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. You’ll discover how to... - Increase your confidence with core math principles and reasoning - Set your students on the path toward eventually developing more complex math skills - Improve student achievement by approaching problems in logical yet creative ways - Overcome common challenges faced by students and teachers - Teach problem solving for different learning styles Every chapter reconsiders well-established ways of teaching all areas of elementary math, from addition and subtraction to statistics and graphs. Helpful examples and tips are scattered throughout the book, offering revisions to the way these topics are often presented in the classroom. Also included are group study ideas for principals and instructional coaches so your school or district can work on the book together. With this practical guide, you’ll be ready to help students truly develop their math understanding. Cover -- Title -- Copyright -- Dedication -- Contents -- Meet the Author -- eResources -- Preface -- 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
