Young Mathematicians at Work Constructing Fractions, Decimals, and Percents

ISBN-10: 0325003556

ISBN-13: 9780325003559

Edition: 2002

Authors: Catherine Twomey Fosnot, Maarten Dolk

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Description:

In our efforts to reform mathematics education, we've learned a tremendous amount about young students' strategies and the ways they construct knowledge, without fully understanding how to support such development over time. The Dutch do. So, funded by the National Science Foundation and ExxonMobil, Mathematics in the City was begun, a collaborative inservice project that pooled the best thinking from both countries. In Young Mathematicians at Work, Catherine Fosnot and Maarten Dolk reveal what they learned after several years of intensive study in numerous urban classrooms. In this third volume in a series of three, Fosnot and Dolk focus on how children in grades 5-8 construct their knowledge of fractions, decimals, and percents. Their book: describes and illustrates what it means to do and learn mathematics. contrasts word problems with true problematic situations which support and enhance investigation and inquiry. provides strategies to help teachers turn their classrooms into math workshops. explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies. defines and gives examples of modeling, noting the importance of context. discusses calculation using number sense and the role of algorithms in computation instruction. describes how to strengthen performance and portfolio assessment. focuses on teachers as learners by encouraging them to see themselves as mathematicians.
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Book details

List price: $31.88
Copyright year: 2002
Publisher: Heinemann
Publication date: 3/26/2002
Binding: Paperback
Pages: 192
Size: 7.75" wide x 9.00" long x 0.25" tall
Weight: 1.100
Language: English

Catherine Twomey Fosnot is the Founding Director of Mathematics in the City and former Professor of Education at The City College of the City of New York. She has twice received the "best writing" award from AERA's Constructivist SIG and she was the recipient of the "young scholar" award by Educational Communication and Technology Journal. She is the lead author of the Contexts for Learning Mathematics series as well as the Young Mathematicians at Work series.

Maarten Dolk is a researcher and developer at the Freudenthal Institute for science and mathematics education in the Netherlands. He is involved in the development and research of in-service and multimedia in-service materials for teachers, staff developers, and teacher educators in a number of countries. He has been a collaborating partner in Mathematics in the City since its inception and is co-author of the first three books in the Young Mathematicians at Work series.

Acknowledgments
Preface
About This Book
"Mathematics" or "Mathematizing"?
Learning and Teaching in the Classroom
What Is Revealed
Back to the Classroom
Teaching and Learning as Development
The Math Congress
What Is Revealed
Strategies, Big Ideas, and Models in a Teaching/Learning Framework
Strategies as Schemes
Big Ideas as Structures
Models as Tools for Thought
Walking the Edge
Summing Up ...
The Landscape of Learning
Describing the Journey
Linear Frameworks
Learning Trajectories
The Role of Context
Word Problems vs. Truly Problematic Situations
Finding Situations for Mathematizing
Building in Constraints
Open vs. Closed Situations
Word Problems vs. Context Problems
Context-Based Investigations and Inquiries
Turning Classrooms into Mathematical Communities
The Edge Between the Individual and the Community
Facilitating Dialogue
Structuring Math Workshop
Investigations
Math Congress
Minilessons
Summing Up ...
Equivalence on the Horizon
Fair Sharing: The Historical Roots of Equivalence
Early Number Systems
Unit Fractions
Measurement Contexts
Sexagesimals
The Rise of Common Fractions
The Rise of Decimal Fractions
Expanding Commercial Markets as a Context
Children's Strategies for Equivalence
Math Congress
Extending Equivalence to Decimals and Percents
Summing Up ...
Developing Big Ideas and Strategies
Big Ideas on the Horizon
Part/Whole Relation
Equivalency vs. Congruency
Connecting Multiplication and Division to Fractions
The Whole Matters: Making Things Equivalent
Relations on Relations
Decimals and Percentage Equivalents
Place Value
Strategies on the Horizon
Summing Up ...
Developing Mathematical Models
What Are Mathematical Models?
Modeling Actions and Situations
Facilitating the Development of Modeling: The Role of Context
Partitive and Quotative Models
Generalizing the Models, Generalizing the Operations
From Models of Thinking to Models for Thinking
Ratio Tables
Double Number Line
Double Number Line and Percentages
The Clock
Arrays
Summing Up ...
Algorithms Versus Number Sense
The History of Algorithms
Teaching for Number Sense
Summing Up ...
Developing Efficient Computation with Minilessons
Minilessons with Mental Math Strings
Choosing the Strategies, Choosing the Numbers, Choosing the Models
Finding a Familiar, Landmark Whole
Choosing a Common Whole
Multiplying Numerators and Denominators
Swapping Numerators and Denominators
Getting Rid of the Fraction
Developing Strategies for Computation with Decimals
Using Money
Using Fractions and Decimals Interchangeably
Summing Up ...
Assessment
Performance-Based Evaluation and Assessment
Portfolio-Based Documentation
Assessing Mathematizing
Capturing Genuine Mathematizing
Linking Contexts to Reality
Providing for Various Levels of Mathematizing
Informing Teaching
Assessment in Reformed Classrooms
Assessing the Landscape of Learning
Assessing in the Moment
Portfolio Assessment
Paper-and-Pencil Assessments
Assessment Results
Mathematizing vs. Traditional Instruction
Standardized Tests
Summing Up ...
Teachers As Mathematicians
Teacher Preparation
Learning to Mathematize
Exploring the Edge
Formulating a Vision
Living in a Mathematical World
Summing Up ...
References
Index
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