This book is about how teachers can use classroom mathematics tasks to support student learning, and presents data on the ways in which teachers used those tasks in a particular research project. It is the product of research findings focusing on teacher practice, teacher learning and knowledge, and student learning. It demonstrates how teachers can use mathematics tasks to promote effective student learning.

This book explores how professionals can engage and inspire parents to support their young children's mathematics learning. Bringing together international experts, researchers and scholars, it proposes a framework for engaging with and supporting parents, including those who are less aware of the crucial development of children's mathematical skills in the early years. Focusing on mathematics learning from birth to 5 years, the book's underlying assumption is that it is possible to offer guidance to professionals working with families with young children concerning how to engage and support families in the area of mathematics learning, including those families who seem alienated from education services. Specifically, the respective chapters present a framework for understanding children's early mathematical development and the important role of families in this regard. They describe effective strategies for engaging families in their children's mathematics learning, including those who are marginalised and experience multiple disadvantages, so that all families can best support their children's mathematical learning and their development of positive attitudes towards learning. In closing, hurdles and opportunities within the systems surrounding family engagement are addressed.

Teacher education seeks to transform prospective and/or practicing teachers from neophyte possibly uncritical perspectives on teaching and learning to more knowledgeable, adaptable, analytic, insightful, observant, resourceful, reflective and confident professionals ready to address whatever challenges teaching secondary mathematics presents.

This transformation occurs optimally through constructive engagement in tasks that foster knowledge for teaching secondary mathematics. Ideally such tasks provide a bridge between theory and practice, and challenge, surprise, disturb, confront, extend, or provoke examination of alternatives, drawn from the context of teaching. We define tasks as the problems or activities that, having been developed, evaluated and refined over time, are posed to teacher education participants. Such participants are expected to engage in these tasks collaboratively, energetically, and intellectually with an open mind and an orientation to future practice. The tasks might be similar to those used by classroom teachers (e.g., the analysis of a graphing problem) or idiosyncratic to teacher education (e.g., critique of videotaped practice).

This edited volume includes chapters based around unifying themes of tasks used in secondary mathematics teacher education. These themes reflect goals for mathematics teacher education, and are closely related to various aspects of knowledge required for teaching secondary mathematics. They are not based on the conventional content topics of teacher education (e.g., decimals, grouping practices), but on broad goals such as adaptability, identifying similarities, productive disposition, overcoming barriers, micro simulations, choosing tools, and study of practice. This approach is innovative and appeals both to prominent authors and to our target audiences.

This volume of newly written chapters on the history and interpretation of Wittgenstein's Tractatus represents a significant step beyond the polemical debate between broad interpretive approaches that has recently characterized the field. Some of the contributors might count their approach as 'new' or 'resolute', while others are more 'traditional', but all are here concerned primarily with understanding in detail the structure of argument that Wittgenstein presents within the Tractatus, rather than with its final self-renunciation, or with the character of the understanding that renunciation might leave behind. The volume makes a strong case that close investigation, both biographical and textual, into the composition of the Tractatus, and into the various influences on it, still has much to yield in revealing the complexity and fertility of Wittgenstein's early thought. Amongst these influences Kant and Kierkegaard are considered alongside Wittgenstein's immediate predecessors in the analytic tradition. The themes explored range across the breadth of Wittgenstein's book, and include his accounts of ethics and aesthetics, as well as issues in metaphysics and the philosophy of mind, and aspects of the logical framework of his account of representation. The contrast of saying and showing, and Wittgenstein's attitude to the inexpressible, is of central importance to many of the contributions. By approaching this concern through the various first-level issues that give rise to it, rather than from entrenched schematic positions, the contributors demonstrate the possibility of a more inclusive, constructive and fruitful mode of engagement with Wittgenstein's text and with each other.

For more than 30 years, the highly regarded Secrets Series (R) has provided students and practitioners in all areas of health care with concise, focused, and engaging resources for quick reference and exam review. Physical Diagnosis Secrets, 3rd Edition, offers practical, up-to-date coverage of the full range of essential topics in physical diagnosis and health assessment. This highly regarded resource features the Secrets' popular question-and-answer format that also includes lists, tables, pearls, memory aids, and an easy-to-read style - making inquiry, reference, and review quick, easy, and enjoyable. The proven Secrets Series (R) format gives you the most return for your time - succinct, easy to read, engaging, and highly effective. Fully revised and updated throughout, with highly illustrated coverage of the history and physical exam, followed by assessment techniques that are weighted based on their clinical importance. Online assessment includes audio clips of the heart and lung. Top 100 Secrets and Key Points boxes provide a fast overview of the secrets you must know for success in practice and on exams. Bulleted lists, mnemonics, practical tips from leaders in the field - all providing a concise overview of important board-relevant content. Multiple-choice questions online provide opportunities for further self-assessment. Portable size makes it easy to carry with you for quick reference or review anywhere, anytime. Enhanced eBook version included with purchase. Your enhanced eBook allows you to access all of the text, figures, and references from the book on a variety of devices.

This book explores how professionals can engage and inspire parents to support their young children's mathematics learning. Bringing together international experts, researchers and scholars, it proposes a framework for engaging with and supporting parents, including those who are less aware of the crucial development of children's mathematical skills in the early years. Focusing on mathematics learning from birth to 5 years, the book's underlying assumption is that it is possible to offer guidance to professionals working with families with young children concerning how to engage and support families in the area of mathematics learning, including those families who seem alienated from education services. Specifically, the respective chapters present a framework for understanding children's early mathematical development and the important role of families in this regard. They describe effective strategies for engaging families in their children's mathematics learning, including those who are marginalised and experience multiple disadvantages, so that all families can best support their children's mathematical learning and their development of positive attitudes towards learning. In closing, hurdles and opportunities within the systems surrounding family engagement are addressed.

