Common Mistakes in Teaching Elementary Math-And How to Avoid Them - Liu, Fuchang

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Meet the Author

Preface

Chapter 1 Counting

Counting Shouldn't Start at 0

What Are Tally Marks for?

It May Not Be Fast-The Purpose of Skip-Counting

Our Number System Is Base-Ten, Not Base-Twelve

Chapter 2 Number Properties

A Red Marble Isn't More Than a Blue One

Playing Cards and Dice Aren't Ideal Things to Make Multidigit Numbers With

It's Odd Not to Consider 0 as Even

14 and 37 Don't Belong in the Same List

Chapter 3 Addition

4 + 4 Isn't Simply 8 Bars Put Together

Make Pictorial Representations More Than a Literal Translation

Don't Hop From Square One

You Can't Add Apples and Oranges Together

Chapter 4 Subtraction

Don't Make the Kittens Disappear

Don't Ever Say Subtract the Smaller Number From the Larger One

Neither a Borrower nor a Lender Be-Why We Shouldn't Borrow

Can We Subtract a Larger Number From a Smaller One?

10 + 5 - 8 = 15 - 8: No Way to Make It Simpler?

Chapter 5 Multiplication

The Formidable 169-Cell Multiplication Table

You Must Put a Zero in the Ones Place

Can You Move Over One Place Value?

Line Multiplication: Why It Won't Work

Chapter 6 Division

The Bigger Number Doesn't Always Go Inside

What's 0 ? 0?

Division Isn't Always Repeated Subtraction

Dad, Mom, Sister, Brother, Rover: Where Is Dad?

Divide Doesn't Always Yield a Smaller Number

Chapter 7 The Order of Operations

Aunt Sally Is Evil - The Order of Operations

The Order M/D Before A/S Isn't Haphazard

Are Negative and Subtract Really Different?

Chapter 8 Algebra

An Equal Sign Means Equal

What Does Adding Up Numbers Landed Have to Do With Finding Factors?

Timelines Aren't Good Candidates for Teaching Negative Numbers

The Worst Example in Teaching Exponents

Chapter 9 Geometry: Bits and Pieces

Don't Count the Diagonals on a Grid

All 3-D Shapes Have an Extra Third Dimension of Height

Don't Use Vertical to Find the Horizontal Value

The Two Sides of a Symmetrical Figure Aren't Exactly the Same

Don't Use Tiles to Figure Out the Perimeter

Chapter 10 Geometry: Common Geometric Figures

Length Doesn't Necessarily Mean Longer

A Rectangle's Orientation Doesn't Matter Either

A Rectangle Has Two Longer Sides and Two Shorter Sides

What's Wrong With Saying Triangles, Rectangles, Squares, and Hexagons?

Base Doesn't Necessarily Mean Side at Bottom

Three Sides Don't Necessarily Make a Triangle

How Many Sides Does a Circle Have?

Chapter 11 Time-Telling

A Quarter in Time Means 15

Does 1 on Analog Clocks Mean 5 Minutes?

Why Does the Time on My Analog Clock Look Weird?

Which Hand Pointing to 12 Makes 12 O'clock?

Why We Shouldn't Jump Around Between 8:00 and 9:00

Chapter 12 Fractions

A Condition for Using Fractions: Equivalent Parts

Bottom Number and Top Number Aren't Nearly Sufficient

for Defining Denominators and Numerators

What Does 1/2x Mean?

A Fraction Doesn't Address How Many

Denominators Should Be Substantially Different for Easy Comparison

Percentage Shouldn't Be Juxtaposed With Fractions and Decimals

Chapter 13 Decimals

Changing the Value Scheme of Base-10 Blocks Not a Good Idea

When Is It Appropriate to Read a Decimal as a Fraction?

25.0 and 25 Aren't Exactly the Same

Keep a Few More Decimal Places

When Rounding at Intermediate Steps

Chapter 14 Simple Statistics and Graphs

Were the Children in Your Class Born, on Average, on the 12.8th?

The Mean Is the Averag...