Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding

“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

Steve Leinwand is Principal Research Analyst at American Institutes for Research in Arlington, Virginia and the author of Accessible Mathematics and Sensible Mathematics, and coauthor of Developing Numerical Fluency. Steve served as Mathematics Supervisor in the Connecticut Department of Education for 22 years and is a former president of the National Council of Supervisors of Mathematics. In 2021, he was awarded the National Council of Teachers of Mathematics' Lifetime Achievement Award.

Honi J. Bamberger is coauthor of Math Misconceptions and Activities to Undo Math Misconceptions, as well as Introduction to Connections (PreK–2, 3–5, and 6–8), part of Heinemann's Math Process Standards Series. She is a professor in the department of mathematics at Towson University. A former classroom teacher, she is a mathematics education researcher, the author of numerous other books and articles, and a nationally recognized speaker on math education.