This book should be a handy tool for teachers of mathematics as they develop plans to confront the problem of misconceptions, which are common with students that often have their own notion of certain mathematical concepts, right or not. The onus is on the teacher to detect those misconceptions and help students remedy them. This book is written for that purpose. Teachers could emulate the presented strategies that the book has elucidated. Teachers may also devise their own strategies based on the source of the misconception as presented in the book. The research segment of each identified misconception will be helpful if teachers want to apprise themselves with what the literature says about the concept. In general, the book is meant for teachers who want to help students engage in mathematics that emphasize conceptual understanding.
Introduction The Purpose of the Book Issues with Misconceptions What are Misconceptions in Mathematics? How do Misconceptions Come About? Why is it Important to Correct Misconceptions? Part One: Arithmetic Misconception 1: Addition Sentence Misconception 2: Subtracting Whole Numbers Misconception 3: Addition of Fractions Misconception 4: Subtraction of Fractions Misconception 5: Rounding Decimals Misconception 6: Comparing Decimals Misconception 7: Multiplying Decimals Misconception 8: More on Multiplying Decimals Misconception 9: Division of Decimals Misconception 10: Percent Problems Misconception 11: Division by a Fraction Misconception 12: Ordering Fractions Misconception 13: Least Common Multiple (LCM) Misconception 14: Addition of Decimal Numbers Misconception 15: Subtraction of Integers Misconception 16: Converting Linear Units Misconception 17: Power to a Base Misconception 18: Order of Operations I Misconception 19: Order of Operations II Misconception 20: Simplifying Square Roots Misconception 21: Comparing Negative Numbers Misconception 22: Addition of Negative Integers Misconception 23: Scientific Notation Misconception 24: Proportional Reasoning Misconception 25: Time Problem Part Two : Algebra Misconception 26: Dividing Rational Expressions Misconception 27: Adding Rational Expressions Misconception 28: Adding Unlike Terms Misconception 29: Adding Like Terms Misconception 30: Distributive Property Misconception 31: Writing a Variable Expression Misconception 32: Simplifying a Variable Expression Misconception 33: Factoring Misconception 34: Exponents Addition Misconception 35: Zero Exponents Misconception 36: Solving Equation by Addition and Subtraction Misconception 37: Solving Equation by Division and Multiplication Misconception 38: Fractional Equations Misconception 39: One-Step Inequality Misconception 40: Absolute Value Misconception 41: Operations with Radical Expressions Misconception 42: Simplifying Polynomials Misconception 43: Systems of Equations Conclusion References Appendix A: List of Manipulatives and their Uses Appendix B: Teaching Standards
