Studies in Reflecting Abstraction


Book Description

This translation of the French Recherches sur l'abstraction reflechissante (1977), make available in English Piaget's only treatise on reflecting abstraction - a process he came to attribute considerable importance to in his later thinking and which he believed to be responsible for many of the advances that take place in human development, especially our understanding of mathematics. Rich with empirical research on reflecting abstraction at work in the thinking of 4 to 12 year olds, the studies in this volume examine its role in many contexts of cognitive development such as: reasoning about mathematics; forming analogies; putting objects in order by size and comparing the resulting series; and navigating through a wire maze. His theoretical discussions explore the relationships between reflecting abstraction and other central processes in his later theory, such as generalization, becoming conscious, and equilibration, as the differentiation of possibilities and their integration into necessities. These discussions indicate which aspects of his later theorizing were settled and which require further thought and investigation. Studies in Reflecting Abstraction will be of interest to developmental and cognitive psychologists, educationalists, philosophers and anyone who seeks to understand human knowledge and its development.




Studies in Reflecting Abstraction


Book Description

This translation of the French Recherches sur l'abstraction reflechissante (1977), make available in English Piaget's only treatise on reflecting abstraction - a process he came to attribute considerable importance to in his later thinking and which he believed to be responsible for many of the advances that take place in human development, especially our understanding of mathematics. Rich with empirical research on reflecting abstraction at work in the thinking of 4 to 12 year olds, the studies in this volume examine its role in many contexts of cognitive development such as: reasoning about mathematics; forming analogies; putting objects in order by size and comparing the resulting series; and navigating through a wire maze. His theoretical discussions explore the relationships between reflecting abstraction and other central processes in his later theory, such as generalization, becoming conscious, and equilibration, as the differentiation of possibilities and their integration into necessities. These discussions indicate which aspects of his later theorizing were settled and which require further thought and investigation. Studies in Reflecting Abstraction will be of interest to developmental and cognitive psychologists, educationalists, philosophers and anyone who seeks to understand human knowledge and its development.




Advanced Mathematical Thinking


Book Description

This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.




Transformation of Knowledge Through Classroom Interaction


Book Description

Transformation of Knowledge through Classroom Interaction examines and evaluates different ways which have been used to support students learning in classrooms.




Transfer of Learning


Book Description

This book provides a common language for and makes connections between transfer research in mathematics education and transfer research in related fields. It generates renewed excitement for and increased visibility of transfer research, by showcasing and aggregating leading-edge research from the transfer research community. This book also helps to establish transfer as a sub-field of research within mathematics education and extends and refines alternate perspectives on the transfer of learning. The book provides an overview of current knowledge in the field as well as informs future transfer research.




Abstractionist Aesthetics


Book Description

An artistic discussion on the critical potential of African American expressive culture In a major reassessment of African American culture, Phillip Brian Harper intervenes in the ongoing debate about the “proper” depiction of black people. He advocates for African American aesthetic abstractionism—a representational mode whereby an artwork, rather than striving for realist verisimilitude, vigorously asserts its essentially artificial character. Maintaining that realist representation reaffirms the very social facts that it might have been understood to challenge, Harper contends that abstractionism shows up the actual constructedness of those facts, thereby subjecting them to critical scrutiny and making them amenable to transformation. Arguing against the need for “positive” representations, Abstractionist Aesthetics displaces realism as the primary mode of African American representational aesthetics, re-centers literature as a principal site of African American cultural politics, and elevates experimental prose within the domain of African American literature. Drawing on examples across a variety of artistic production, including the visual work of Fred Wilson and Kara Walker, the music of Billie Holiday and Cecil Taylor, and the prose and verse writings of Ntozake Shange, Alice Walker, and John Keene, this book poses urgent questions about how racial blackness is made to assume certain social meanings. In the process, African American aesthetics are upended, rendering abstractionism as the most powerful modality for Black representation.




New Directions for Situated Cognition in Mathematics Education


Book Description

This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. No other books are available which take this view specifically in mathematics education. Thus it provides an up-to-date overview of developments and applications to which other researchers can refer and which will inspire future research.




Jean Piaget and Neuchâtel


Book Description

Jean Piaget is widely acknowledged as one of the most important scholars of the twentieth century. His passionate philosophical search for an understanding of the nature of knowledge led him to make major contributions to the study of child development and epistemology. But how did his early life in Neuchâtel inspire him to embark on this search? Taking a socio-historical and cultural perspective, this book outlines the development of Piaget's understanding of major issues regarding mind, faith, science, logic, peace, and social rights in a time of anxiety. and world wars The international and multidisciplinary contributors investigate Piaget the adolescent as he begins his quest for autonomy of reason and sets out to create his own explanatory system for cognitive growth. The latter part of the book goes on to consider the early reception of Piaget's work in different cultural contexts and his impact on issues of psychology and educational reform. Piaget's theoretical system can be seen as an expression of the values he developed during his childhood and adolescence as he searched for the conditions of reciprocal relationships and rational dialogues. Jean Piaget and Neuchâtel demonstrates that in today's climate, the questions Piaget addressed remain very relevant and invite new enquiries from different standpoints. This book will therefore be of interest to psychologists, educators, and philosophers. This book is published with the support of Pro Helvetia, Swiss Arts Council.




Thinking Visually


Book Description

Language is a marvelous tool for communication, but it is greatly overrated as a tool for thought. This volume documents the many ways pictures, visual images, and spatial metaphors influence our thinking. It discusses both classic and recent research that support the view that visual thinking occurs not only where we expect to find it, but also where we do not. Much of comprehending language, for instance, depends on visual simulations of words or on spatial metaphors that provide a foundation for conceptual understanding. Thinking Visually supports comprehension by reducing jargon and by providing many illustrations, educational applications, and problems for readers to solve. It provides a broad overview of topics that range from the visual images formed by babies to acting classes designed for the elderly, from visual diagrams created by children to visual diagrams created by psychologists, from producing and manipulating images to viewing animations. The final chapters discuss examples of instructional software and argue that the lack of such software in classrooms undermines the opportunity to develop visual thinking. The book includes the Animation TutorTM downloadable resources to illustrate the application of research on visual thinking to improve mathematical reasoning.




New Trends in Software Methodologies, Tools and Techniques


Book Description

Annotation. The Lyee International Workshop (Lyee-W02) is a means for presenting the results of the Lyee International research project, oriented for new software generation techniques based on Lyee technologies. Lyee-W02 will help to build a forum for exchanging ideas and experiences in the field of new directions on software development methodologies and its tools and techniques. Lyee methodology captures the essence of the innovations, controversies, challenges, and possible solutions of the software industry. This theory is born from experience and it is the time to stimulate the academic research on software science initiated from experience to theory through this workshop and its coming series.