This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.
This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.
No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.
The concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.
This book's innovative transformative stance revives the critical-activist gist of Vygotsky's project to move beyond theoretical-ideological canons in addressing the crisis of inequality.
What does it mean to be an expert primary science practitioner? How do primary teachers use science subject knowledge in their practice? This book addresses these questions from a sociocultural perspective, challenging currently influential constructivist accounts. It treats the nature of teacher expertise as a dynamic capacity exemplified by those who are recognised as experts in their local communities of practice. In line with this, it provides an in-depth case study of the perspective and practices of a primary science teacher who is locally and more widely recognised as an expert practitioner. One of the conclusions is that primary science expertise is eclectic in character, requiring the employment, in a flexible way, of a variety of forms of knowledge, views of learning, and teaching strategies in order to deal successfully with the contingent situations faced in the classroom. The study of expertise-in-action is particularly important at a time when teaching is increasingly configured in terms of competencies and standards. Its implications for the education of primary science practitioners are profound. Students on education courses, teachers, and researchers will find this book of value for its careful exploration of arguments about the nature of knowledge and learning, and how these are implicated in classroom practice.
This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates more generally the development of mathematical scientists for a variety of workplaces, and includes the experiences of those who were not successful in the transition to the workplace as mathematicians. The research presented is based on interviews, observations and surveys of students and graduates as they are finding their identity as a mathematician. The book contains material from the research carried out in South Africa, Northern Ireland, Canada and Brunei as well as Australia.
This book tells a story of Polish and Slovak Holocaust survivors returning to homes that no longer existed in the aftermath of the Second World War. It focuses on their daily efforts to rebuild their lives in the radically changed political and social landscape of post-war Eastern Europe. Such an analysis shifts the perspective from post-war violence and emigration to post-war reconstruction. Using a comparative approach, Anna Cichopek-Gajraj discusses survivors' journeys home, their struggles to retain citizenship and repossess property, their coping with antisemitism, and their efforts to return to 'normality'. She emphasizes the everyday communal and personal experiences of survivors in the context of their relationships with non-Jews. In essence, by focusing on the daily efforts of Polish and Slovak Jews to rebuild their lives, the author investigates the limits of belonging in Eastern Europe after the Holocaust.
One woman’s national, political, ethnic, social, and personal identities impart an extraordinary perspective on the histories of Europe, Polish Jews, Communism, activism, and survival during the twentieth century. Tonia Lechtman was a Jew, a loving mother and wife, a Polish patriot, a committed Communist, and a Holocaust survivor. Throughout her life these identities brought her to multiple countries—Poland, Palestine, Spain, France, Germany, Switzerland, and Israel—during some of the most pivotal and cataclysmic decades of the twentieth century. In most of those places, she lived on the margins of society while working to promote Communism and trying to create a safe space for her small children. Born in Łódź in 1918, Lechtman became fascinated with Communism in her early youth. In 1935, to avoid the consequences of her political activism during an increasingly antisemitic and hostile political environment, the family moved to Palestine, where Tonia met her future husband, Sioma. In 1937, the couple traveled to Spain to participate in the Spanish Civil War. After discovering she was pregnant, Lechtman relocated to France while Sioma joined the International Brigades. She spent the Second World War in Europe, traveling with two small children between France, Germany, and Switzerland, at times only miraculously avoiding arrest and being transported east to Nazi camps. After the war, she returned to Poland, where she planned to (re)build Communist Poland. However, soon after her arrival she was imprisoned for six years. In 1971, under pressure from her children, Lechtman emigrated from Poland to Israel, where she died in 1996. In writing Lechtman’s biography, Anna Müller has consulted a rich collection of primary source material, including archival documentation, private documents and photographs, interviews from different periods of Lechtman’s life, and personal correspondence. Despite this intimacy, Müller also acknowledges key historiographical questions arising from the lacunae of lost materials, the selective preservation of others, and her own interpretive work translating a life into a life story.
Includes audio and video of transcript annotations and commentary; "additional materials including a PowerPont presentation of the NSF TalkBank project which funded the CD and a transcript from an earlier special issue of "Discourse processes" on problem-based leaning published by Lawrence Erlbaum Associates and edited by Tim Koschmann.
Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.
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