Paul Cobb – författare

In Systems for Instructional Improvement, Paul Cobb and his colleagues draw on their extensive research to propose a series of specific, empirically grounded recommendations that together constitute a theory of action for advancing instruction at scale. The authors outline the elements of a coherent instructional system; describe productive practices for school leaders in supporting teachers’ growth; and discuss the role of district leaders in developing school-level capacity for instructional improvement.Based on the findings of an eight-year research-practice partnership with four large urban districts investigating their efforts to enhance middle school math instruction, the authors seek to bridge the gap between the literature on improving teaching and learning and the literature on policy and leadership. They look at the entire education system and make recommendations on improvement efforts with a focus on student learning and teachers’ instructional vision. In particular, the authors offer insights on the interplay among various supports for teacher learning, including pullout professional development, coaching, collaborative inquiry, the most instructionally productive uses of principals’ time, and the tensions that tend to emerge at the district level. They provide a guide for district-level leaders in organizing their work to support significant teacher learning.Systems for Instructional Improvement provides an invaluable resource for school and district leaders, while outlining a clearly focused agenda for future research.

The studies presented in this book should be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The 'eaching experiment· was carried out with half a dozen children entering first grade over two years in biweekly sessions. Methodologically the authors' research is original. It is a longitudinal but not a naturalistic study, since the experimenter-teachers directed their interaction with each individual child with a view to his or her possible progress. It is experimental in the sense that two groups of subjects were selected according to criteria derived from an earlier study (Steffe, von Glasersfeld, Richards & Cobb, 1983) and that the problems proposed were comparable, though far from identical across the subjects; but unlike more rigid and shorter "learning" or ''training" studies it does not include pre-and posttests, or predetermined procedures. Theoretically, the authors subscribe to Piagefs constructivism: numbers are made by children, not found (as they may find some pretty rocks, for example) or accepted from adults (as they may accept and use a toy). The authors interpret changes in the children's counting behaviors in terms of constructivist concepts such as assimilation, accommodation, and reflective abstraction, and certain excerpts from protocols provide on-line examples of such processes at work. They also subscribe to Vygotsky's proposal for teachers '0 utilize the zone of proximal development and to lead the child to what he (can) not yet do· (1965, p. 104).

The first five contributions to this Special Issue on Theories of Mathematical Learning take a cognitive perspective whereas the sixth, that by Voigt, takes an interactionist perspective. The common theme that links the six articles is the focus on students' inferred experiences as the starting point in the theory-building process. This emphasis on the meanings that objects and events have for students within their experiential realities can be contrasted with approaches in which the goal is to specify cognitive behaviors that yield an input-output match with observed behavior. It is important to note that the term 'experience' as it is used in these articles is not restricted to physical or sensory-motor experience. A perusal of the first five articles indicates that it includes reflective experiences that involve reviewing prior activity and anticipating the results of potential activity. In addition, by emphasizing interaction and communication, Voigt's contribution reminds us that personal experiences do not arise in a vacuum but instead have a social aspect. In taking a cognitive perspective, the first five contributions analyze the pro­ cesses by which students conceptually reorganize their experiential realities and thus construct increasingly sophisticated mathematical ways of knowing. The conceptual constructions addressed by these theorists, ranging as they do from fractions to the Fundamental Theorem of Calculus, indicate that experiential approaches to mathematical cognition are viable at all levels of mathematical development. Although the authors use different theoretical constructs, several additional commonalities can be discerned in their work.

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.

Chemists, working with only mortars and pestles, could not get very far unless they had mathematical models to explain what was happening "inside" of their elements of experience -- an example of what could be termed mathematical learning.This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.

This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

This volume grew out of a symposium on discourse, tools, and instructional design at Vanderbilt University in 1995 that brought together a small international group to grapple with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. The participants invited to develop chapters for this book--all internationally recognized scholars in their respective fields--were selected to represent a wide range of theoretical perspectives including mathematics education, cognitive science, sociocultural theory, and discourse theory. The work is distinguished by the caliber of the contributors, the significance of the topics addressed in the current era of reform in mathematics education, and the diversity of perspectives taken to a common set of themes and issues.The book is intended for those who are seeking to expand their understanding of the complexity of learning in order to enhance the learning experiences students have in schools, primarily researchers, instructional designers, and graduate students in mathematics education, as well as those in other fields including science education, instructional design in general, discourse theory, and semiotics.

This volume grew out of a symposium on discourse, tools, and instructional design at Vanderbilt University in 1995 that brought together a small international group to grapple with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. The participants invited to develop chapters for this book--all internationally recognized scholars in their respective fields--were selected to represent a wide range of theoretical perspectives including mathematics education, cognitive science, sociocultural theory, and discourse theory. The work is distinguished by the caliber of the contributors, the significance of the topics addressed in the current era of reform in mathematics education, and the diversity of perspectives taken to a common set of themes and issues.The book is intended for those who are seeking to expand their understanding of the complexity of learning in order to enhance the learning experiences students have in schools, primarily researchers, instructional designers, and graduate students in mathematics education, as well as those in other fields including science education, instructional design in general, discourse theory, and semiotics.

