Search Mobile Navigation

Math Misconceptions, PreK-Grade 5

From Misunderstanding to Deep Understanding

By Honi J Bamberger, Christine Oberdorf, Karren Schultz-Ferrell
Foreword by Steven Leinwand

Identify and investigate the source of some of your students’ most common mathematical errors. See how you can correct the misconception they already have and ensure that the mathematics you are introducing and reinforcing is accurate.

Special Offer: Save 30% off our list price automatically when you buy 15 or more.


In Stock

List Price: $30.00

Web/School Price: $24.00

eBook + Print Bundle
Full Description

“In this wonderfully insightful book, Honi, Christine, and Karren not only describe a vast array of perfectly understandable mathematical misconceptions that students have across the elementary curriculum, they also provide numerous practical instructional strategies and activities for helping remediate and “undo” the misconceptions.  The classroom vignettes they describe will ring true to everyone who has tried to teach mathematics to young, and not-so-young, children.”
—Steven Leinwand

Children enter school filled with all kinds of ideas about numbers, shapes, measuring tools, time, and money—ideas formed from the expressions they hear…the things they see on television…the computer screen…in children’s books…all around them. It’s no wonder some children develop very interesting and perhaps incorrect ideas about mathematical concepts.

“How can we connect the informal knowledge that students bring to our classrooms with the mathematics program adopted by our school system? Just as important, how do we ensure that the mathematics we are introducing and reinforcing is accurate and will not need to be re-taught in later years?” 

Math Misconceptions answers these questions by:

  • identifying the most common errors relative to the five NCTM content strands (number and operations, algebra, geometry, measurement, and data analysis and probability)
  • investigating the source of these misunderstandings
  • proposing ways to avoid as well as “undo” misconceptions.

Using classroom vignettes that highlight common misconceptions in each content area, followed by applicable research about the root causes of the confusion, the authors offer numerous instructional ideas and interventions designed to prevent or correct the misconception. 

Untangle your students’ math misconceptions.  This practical resource will help make it all make sense, and raise math achievement in your classroom.

Related Resources:

Activities to Undo Math Misconceptions, Grades PreK-2

Activities to Undo Math Misconceptions, Grades 3-5

Additional Resource Information

(click any section below to continue reading)


1.  Number and Operations

     Counting with Number Words

     Thinking Addition Means "Join Together" and Subtraction Means "Take Away"

     Renaming and Regrouping When Adding and Subtracting Two-Digit Numbers

     Misapplying Addition and Subtraction Strategies to Multiplication and Division

     Understanding the Division Algorithm

     Adding and Subtracting Fractions

     Representing, Ordering, and Adding/Subtracting Decimals

2.  Algebra

     Understanding Patterns

     Meaning of Equals

     Identifying Functional Relationships

     Interpreting Variables

     Algebraic Representations

3.  Geometry

     Categorizing Two-Dimensional Shapes

     Naming Three-Dimensional Figures

     Navigating Coordinate Geometry

     Applying Reflection

     Solving Spatial Problems

4.  Measurement

     Reading and Analog Clock

     Determining the Value of Coins

     Units Versus Numbers

     Distinguishing Between Area and Perimeter

     Overgeneralizing Base-Ten Renaming

5.  Data Analysis and Probability

     Sorting and Classifying

     Choosing and Appropriate Display

     Understanding Terms for Measures of Central Tendency

     Analyzing Data


6.  Assessing Children's Mathematical Progress

     Assessment:  The Received View

     Assessment from a Better Angle

     Types of Formative Assessments

     Why Assess?

     Final Thoughts




"An excellent set of resources to supply student-focused, Standards-based activities,these books also provoke deeper thought among teachers about our students' learning.  Although appropriate for use by individual teachers, the books have the potential to be even more powerful when used for collaborative study."--Teaching Children Mathematics

Related PD Services



Email if you would like to contact Honi J Bamberger directly about professional development support.


Email if you would like to contact Christine Oberdorf directly about professional development support.


Email if you would like to contact Karren Schultz-Ferrell directly about professional development support.

Customers who liked this also liked