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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.
This book deals with the development of thinking under different cultural conditions, focusing on the evolution of mathematical thinking in the history of science and education. Starting from Piaget's genetic epistemology, it provides a conceptual framework for describing and explaining the development of cognition by reflective abstractions from systems of actions.
This unusual volume presents an overview of Jean Piaget's work in psychology--from his earliest writings to posthumous publications. It also contains a glossary of the essential explanatory concepts found in this work. The focus is on Piaget's psychological studies and on the underlying epistemological theses. The book may be consulted in various ways depending on whether one is looking for an introduction to Piaget's theory, details about a particular concept, a survey of his body of work, or a historical perspective. Readers who are relatively unfamiliar with Piaget's ideas and seek access to them through this book will not necessarily proceed in the same way as those who are acquainted with Piaget's work and wish to refresh, synthesize, or complete their knowledge. The volume is divided into two major sections with several subdivisions as follows: * The Chronological Overview presents Piaget's early ideas and the most important sources of his inspiration, and reviews his research work dividing it into four main periods plus a transitional one. * The Glossary covers a number of explanatory concepts which are essential to Piaget's theory.
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.
This book constitutes the thoroughly refereed proceedings of the 19th International Symposium on Static Analysis, SAS 2012, held in Deauville, France, in September 2012. The 25 revised full papers presented together with 4 invited talks were selected from 62 submissions. The papers address all aspects of static analysis, including abstract domains, abstract interpretation, abstract testing, bug detection, data flow analysis, model checking, new applications, program transformation, program verification, security analysis, theoretical frameworks, and type checking.
The Creative Enterprise of Mathematics Teaching Research presents the results and methodology of work of the teaching-research community of practice of the Bronx (TR Team of the Bronx). It has a twofold aim of impacting both teachers of Mathematics and researchers in Mathematics Education. This volume can be used by teachers of mathematics who want to use research to reflect upon and to improve their teaching craft, as well as by researchers who are interested in uncovering riches of classroom learning/teaching for research investigations. This book represents the results of a collaboration of instructors discussing their own instruction research, analyzed through a conceptual framework obtained via the synthesis of creativity research and educational learning theories, based upon the work of Piaget and Vygotsky. The editors see an urgent need for creative synthesis of research and teaching, an example of which is presented in the book. Two central themes of the book are the methodology of TR/NYCity model and creativity, more precisely, creativity of the Aha moment formulated by Arthur Koestler (1964) in a very profound but little known theory of bisociation exposed in his work “The Act of Creation”. Incorporation of the theory of bisociation into classroom teaching of mathematics provides the key to enable students who may struggle with mathematics to engage their own creativity, become involved in their learning process and thus reach their full potential of excellence. Creativity in teaching remedial mathematics is teaching gifted students how to access their own giftedness.
On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.
This major text provides the first comprehensive anthology of the key topics arising in the philosophy of psychology. Bringing together internationally renowned authors, including Herb Simon, Karl Pribram, Joseph Rychlak, Ullin T Place and Adolf Gr[um]unbaum, this volume offers a stimulating and informative addition to contemporary debate. With the cognitive revolution of the 1960s, there has been a resurgence of interest in the study of the philosophical assumptions and implications of psychology. Several significant themes, such as the foundations of knowledge, behaviourism, rationality, emotion and cognitive science span both philosophy and psychology, and are covered here along with a wide range of issues in the fields of folk psychology, clinical psychology, neurophysiology and professional ethics.
The first full-length study of Jean Piaget as a philosopher and evolutionist. Messerly traces Piaget's earliest conjectures about knowledge through its further developments to its mature formulation as 'genetic epistemology.' Messerly analyzes Piaget's constructivist theory of the evolution of human knowledge as continuous with, yet partially transcending, the biological process of adaptation to the environment. Messerly's study serves as an invitation to further explorations with Paiget's theory and will interest philosophers, biologists, and psychologists.
The intent of this monograph is to showcase successful implementation of mathematical discourse in the classroom. Some questions that might be addressed are: * How does a teacher begin to learn about using discourse purposefully to improve mathematics teaching and learning? * How is discourse interwoven into professional development content courses to provide teachers with the tools necessary to begin using discourse in their own classrooms? * What does a discourse-rich classroom look like and how is it different from other classrooms, from both the teacher's and the students' perspectives? * How can teachers of pre-service teachers integrate discourse into their content and methods courses? * How can we use discourse research to inform work with teachers, both pre- and in-service, for example, to help them know how to respond to elicited knowledge from students in their classrooms? * What are the discourse challenges in on-line mathematics courses offered for professional development? Can on-line classrooms also be discourse-rich? What would that look like? * In what ways does mathematical discourse differ from discourse in general?