This book is the only one of its kind that instructs teachers to identify typical error patterns, to receive feedback on their diagnosis, and to gain insight regarding why a child may have adopted an incorrect procedure. Revised to link content to the new NCTM Standards, this new edition emphasizes the meaning of operations and using the appropriate method of computation. As in previous editions, it retains its focus on placing paper-and pencil instructional activities within the context of problem solving. Chapter topics cover diagnosing misconceptions and error patterns in computation, providing needed instruction in computation, and helping students who have learned error patterns. For mathematics teachers of special education classes or at the middle school level.
As your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket.
As your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket.
Exploring Cognition: Damaged Brains and Neural Networks analyses the contribution made by cognitive neuropsychology and connectionist modelling to theoretical explanations of cognitive processes. Bringing together evidence from both damaged brains and neural networks, this exciting and innovative approach leads to re-evaluation of traditional theories: connectionist models lesioned to mimic the residual function of the damaged brain and rehabilitated to simulate the process of recovery suggest underlying mechanisms and challenge previous interpretations. In this reader key articles by leading international researchers are combined with linking commentaries that provide a context, highlight the conceptual themes and evaluate the evidence. Carefully selected to include hotly debated topics, the papers cover, among others, the controversies surrounding explanations for category specificity in object recognition and for covert recognition of faces and words; the mechanisms underlying the use of regular and irregular past tenses; and the reading of regularly and irregularly spelled words. The challenges posed by connectionist models to assumptions about the nature of dissociations, the need for symbolic rule-based operations in language processing and the modularity and localisation of processes are assessed. Exploring Cognition: Damaged Brains and Neural Networks will be of interest to advanced undergraduates, postgraduates and researchers in cognitive neuropsychology and cognitive neuroscience.
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
This book reports recent research on mechanisms of normal formulation and control in speaking and in language disorders such as stuttering, aphasia and verbal dyspraxia. The theoretical claim is that such disorders result both from deficits in a component of the language production system and interactions between this component and the system that 'monitors' for errors and undertakes a corrective behaviour. In particular, the book focuses on phonological encoding in speech (the construction of a phonetic plan for utterances), on verbal self-monitoring (checking for correctness and initiating corrective action if necessary), and on interactions between these processes. Bringing together sixteen original chapters by leading international researchers, this volume represents a coherent statement of current thinking in this exciting field. The aim is to show how psycholinguistic models of normal speech processing can be applied to the study of impaired speech production. This book will prove invaluable to any researcher, student or speech therapist looking to bridge the gap between the latest advances in theory and the implications of these advances for language and speech pathology.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
