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Unpacking fractions [electronic resource] : classroom-tested strategies to build students' mathematical understanding

Unpacking fractions [electronic resource] : classroom-tested strategies to build students' mathematical understanding

Material type
E-Book(소장)
Personal Author
Neagoy, Monica.
Title Statement
Unpacking fractions [electronic resource] : classroom-tested strategies to build students' mathematical understanding / Monica Neagoy.
Publication, Distribution, etc
Alexandria, Virginia :   ASCD/National Council of Teachers of Mathematics,   c2017.  
Physical Medium
1 online resource (xii, 286 p.).
ISBN
9781416621256 (electronic bk.) 1416621253 (electronic bk.) 9781416621263 1416621261 9781416621232 (pbk.)
요약
Monica Neagoy draws on decades of research and experience to address seven big ideas in the teaching and learning of fractions in grades 2-6.
General Note
Title from e-Book title page.  
Content Notes
Introduction : the challenge of fractions -- Convey the many meanings of a/b -- Use visual and tactile models -- Focus on the unit -- Teach the concept of equivalence (not just the rule) -- Compare and order fractions meaningfully -- Let algorithms emerge naturally -- Connect fractions and decimals -- Conclusion : moving from rote to reason.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Fractions --Study and teaching (Elementary). Fractions --Study and teaching (Middle school). Fractions --Study and teaching (Secondary).
Short cut
URL
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100 1 ▼a Neagoy, Monica.
245 1 0 ▼a Unpacking fractions ▼h [electronic resource] : ▼b classroom-tested strategies to build students' mathematical understanding / ▼c Monica Neagoy.
260 ▼a Alexandria, Virginia : ▼b ASCD/National Council of Teachers of Mathematics, ▼c c2017.
300 ▼a 1 online resource (xii, 286 p.).
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a Introduction : the challenge of fractions -- Convey the many meanings of a/b -- Use visual and tactile models -- Focus on the unit -- Teach the concept of equivalence (not just the rule) -- Compare and order fractions meaningfully -- Let algorithms emerge naturally -- Connect fractions and decimals -- Conclusion : moving from rote to reason.
520 ▼a Monica Neagoy draws on decades of research and experience to address seven big ideas in the teaching and learning of fractions in grades 2-6.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Fractions ▼x Study and teaching (Elementary).
650 0 ▼a Fractions ▼x Study and teaching (Middle school).
650 0 ▼a Fractions ▼x Study and teaching (Secondary).
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1485404
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 372.72 Accession No. E14006057 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

