69´«Ã½

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
Email Copy URL

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)

69´«Ã½ 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

¶Ù·¡°ä°¿²Ñ±ÊO³§±õ°Õ±õ°¿±·

69´«Ã½ 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

69´«Ã½ 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
Artificial Intelligence Webinar
AI and Educational Leadership: Driving Innovation and Equity
Discover how to leverage AI to transform teaching, leadership, and administration. Network with experts and learn practical strategies.
Content provided by 
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
School Climate & Safety Webinar
Investing in Success: Leading a Culture of Safety and Support
Content provided by 
Assessment K-12 Essentials Forum Making Competency-Based Learning a Reality
Join this free virtual event to hear from educators and experts working to implement competency-based education.

EdWeek Top School Jobs

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

Read Next

Mathematics Video Here's How All 69´«Ã½ Can Learn to Enjoy Word Problems
Teachers should weave students' cultural context into word problems, says math expert David Dai.
1 min read
Mathematics Q&A Word Problems Get a Bad Rap in Math Class. Here’s How to Get Them Right
Kevin Dykema, a math expert, shares strategies for teachers to help students tackle word problems.
5 min read
Education Week Math Mini-Course, Week 4, Word Problems, 2700 x 1806
EglÄ— PlytnikaitÄ— for Education Week
Mathematics Can Kindergarten Math Lay the Foundation for Algebra? New Study Aims to Find Out
Teaching algebraic thinking skills early—like generalizing, representing, and reasoning—can set students up for success, researchers say.
4 min read
Illustration of a young boy writing in a notepad with Algebra equations floating all around him
iStock/Getty
Mathematics Q&A Fractions Are Tough to Teach and to Learn. These Strategies Can Help
Here's how teachers can build students' conceptual understanding.
4 min read
Education Week Math Mini-Course, Week 3, Fractions, 2700 x 1806
EglÄ— PlytnikaitÄ— for Education Week