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Descriptors:
Mathematics Instruction; Problem Solving; Educational Research; Evidence; Teaching Methods; Mathematical Applications; Group Instruction; Self Management; Reflection; Visual Aids; Protocol Analysis; Discussion (Teaching Technique); Mathematical Concepts; Algebra; Grade 4; Grade 5; Grade 6; Grade 7; Grade 8

Abstract:
The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these challenges. The authors rate the strength of the research evidence supporting each of their recommendations. The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of improving mathematical problem solving in grades 4 through 8. The guide provides practical, clear information on critical topics related to improving mathematical problem solving and is based on the best available evidence as judged by the authors. Appended are: (1) Postscript from the Institute of Education Sciences; (2) About the Authors; (3) Disclosure of Potential Conflicts of Interest; and (4) Rationale for Evidence Ratings. (Contains 9 tables, 21 examples and 303 endnotes.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Mathematics Education; Geometry; Educational Change; Middle School Teachers; Faculty Development; Pedagogical Content Knowledge; Teaching Methods; Video Technology; Educational Objectives; Material Development

Abstract:
Although there are increasing numbers of professional development (PD) materials intended to foster teachers' mathematical knowledge for teaching within the topics of number and algebra, little attention has been given to geometry. In this article we describe the Learning and Teaching Geometry project's approach to the development of PD materials aimed at supporting middle grades teachers to meet the challenges of teaching similarity. We discuss the design research approach of the project, including developing a mathematical learning trajectory, videotaping in classrooms, and selecting videoclips to support our learning goals. We use a sample videocase to illustrate the design process. (Contains 3 notes and 4 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Faculty Development; Professional Development; Coaching (Performance); Instructional Improvement; Excellence in Education; Teacher Effectiveness; Listening Skills; Classroom Observation Techniques

Abstract:
Because the author and his colleagues at the Center for Leadership and Learning Communities believe that instructional coaching is one of the most exciting developments in education in a long time, they have examined the questions this new strategy has raised for education leaders: Should coaching replace some traditional forms of teacher professional development? If not, how can coaching be integrated with other forms of professional development in the lives of teachers? How much group professional development is needed along with coaching? They have concluded that the relationship between coaching and group professional development should not be thought of in "either-or" terms, but rather "both-and." (Contains 2 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Health Behavior; Smoking; Public Policy; Youth; Health Promotion; Intervention; Community Programs

Abstract:
This brief paper reports the results of two observational studies examining the impact of fines for youth tobacco possession on public smoking among youth. Preliminary findings are presented that suggest that when police issued warnings and tickets to reduce underage youth possession of tobacco, in both towns the number of youth smoking in public declined. The study focused on an important health behavior; application of a potentially powerful, community-wide intervention; the use of two distinct communities; and unobtrusive assessment of adult and youth smoking rates. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Algebra; Cognitive Processes; Curriculum Development; Grade 7; Learning Strategies; Mathematics Education; Professional Development; Secondary Education; Thinking Skills

Abstract:
This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials focus on how students think about mathematics and helping teachers to understand students' thinking through the analysis of different kinds of data such as student work and classroom observation. Instructional implications are also considered from the perspective of an understanding of how algebraic thinking develops. This material is a self-study guide and offers the following: (1) hands-on investigation, discussion, and reflection aimed at a deeper understanding of algebraic thinking; (2) language for talking and thinking about algebraic thinking; (3) structured approaches to gathering and analyzing data about students' mathematical thinking; (4) structured approaches to discussion among teachers about mathematics, student thinking, and other issues related to teachers' practice; and (5) mathematics problems that both elicit and develop algebraic thinking. (KHR) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Algebra; Educational Strategies; Mathematics Activities; Mathematics Instruction; Professional Development; Secondary Education; Teacher Education

Abstract:
This book was written as a resource for middle and high school teachers hoping to ease their students' transition to algebra. Drawing on experiences with three professional development programs, key "habits of thinking" that characterize the successful learning and use of algebra are outlined. Strategies teachers can use to cultivate these habits of thinking and guidelines for assessing students' development are presented. The book is organized according to the critical challenges algebra teachers face such as: How can they help students build on number sense and arithmetic skills to develop their algebraic thinking? What kinds of questions can foster algebraic thinking? and When is it best to use them? Excerpts from discussions among the classroom teachers who participated in the professional development projects are used to place these issues in context. Each chapter also includes activities to encourage teachers to reflect on how they think about algebra and how that thinking informs their practice. There are also samples and analyses of student work to help teachers identify patterns of algebraic thinking along with questions and strategies that can be used to guide and extend students' thinking. (MM) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Educational Assessment; Elementary Secondary Education; Evaluation Criteria; Evaluation Methods; Mathematics Activities; Mathematics Education; Problem Solving

