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Pub Date: |
2010-09-00 |
Pub Type(s): |
Guides - Classroom - Teacher; Reports - Descriptive |
Peer Reviewed: |
Yes |
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Descriptors:
Mathematics; Problem Solving; Young Children; Elementary Education; Instructional Effectiveness; Educational Practices; Guides; Mathematical Concepts; Comprehension; Cognitive Processes
Abstract:
This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and computations that involve fractions; to proposals intended to help students apply their understanding of fractions to solve problems involving ratios, rates, and proportions. Improving students' learning about fractions will require teachers' mastery of the subject and their ability to help students master it; therefore, a recommendation regarding teacher education also is included. Appendices include: (1) Postscript from the Institute of Education Sciences; (2) About the Authors; (3) Disclosure of Potential Conflicts of Interest; (4) Rationale for Evidence Ratings; and (5) Evidence Heuristic. A glossary and index are also provided. (Contains 5 tables, 10 figures, and 250 endnotes.)
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Pub Date: |
2005-00-00 |
Pub Type(s): |
Books; Collected Works - General |
Peer Reviewed: |
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Descriptors:
Teaching Methods; Science Instruction; Mathematics Instruction; Mathematics Education; Faculty Development; Instructional Design; Educational Change; Educational Research; Learning Strategies; Teacher Role; Evaluation Methods; Student Evaluation; Academic Standards; Knowledge Level; Thinking Skills; Elementary School Mathematics; Secondary School Mathematics; Comprehension; Teacher Collaboration; Mathematical Concepts; Scientific Concepts; Elementary School Science; Secondary School Science
Abstract:
The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics and Science--established in 1996 as a research center and funded by the U.S. Department of Education--was instrumental in developing instructional practices supportive of high student achievement in and understanding of mathematics and science concepts. NCISLA researchers worked with teachers, students, and administrators to construct learning environments that exemplify current research and theory about effective learning of mathematics and science. The careful programs of research conducted examined how instructional content and design, assessment, professional development, and organizational support can be designed, implemented, and orchestrated to support the learning of all students. This book presents a summary of the concepts, findings, and conclusions of the Center's research from 1996-2001. In the Introduction, the chapters in this book are situated in terms of the reform movement in school mathematics and school science. Three thematically structured sections focus on, respectively, research directed toward what is involved when students learn mathematics and science with understanding; research on the role of teachers and the problems they face when attempting to teach their students mathematics and science with understanding; and a collaboration among some of the contributors to this volume to gather information about classroom assessment practices and organizational support for reform. Following a preface, this book is divided into four parts. Part I, Introduction, presents the initial chapter of the book: (1) Standards-Based Reform and Teaching for Understanding (T. A. Romberg, T.P. Carpenter, and J. Kwako). Part II, Learning with Understanding, includes: (2) Developing Modeling and Argument in the Elementary Grades (R. Lehrer and L. Schauble); (3) The Generative Potential of Students' Everyday Knowledge in Learning Science (A. S. Rosebery, B. Warren, C. Ballenger, and A. Ogonowski); (4) Developing Algebraic Reasoning in the Elementary School (T. P. Carpenter, L. Levi, P. W. Berman, and M. Pligge); (5) A Teacher-Centered Approach to Algebrafying Elementary Mathematics (J. J. Kaput and M. L. Blanton); (6) Statistical Data Analysis: A Tool for Learning (K. McCain, P. Cobb, and K. Gravemeijer); (7) Modeling for Understanding in Science Education (J. Stewart, C. Passmore, J. Cartier, J. Rudolph, and S. Donovan); (8) Learning Mathematics in High School: Symbolic Places and Family Resemblances (R. Nemirovsky, A. Barros, T. Noble, M. Schnepp, and J. Solomon). Part III, Teaching for Understanding (M. Franke and E. Kazemi) includes: (9) Changing Teachers' Professional Work in Mathematics: One School's Journey (J. Shih, S. Biagetti, and D. Battey); (10) Teacher Collaboration: Focusing on Problems of Practice (D. C. Webb, T. A. Romberg, M. J. Ford, and J. Burrill); and (11) Managing Uncertainty and Creating Technical Knowledge (W. G. Secada and T. Williams). Part IV, Cross-Cutting Studies, includes the final chapters: (12) Research in Assessment Practices (J. de Lange and T. A. Romberg); and (13) Capacity for Change: Organizational Support for Teaching for Understanding (A. Gamoran).
