Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. Whether in the classroom, university or workplace, there is a growing requirement to use and interpret a large variety of external representational forms and tools for knowledge acquisition, problem solving, and to communicate with others. Use of Representations in Reasoning and Problem Solving brings together contributions from some of the world’s leading researchers in educational and instructional psychology, instructional design, and mathematics and science education to document the role which external representations play in our understanding, learning and communication. Traditional research has focused on the distinction between verbal and non-verbal representations, and the way they are processed, encoded and stored by different cognitive systems. The contributions here challenge these research findings and address the ambiguity about how these two cognitive systems interact, arguing that the classical distinction between textual and pictorial representations has become less prominent. The contributions in this book explore: how we can theorise the relationship between processing internal and external representations what perceptual and cognitive restraints can affect the use of external representations how individual differences affect the use of external representations how we can combine external representations to maximise their impact how we can adapt representational tools for individual differences. Using empirical research findings to take a fresh look at the processes which take place when learning via external representations, this book is essential reading for all those undertaking postgraduate study and research in the fields of educational and instructional psychology, instructional design and mathematics and science education.

Within an increasingly multimedia focused society, the use of external representations in learning, teaching and communication has increased dramatically. This book explores: how we can theorise the relationship between processing internal and external representations.

The Cambridge Handbook of Thinking and Reasoning is the first comprehensive and authoritative handbook covering all the core topics of the field of thinking and reasoning. Written by the foremost experts from cognitive psychology, cognitive science, and cognitive neuroscience, individual chapters summarize basic concepts and findings for a major topic, sketch its history, and give a sense of the directions in which research is currently heading. The volume also includes work related to developmental, social and clinical psychology, philosophy, economics, artificial intelligence, linguistics, education, law, and medicine. Scholars and students in all these fields and others will find this to be a valuable collection.

The rise in computing and multimedia technology has spawned an increasing interest in the role of diagrams and sketches, not only for the purpose of conveying information but also for creative thinking and problem-solving. This book attempts to characterise the nature of "a science of diagrams" in a wide-ranging, multidisciplinary study that contains accounts of the most recent research results in computer science and psychology. Key topics include: cognitive aspects, formal aspects, and applications. It is a well-written and indispensable survey for researchers and students in the fields of cognitive science, artificial intelligence, human-computer interaction, and graphics and visualisation.

The 6th International Conference on the Theory and Application of Diagrams – Diagrams 2010 – was held in Portland, USA in August 2010. Diagrams is an international and interdisciplinary conference series, which continues to present the very best work in all aspects of research on the theory and application of diagrams. Some key questions that researchers are tackling concern gaining an insight into how diagrams are used, how they are rep- sented, which types are available and when it is appropriate to use them. The use of diagrammatic notations is studied for a variety of purposes including communication, cognition, creative thought, computation and problem-solving. Clearly, this must be pursued as an interdisciplinary endeavor, and Diagrams is the only conference series that provides such a united forum for all areas that are concerned with the study of diagrams: for example, architecture, arti?cial intelligence,cartography,cognitivescience,computer science,education,graphic design, history of science, human–computer interaction, linguistics, logic, ma- ematics, philosophy, psychology, and software modelling. The articles in this volume re?ect this variety and interdisciplinarity of the ?eld.

Empower students to build new mathematical knowledge, solve problems in context, apply and adapt appropriate strategies, and reflect on the problem solving process with these reproducible worksheets. The content in this book supports and is divided by the NCTM content standards: number and operations, algebra, geometry, measurement, and data analysis and probability. Timesaving teaching aids such as skill checks and cumulative tests are included along with an NCTM correlation chart, pretests, answer key, and vocabulary cards

ABC of Clinical Reasoning Being a good clinician is not only about knowledge — how doctors and other healthcare professionals think, reason, and make decisions is arguably their most critical skill. The second edition of the ABC of Clinical Reasoning breaks down clinical reasoning into its core components and explores each of these in more detail, including the applications for clinical practice, teaching, and learning. Informed by the latest evidence from cognitive psychology, education, and studies of expertise, this edition has been extensively re-written and updated, and covers: Key components of clinical reasoning: evidence-based history and examination, choosing and interpreting diagnostic tests, problem identification and management, and shared decision-making Key concepts in clinical reasoning, such dual process theories, and script theory Situativity and human factors Metacognition and cognitive strategies Teaching clinical reasoning From a team of expert authors, the ABC of Clinical Reasoning is essential reading for all students, clinical teachers, curriculum planners and clinicians involved in diagnosis. About the ABC series The ABC series has been designed to help you access information quickly and deliver the best patient care, and remains an essential reference tool for GPs, junior doctors, medical students and healthcare professionals. Now offering over 80 titles, this extensive series provides you with a quick and dependable reference on a range of topics in all the major specialties. The ABC series is the essential and dependable source of up-to-date information for all practitioners and students in primary healthcare. To receive automatic updates on books and journals in your specialty, join our email list. Sign up today at www.wiley.com/email

Your Guide to Engaging and Effective Math Instruction With the latest research on what works best in teaching and learning, The Mathematics Playbook is your comprehensive guide to enhancing mathematics teaching and learning. With a focus on fostering equity and maximizing student learning, the authors provide practical modules that integrate the latest research on effective teaching practices, and answer four critical questions: How do we foster, nurture, and sustain mathematics learning? How do we ensure all learners have equity of access and opportunity? What are the non-negotiables in a high-quality mathematics task? How do we know if learners really "get it"? Through real-life examples and an emphasis on self-assessment and reflection, this playbook empowers you to create engaging and impactful learning experiences in mathematics.

Pioneering work shows how using Diagrams facilitates the design of better AI systems The publication of Diagrammatic Reasoning in AI marks an important milestone for anyone seeking to design graphical user interfaces to support decision-making and problem-solving tasks. The author expertly demonstrates how diagrammatic representations can simplify our interaction with increasingly complex information technologies and computer-based information systems. In particular, the book emphasizes how diagrammatic user interfaces can help us better understand and visualize artificial intelligence (AI) systems. It examines how diagrammatic reasoning enhances various AI programming strategies used to emulate human thinking and problem-solving, including: Expert systems Model-based reasoning Inexact reasoning such as certainty factors and Bayesian networks Logic reasoning A key part of the book is its extensive development of applications and graphical illustrations, drawing on such fields as the physical sciences, macroeconomics, finance, business logistics management, and medicine. Despite such tremendous diversity of usage, in terms of applications and diagramming notations, the book classifies and organizes diagrams around six major themes: system topology; sequence and flow; hierarchy and classification; association; cause and effect; and logic reasoning. Readers will benefit from the author's discussion of how diagrams can be more than just a static picture or representation and how diagrams can be a central part of an intelligent user interface, meant to be manipulated and modified, and in some cases, utilized to infer solutions to difficult problems. This book is ideal for many different types of readers: practitioners and researchers in AI and human-computer interaction; business and computing professionals; graphic designers and designers of graphical user interfaces; and just about anyone interested in understanding the power of diagrams. By discovering the many different types of diagrams and their applications in AI, all readers will gain a deeper appreciation of diagrammatic reasoning.

Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website.