Learning To Reason

Learn how to develop your reasoning skills and how to writewell-reasoned proofs Learning to Reason shows you how to use the basic elements ofmathematical language to develop highly sophisticated, logicalreasoning skills. You'll get clear, concise, easy-to-followinstructions on the process of writing proofs, including thenecessary reasoning techniques and syntax for constructingwell-written arguments. Through in-depth coverage of logic, sets,and relations, Learning to Reason offers a meaningful, integratedview of modern mathematics, cuts through confusing terms and ideas,and provides a much-needed bridge to advanced work in mathematicsas well as computer science. Original, inspiring, and designed formaximum comprehension, this remarkable book: * Clearly explains how to write compound sentences in equivalentforms and use them in valid arguments * Presents simple techniques on how to structure your thinking andwriting to form well-reasoned proofs * Reinforces these techniques through a survey of sets--thebuilding blocks of mathematics * Examines the fundamental types of relations, which is "where theaction is" in mathematics * Provides relevant examples and class-tested exercises designed tomaximize the learning experience * Includes a mind-building game/exercise space atwww.wiley.com/products/subject/mathematics/

Unique in that it collects, presents, and synthesizes cutting edge research on different aspects of statistical reasoning and applies this research to the teaching of statistics to students at all educational levels, this volume will prove of great value to mathematics and statistics education researchers, statistics educators, statisticians, cognitive psychologists, mathematics teachers, mathematics and statistics curriculum developers, and quantitative literacy experts in education and government.

How can teachers help children to develop reasoning skills? What is reasoning and how do we teach it? Much is being said in schools and education about the importance of reasoning skills. This book explores what reasoning is and what it is not. It includes examples of how reasoning in primary mathematics and science classes can develop. It shows how a connection between the ′skills′ of mathematics and science can help children to gain a better understanding of reasoning. What is a conjecture? What makes you think? What makes you think about your thinking? What does reasoning look like? With links to classroom practice and examples of effective teaching throughout, this book not only provides an exploration of what reasoning is and why it′s important—it also show you how to develop children′s reasoning skills in your classroom.

Learning in the Age of Digital Reason contains 16 in-depth dialogues between Petar Jandrić and leading scholars and practitioners in diverse fields of history, philosophy, media theory, education, practice, activism, and arts. The book creates a postdisciplinary snapshot of our reality, and the ways we experience that reality, at the moment here and now. It historicises our current views to human learning, and experiments with collective knowledge making and the relationships between theory and practice. It stands firmly at the side of the weak and the oppressed, and aims at critical emancipation. Learning in the Age of Digital Reason is playful and serious. It addresses important issues of our times and avoids the omnipresent (academic) sin of pretentiousness, thus making an important statement: research and education can be sexy. Interlocutors presented in the book (in order of appearance): Larry Cuban, Andrew Feenberg, Michael Adrian Peters, Fred Turner, Richard Barbrook, McKenzie Wark, Henry Giroux, Peter McLaren, Siân Bayne, Howard Rheingold, Astra Taylor, Marcell Mars, Tomislav Medak, Ana Kuzmanić, Paul Levinson, Kathy Rae Huffman, Ana Peraica, Dmitry Vilensky (Chto Delat?), Christine Sinclair, and Hamish Mcleod.

Mathematics teaching and professional development of mathematics teachers are areas where research has increased substantially in recent years. In this dynamic field, mathematics teaching practices, pedagogical knowledge of mathematics teachers and professional development via collaboration between mathematics teachers have emerged as vital domains of inquiry. Professional Development and Knowledge of Mathematics Teachers addresses the underlying characteristics of mathematics teacher education, and those professional development contexts that have a positive impact on teachers’ professional learning. Recognizing the impact of broader institutional settings on mathematics teaching and teacher professional development, the editors suggest bridging the gaps between theoretical practices and methodological approaches in the field by focusing on and conceptualizing the following relational factors: The study of mathematics teaching and classroom situations Researching teacher and teacher educator knowledge, since these issues inform the quality of mathematics teaching directly Mathematics teacher education and professional development, focusing on design principles and the impact they have on teacher professional learning Combining central issues of mathematics teaching, knowledge and professional development, the chapters in this volume address each of the above factors and provide profound considerations on both theoretical and practical levels. This book will be an essential resource for researchers, teachers and students working in the fields of mathematics teaching and mathematics teacher professional development.

This title includes the following features: A new volume in the renowned Oxford Cognitive Science Series; Presents important new findings on human reasoning and reasoning skills; Explores the relationship between cognitive and social aspects of communication and reasoning; Trulyinterdisciplinary - accessible to both psychologists and philosophers

An argument that qualitative representations—symbolic representations that carve continuous phenomena into meaningful units—are central to human cognition. In this book, Kenneth Forbus proposes that qualitative representations hold the key to one of the deepest mysteries of cognitive science: how we reason and learn about the continuous phenomena surrounding us. Forbus argues that qualitative representations—symbolic representations that carve continuous phenomena into meaningful units—are central to human cognition. Qualitative representations provide a basis for commonsense reasoning, because they enable practical reasoning with very little data; this makes qualitative representations a useful component of natural language semantics. Qualitative representations also provide a foundation for expert reasoning in science and engineering by making explicit the broad categories of things that might happen and enabling causal models that help guide the application of more quantitative knowledge as needed. Qualitative representations are important for creating more human-like artificial intelligence systems with capabilities for spatial reasoning, vision, question answering, and understanding natural language. Forbus discusses, among other topics, basic ideas of knowledge representation and reasoning; qualitative process theory; qualitative simulation and reasoning about change; compositional modeling; qualitative spatial reasoning; and learning and conceptual change. His argument is notable both for presenting an approach to qualitative reasoning in which analogical reasoning and learning play crucial roles and for marshaling a wide variety of evidence, including the performance of AI systems. Cognitive scientists will find Forbus's account of qualitative representations illuminating; AI scientists will value Forbus's new approach to qualitative representations and the overview he offers.

Improve the quality of organizational learning in your school and address how current demands for rapid change and accountability contribute to levels of fear and stress. The author draws on educational, psychological, and neuroscientific research to show how leaders can change the prevailing emotional climate or tone of a school to promote deeper learning at all levels.