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Pub Date: |
2004-09-00 |
Pub Type(s): |
Journal Articles; Reports - Descriptive |
Peer Reviewed: |
Yes |
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Descriptors:
Inquiry; Educational Change; Case Studies; Mathematics Teachers; Teaching Methods; Teacher Student Relationship; Mathematics Instruction; Mathematics Skills; Children; Thinking Skills; Cognitive Processes
Abstract:
In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's engagement with children's thinking changed dramatically in a period of only a few months; observations and interviews several years later confirm she sustained this change. Our analysis focuses on the mathematical discussions she had with her students, and suggests this talk with children about their thinking in instruction served both as an index of change, and, in combination with other factors, as a mechanism for change. We identified four phases in Ms. Statz's growth toward practical inquiry, distinguished by her use of interactive talk with children. Motivating the evolution of phases were two sorts of mechanisms: scaffolded examination of her students' thinking; and asking and answering questions about individual students' thinking. Processes for generating and testing knowledge about children's thinking ultimately became integrated into Ms. Statz's instructional practices as she created opportunities for herself, and then students, to hear and respond to children's thinking.
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Pub Date: |
2003-00-00 |
Pub Type(s): |
Books; Reports - Descriptive |
Peer Reviewed: |
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Descriptors:
Algebra; Arithmetic; Elementary Education; Mathematics Activities; Mathematics Instruction; Problem Solving; Teaching Methods; Thinking Skills
Abstract:
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what problems and questions help elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students. Teacher Commentaries captures the voices of a number of teachers providing realistic portrayals of what happens in class. The Challenge offers a variety of problems and activities for teachers to increase their own knowledge of mathematics and help their students develop algebraic thinking. The accompanying CD provides rich illustrations of ideas in the book clearly linked to the text. (KHR)
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Pub Date: |
2000-09-00 |
Pub Type(s): |
Reports - Descriptive |
Peer Reviewed: |
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Descriptors:
Academic Achievement; Elementary Education; Faculty Development; Mathematics Education; Teacher Attitudes; Teacher Education
Abstract:
This paper describes a research-based teacher professional development program for elementary school mathematics and includes an overview of cognitively guided instruction (CGI). Also described are the CGI professional development program and the research base for CGI with regard to children's thinking; teachers' knowledge and beliefs about children's thinking and the relation of teachers' knowledge and beliefs to their student's achievement; the effect of the CGI professional development program on teachers' knowledge, beliefs, and practice; and the achievement of students in CGI classes. (Contains 27 references.) (MM)
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Pub Date: |
2000-10-00 |
Pub Type(s): |
Reports - Research |
Peer Reviewed: |
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Descriptors:
Algebra; Elementary Education; Mathematics Curriculum; Mathematics Instruction; Thinking Skills
Abstract:
This report describes a research project that investigated how to design instruction to help children take the step to generalizing and formalizing their knowledge into powerful abstract systems for representing and operating mathematical ideas. The studies build on existing research on cognitively guided instruction (CGI). The goal of this paper is to begin to understand how to provide support for children to reflect on their procedures in order to form generalizations from them and construct notations for representing their procedures and generalizations abstractly. The conclusion is that overall it appears that students in the primary grades can engage in formulating, representing, and justifying conjectures even though their justifications might not always be sufficient to validate all of the conjectures they are capable of identifying. (Contains 20 references.) (MM)
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Pub Date: |
2000-00-00 |
Pub Type(s): |
Collected Works - Serials; Guides - Non-Classroom; Reports - Descriptive |
Peer Reviewed: |
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Descriptors:
Abstract Reasoning; Algebra; Arithmetic; Educational Change; Elementary Education; Elementary School Mathematics; Mathematics Instruction; Professional Development; Teaching Methods
Abstract:
"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic in ways that build their capacity for algebraic reasoning. The research summarized in this article shows that with appropriate teacher professional development, teachers can learn to help students learn mathematics in ways that both enhance their understanding of arithmetic and provide a foundation for learning algebra. Teaching and policy considerations for learning algebra in the elementary grades are attached. (ASK)
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