Common Misconceptions in Mathematics (eBook)

Bobby Ojose is an assistant professor of mathematics education at the University of Redlands. He obtained his doctorate in mathematics and science education from the University of Southern California. Dr. Ojose teaches courses in mathematics and science education in the preliminary teaching credential program and the quantitative research methods courses for the MA and doctoral programs. His research agenda is focused on mathematics education.

IntroductionThe Purpose of the BookIssues with MisconceptionsWhat 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 FractionsMisconception 4: Subtraction of Fractions Misconception 5: Rounding Decimals Misconception 6: Comparing Decimals Misconception 7: Multiplying Decimals Misconception 8: More on Multiplying DecimalsMisconception 9: Division of DecimalsMisconception 10: Percent Problems Misconception 11: Division by a FractionMisconception 12: Ordering Fractions Misconception 13: Least Common Multiple (LCM) Misconception 14: Addition of Decimal NumbersMisconception 15: Subtraction of IntegersMisconception 16: Converting Linear Units Misconception 17: Power to a BaseMisconception 18: Order of Operations IMisconception 19: Order of Operations IIMisconception 20: Simplifying Square RootsMisconception 21: Comparing Negative NumbersMisconception 22: Addition of Negative Integers Misconception 23: Scientific Notation Misconception 24: Proportional Reasoning Misconception 25: Time Problem Part Two : AlgebraMisconception 26: Dividing Rational ExpressionsMisconception 27: Adding Rational ExpressionsMisconception 28: Adding Unlike Terms Misconception 29: Adding Like Terms Misconception 30: Distributive PropertyMisconception 31: Writing a Variable Expression Misconception 32: Simplifying a Variable ExpressionMisconception 33: FactoringMisconception 34: Exponents AdditionMisconception 35: Zero Exponents Misconception 36: Solving Equation by Addition and SubtractionMisconception 37: Solving Equation by Division and Multiplication Misconception 38: Fractional EquationsMisconception 39: One-Step Inequality Misconception 40: Absolute Value Misconception 41: Operations with Radical Expressions Misconception 42: Simplifying Polynomials Misconception 43: Systems of Equations Conclusion ReferencesAppendix A: List of Manipulatives and their Uses Appendix B: Teaching Standards