Common Misconceptions in Mathematics: Strategies to Correct Them

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.

Table of Contents:
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

About the Author :
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.

Review :
One of the book’s strengths lies in its organizational structure. Teachers can easily navigate to relevant topics because each misconception section is organized and presented in the same way. . . .The author offers a wide range of potential solutions to correct each misconception. . . .The book offers a wealth of information that would be good for K–grade 12 teachers to have at their disposal. This book would be best used in undergraduate or master’s level teacher education courses that specifically address learning mathematics. . . .The descriptions of what teachers can do are useful and straightforward, and they discuss various ways for students to understand the concept of an algorithm. The research notes are useful summaries of research that has been conducted concerning each misconception; this research can be used as a platform for further investigation. What a great idea for a book! What I really mean is, what a great idea for reaching teachers and helping them understand and teach mathematics better!...Being able to focus on one misconception at a time will allow teachers to think about and understand concepts more than they usually do. This book is a useful resource for the classroom math teacher as it provides many examples of student errors, and also provides some practical ways to help remedy such errors.