The Construction of New Mathematical Knowledge in Classroom Interaction PDF Download

Author: Heinz Steinbring
Publisher: Springer Science & Business Media
ISBN: 0387242538
Category : Education
Languages : en
Pages : 242

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Book Description
Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.

Author: Falk Seeger
Publisher: Cambridge University Press
ISBN: 9780521571074
Category : Psychology
Languages : en
Pages : 276

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Book Description
The culture of the mathematics classroom is becoming an increasingly salient topic of discussion in mathematics education. Studying and changing what happens in the classroom allows researchers and educators to recognize the social character of mathematical pedagogy and the relationship between the classroom and culture at large. This volume is divided into three sections, reporting findings gained in both research and practice. The first part presents several attempts to change classroom culture by focusing on the education of mathematics teachers and on teacher-researcher collaboration. The second section shifts to the interactive processes of the mathematics classroom and to the communal nature of learning. The third section discusses the means of constructing, filtering, and establishing mathematical knowledge that are characteristic of classroom culture. This internationally relevant volume will be of particular interest to educators and educational researchers.

Author: Alan Bishop
Publisher: Springer Science & Business Media
ISBN: 9401721955
Category : Education
Languages : en
Pages : 214

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Book Description
In the first BACOMET volume different perspectives on issues concerning teacher education in mathematics were presented (B. Christiansen, A. G. Howson and M. Otte, Perspectives on Mathematics Education, Reidel, Dordrecht, 1986). Underlying all of them was the fundamental problem area of the relationships between mathematical knowledge and the teaching and learning processes. The subsequent project BACOMET 2, whose outcomes are presented in this book, continued this work, especially by focusing on the genesis of mathematical knowledge in the classroom. The book developed over the period 1985-9 through several meetings, much discussion and considerable writing and redrafting. Our major concern was to try to analyse what we considered to be the most significant aspects of the relationships in order to enable mathematics educators to be better able to handle the kinds of complex issues facing all mathematics educators as we approach the end of the twentieth century. With access to mathematics education widening all the time, with a multi tude of new materials and resources being available each year, with complex cultural and social interactions creating a fluctuating context of education, with all manner of technology becoming more and more significant, and with both informal education (through media of different kinds) and non formal education (courses of training etc. ) growing apace, the nature of formal mathematical education is increasingly needing analysis.

Author: Tim Rowland
Publisher: Springer Science & Business Media
ISBN: 904819766X
Category : Education
Languages : en
Pages : 304

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Book Description
The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.

Author: Margaret Walshaw
Publisher: IAP
ISBN: 1607524295
Category : Education
Languages : en
Pages : 311

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Book Description
This volume represents a serious attempt to understand what it is that structures the pedagogical experience. In that attempt there are two main objectives. One is a theoretical interest that involves examining the issue of the subjectivity of the teacher and exploring how intersubjective negotiations shape the production of classroom practice. A second objective is to apply these understandings to the production of mathematical knowledge and to the construction of identities in actual mathematics classrooms. To that end book contains substantial essays that draw on postmodern philosophies of the social to explore theory's relationship with the practice of mathematics pedagogy. Unpacking Pedagogy takes new ideas seriously and engages readers in theory development. Groundbreaking in content, the book investigates how our thinking about classroom practice in general, and mathematics teaching (and learning), in particular, might be transformed. As a key resource for interrogating and understanding classroom life, the book's sophisticated analyses allow readers to build new knowledge about mathematics pedagogy. In turn, that new knowledge will provide them with the tools to engage more actively in educational criticism and to play a role in educational change.

Author: Steve Lerman
Publisher: Springer Science & Business Media
ISBN: 9401711992
Category : Education
Languages : en
Pages : 212

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Book Description
Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in social practices, including the market place and the home, have initiated a shift of focus. Culture has become identified as a key to understanding the basis on which the learner appropriates meaning. The chapters in this timely book attempt to engage with this shift of focus and offer original contributions to the debate about mathematics teaching and learning. They adopt theoretical perspectives while drawing on the classroom as both the source of investigation and the site of potential change and development. The book will be of fundamental interest to lecturers and researchers and to teachers concerned with the classroom as a cultural phenomenon.

