Computational Fluency

What is Fluency Anyway?

Computational fluency is the ability for people to work flexibly and fluently with numbers. While one aspect of fluency includes automaticity with facts, the automaticity develops out of a deep understanding of how numbers work (number sense) that is developed through frequent and varied experiences working with numbers. In this sense, fluency is as much about how we get the answer as it is about the answer itself.

Free resources for learning about teaching for computational fluency: While some of these resources were designed for teachers, they will also be useful for parents, who want to better understand how to support their children in becoming more fluent when working with numbers.

Christina Tondovold’s 6 part video series
Jo Boaler’s Article Fluency Without Fear
Jennifer Katz’s Rubrics for assessing math for BC teachers (look at the flow for number sense and computational fluency across the grades.
Joe Roicki’s blog post explaining this graphic of the components of fluency
Dan Meyer’s blog about what fluency is not for those who learn best from non-examples. The post includes lots of Tweets from teachers.
My multimedia presentation slide-deck (pdf)

Building Fluency 

Games, stories and rich math tasks/routines are the best way to build fluency.  Fluency, unlike memorization is developed from a deep understanding of how numbers work.  Unlike memorized facts, computational fluency allows students to work efficiently in any context with flexibility and confidence.  The resources on this page support the development of computational fluency through activating deep thinking about how numbers work, how they go together and how they come apart. 

Questions to ask when choosing resources for developing fluency: 

  1. Does this resource/tool/activity develop understanding of how numbers work, rather than focusing on speed and accuracy? 
  1. Does this resource/tool/activity activate thinking? (memorization activates recall, not thinking) 
  1. Does this resource/tool/activity allow for flexibility of strategies and thinking to be practiced and acknowledged? 
  1. Does this resource/tool/activity allow for each child to operate within their development zone (unproductive struggle = frustration; unnecessary repetition = boredom) 
  1. Does this resource/tool/activity allow for moments of DISCOVERY and JOY as the learner makes deeper connections to how numbers work in the world? 

Teachers: Always remember to preview any resources for compatibility with the technology available AND compliance with your districts curriculum and privacy requirements.

Steve Wyborney’s Multiplication Course (and activities)

Christina Tondevold:

Youcubed:

Dan Finkel:

Carole Fullerton

Mathigon: 

Berkeley Everett: 

  • Visual Animations of operations and information on visual math 
  • Math Flips (alternative to flashcards; digital and hard copy)   

Jen Barker:  

Janice Novakowski: 

Graham Fletcher: 

Global Math Project: 

BC Numeracy Network (Balanced Numeracy)

Andrew Fenner (Number Shapes)