Ratio and Proportion: Research and Teaching in Mathematics Teachers’ Education

(Pre- and In-Service Mathematics Teachers of Elementary and Middle School Classes)

David Ben-Chaim (The Technion-Israel Institute of Technology, Israel), 
Yaffa Keret (The Open University of Israel, Israel) 
Bat-Sheva Ilany (Beit Berl Academic College, Israel)

Sense Publishers | 2012 | 283 páginas | pdf | 4,7 Mb

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Ratio and Proportion-Research and Teaching in Mathematics Teachers' Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their specific needs. The book reports on hands-on experience in the college classes plus teachers' experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.

TABLE OF CONTENTS
Chapter 1: Introduction ... 1
PART I: STRUCTURE OF BOOK AND TEACHING MODEL 5
Chapter 2: Structure of Book... 7
Chapter 3: A Model for Teaching Ratio and Proportion Using Authentic Investigative Activities .... 13
PART II: THEORETICAL BACKGROUND 21
Chapter 4: A Mathematical Perspective of Ratio and Proportion ... 23
Chapter 5: Proportional reasoning—A psychological-didactical view ... 49
Chapter 6: Research and new approaches in pre- and
in-service mathematics teacher education ... 61
PART III: AUTHENTIC INVESTIGATIVE ACTIVITIES, INCLUDING DIDACTIC COMMENTS AND EXPLANATIONS 71
Chapter 7: Authentic investigative activities— Introduction .. 73
Chapter 8: Group 1: Introductory activities .. 83
Chapter 9: Group 2: Rate activities . 95
Chapter 10: Group 3: Ratio activities .. 125
Chapter 11: Group 4: Stretching and Shrinking: Scaling Activities .. 145
Chapter 12: Group 5: Indirect Proportion Activities ... 181
Chapter 13: Group 6: Additional Activities
for Practice and Enrichment (All topics). 195
PART IV: ASSESSMENT TOOLS 219
Chapter 14: Introduction to Assessment Tools .. 221
Chapter 15: Questionnaire: Attitude Toward Ratio and Proportion .. 225
Chapter 16: Diagnostic Questionnaire in Ratio and Proportion ... 233
Chapter 17: Assessing Research Reports and Building a Student Portfolio . 245
PART V: ANNOTATED RESOURCES AND BIBLIOGRAPHY 253
Chapter 18: Annotated Resources .... 255

Chapter 19: Bibliography ... 269

Second Handbook of Research on Mathematics Teaching and Learning

Frank K. Jr. Lester

Information Age Publishing | 2007 | 1381 páginas | rar - pdf | 11,4 Mb

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The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.

Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community. 