Author: Baruch Schwarz
Publisher: Routledge
ISBN: 1134007310
Category : Education
Languages : en
Pages : 336

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Book Description
Classrooms provide extremely varied settings in which learning may take place, including teacher-led conversations, small group unguided discussions, individual problem solving or computer supported collaborative learning (CSCL). Transformation of Knowledge through Classroom Interaction examines and evaluates different ways which have been used to support students learning in classrooms, using mathematics and science as a model to examine how different types of interactions contribute to students’ participation in classroom activity, and their understanding of concepts and their practical applications. The contributions in this book offer rich descriptions and ways of understanding how learning occurs in both traditional and non-traditional settings. Combining theoretical perspectives with practical applications, the book includes discussions of: the roles of dialogue and argumentation in constructing knowledge the role of guidance in constructing knowledge abstracting processes in mathematics and science classrooms the effect of environment, media and technology on learning processes methodologies for tracing transformation of knowledge in classroom interaction. Bringing together a broad range of contributions from leading international researchers, this book makes an important contribution to the field of classroom learning, and will appeal to all those engaged in academic research in education.

Author: Terry Wood
Publisher: Routledge
ISBN: 1135658722
Category : Education
Languages : en
Pages : 324

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Book Description
The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

Author: Baruch Schwarz
Publisher: Routledge
ISBN: 1134007329
Category : Education
Languages : en
Pages : 335

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Book Description
Classrooms provide extremely varied settings in which learning may take place, including teacher-led conversations, small group unguided discussions, individual problem solving or computer supported collaborative learning (CSCL). Transformation of Knowledge through Classroom Interaction examines and evaluates different ways which have been used to support students learning in classrooms, using mathematics and science as a model to examine how different types of interactions contribute to students’ participation in classroom activity, and their understanding of concepts and their practical applications. The contributions in this book offer rich descriptions and ways of understanding how learning occurs in both traditional and non-traditional settings. Combining theoretical perspectives with practical applications, the book includes discussions of: the roles of dialogue and argumentation in constructing knowledge the role of guidance in constructing knowledge abstracting processes in mathematics and science classrooms the effect of environment, media and technology on learning processes methodologies for tracing transformation of knowledge in classroom interaction. Bringing together a broad range of contributions from leading international researchers, this book makes an important contribution to the field of classroom learning, and will appeal to all those engaged in academic research in education.

Author: Elizabeth Fennema
Publisher: Routledge
ISBN: 1136496394
Category : Education
Languages : en
Pages : 455

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Book Description
This book addresses the need of professional development leaders and policymakers for scholarly knowledge about influencing teachers to modify mathematical instruction to bring it more in alignment with the recommendations of the current reform movement initiated by the National Council of Teachers of Mathematics. The book presents: * theoretical perspectives for studying, analyzing, and understanding teacher change; * descriptions of contextual variables to be considered as one studies and attempts to understand teacher change; and * descriptions of professional development programs that resulted in teacher change. One chapter builds a rationale for looking to developmental psychology for guidance in constructing models of reconstructing new forms of mathematical instruction. Another highlights the relevance to mathematics teacher development of research-based knowledge about how children construct mathematical ideas. Other chapters explore the relationships between the various contexts of schooling and instructional change. Included also are chapters that describe and analyze major reform efforts designed to assist teachers in modifying their instructional practices (Cognitively Guided Instruction, Math-Cubed, Project Impact, Mathematics in Context, and the Case-Based Project). Finally, the current state of knowledge about encouraging teachers to modify their instruction is discussed, the implications of major research and implementation findings are suggested, and some of the major questions that need to be addressed are identified, such as what we have learned about teacher change.