Resources mentioned in this episode:

Developing Computational Fluency with Whole Numbers by Susan Jo Russell (NCTM members only can access)

Developing Computational Fluency with Whole Numbers by Susan Jo Russell (NCTM members only can access)

Developing Computational Fluency with Whole Numbers in the Elementary Grades by Susan Jo Russell (TERC article)

The Flexibility Formula K-2, online math PD course for Kindergarten through 2nd grade teachers

The Flexibility Formula 3rd-5th, online math PD course for 3rd through 5th grade teachers

Welcome fellow Recovering Traditionalists to Episode 144.  Today we’re answering the question, What is Computational Fluency?

I want to start off with a little bit of my backstory in this podcast and then I’ll share a snippet from one of my favorite articles about math fluency.

While I was getting my Master’s degree in Curriculum & Instruction with an emphasis in Mathematics back in 2003-2005, I was introduced to the research of Cognitively Guided Instruction, John Van de Walle, and Cathy Fosnot.

Even though most of what I was reading was about early elementary (Prek-2nd grade), I saw a connection to my 6th graders and their lack of mathematical understanding.

To make a long story short, a lot of the research talked about building students’ number sense in the early grades. I saw that my 6th graders did not have number sense, they could compute and get answers, but they lacked an understanding of how numbers work, and that was keeping them from being able to think flexibly about math problems.

I took those ideas I had learned, read even more research about number sense, and worked on helping my students build their number sense.  I even started presenting at national conferences about the impact of number sense.

I was soon being asked to travel across the United States and into Canada to do in-person workshops for teachers about what number sense is and how to help students build it.

But at the same time I was starting my family.  I had 4 kids in under 6 years, while still working and in my “spare time” traveling to do workshops at schools.

In 2015, when my youngest child was about 1 ½, I (and my husband and kids) had had enough of me traveling.  

I was listening to podcasts a lot during my travels and happened upon one talking about turning what you know into an online course.  It got me thinking.

So in January of 2016, I took the training that I was doing out in the schools, recorded videos of the information, and created a course called Number Sense 101 for Prek-2nd grade teachers.

I had thousands of teachers take that online course and even created Number Sense 201 for 3rd-5th grade teachers.

I loved being able to have teachers do my workshop without me having to travel.  Without them needing substitute teachers.  And without districts having to pay thousands of dollars to have a PD presenter like me come into the school for 1 day of training.  

However, I don’t actually offer the Number Sense courses anymore.  Since the time that I made the courses, I’ve learned more through new research.  I also learned from past participants in the Number Sense courses that there were certain misconceptions about the teaching, and learning, of number sense they were taking away.

So I revamped the courses to make them better and they are now called The Flexibility Formula.  There is one for K-2 and one for 3rd-5th grade teachers.  If you are interested in taking one of these courses, you can go to to join.

The courses still have a huge focus on how we can help kids develop number sense, but the main reason to focus on number sense is really to help your students become flexible thinkers; to build their flexibility in mathematics.

The reason I want to build flexibility is because it’s the part that’s typically missing in our math fluency instruction.  Which leads me to one of my favorite articles and why I called the revamped course The Flexibility Formula.

In 2000, Susan Jo Russell wrote an article for the National Council of Teachers of Mathematics’ journal Teaching Children Mathematics.  You can only access the article if you are a member of NCTM, however she also published a similar article for TERC that you can access and I’ll link up both articles at

In both articles, she talks about Computational Fluency including 3 ideas.  This is what is written on page 5 of the TERC article:

“• Efficiency implies that the student does not get bogged down in too many steps or lose track of the logic of the strategy. An efficient strategy is one that the student can carry out easily, keeping track of subproblems and making use of intermediate results to solve the problem. 

  • Accuracy depends on several aspects of the problem-solving process, among them careful recording, knowledge of number facts and other important number relationships, and double-checking results. 
  • Flexibility requires the knowledge of more than one approach to solving a particular kind of problem, such as two-digit multiplication. Students need to be flexible in order to choose an appropriate strategy for the problem at hand, and also to use one method to solve a problem and another method to double-check the results.”

Most instruction around math fluency is focused on the first two: Efficiency & Accuracy.  We work to help kids to get correct answers quickly.

However, when we focus on that, we get kids who can produce answers but often don’t have understanding built.  They are just good memorizers and rule followers.  

I was one of those kids and I was that way as an adult as well.  I could follow the steps and procedures that I was taught, but I wasn’t able to really problem solve.  I had Efficiency & Accuracy, but NO Flexibility.

That’s why I changed the name of the courses to The Flexibility Formula.  Yes, I want to help you learn about building your students’ number sense, but really it’s about much more than that.  It’s about helping kids become TRULY fluent and to do that we need to help them build their flexibility.

As math standards have changed, textbooks have put more of an emphasis on teaching students different ways to compute.  It’s their way of trying to build kids’ math flexibility, but it’s the wrong way.  We now have 5 ways to solve an addition problem instead of just one.  However, what we’ve seen is that instead of building students’ flexibility, it just confuses them.

Well there’s a reason for that, but I’m going to save that for our next episode.

Until then, I want you to really reflect about what your curriculum is focusing on through the teaching of strategies.

Is it teaching the strategies as procedures to be followed for a specific set of questions in the textbook?  

Or is it helping students to, as Susan Jo Russell said, “be flexible in order to choose an appropriate strategy for the problem at hand”?

Until next week my Fellow Recovering Traditionalists, keep Building Math Minds.

These episodes are sponsored by the online trainings that I do for elementary educators.  Registration for The Flexibility Formula K-2 and 3rd-5th is now open.  These courses help you understand the foundation of number sense, how number sense builds kids’ flexibility with numbers, and how that impacts their ability to become fluent with the mathematics at your grade level.  Go to to learn more about each course and get enrolled.

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As you start off the school year, I want you to keep in mind what is really important as we're trying to teach mathematics to our students.