Middle Grade Teachers Mathematical Knowledge And Its Relationship To Instruction

Author : Judith Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle
Publisher : State University of New York Press
Page : 240 pages
File Size : 40,7 Mb
Release : 1998-07-16
Category : Education
ISBN : 9781438420721

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Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction by Judith Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle Pdf

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.

Author : Judith T. Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle
Publisher : SUNY Press
Page : 240 pages
File Size : 44,5 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 0791438414

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Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction by Judith T. Sowder,Randolph A. Philipp,Barbara E. Armstrong,Bonnie P. Schappelle Pdf

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.

Author : Anonim
Publisher : BRILL
Page : 319 pages
File Size : 45,6 Mb
Release : 2008-01-01
Category : Education
ISBN : 9789087906184

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Teacher Knowledge and Practice in Middle Grades Mathematics by Anonim Pdf

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.

Author : Elizabeth Fennema,Thomas P. Carpenter,Susan J. Lamon
Publisher : State University of New York Press
Page : 242 pages
File Size : 50,8 Mb
Release : 1991-08-06
Category : Education
ISBN : 9781438402581

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Integrating Research on Teaching and Learning Mathematics by Elizabeth Fennema,Thomas P. Carpenter,Susan J. Lamon Pdf

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.

Author : National Research Council,Center for Science, Mathematics, and Engineering Education
Publisher : National Academies Press
Page : 271 pages
File Size : 47,6 Mb
Release : 2000-02-11
Category : Education
ISBN : 9780309172271

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Mathematics Education in the Middle Grades by National Research Council,Center for Science, Mathematics, and Engineering Education Pdf

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.

Author : Judith Sowder,Bonnie P. Schappelle
Publisher : State University of New York Press
Page : 348 pages
File Size : 43,8 Mb
Release : 1995-08-03
Category : Education
ISBN : 9781438420738

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Providing a Foundation for Teaching Mathematics in the Middle Grades by Judith Sowder,Bonnie P. Schappelle Pdf

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.

Author : Conference Board of the Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 44,8 Mb
Release : 2001
Category : Education
ISBN : 0821828991

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The Mathematical Education of Teachers by Conference Board of the Mathematical Sciences Pdf

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.

Author : Bindu Elizabeth Pothen
Publisher : Stanford University
Page : 253 pages
File Size : 42,8 Mb
Release : 2011
Category : Electronic
ISBN : STANFORD:ck171qs7892

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Refining the Mathematics Knowledge Base by Bindu Elizabeth Pothen Pdf

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.

Author : Tim Rowland,Kenneth Ruthven
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 41,5 Mb
Release : 2011-01-06
Category : Education
ISBN : 9789048197668

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Mathematical Knowledge in Teaching by Tim Rowland,Kenneth Ruthven Pdf

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 : Douglas T. Owens,Sigrid Wagner
Publisher : MacMillan Reference Library
Page : 350 pages
File Size : 55,7 Mb
Release : 1993
Category : Mathematics
ISBN : 0028957954

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Middle Grades Mathematics by Douglas T. Owens,Sigrid Wagner Pdf

Author : Heinz Steinbring
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 53,5 Mb
Release : 2006-03-30
Category : Education
ISBN : 9780387242538

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The Construction of New Mathematical Knowledge in Classroom Interaction by Heinz Steinbring Pdf

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 : Gerald Kulm
Publisher : Brill / Sense
Page : 330 pages
File Size : 45,7 Mb
Release : 2008
Category : Education
ISBN : STANFORD:36105132226551

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Teacher Knowledge and Practice in Middle Grades Mathematics by Gerald Kulm Pdf

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. Based on the analysis of video data collected over a six-year project, the chapters present new and accessible research on the learning of fractions, early concepts of algebra, and basic statistics and probability. The three sections of the book contain chapters that address research on the development of mathematics knowledge for teaching at the undergraduate level, instructional practices of middle-grades teachers, and the implications of teacher knowledge of mathematics for student learning. The chapters are written by members of a research team led by the Editor that has been working for the past six years to develop practical and useful theories and findings on variables that affect teaching and learning of middle grades mathematics. Mathematics knowledge for teaching is a topic of great current interest. This book is a valuable resource for mathematics education researchers, graduate students, and teacher educators. In addition, professional developers and school district supervisor and curriculum leaders will find the concrete examples of effective teaching strategies useful for teacher workshops.

Author : Hamsa Venkat,Marissa Rollnick,John Loughran,Mike Askew
Publisher : Routledge
Page : 263 pages
File Size : 51,6 Mb
Release : 2014-05-09
Category : Education
ISBN : 9781134683710

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Exploring Mathematics and Science Teachers' Knowledge by Hamsa Venkat,Marissa Rollnick,John Loughran,Mike Askew Pdf

Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists are teaching mathematics and science at both primary and secondary levels, and research evidence has revealed how gaps and limitations in teachers’ content understandings can lead to classroom practices that present barriers to students’ learning. This book addresses these issues by investigating how teachers’ content knowledge interacts with their pedagogies across diverse contexts and perspectives. This knowledge-practice nexus is examined across mathematics and science teaching, traversing schooling phases and countries, with an emphasis on contexts of disadvantage. These features push the boundaries of research into teachers’ content knowledge. The book’s combination of mathematics and science enriches each discipline for the reader, and contributes to our understandings of student attainment by examining the nature of specialised content knowledge needed for competent teaching within and across the two domains. Exploring Mathematics and Science Teachers’ Knowledge will be key reading for researchers, doctoral students and postgraduates with a focus on Mathematics, Science and teacher knowledge research.

Author : Reagan Curtis,Darran R. Cairns,Johnna J. Bolyard
Publisher : Teachers College Press
Page : 169 pages
File Size : 43,8 Mb
Release : 2023-03-24
Category : Education
ISBN : 9780807767801

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Design Thinking in the Middle Grades by Reagan Curtis,Darran R. Cairns,Johnna J. Bolyard Pdf

Too often, mathematics and science are taught in isolation from each other and from meaningful problems that matter to students. This book draws on the authors' experiences with teacher colleagues, including time spent in their classrooms co-developing and refining lessons. The core of their approach is to encourage learners to pursue solutions to everyday challenges through design-based learning cycles. Students use mathematical modeling to describe or summarize a phenomenon, predict which potential solutions may be successful, and/or to test actual performance against predictions. The authors emphasize connecting grade-appropriate science and math content standards and integrating literacy with evidence-based argument through design briefs and presentations. Teachers will learn how to support productive struggle and structure group learning that promotes equity, while teaching in the classroom or virtually as needed. The middle grades are a pivotal time to engage the next generation so that they are prepared to solve tomorrow's challenges. Classroom teachers, preservice educators, and faculty in teacher education programs can use Design Thinking in the Middle Grades as a foundational text for math, science, and integrated STEM teaching.

Author : Randall E. Groth
Publisher : SAGE
Page : 513 pages
File Size : 49,7 Mb
Release : 2012-08-10
Category : Education
ISBN : 9781412995689

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Teaching Mathematics in Grades 6 - 12 by Randall E. Groth Pdf

Teaching Mathematics in grades 6-12 by Randall E. Groth is a core methods text that introduces students to the vibrant and intriguing world of mathematics education. The author shows preservice mathematics teachers the value of being a "researcher"--constantly experimenting with methods for developing students' mathematical thinking--and connecting this research to practices that enhance students' understanding of the types of mathematical knowledge students bring to school and how students' thinking may develop in response to different teaching strategies.