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    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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  • Sparse Polynomial Approximation of High-Dimensional Functions
    Sparse Polynomial Approximation of High-Dimensional Functions

    Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions.These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data.This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods.These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations.It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing.It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code.The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

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

    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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  • What is the difference between a polynomial and a polynomial function?

    A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or roots. A polynomial function, on the other hand, is a specific type of function that can be defined by a polynomial expression. In other words, a polynomial function is a function that can be expressed as a polynomial. So, while a polynomial is simply an algebraic expression, a polynomial function is a specific type of mathematical function.

  • What are polynomial functions?

    Polynomial functions are mathematical functions that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. These functions can have multiple terms, each with a different power of the variable. Polynomial functions are continuous and smooth, and they can be used to model a wide range of real-world phenomena. They are commonly used in algebra, calculus, and other branches of mathematics to analyze and solve various problems.

  • What is double polynomial division?

    Double polynomial division is a method used to divide one polynomial by another polynomial. It involves dividing the leading term of the dividend by the leading term of the divisor to determine the first term of the quotient. This process is repeated for each subsequent term until the entire dividend is divided by the divisor. The result is a quotient and a remainder, if any.

  • What is a polynomial space?

    A polynomial space is a vector space whose elements are polynomials. In other words, it is a set of all polynomials of a certain degree, along with the operations of addition and scalar multiplication. The dimension of a polynomial space is determined by the highest degree of the polynomials in the space. Polynomial spaces are commonly used in mathematics and engineering to represent and manipulate functions and data.

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    Education, Teaching, and Learning : Discourses, Cultures, Conversations


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    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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  • Teaching in Post-14 Education & Training
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    Teaching in Post-14 Education & Training provides a skilfully balanced mix of essential theory and practical guidance to support you if you are studying an ‘education and training’ qualification.It covers fundamental background information such as key philosophies and concepts, current policy and practice, key thinkers and ideas, and includes a useful chronology. More importantly it also provides the tools to help you approach the classroom with confidence, covering fundamental issues such as teaching and learning, assessment, resources, and course design. Through its pedagogical features the book also offers you opportunities to pause and reflect, as well as practical exercises, templates and examples of student work. Key features of this new edition include:• Links to the latest Professional Standards for Teachers and Trainers• Updating of the legislative and policy context• Supporting learning with technology• Planning for equality and diversity• Embedding language and literacyThis is the definitive textbook on teaching, learning and assessment for those training to work in the post-14 sector. "The latest edition of this popular book helps educators to reclaim their professional identity through stretching and thought-provoking commentary and critical questioning ...This is a valuable resource for students and teachers alike.It provides a useful framework for assignment and classroom work, balancing theory and practical teaching strategies."In Tuition, Issue 24/Summer 2016

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  • Is 2x a polynomial function?

    Yes, 2x is a polynomial function. A polynomial function is a function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. In the case of 2x, it can be written as 2x^1, which fits the definition of a polynomial function.

  • "Is my polynomial function correct?"

    To determine if your polynomial function is correct, you should first check if it satisfies the given conditions or constraints. Then, you can verify if the function produces the expected output for a range of input values. Additionally, you can compare your function with other known correct polynomial functions to see if they match. If your function meets all these criteria, it is likely correct. However, it's always a good idea to double-check your work and seek feedback from others to ensure accuracy.

  • What is the polynomial form?

    The polynomial form is a mathematical expression consisting of variables, coefficients, and exponents. It is a sum of terms, where each term is a variable raised to a non-negative integer power, multiplied by a coefficient. The polynomial form is used to represent various mathematical functions and equations, and it can be manipulated through operations such as addition, subtraction, multiplication, and division. The degree of a polynomial is determined by the highest exponent of the variables present in the expression.

  • What is a constant polynomial?

    A constant polynomial is a polynomial function that has a degree of zero, meaning it does not contain any variables. It is simply a constant value, such as 5 or -3. Constant polynomials are represented in the form f(x) = c, where c is a constant value. These polynomials do not change in value as x varies, hence the term "constant."

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