Common Mistakes in Teaching Elementary Math And How to Avoid Them 1st Edition by Fuchang Liu 1138201456 9781138201453

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ISBN-10 :  1138201456 

ISBN-13 :  9781138201453

Author: Fuchang Liu 

  Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students can achieve success.

Common Mistakes in Teaching Elementary Math And How to Avoid Them 1st Table of contents:

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-10, Not Base-12
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
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
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 − 7 = 15 − 7: No Way to Make It Easier?
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 Doesn’t Work
6 Division
The Larger Number Doesn’t Always Go Inside
What’s 0 ÷ 0?
Division Isn’t Always Repeated Subtraction
“Dad, Mom, Sister, Brother, Rover”: Where Is Dad?
Division Doesn’t Always Yield a Smaller Number
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?
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
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
10 Geometry: Common Geometric Shapes
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?
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 12:00?
Why We Shouldn’t Jump Around Between 8:00 and 9:00
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
13 Decimals
Changing the Value Scheme of Base-10 Blocks Is 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
14 Simple Statistics and Graphs
Were the Children in Your Class Born, on Average, on the 12.8th?
“The Mean Is the Average”
Where in the World Does the Mode Ever Get Used?
Do All Your Children Have an Equal Chance of Winning?
Use Different Types of Data for a Beginning Lesson on Graphs
15 Measurement
Why Do We Need Nonstandard Measurement?
What Is Standard Measurement?
What Are Centimeters Used to Measure?
Leave Out Units of Measure at Intermediate Steps
How Do You Say the Word for “1000 Meters”?
Fractions Don’t Belong with Metric Measurements
16 Computational Estimation
Is Computational Estimation an Educated Guess?
Are All Estimates Good Ones?
How Practical Is an Estimate If It Takes 4 Minutes?
Be Extremely Careful When Rounding 1-Digit Numbers
There Is Often More Than One Way to Round a Number

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Tags: Common Mistakes, Teaching Elementary, Fuchang Liu