomies and competencies from the first edition.

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  • Mathematical Properties of Population-Genetic Statistics : Quadratic Forms Most Beautiful
    Mathematical Properties of Population-Genetic Statistics : Quadratic Forms Most Beautiful

    A powerful new approach to interpreting population-genetic data in evolution and ecologyPopulation genetics uses statistical analysis to catalog genetic variation among populations and species.Summary statistics computed from allele frequencies—mathematical functions that measure features of genetic similarity and diversity—are key to this global effort.Yet despite their widespread use in evolutionary biology, ecology, and conservation biology, their mathematical properties have largely been overlooked.This book shows how to use the mathematical bounds on summary statistics to make better interpretations of population-genetic data. Noah Rosenberg discusses how the behavior of these statistics depends not only on the biology of the populations they seek to describe but also on the mathematical properties of the functions used to compute them, properties that produce constraints on the values of the statistics and influence their interpretation.Focusing on the concept of homozygosity—a quadratic function of allele frequencies in a population—he demonstrates how to account for mathematical constraints when measuring genetic similarity and diversity.Rosenberg illustrates the results using examples from empirical data and shares strategies that readers can use to apply this mathematical perspective to different kinds of summary statistics, including those for measuring biodiversity in ecological communities. Drawing inspiration from Charles Darwin, who marveled at evolution’s “endless forms most beautiful and most wonderful,” this book presents a groundbreaking approach to the study of genetic variation.It is sure to stimulate new research in population biology and deeper thinking about the meaning and interpretation of essential measurements of the world’s genomes.

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  • Quadratic Number Theory : An Invitation to Algebraic Methods in the Higher Arithmetic
    Quadratic Number Theory : An Invitation to Algebraic Methods in the Higher Arithmetic

    This text is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra.With its exceptionally clear prose, hundreds of exercises, and historical motivation, it would make an excellent textbook for a second undergraduate course in number theory or a terrific choice for independent reading.

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  • Are quadratic functions the same as quadratic equations?

    Quadratic functions and quadratic equations are related, but they are not the same. A quadratic function is a mathematical expression that can be graphed as a parabola, while a quadratic equation is a specific type of equation that can be solved to find the values of the variable that satisfy the equation. In other words, a quadratic function represents a relationship between inputs and outputs, while a quadratic equation represents an equality involving a variable raised to the second power.

  • Why is the quadratic formula called the quadratic formula?

    The quadratic formula is called the quadratic formula because it is used to solve quadratic equations, which are equations of the form ax^2 + bx + c = 0. The formula provides a method for finding the roots, or solutions, of these equations. It is derived from the process of completing the square and is a fundamental tool in algebra for solving quadratic equations. The term "quadratic" comes from the Latin word "quadratus," meaning "square," which reflects the presence of the squared term in the quadratic equation.

  • Why is the quadratic formula actually called the quadratic formula?

    The quadratic formula is called the quadratic formula because it is specifically used to solve quadratic equations. A quadratic equation is a second-degree polynomial equation, and the quadratic formula provides a way to find the roots or solutions of such equations. The formula is derived from the process of completing the square, and it is a fundamental tool in algebra for solving quadratic equations of the form ax^2 + bx + c = 0. Therefore, it is named the quadratic formula to reflect its direct application to quadratic equations.

  • What is the difference between quadratic equations and quadratic functions?

    Quadratic equations are mathematical expressions that are set equal to zero and can be solved to find the values of the variable that satisfy the equation. Quadratic functions, on the other hand, are mathematical functions that can take any input value and produce an output value based on the quadratic equation. In other words, a quadratic equation is a specific instance of a quadratic function, where the function is defined by the equation. Additionally, quadratic functions can be graphed as parabolas, while quadratic equations are typically solved for specific values of the variable.

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    This textbook gives you guidance and insights into the knowledge, values and commitments necessary to succeed in the primary classroom, supported by links to theory and research literature and realistic scenarios you may encounter as a new teacher. Fully updated throughout, key features of this second edition include:· A new chapter on inclusive education· Newly expanded coverage of digital learning, engaging with educational research and the role of the primary teacher· New ‘View from Practice’ examples· Cross-referenced links to the Teachers’ Standards in England and the GTCS Professional Standards in Scotland and where they are covered within the bookThis is essential reading for professional studies modules on primary initial teacher education courses, including university-based (PGCE, PGDE, BA QTS, BEd), school-based (SCITT, School Direct) and employment-based routes into teaching.

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    This book is essential reading for teaching staff and librarians to assist them in briefing the project design teams.It should also be a reference book for architects and interior designers.Student's need for social learning, collaborative and interactive facilities have had the greatest impact on the design of new teaching and learning spaces.The author, Brian Griffin, Architect researched this subject over many years and has included a large number of international Case Studies of successful designs.He is also the author of 'Laboratory Design Guide' 3rd Ed 2012 Routledge.

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  • Reflective Teaching and Learning in Further Education
    Reflective Teaching and Learning in Further Education

    This book looks at critical reflection as a key skill for all teachers in further education (FE) and an important part of the new Professional Standards.In particular the text explores the key themes of self-awareness, planning, managing behaviour and CPD in relation to reflective practice to demonstrate how it can support those areas of teaching that most often cause concern.The limitations and benefits of reflection are analysed and action research is identified as an important facet in developing professional reflective practice which can in turn enhance both the personal and professional life of FE teachers. Â

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  • What is the quadratic formula and how does quadratic completion work?

    The quadratic formula is a formula used to find the solutions to a quadratic equation of the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b^2 - 4ac)) / 2a. Quadratic completion is a method used to rewrite a quadratic expression in the form of (x + p)^2 + q, where p and q are constants. This method involves adding and subtracting a term inside the parentheses to create a perfect square trinomial, which can then be factored easily.

  • What are quadratic relationships?

    Quadratic relationships are mathematical relationships that involve a variable raised to the second power. In other words, they are relationships that can be represented by a quadratic equation of the form y = ax^2 + bx + c, where x is the independent variable, y is the dependent variable, and a, b, and c are constants. Quadratic relationships often form a U-shaped curve when graphed, known as a parabola. These relationships are commonly seen in physics, engineering, economics, and many other fields to model various real-world phenomena.

  • What is quadratic growth?

    Quadratic growth is a type of growth pattern where a quantity increases at an accelerating rate. In quadratic growth, the rate of increase is proportional to the square of the quantity itself. This results in a curve that starts off slowly, then increases rapidly, creating a parabolic shape. Quadratic growth is commonly seen in natural phenomena and mathematical models where the growth rate is influenced by the current quantity.

  • What are quadratic functions?

    Quadratic functions are a type of polynomial function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. These functions graph as a parabola, which is a U-shaped curve. The highest or lowest point of the parabola, called the vertex, depends on the value of the coefficient a. Quadratic functions are commonly used to model real-world situations where the relationship between two variables is nonlinear.

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