CONTENTS

Preface. 
Acknowledgements.
Part I: Foundations. 
Putting Philosophy to Work: Coping With Multiple Theoretical Perspectives, Paul Cobb.
Theory in Mathematics Education Scholarship, Edward A. Silver & Patricio G. Herbst
Method, Alan H. Schoenfeld. 
Part II: Teachers and Teaching. 
Assessing Teachers' Mathematical Knowledge: What Knowledge Matters and What Evidence Counts? Heather C. Hill, Laurie Sleep, Jennifer M. Lewis, & Deborah Loewenberg Ball. 
The Mathematical Education and Development of Teachers, Judith T. Sowder.
Understanding Teaching and Classroom Practice in Mathematics, Megan Loef Franke, Elham Kazemi and Daniel Battey. 
Mathematics Teachers' Beliefs and Affect, Randolph A. Philipp. 
Part III: Influences on Student Outcomes. 
How Curriculum Influences Student Learning, Mary Kay Stein, Janine Remillard and Margaret Smith. 
The Effects of Classroom Mathematics Teaching on Students' Learning, James S. Hiebert and Douglas A. Grouws. 
Culture, Race, Power, and Mathematics Education, Diversity in Mathematics Education Center for Learning and Teaching. 
The Role of Culture in Teaching and Learning Mathematics, Norma G. Presmeg. 
Part IV: Students and Learning. 
Early Childhood Mathematics Learning, Douglas H. Clements and Julie Sarama. 
Whole Number Concepts and Operations, Lieven Verschaffel, Brian Greer, and Erik DeCorte.
Rational Numbers and Proportional Reasoning: Toward a Theoretical Framework for Research, Susan J. Lamon. Early Algebra, David W. Carraher and Analucia D. Schliemann. 
Learning and Teaching of Algebra at the Middle School through College Levels: Building Meaning for Symbols and Their Manipulation, Carolyn Kieran. 
Problem Solving and Modeling, Richard Lesh and Judith Zawejewski. 
Toward Comprehensive Perspectives on the Learning and Teaching of Proof, Guershon Harel and Larry Sowder. 
The Development of Geometric and Spatial Thinking, Michael T. Battista. 
Research in Probability: Responding to Classroom Realities, Graham A. Jones, Cynthia W. Langrall and Edward S. Mooney. 
Research on Statistics Learning and Reasoning, J. Michael Shaughnessy. 
Mathematics Thinking and Learning at Post-secondary Level, Michele Artigue, Carmen Batanero and Phillip Kent. 
Part V: Assessment. 
Keeping Learning on Track: Classroom Assessment and the Regulation of Learning, Dylan Wiliam. 
High Stakes Testing in Mathematics, Linda Dager Wilson. 
Large-scale Assessment of Mathematics Education, Jan DeLange. 
Part VI: Issues and Perspectives. 
Issues in Access and Equity in Mathematics Education, Alan J. Bishop and Helen J. Forgasz. 
Research on Technology in Mathematics Education: The Perspective of Constructs, Rose Mary Zbiek, M. Kathleen Heid, Glendon Blume and Thomas P. Dick. 
Engineering Change in Mathematics Education: Research, Policy, and Practice, William F. Tate and Celia Rousseau. 
Educational Policy Research and Mathematics Education, Joan Ferrini-Mundy & Robert Floden. 
Mathematics Content Specification in the Age of Assessment, Norman L. Webb. 
Reflections on the State and Trends in Research on Mathematics Teaching and Learning: From Here to Utopia, Mogens Niss.

Percents and Ratios

(Math Success)
Lucille Caron, Philip M. St. Jacques

Enslow Publishers | 2000 | 64 páginas | rar -pdf | 1,9 Mb

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Improving Instruction in Rational Numbers and Proportionality

(Using Cases to Transform Mathematics Teaching and Learning, Vol 1)
Margaret Schwan Smith, Edward A. Silver, e Mary Kay Stein


Teachers College Press | 2005 | 140 páginas  | PDF | 1,5 MB


p4mriunpat.files.wordpress.com (link direto)
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referência em: te-mat

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. 

Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features: 
* Cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction. 
* The teachers’ perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content. 
* Cognitively challenging mathematics activities that are built around samples of authentic classroom practice. 
* Facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacher’s own practice. 

As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

The Illusion of Linearity: From Analysis to Improvement

Mathematics Education Library , Vol. 41

Dirk De Bock, Wim Van Dooren, Dirk Janssens, Lieven Verschaffel

Springer | 2007 |   186 páginas | PDF | 845 kb

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Referência em: MathEduc

Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students have a strong tendency to apply the linear model also in situations wherein it is not applicable. This overgeneralization of linearity is sometimes referred to as the "illusion of linearity" and has a strong negative impact on students’ reasoning and problem solving skills.

"The Illusion of Linearity: From Analysis to Improvement" presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. Although the empirical study of students’ improper linear reasoning clearly constitutes a new line of research, it owes a great deal to prior work in mathematics education research community such as the work of the scholars of the Freudenthal Institute on realistic mathematics education.

Based on both quantitative and qualitative research, "The Illusion of Linearity: From Analysis to Improvement" discusses the following issues: (1) how the illusion of linearity appears in diverse domains of mathematics and science and how it is conceptually related to other more general misconceptions identified in the research literature, (2) what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon, and (3) how the illusion of linearity can be remedied by appropriate instruction.

"The Illusion of Linearity: From Analysis to Improvement" is essential to those working in mathematics education, particularly teacher educators and curriculum research and development.