Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Author: Judith Sowder

Publisher: State University of New York Press

Published: 1998-07-16

Total Pages: 240

ISBN-13: 1438420722

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The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.


Book Synopsis Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction by : Judith Sowder

Download or read book Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction written by Judith Sowder and published by State University of New York Press. This book was released on 1998-07-16 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.

Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Author: Judith T. Sowder

Publisher: SUNY Press

Published: 1998-01-01

Total Pages: 240

ISBN-13: 9780791438411

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The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.


Book Synopsis Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction by : Judith T. Sowder

Download or read book Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction written by Judith T. Sowder and published by SUNY Press. This book was released on 1998-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.

Teacher Knowledge and Practice in Middle Grades Mathematics

Teacher Knowledge and Practice in Middle Grades Mathematics

Author:

Publisher: BRILL

Published: 2008-01-01

Total Pages: 319

ISBN-13: 9087906188

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This book presents a coherent collection of research studies on teacher knowledge and its relation to instruction and learning in middle-grades mathematics. The authors provide comprehensive literature reviews on specific components of mathematics knowledge for teaching that have been found to be important for effective instruction.


Book Synopsis Teacher Knowledge and Practice in Middle Grades Mathematics by :

Download or read book Teacher Knowledge and Practice in Middle Grades Mathematics written by and published by BRILL. This book was released on 2008-01-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent collection of research studies on teacher knowledge and its relation to instruction and learning in middle-grades mathematics. The authors provide comprehensive literature reviews on specific components of mathematics knowledge for teaching that have been found to be important for effective instruction.

Integrating Research on Teaching and Learning Mathematics

Integrating Research on Teaching and Learning Mathematics

Author: Elizabeth Fennema

Publisher: SUNY Press

Published: 1991-01-01

Total Pages: 242

ISBN-13: 9780791405222

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During the last decade there were significant advances in the study of students' learning and problem solving in mathematics, and in the study of classroom instruction. Because these two research programs usually have been conducted individually, it is generally agreed now that there is an increasing need for an integrated research program. This book represents initial discussions and development of a unified paradigm for studying teaching in mathematics that builds upon both cognitive as well as instructional research.


Book Synopsis Integrating Research on Teaching and Learning Mathematics by : Elizabeth Fennema

Download or read book Integrating Research on Teaching and Learning Mathematics written by Elizabeth Fennema and published by SUNY Press. This book was released on 1991-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade there were significant advances in the study of students' learning and problem solving in mathematics, and in the study of classroom instruction. Because these two research programs usually have been conducted individually, it is generally agreed now that there is an increasing need for an integrated research program. This book represents initial discussions and development of a unified paradigm for studying teaching in mathematics that builds upon both cognitive as well as instructional research.

Mathematics Education in the Middle Grades

Mathematics Education in the Middle Grades

Author: National Research Council

Publisher: National Academies Press

Published: 2000-02-11

Total Pages: 271

ISBN-13: 0309172276

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In September 1998, the Math Science Education Board National held a Convocation on Middle Grades Mathematics that was co-sponsored by the National Council of Teachers of Mathematics, the National Middle School Association, and the American Educational Research Association. The Convocation was structured to present the teaching of middle school mathematics from two points of view: teaching mathematics with a focus on the subject matter content or teaching mathematics with a focus on the whole child and whole curriculum. This book discusses the challenges before the nation's mathematical sciences community to focus its energy on the improvement of middle grades mathematics education and to begin an ongoing national dialogue on middle grades mathematics education.


Book Synopsis Mathematics Education in the Middle Grades by : National Research Council

Download or read book Mathematics Education in the Middle Grades written by National Research Council and published by National Academies Press. This book was released on 2000-02-11 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 1998, the Math Science Education Board National held a Convocation on Middle Grades Mathematics that was co-sponsored by the National Council of Teachers of Mathematics, the National Middle School Association, and the American Educational Research Association. The Convocation was structured to present the teaching of middle school mathematics from two points of view: teaching mathematics with a focus on the subject matter content or teaching mathematics with a focus on the whole child and whole curriculum. This book discusses the challenges before the nation's mathematical sciences community to focus its energy on the improvement of middle grades mathematics education and to begin an ongoing national dialogue on middle grades mathematics education.

Providing a Foundation for Teaching Mathematics in the Middle Grades

Providing a Foundation for Teaching Mathematics in the Middle Grades

Author: Judith Sowder

Publisher: State University of New York Press

Published: 1995-08-03

Total Pages: 348

ISBN-13: 1438420730

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This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach. In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction. The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.


Book Synopsis Providing a Foundation for Teaching Mathematics in the Middle Grades by : Judith Sowder

Download or read book Providing a Foundation for Teaching Mathematics in the Middle Grades written by Judith Sowder and published by State University of New York Press. This book was released on 1995-08-03 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach. In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction. The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.

Mathematical Knowledge in Teaching

Mathematical Knowledge in Teaching

Author: Tim Rowland

Publisher: Springer Science & Business Media

Published: 2011-01-06

Total Pages: 300

ISBN-13: 904819766X

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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.


Book Synopsis Mathematical Knowledge in Teaching by : Tim Rowland

Download or read book Mathematical Knowledge in Teaching written by Tim Rowland and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Refining the Mathematics Knowledge Base

Refining the Mathematics Knowledge Base

Author: Bindu Elizabeth Pothen

Publisher: Stanford University

Published: 2011

Total Pages: 253

ISBN-13:

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Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.


Book Synopsis Refining the Mathematics Knowledge Base by : Bindu Elizabeth Pothen

Download or read book Refining the Mathematics Knowledge Base written by Bindu Elizabeth Pothen and published by Stanford University. This book was released on 2011 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.

The Construction of New Mathematical Knowledge in Classroom Interaction

The Construction of New Mathematical Knowledge in Classroom Interaction

Author: Heinz Steinbring

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 242

ISBN-13: 0387242538

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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.


Book Synopsis The Construction of New Mathematical Knowledge in Classroom Interaction by : Heinz Steinbring

Download or read book The Construction of New Mathematical Knowledge in Classroom Interaction written by Heinz Steinbring and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematical Education of Teachers

The Mathematical Education of Teachers

Author: Conference Board of the Mathematical Sciences

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 164

ISBN-13: 9780821828991

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Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.


Book Synopsis The Mathematical Education of Teachers by : Conference Board of the Mathematical Sciences

Download or read book The Mathematical Education of Teachers written by Conference Board of the Mathematical Sciences and published by American Mathematical Soc.. This book was released on 2001 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.