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Book Cover
E-book
Author Lamon, Susan J., 1949-

Title Teaching fractions and ratios for understanding : essential content knowledge and instructional strategies for teachers / Susan J. Lamon
Edition 2nd ed
Published Mahwah, N.J. : Lawrence Erlbaum Associates, 2006

Copies

Description 1 online resource (xvi, 237 pages) : illustrations
Contents 1. Fractions and proportional reasoning : an overview -- 2. Fractions and rational numbers -- 3. Relative and absolute thinking -- 4. Measurement -- 5. Quantities and covariation -- 6. Reasoning up and down -- 7. Unitizing -- 8. Sharing and comparing -- 9. Proportional reasoning -- 10. Reasoning with fractions -- 11. Part-whole comparisons with unitizing -- 12. Partitioning and quotients -- 13. Rational numbers as operators -- 14. Rational numbers as measures -- 15. Ratios and rates -- 16. Distance-rate-time relationships -- 17. Similarity and percents -- 18. Changing fraction instruction
1. Proportional Reasoning: An Overview -- Student Strategies -- Introduction -- The Constant of Proportionality -- Reasoning: Beyond Mechanization -- Invariance and Covariance -- Solving Proportions Using k -- Multiplicative Thinking -- Critical Components of Powerful Reasoning -- Getting Started -- Analyzing Children's Thinking -- Activities -- 2. Fractions and Rational Numbers -- Student Strategies -- New Units and a New Notational System
The Compensatory PrincipleThe Approximation Principle -- Recursive Partitioning Principle -- Measuring More Abstract Qualities -- Other Strategies -- Activities -- 4. Quantities and Covariation -- Student Strategies -- Building on Children's Informal Knowledge -- Quantities Unquantified -- Quantifiable Characteristics -- Discussing Proportional Relationships in Pictures -- Visualizing, Verbalizing, and Symbolizing Changing Relationships -- Covariation and Invariance -- Cuisenaire Strips -- Scale Factors -- Similarity -- Indirect Measurement -- Testing for Similarity -- Mockups and Pudgy People -- Activities
5. Proportional ReasoningStudent Strategies -- The Unit -- Unit s. Defined Implicitly -- Using Units of Various Types -- Reasoning Up and Down -- Unit s. and Unitizing -- Unit izing. Notation -- Flexibility in Unitizing -- Children's Thinking -- Classroom Activities to Encourage Unitizing -- Visual Activities -- Reasoning with Ratio Tables -- Problem Types -- Ratio Tables -- Increasing the Difficulty -- Analyzing Relationships -- Percent -- Percents as an Instructional Task -- Reasoning with Percents -- Activities -- 6. Reasoning with Fractions -- Student Strategies -- Visualizing Operations
Equivalent Fractions and UnitizingComparing Fractions -- Fractions in Between -- Activities -- 7. Fractions as Part-Whole Comparisons -- Student Strategies -- Part-Whole Fractions: The Big Ideas -- Unit izing. and Equivalence -- Problems in Current Instruction -- Fraction Models -- Fraction Strips -- Comparing Part-Whole Fractions -- Discrete Units -- Multiplication -- Part itive. and Quotative Division -- Division -- Other Rational Number Interpretations -- Activities -- 8. Fractions as Quotients -- Quotients -- Part itioning. as Fair Sharing -- Part itioning. Activities -- Children's Partitioning -- Equivalence
Should We Reduce
Summary This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking - without falling back on rules and procedures they have relied on throughout their lives. Written in a conversational and easy to underst
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Fractions -- Study and teaching (Elementary)
Ratio and proportion -- Study and teaching (Elementary)
EDUCATION -- Teaching Methods & Materials -- Mathematics.
Fractions -- Study and teaching (Elementary)
Ratio and proportion -- Study and teaching (Elementary)
Form Electronic book
ISBN 1410617130
9781410617132
9780805852103
0805852107
9781135606732
1135606730
9781135606770
1135606773
9781135606787
1135606781