Common Mistakes in Teaching Elementary Math—And How to Avoid Them

Fuchang Liu is Associate Professor of Mathematics Education at Wichita State University. Previously, he taught high school math in Louisiana and Texas.

• Meet the Author PrefaceChapter 1 Counting Counting Shouldn't Start at 0 What Are Tally Marks for?It May Not Be Fast—The Purpose of Skip-CountingOur Number System Is Base-Ten, Not Base-TwelveChapter 2 Number Properties A Red Marble Isn't More Than a Blue OnePlaying Cards and Dice Aren't Ideal Things to Make Multidigit Numbers WithIt's Odd Not to Consider 0 as Even14 and 37 Don't Belong in the Same ListChapter 3 Addition 4 + 4 Isn't Simply 8 Bars Put TogetherMake Pictorial Representations More Than a "Literal" TranslationDon’t Hop From Square OneYou Can't Add Apples and Oranges TogetherChapter 4 SubtractionDon't Make the Kittens DisappearDon't Ever Say "Subtract the Smaller Number From the Larger One""Neither a Borrower nor a Lender Be"—Why We Shouldn't BorrowCan 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 WorkChapter 6 Division The Bigger Number Doesn't Always Go InsideWhat's 0 ¸ 0? Division Isn't Always Repeated Subtraction "Dad, Mom, Sister, Brother, Rover": Where Is Dad?Divide Doesn't Always Yield a Smaller NumberChapter 7 The Order of Operations Aunt Sally Is Evil – The Order of OperationsThe Order "M/D Before A/S" Isn't Haphazard Are Negative and Subtract Really Different?Chapter 8 Algebra An Equal Sign Means EqualWhat Does Adding Up Numbers Landed Have to Do With Finding Factors?Timelines Aren't Good Candidates for Teaching Negative NumbersThe Worst Example in Teaching ExponentsChapter 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 ValueThe Two Sides of a Symmetrical Figure Aren't Exactly the SameDon't Use Tiles to Figure Out the PerimeterChapter 10 Geometry: Common Geometric Figures Length Doesn't Necessarily Mean LongerA 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 9:00Chapter 12 Fractions A Condition for Using Fractions: Equivalent Parts "Bottom Number" and "Top Number" Aren't Nearly Sufficientfor Defining Denominators and NumeratorsWhat Does 1/2x Mean? A Fraction Doesn't Address "How Many"Denominators Should Be Substantially Different for Easy ComparisonPercentage Shouldn't Be Juxtaposed With Fractions and DecimalsChapter 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 PlacesWhen Rounding at Intermediate StepsChapter 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 Chapter 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 StepsHow Do You Say the Word for "1000 Meters"?Fractions Don't Belong With Metric MeasurementsChapter 16 Computational Estimation Is Computational Estimation an Educated Guess?Are All Estimates Good Ones?How Practical Is an Estimate If It Takes Four Minutes?Be Extremely Careful When Rounding Single-Digit Numbers There Is Often More Than One Way to Round a Number Chapter 17 Odds and Ends Appendix: Suggestions for Using Common Mistakes in Teaching Elementary Math with Study Groups

Children’s misunderstandings about mathematics ideas stand in their ways to learn mathematics well and effectively in elementary schools. Common Mistakes in Teaching Elementary Math and How to Avoid Them, is the first book, I know, that directly explains teachers’ own misunderstandings about mathematics ideas, how they reproduce them among their students, and more importantly, what they can do to address these issues in their mathematics teaching. Dr. Liu accomplished all the above successfully by engaging readers in experiencing what teachers do and how students react in elementary classrooms using a series of stories. A great book for mathematics teachers, teacher educators, and policy makers.----Jian Wang, Helen DeVitt Jones Chair in Teacher Education, Texas Tech University This book appeals to pre-service and elementary teachers who are not math content knowledge experts. Fuchang Liu offers a "quick-fix" for those elementary teachers who are aware that they are struggling as math teachers, and are seeking help. --- Elizabeth Simpson, Math Coach, Lamphere School District, MI