Heinemann | 2010 | 200 páginas | mobi | 4,3 Mb
"In this wonderfully insightful book, Honi, Christine, and Karren not only describe a vast array of perfectly understandable mathematical misconceptions that students have across the elementary curriculum, they also provide numerous practical instructional strategies and activities for helping remediate and "undo" the misconceptions. The classroom vignettes they describe will ring true to everyone who has tried to teach mathematics to young, and not-so-young, children."
-Steven Leinwand
- identifying the most common errors relative to the five NCTM content strands (number and operations, algebra, geometry, measurement, and data analysis and probability)
- investigating the source of these misunderstandings
- proposing ways to avoid as well as "undo" misconceptions.
Children enter school filled with all kinds of ideas about numbers, shapes, measuring tools, time, and money-ideas formed from the expressions they hear...the things they see on television...the computer screen...in children's books...all around them. It's no wonder some children develop very interesting and perhaps incorrect ideas about mathematical concepts.
"How can we connect the informal knowledge that students bring to our classrooms with the mathematics program adopted by our school system? Just as important, how do we ensure that the mathematics we are introducing and reinforcing is accurate and will not need to be re-taught in later years?"
Math Misconceptions answers these questions by:
Using classroom vignettes that highlight common misconceptions in each content area, followed by applicable research about the root causes of the confusion, the authors offer numerous instructional ideas and interventions designed to prevent or correct the misconception.
Untangle your students' math misconceptions. This practical resource will help make it all make sense, and raise math achievement in your classroom.
Foreword .v
Acknowledgments . .ix
Introduction . . .xi
Counting with Number Words 2
Thinking Addition Means “Join Together” and Subtraction Means “Take Away” 7
Renaming and Regrouping When Adding and Subtracting Two-Digit Numbers 13
Misapplying Addition and Subtraction Strategies to Multiplication and Division 20
Multiplying Two-Digit Factors by Two-Digit Factors 24
Understanding the Division Algorithm 29
Understanding Fractions 34
Adding and Subtracting Fractions 40
Representing, Ordering, and Adding/Subtracting Decimals 43
Understanding Patterns 50
Meaning of Equals 55
Identifying Functional Relationships 61
Interpreting Variables 66
Algebraic Representations 71
CHAPTER 3 Geometry . . .78
Categorizing Two-Dimensional Shapes 78
Naming Three-Dimensional Figures 84
Navigating Coordinate Geometry 88
Applying Reflection 95
Solving Spatial Problems 100
CHAPTER 4 Measurement .108
Reading an Analog Clock 108
Determining the Value of Coins 116
Units Versus Numbers 121
Distinguishing Between Area and Perimeter 127
Overgeneralizing Base-Ten Renaming 132
CHAPTER 5 Data Analysis and Probability . . .137
Sorting and Classifying 137
Choosing an Appropriate Display 142
Understanding Terms for Measures of Central Tendency 148
Analyzing Data 152
Probability 158
CHAPTER 6 Assessing Children’s Mathematical Progress . . .164
Assessment: The Received View 164
Assessment from a Better Angle 165
Types of Formative Assessments 166
Why Assess? 170
Final Thoughts 171
References 173
Index ..179