Abstract:
Increased attention has been given to issues of assessment in recent years. Teachers of mathematics have been working to change both the way they elicit evidence of their students' mathematical thinking and the way they use that evidence to monitor students' progress and guide instructional decision making. This publication is based on work done with teachers and administrators in the Classroom Assessment in Mathematics network and the Assessment Communities of Teachers project. This book presents guidelines for designing and facilitating these investigations. Emphasis is placed on experiencing a task, observing problem solving, examining students' work, developing tasks, developing rubrics, and planning assessment. Half of the text is comprised of appendices. (Contains 35 references and resources.) (ASK) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Alternative Assessment; Mathematics Education; Mathematics Instruction; Misconceptions; Secondary Education; Secondary School Mathematics; Student Evaluation

Abstract:
Discusses the integration of assessment into instruction using a four-step framework: planning the activity, gathering evidence, interpreting evidence, and using evidence. (MKR)

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Descriptors:
Computer Assisted Instruction; Core Curriculum; Demonstration Programs; Educational Quality; Elementary School Students; Elementary Secondary Education; Equal Education; Females; Instructional Innovation; Learning Strategies; Mathematics Curriculum; Mathematics Instruction; Mathematics Teachers; Microcomputers; Minority Group Children; Multicultural Education; Secondary School Students; Teacher Education

Abstract:
The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together to give mathematics teachers the opportunity to recount their stories of success in achieving that goal. The 17 chapters in this book describe programs that range from minimal to revolutionary efforts to widen the participation and success of students from underrepresented groups. This book is divided into four parts. Part 1 contains 4 articles taking a global view at reaching students: (1) "Introduction. Reaching all students: A vision of learning mathematics" (L. Stiff); (2) "If everybody counts, why do so few survive?" (Z. Usiskin); (3) "Educators and parents working together to help all students live up to their dreams with mathematics" (N. Bezuk, B. Armstrong, A. Ellis, F. Holmes, and L. Sowder); and (4) "Multicultural mathematics: One road to the goal of mathematics for all" (C. Zaslavsky). Part 2 contains four articles on changing what students learn: (5) "Equation for success: Project SEED" (S. Phillips and H. Ebrahimi); (6) "The Mathematics and Science Microcomputer Project: A model for success" (H. Johnson and J. Leonard); (7) "Blending equity and excellence: UMTYMP's efforts to reach all students" (H. Keynes); and (8) "Algebra Transition Project: A work in progress" (S. Stetzer). Part 3 contains 5 articles on changing how teachers teach: (9) "Mathematics Specialist-Teacher Program: An intervention strategy for all" (V. Camerlengo); (10) "Meeting the NCTM communication standards for all students" (F. Santiago and G. Spanos); (11) "Geometry for all students: Phase-based instruction" (J. Bobango); (12) "Females, minorities, and the physically handicapped in mathematics and science: A model program" (C. Heid and T. Jump); and (13) "Helping inner-city girls succeed: The METRO Achievement Program (D. Thompson and N. Jakucyn). Part 4 contains 4 articles on changing how students learn: (14) "Homogenized is only better for milk" (E. Davidson and J. Hammerman); (15) "They can learn" (N. MacDowell); (16) "Using children's word-problem compositions for problem-solving instruction: A way to reach all children with mathematics" (H. Bebout); and (17) "Equity? We're just trying to survive here" (C. Healy). (MDH) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Curriculum; Demonstration Programs; Elementary Secondary Education; Mathematics Curriculum; Mathematics Education; Mathematics Instruction

Abstract:
This report discusses the change in mathematics curriculum influenced by researchers, society, and the mathematics field. Many research results suggest that students should learn mathematics by experience. Students' misconceptions may be formed because of the sudden shift from arithmetic to algebra. Up to the eighth grade, mathematical content has been heavily repeated. For more of the active doing of mathematics, four common activities (abstracting, inventing, proving, and applying) and four processes (generalizing, conjecturing, convincing, and specializing) are recommended. The curriculum standards developed by the National Council of Teachers of Mathematics, the curriculum framework developed by the National Academy of Sciences, some projects sponsored by the National Science Foundation, the University of Chicago School Mathematics Project, and other projects are described. Constraints against curricular change are listed and teacher collaboration is emphasized as accessary to obtain change in mathematics curriculum. Six schools selected as exemplary programs are introduced. Addresses of five mathematics curriculum projects and project directors involved in the Urban Mathematics Collaborative project are listed. (YP) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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