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E-raamat: How the Math Gets Done: Why Parents Don't Need to Worry about New vs. Old Math

  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-Oct-2017
  • Kirjastus: Rowman & Littlefield Publishers
  • Keel: eng
  • ISBN-13: 9781475834246
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-Oct-2017
  • Kirjastus: Rowman & Littlefield Publishers
  • Keel: eng
  • ISBN-13: 9781475834246

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How the Math Gets Done: Why Parents Don't Need to Worry About New vs. Old Math provides a roadmap to understanding what the symbols for math operations (add, subtract, multiply, and divide) really mean, what the clues are to interpret these symbols, and a kind of short story of how they evolved over time. to decipher the enigmatic squiggles of those verbs called operations. How the Math Gets Done: Why Parents Don't Need to Worry About New vs. Old Math compares the old and the new methods for math procedures from a Big Idea perspective by organizing the information in four sections: Definition, Organization, Relationships and Patterns, and Connections. Each section contains three chapters that clarify the issues related to each Big Idea section. The Conclusion offers parents even more hints and guidelines to help their child through this math country of procedures for calculating in math.

Arvustused

How the Math Gets Done is not a quick fix to raise the child's math grade for tomorrows test, but about deciphering the child's thinking and establishing real math understanding for the long haul. Once a kid is in trouble, parents will not feel there is time to immediately get to the bottom of the issues, so they may want to skip around the book to locate the particular topic that is giving their child difficulty. This is the book that will wake parents (and teachers) up to the notion that multiple strategies are helpful and that opportunities for misunderstandings are lying in the path like so many land mines! -- Ann Hammond McCamy, Parent and Assistant Director, Delmont Public Library. Former curriculum writer for Lambert Book House, Education Coordinator at The House of the Seven Gables, and public and private school teacher Oh my goodness, this book is brilliant and so helpful. As an educator and a mother, I can't help thinking that this is a book for everyone not just parents. How the Math Gets Done spotlights and breaks down into understandable nuggets the most intimate mathematical thinking of our children. While illuminating for us their understandings and misunderstandings, it pushes us -the adults- to think our very own understandings in the most non-threatening way, so that we can support our kids.  -- Regine Philippeaux-Pierre, Mother of Two Children, Director, Excellence for All, Boston Public Schools

Foreword xi
Preface xiii
Introduction xv
PART I DEFINITION
1(32)
1 Math According to Jen, Bobby, and Others
3(8)
Jen's Deductions
3(2)
Bobby's Experience with Multiplication and Number Arrangements
5(2)
Children's Descriptions about Making Sense
7(1)
Trevor and Jim Invent Their Own Multiplication Methods
7(1)
Keep in Mind
8(3)
2 Math Grammar of Nouns, Verbs, and Stories
11(12)
"Putting Together" Verbs for Addition and Multiplication
11(2)
"Taking Apart" Verbs for Subtraction and Division
13(3)
A Short Interlude about the Use of That Negative Sign
16(1)
Word Problems Put Math Verbs in Stories
16(6)
Keep in Mind
22(1)
3 The Choice between Two Rs: Rote Memorization or Reasoning
23(10)
Sound Bites That Bite Back
24(3)
Memorization vs. Organization
27(3)
Acronyms: Sense or Nonsense
30(1)
Keep in Mind
30(3)
PART II ORGANIZATION
33(36)
4 In Search of Like Terms: Classification Revisited
35(10)
Like Terms, Common Denominators, and Same Units
35(2)
Place Value Columns Have Like Terms Categories
37(2)
What's Wrong with This Picture?
39(3)
Adding Percentages
42(1)
A Note about Multiplication and Division
42(1)
Keep in Mind
43(2)
5 Artful Assembly of Operations
45(12)
Facts, Frogs, and Formats
45(4)
Jackie's Thinking about Number Operations
49(3)
James, Janie, and Napier's Lattice Multiplication
52(1)
Division Interpretations That Made Sense
53(2)
Keep in Mind
55(2)
6 Same Math, Same Meaning, Different Organization: New vs. Old
57(12)
"If It Ain't Broke, Don't Fix It"
58(1)
Multiplication Organization Sense
59(2)
Digit Alignment Continues
61(2)
Zeke, Jake, and Long Division
63(4)
Keep in Mind
67(2)
PART III RELATIONSHIPS AND PATTERNS
69(28)
7 "Seeing" Math Patterns with Viewfinders
71(10)
Multiplication Table Patterns
72(4)
Addition Table Patterns
76(2)
Kathy's and Rudy's Fraction Viewfinders
78(2)
Keep in Mind
80(1)
8 Spelunking for Patterns with More Viewfinders
81(10)
Reflections on Addition and Multiplication
81(2)
Subtraction, Division, and Missy's Different "Family"
83(3)
A Few Rules of Engagement for Working with Numbers
86(2)
Keep in Mind
88(3)
9 Functions, Predictability, and Balance
91(6)
Predictability and Functions
91(1)
One Answer or Many Answers, Same Balance
92(4)
Keep in Mind
96(1)
PART IV CONNECTIONS
97(34)
10 A Multiplication Area Image for the Ages
99(8)
From Theon to Dienes: A Bridge across the Centuries
100(1)
Same Design for Mixed Numbers, Fractions, and Decimals
101(4)
Visual-Spatial Multiple-Digit Multiplication
105(1)
Keep in Mind
106(1)
11 Ratios, Proportions, and Rate of Change
107(12)
Fractions as Gatekeepers
109(2)
David's Decluttering Fractions 109 Changing Numbers, Changing Locations, and Moving Targets in Proportions
111(5)
Slope as a Rate of Change
116(1)
Keep in Mind
117(2)
12 Algebraic Thinking
119(12)
The Shapes for an Algebra Transition
119(2)
From Multiplication Tables to Coordinate Tables
121(1)
Jill's Graphic Solutions
122(3)
FOIL'ed Again
125(1)
Keep in Mind
125(2)
Conclusion: What Parents Can Do
127(1)
Problem Solving beyond Word Problems
128(1)
Right Tool for the Right Job: A Hard Look at Technology
129(1)
Keep in Mind
130(1)
Glossary 131(4)
References 135(4)
About the Author 139
Catheryne Draper has been learning from her students for over half a century of teaching, supervising the math program in a school district, advising math education at the state level, coaching math in schools, and presenting math workshops for teachers.

She is the author of The Algebra Game, a hands-on multi-deck algebra program in four topics covering Linear Graphs, Quadratic Equations, Conic Sections, and Trig Functions that allows students to work together in cooperative groups, or individually, to identify the algebra relationships and patterns in the each topic and in the organization across the topics. In addition to contributing many published articles, Draper is also the author of Winning the Math Homework Challenge: Insights for Parents To See Math Differently and User-Friendly Math for Parents: Learning and Understanding the Language of Numbers is Key.