Intro -- Foreword -- Introduction—The Challenge of Fractions -- Appreciate the Fraction Challenge -- From Natural Numbers to Real Numbers -- A Word on the Word Fraction -- Cognitive Shifts to Consider -- The Rush to Algorithms -- What Can You Expect from This Book? -- CHAPTER 1—Convey the Many Meanings of a/b -- Roberto’s Story -- Recognizing Misconceptions -- Limited Ideas About the Meaning of a Fraction -- Difficulty Conceptualizing a Fraction as a Single Number -- Unpacking the Mathematical Thinking -- The Part-Whole Meaning of a/b -- The Measure Meaning of a/b -- The Quotient Meaning of a/b -- The Ratio Meaning of a/b -- The Multiplicative Operator Meaning of a/b -- The Rational Number Meaning of a/b Embodied by the Number Line -- Targeting Misconceptions with Challenging Problems -- CHAPTER 2—Use Visual and Tactile Models -- Maya’s Story -- Beyond Misconceptions of Fractions -- Limited Repertoire of Fraction Models -- Lack of Connectedness Among Models -- Unpacking the Mathematical Thinking -- Continuous Models -- Discrete Models -- Discussing and Connecting Models -- Targeting Misconceptions with Challenging Problems -- Maya’s Story, Part 2 -- Recognizing Misconceptions -- The Parts Need Not Be Equal -- The Parts Must Be Clearly Delineated -- The Parts Must Have the Same Shape -- The Shaded Regions Must Be Grouped into One Part -- Unpacking the Mathematical Thinking -- The Importance of Equal Parts -- Area, Not Shape, Is the Focus -- Targeting Misconceptions with Challenging Problems -- Maya’s Story: Epilogue -- CHAPTER 3—Focus on the Unit -- Ed’s Story -- Recognizing Misconceptions -- The Whole Is Made of One Piece -- A Fraction Is Smaller Than the Whole, the Unit, or the “1” -- Difficulty Conceiving of or Writing Fractions Greater Than 1 -- Limited Experience with Non-continuous Units -- Unpacking the Mathematical Thinking -- The Unit Is Defining -- Working with a Variety of Units -- Revisiting the Partition and Iteration Process -- Targeting Misconceptions with Challenging Problems -- Two Vignettes -- Linda’s Story -- Jason’s Story -- Recognizing Misconceptions -- Difficulty Going from Part to Whole -- Difficulty Discriminating Between What Is Relevant and What Is Not -- Unpacking the Mathematical Thinking -- A Fraction Is a Relation Between Two Quantities -- Proceeding from Part to Whole -- Infusing Problems with Distractors: Trapping or Stimulating Students? -- Targeting Misconceptions with Challenging Problems -- A Final Note -- CHAPTER 4—Teach the Concept of Equivalence (Not Just the Rule) -- Lisa’s Story -- Recognizing Misconceptions -- Different Fraction Names for the Same Quantity or Number -- Overreliance on Physical Models (3rd Grade and Up) -- Difficulty with Discrete Quantities (3rd Grade and Up) -- Limited Concept of the Equals Sign (4th Grade and Up) -- Rote Application of a/b = (n × a)/(n × b) (4th Grade and Up) -- The Misuse of Language (All Grades) -- A Partial View of the EFA (5th Grade and Up) -- Additive Thinking -- Un.
packing the Mathematical Thinking -- Build on Students’ Informal Experiences with Equivalence -- Cultivate the Equivalence Meaning of Equality -- Explain Equivalence by Connecting Fractions to Multiplication and Division -- Begin with Equal-Sharing Problem Situations -- Model Equivalence Using Different Interpretations of Fractions -- Be Mindful That Models Lead to Concept Building -- Targeting Misconceptions with Challenging Problems -- CHAPTER 5—Compare and Order Fractions Meaningfully -- Nicole’s Story -- Recognizing Misconceptions -- Overreliance on Ready-Made Models -- Difficulty Comparing Fractions Without the Common Algorithm -- Lack of Attention to the Unit -- Inappropriate Whole-Number Reasoning -- Predominance of Additive Thinking -- Unpacking the Mathematical Thinking -- Using Models -- Reasoning with Unit Fractions -- Using the Concept of Equivalence (Common Denominators or Numerators) -- Comparing to Benchmarks -- Using Multiplicative Thinking -- Noticing Patterns -- Looking Ahead: Visualizing the “Cross-Product” Method -- Targeting Misconceptions with Challenging Problems -- CHAPTER 6—Let Algorithms Emerge Naturally -- Vignette 1: Division of a Whole Number by a Fraction -- Vignette 2: Multiplication of a Whole Number by a Fraction -- Recognizing Misconceptions -- Difficulty Seeing Fractions as Numbers -- Rote or Incorrect Application of Algorithms -- Knowing Fractions Means Knowing the Algorithms -- Lack of Fraction Operation Sense -- False Beliefs About the Effects of Operations on Numbers or Quantities -- Lack of Attention to the Unit -- Unpacking the Mathematical Thinking -- Begin with Problem Situations That Students Can Tackle -- Allow Students to Devise Their Own Algorithms -- Revisit Meanings of Addition and Subtraction -- Revisit Meanings of Multiplication and Division -- Emphasize That Relationships and Properties Still Hold -- Highlight Important Changes in Ways of Thinking -- Targeting Misconceptions with Challenging Problems -- CHAPTER 7—Connect Fractions and Decimals -- Denis’s Story -- Recognizing Misconceptions -- Scarce Contact with Decimals in Daily Life -- Lack of Connectedness Between Fractions and Decimals -- Difficulty with Symbol Meaning -- Overreliance on the Money Model -- Poor Understanding of Decimal Magnitude -- Rote or Incorrect Application of Decimal Algorithms -- Unpacking the Mathematical Thinking -- Extending Place Value to Tenths and Hundredths -- The Models We Use Are Important -- Comparing Decimals Meaningfully -- Importance of the Unit -- Sensing Approximate Values -- Making Sense of Operations -- Targeting Misconceptions with Challenging Problems -- CONCLUSION—Moving from Rote to Reason -- Foster These Seven Habits of Mind -- Teach Meanings First, Algorithms Last -- Look Ahead to Ratios, Proportions, Proportional Relations, and Linear Functions -- From Fractions to Ratios -- From Ratios to Proportions -- From Proportions to Proportional Relationships -- From Proportional Relationships to Linear .
Functions -- Concluding Thoughts -- References -- Index -- About the Author -- .

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