Special Report
Mathematics Explainer

How Addition Fluency Develops: A Visual Explainer

By Vanessa Solis & Stephen Sawchuk — May 11, 2023 1 min read
Illustration of a giant red addition symbol on a field of numbers
  • Save to favorites
  • Print

As surely as 2+2=4, it also equals a beginning step on students’ mathematics journey.

Single-digit addition facts like these are so heavily used in mathematics that it’s critical that students ultimately commit them to memory so they don’t have to compute each time they appear.

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS

Research indicates that most students use a variety of increasingly sophisticated strategies as they learn their math facts, and that these strategies ultimately help them store the sums in their long-term memory so they can instantly recall them later. (Some research, in fact, indicates that adults continue to use these strategies long after they’ve become fluent in addition facts—though generally to a lesser degree.)

Take a look at how these strategies develop.

Then, check out our report on math foundations, where you’ll find an explainer and bibliography on math facts, and another aimed at helping teachers and curriculum planners craft a strong approach to fact fluency.

COUNTING ALL

Young students first learn to add by counting every number up to the sum.

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS Counting ON

COUNTING ON (OR COUNTING UP)

Students realize that the sum is six more than 4 in the counting sequence, and they can simply begin counting from 4.

Eventually, no matter the order of the numbers to be added, or “addends,” they automatically choose the larger and count from there.

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS Conting GIF

DECOMPOSITION

Students see that a number can be decomposed into various parts and use that knowledge to make addition easier.

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS decomposition a

There are various strategies that rely on decomposition for larger sums, including

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS  decomposition final

DIRECT RETRIEVAL

Students have stored the math fact in long-term memory and can retrieve it without falling back on a strategy.

ARTICLE 32SRMATH How Addition Fact Fluency develops Stephen VS

Related Tags:

Vanessa Solis, Associate Design Director and Stephen Sawchuk, Assistant Managing Editor contributed to this article.

Events

This content is provided by our sponsor. It is not written by and does not necessarily reflect the views of Education Week's editorial staff.
Sponsor
College & Workforce Readiness Webinar
The Road to Opportunity: Making CTE Accessible for All
The most valuable CTE happens off campus. For too many students, transportation is the barrier that keeps opportunity out of reach.
Content provided by HopSkipDrive
This content is provided by our sponsor. It is not written by and does not necessarily reflect the views of Education Week's editorial staff.
Sponsor
Recruitment & Retention Webinar
New Hire, No Laptop, No Login: Preventing Day-One Disruption
What happens before day one matters. Discover how districts are improving the new hire experience.
Content provided by Frontline Education
Teaching Profession K-12 Essentials Forum Supporting the New K-12 Workforce: What Teachers Need to Stay at School
 Join this free virtual event to discover what teachers say they need to feel supported to stay in classrooms for the long haul.

EdWeek Top School Jobs

Teacher Jobs
Search over ten thousand teaching jobs nationwide — elementary, middle, high school and more.
View Jobs
Principal Jobs
Find hundreds of jobs for principals, assistant principals, and other school leadership roles.
View Jobs
Administrator Jobs
Over a thousand district-level jobs: superintendents, directors, more.
View Jobs
Support Staff Jobs
Search thousands of jobs, from paraprofessionals to counselors and more.
View Jobs

Read Next

Mathematics Opinion How to Overhaul High School Math Pathways (and Why You Should)
What should count for math credit? This state ed. commissioner explains why the answer matters.
Angélica Infante-Green
5 min read
Vision, goal conquering, on the path to accomplishment, with xxx flags and Doodle math. Algebra and geometry school equation and graphs, hand drawn physics science formulas in the background
Vanessa Solis/Education Week + iStock/Getty Images
Mathematics Letter to the Editor How to Solve the College Math-Readiness Problem
Are our K-12 systems designed for how students actually learn math?
1 min read
Education Week opinion letters submissions
Gwen Keraval for Education Week
Mathematics Opinion Why There’s Still No ‘Science of Reading’ Equivalent for Math Instruction
A leading curriculum designer lays out the biggest problem in math instruction today.
10 min read
The United States Capitol building as a bookcase filled with red, white, and blue policy books in a Washington DC landscape.
Luca D'Urbino for Education Week
Mathematics Video The Algebra Hurdle: One School's Strategy to Help Students Clear It
An EdWeek video describes an Indiana school's use of tutoring and courses with different levels of rigor to help students.
1 min read