This book is about how teachers can use classroom mathematics tasks to support student learning, and presents data on the ways in which teachers used those tasks in a particular research project. It is the product of research findings focusing on teacher practice, teacher learning and knowledge, and student learning. It demonstrates how teachers can use mathematics tasks to promote effective student learning.

Teacher education seeks to transform prospective and/or practicing teachers from neophyte possibly uncritical perspectives on teaching and learning to more knowledgeable, adaptable, analytic, insightful, observant, resourceful, reflective and confident professionals ready to address whatever challenges teaching secondary mathematics presents.

This transformation occurs optimally through constructive engagement in tasks that foster knowledge for teaching secondary mathematics. Ideally such tasks provide a bridge between theory and practice, and challenge, surprise, disturb, confront, extend, or provoke examination of alternatives, drawn from the context of teaching. We define tasks as the problems or activities that, having been developed, evaluated and refined over time, are posed to teacher education participants. Such participants are expected to engage in these tasks collaboratively, energetically, and intellectually with an open mind and an orientation to future practice. The tasks might be similar to those used by classroom teachers (e.g., the analysis of a graphing problem) or idiosyncratic to teacher education (e.g., critique of videotaped practice).

This edited volume includes chapters based around unifying themes of tasks used in secondary mathematics teacher education. These themes reflect goals for mathematics teacher education, and are closely related to various aspects of knowledge required for teaching secondary mathematics. They are not based on the conventional content topics of teacher education (e.g., decimals, grouping practices), but on broad goals such as adaptability, identifying similarities, productive disposition, overcoming barriers, micro simulations, choosing tools, and study of practice. This approach is innovative and appeals both to prominent authors and to our target audiences.

"A remarkable book capable of reshaping what one takes philosophy to be." -Cora Diamond, Kenan Professor of Philosophy Emerita, University of Virginia Could there be a logical alien-a being whose ways of talking, inferring, and contradicting exhibit an entirely different logical shape than ours, yet who nonetheless is thinking? Could someone, contrary to the most basic rules of logic, think that two contradictory statements are both true at the same time? Such questions may seem outlandish, but they serve to highlight a fundamental philosophical question: is our logical form of thought merely one among many, or must it be the form of thought as such? From Descartes and Kant to Frege and Wittgenstein, philosophers have wrestled with variants of this question, and with a range of competing answers. A seminal 1991 paper, James Conant's "The Search for Logically Alien Thought," placed that question at the forefront of contemporary philosophical inquiry. The Logical Alien, edited by Sofia Miguens, gathers Conant's original article with reflections on it by eight distinguished philosophers-Jocelyn Benoist, Matthew Boyle, Martin Gustafsson, Arata Hamawaki, Adrian Moore, Barry Stroud, Peter Sullivan, and Charles Travis. Conant follows with a wide-ranging response that places the philosophical discussion in historical context, critiques his original paper, addresses the exegetical and systematic issues raised by others, and presents an alternative account. The Logical Alien challenges contemporary conceptions of how logical and philosophical form must each relate to their content. This monumental volume offers the possibility of a new direction in philosophy.

School leaders have ready access to assessment data, motivating efforts to improve the numeracy outcomes of their students, but it can be difficult for principals to decide how to achieve these goals within their school's existing strategic plans and policies. Emeritus Professor Peter Sullivan brings his decades of experience and research in mathematics teaching and education to a carefully curated selection of proven practices and effective approaches that will help school leaders empower teachers and achieve improved numeracy outcomes for their students. With links to the OECD's Future of Education and Skills 2030 framework and the Victorian Education Department's high impact teaching strategies, the book gives school leaders insights into professional learning opportunities and high-impact practices that can align improvement visions and goals with effective classroom approaches. Quality learning experiences, lesson structure, learning sequences, classroom culture, collaborative planning and effective teaching are addressed in ways that will help school leaders improve not only students' numeracy and mathematics outcomes, but also their critical and creative thinking skills, enabling classroom learning to be transferred to real-life contexts. Leading Improvements in Mathematics Teaching and Learning provides a framework for a set of high-impact strategies that individually and together can be the focus of teacher professional learning, school improvement and student numeracy achievement. High Impact Strategies for School Leaders is a suite of resources to help busy principals decide on the strategies that will move their school towards its long- and short-term goals of improving outcomes for all learners, and to understand the details of implementation, resourcing, monitoring and evaluation.

Kant's introduction of a distinctive form of philosophical investigation and proof, known as transcendental, inaugurated a new philosophical tradition. Transcendental Philosophy and Naturalism assesses the present state and contemporary relevance of this tradition. The contributors aim to understand the theoretical structures involved in transcendental explanation, and to assess the contemporary relevance of the transcendental orientation, in particular with respect to contemporary philosophical naturalism. These issues are approached from both naturalistic and transcendental perspectives.

Challenging Mathematical Tasks supports the idea that students learn best when they work on problems that they do not yet know how to solve. Peter Sullivan's research shows that many students do not fear challenges in mathematics, but welcome them. And rather than having teachers instruct them, these students prefer to work out solutions for themselves.

Open-Ended Maths Activities discusses the features of 'good' mathematical questions. It provides practical advice on how teachers can create their own open-ended and problem-solving questions and use them effectively in the classroom.