University Press of America

Pages: 116
•
Trim: 6⅛ x 9

978-0-7618-5885-0 • Paperback • May 2015 • $31.99 • (£25.00)

978-0-7618-5886-7 • eBook • May 2015 • $30.00 • (£25.00)

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.

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

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.

**— ****National Council of Teachers of Mathematics**

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.

**— ****Mathematics Teaching in the Middle School**

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.

**— ****Janet Beery, Ph.D., mathematics professor, University of Redlands, California**

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.

**— ****Ramakrishnan Menon, PhD., mathematics education professor, George Gwinnett College, Georgia**