<img height="1" width="1" alt="" style="display:none" src="https://www.facebook.com/tr?id=940171109376247&amp;ev=PageView&amp;noscript=1">

Dedicated to Teachers

Teaching for Authentic Fluency, Not Rote Memorization

E10732_Davenport_Henry_Clements_Sarama_BlogAnyone who wishes to be mathematically proficient needs to “just know” simple arithmetic — 4 + 9 = 13, for example, or 3 × 7 = 21. Students who do not learn such facts tend to have difficulties learning more advanced mathematics.

Download a sample chapter of No More Math Fact Frenzy

The reason for this is not that children cannot solve, for example, a multidigit arithmetic problem without knowing these basic facts, but rather that it is far more difficult to do so. When students achieve “automaticity” easy access to these facts—they free up mental resources that they can use to think about other aspects of the math, such as place value, complexities of renaming, and, of course, the problem they were solving in the first place. In general, they can give more attention to more complex matters. Without automaticity, students have a hard time learning multidigit calculations—both written and mental. They also face a roadblock in learning multiplication and division and then in understanding and later calculating with fractions. 

Many teachers assume that students must “just memorize” their basic facts by rote. To them, that implies timed practices, worksheets, and flash cards. If you have to memorize facts, you need to practice each one separately, again and again, quickly. They often believe, “That’s how we learned them, and that worked well.”

The problem is, worldwide research shows that the way most people in the United States think about arithmetic facts and children’s learning of them, and the language they use, may harm more than help. To see why, we have to step back and rethink each of these assumptions.

There are three primary misconceptions embedded in these assumptions:


Misconception 1: Arithmetic Facts Are Disconnected Items

To many people, the term fact often means a piece of disconnected information.But almost nothing in mathematics is disconnected. Knowing an arithmetic fact well—that is, fluently—means far more than knowing a simple, isolated piece of information.

Misconception 2: Learning = Memorization 

Research suggests that producing basic facts is not just a simple process of “rotely memorizing” each fact and then mentally “looking each up” in our memories. Retrieval of arithmetic facts is part of a complex process.

Misconception 3: Students Learn Through Rote Practice 

Memorization without understanding, drill without developing concepts and strategies, are not effective ways to teach or learn arithmetic facts, much less the edifice that is mathematics.


An important goal of early mathematics is students’ flexible, fluent, and accurate knowledge of arithmetic facts. Learning these facts is not about rote memorization. Seeing and using patterns, and building relationships, can free children’s cognitive resources to be used in other tasks. Number fact instruction that focuses on encouraging children to look for patterns and relations can generalize to problem-solving situations and can free attention and effort for other tasks.

Learn more about No More Math Fact Frenzy at Heinemann.com

Download a sample chapter of No More Math Fact Frenzy

glyph-logo_May2016Follow us on Instagram @heinemannpub to stay up to date on the latest books, your favorite authors, and upcoming events!

Linda Ruiz Davenport is the Director of K–12 Mathematics for Boston Public Schools and supports mathematics teaching and learning district-wide.

Follow her on Twitter @LindaD_BPSMath

Connie S. Henry is an Assistant Director of K–12 Mathematics for Boston Public Schools. She has taught and coached math for many years.

Follow her on Twitter @ConnieS_Henry

Douglas H. Clements is the Kennedy Endowed Chair in Early Childhood Learning and Distinguished University Professor at the University of Denver.

Follow him on Twitter @DHClements

Julie Sarama is the Kennedy Endowed Chair in Innovative Technologies and Distinguished University Professor at the University of Denver. 

Follow her on Twitter @JulieSarama

Topics: M. Colleen Cruz, Mathematics, Not This But That, Nell K. Duke, No More Math Fact Frenzy, Linda Ruiz Davenport, Julie Sarama, Connie S. Henry, Douglas H. Clements

Date Published: 04/22/19

Related Posts

SUMMER SALE: Heinemann Audiobooks

Heinemann Audiobooks are discounted Memorial Day 2022 through Labor Day 2022 ONLY at Apple, Google Play, ...
May 31, 2022 8:44:40 AM

Celebrate World Read Aloud Day with Heinemann Audiobooks

As Rebecca Bellingham reminds us in the Artful Read-Aloud: "We don't age out of the read-aloud experience...
Jan 31, 2022 2:35:46 PM

Heinemann Authors at Literacy for All

Heinemann is proud to sponsor the 2021 Literacy for All Conference, a national literacy and Reading Recov...
Oct 8, 2021 8:45:00 AM

Create a Classroom Culture That Values Learning from Mistakes Over Compliance

After talking to countless teachers, I’ve come to believe specific things in our practice create a pseudo...
Jul 29, 2021 2:39:16 PM