In this book, key experts with extensive research and classroom experience examine how the multiple dimensions of race, class, culture, power, and knowledge interact in mathematics classrooms to foster and create inequities. Its chapters explore new theoretical perspectives, describe successful classroom practices, and offer insights into how we might develop an effective sociocultural approach to equity in math education.Seeing diversity as an instructional resource rather than as an obstacle to be overcome, this forward-looking volume: helps us to understand the process by which diverse learners experience mathematics education; examines the way students' identities can influence their mathematics learning; describes mathematics education programs that have demonstrated their success with poor, urban, and rural students of color; explains why certain teaching and learning interventions are successful; offers culturally based approaches to mathematics education, including activities for the classroom.

A first-in-field compilation of best practices for the design and implementation of practical measurement for improvement in K-12 educationIn Measuring to Improve, Paul G. LeMahieu, Paul Cobb, and contributors introduce educational practitioners, administrators, and policymakers to the foundational elements of practical measurement to support continuous improvement efforts in K–12 schools. They begin by defining practical measurement as data collection and analysis that is relevant to practice, useful to practitioners, and designed to guide and even be integrated into practice. LeMahieu and Cobb discuss the importance of practical measurement as it relates to and informs the core principles of improvement science. Contributors present five detailed case studies of practical measurement in action across a variety of contexts and improvement efforts in districts throughout the United States. The outcomes of these research-practice partnerships show how solutions to issues—including increasing high school graduation rates, improving college entrance rates, redesigning mathematics instruction, enhancing student literacy and writing skills, and redressing systemic inequities—can be informed by practical measurement. And they describe proven approaches for the design and implementation of measurement systems that align with a validity framework. They provide actionable suggestions for core elements such as tracking, testing, administering exit tickets and surveys, and collaboration.This useful work provides a blueprint that can guide practitioners in incorporating practical measurement as a central element of educational improvement efforts.

In 1031, an Arab scientist, a Jewish astronomer and a Christian monk gather under the dome of an observatory in Spain. A foretelling written on the blade of a knife tells of a new ruler, whose power will come from the knowledge in a centuries old book. As its guardians begin to covet this knowledge for themselves, the book is drawn into the conflict between the houses of Wessex and Godwin, and England’s destiny. It will carry a secret at the heart of the succession to the English throne. But the book is in danger, from those who will use it for the wealth and power it can bring — or who want to destroy it. From Spain to Normandy and England, The Book and the Knife: Thegn of Berewic is the story of the power of knowledge, of a generation—spanning blood feud, and of the struggle for control of England before the Norman invasion of 1066. A story of loyalty and treachery, love and hate.

In honor of Fred M. Donner's long and distinguished career as one of the foremost interpreters of early Islam, this volume collects more than a dozen original studies by his students. They range over a wide array of sub-fields in Islamic history and Islamic studies, including early history, historiography, Islamic law, religious studies, Qur'anic studies and Islamic archaeology. The book also includes a bibliography of Donner's works and a biographical sketch of sorts. Taken together, these essays are a clear testament to Donner's wide-ranging and continuing impact on the field.Contributors include: Sean W. Anthony, Jonathan A. C. Brown, David Cook, Vaness De Gifis, Asa Eger, Tracy Hoffman, Marion H. Katz, Kathryn M. Kueny, Shari Lowin, Jens Scheiner, Robert Schick, Stuart Sears, Elizabeth Urban, Tasha Vorderstrasse, Brannon Wheeler, and Hayrettin Yücesoy.

The first five contributions to this Special Issue on Theories of Mathematical Learning take a cognitive perspective whereas the sixth, that by Voigt, takes an interactionist perspective. The common theme that links the six articles is the focus on students' inferred experiences as the starting point in the theory-building process. This emphasis on the meanings that objects and events have for students within their experiential realities can be contrasted with approaches in which the goal is to specify cognitive behaviors that yield an input-output match with observed behavior. It is important to note that the term 'experience' as it is used in these articles is not restricted to physical or sensory-motor experience. A perusal of the first five articles indicates that it includes reflective experiences that involve reviewing prior activity and anticipating the results of potential activity. In addition, by emphasizing interaction and communication, Voigt's contribution reminds us that personal experiences do not arise in a vacuum but instead have a social aspect. In taking a cognitive perspective, the first five contributions analyze the pro­ cesses by which students conceptually reorganize their experiential realities and thus construct increasingly sophisticated mathematical ways of knowing. The conceptual constructions addressed by these theorists, ranging as they do from fractions to the Fundamental Theorem of Calculus, indicate that experiential approaches to mathematical cognition are viable at all levels of mathematical development. Although the authors use different theoretical constructs, several additional commonalities can be discerned in their work.