What does it mean to be computationally fluent?  Has this definition changed?  A generation ago, being good at math meant being fast and accurate.  I’m not sure anyone was thinking about the bigger picture of computational fluency but if they were, I think they were thinking about who was able to manipulate numbers quickly to get the right answer.  At that time, speed was always an important piece of the definition.

More recent research has shown us that we need to move away from speed as a factor in being computationally fluent.  Building on the work of others at NCTM and NSF, Susan Jo Russell developed the definition of computational fluency that is now commonly agreed upon.  Being computationally fluent is about being able to find a solution efficiently, being accurate in one’s calculations and being flexible – using one method to solve a problem and then using another strategy to check one’s work.  Number sense and knowledge of a variety of strategies is more important than speed.  Let’s look at the exact wording….

Definition of Computational Fluency

Efficiency

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

Accuracy

Accuracy depends on several aspects of the problem-solving process, among them careful recording, the knowledge of basic number combinations and other important number relationships, and concern for double-checking results.

Flexibility

Flexibility requires the knowledge of more than one approach to solving a particular kind of problem. Students need to be flexible and choose an appropriate strategy for solving the problem at hand. They can use one method to solve a problem and another method to double-check the results.

Digging Deeper

Using this definition, students need to be able to work efficiently by understanding the process they are using.  They need to be able to follow the logic of the problem.  If they are using a process that is too abstract for them and does not make sense to them, they are not using an efficient strategy.  This can often mean they are using a strategy that is different from the one that the adults around them consider to be most efficient.  This is OK!  All brains work differently so we won’t all agree on what is most efficient.  

Being accurate means having a concern for double-checking results.  In order to be concerned about it, students must have some sense about whether their answer is correct or not.  

Finally, flexibility calls upon students to have more than one way to solve a problem.  They need to be strategic and choose an appropriate strategy for the problem they are trying to solve and they need to use ANOTHER strategy to check their work.  It doesn’t help to solve a problem and then check one’s work by solving the problem exactly the same way because students will usually make the same mistake the second time that they made the first time.  They will get the same answer and therefore assume that their first answer was correct.  However, if they use a different strategy to solve it the second time and get a different answer, they can then investigate to find the error.  

The Matter of Speed

Note that in the definition, the words “speed” or “fast” or “quickly” are not present.  “The knowledge of basic number combinations and other important number relationships…” is part of the definition but being able to solve a certain number of problems in a minute is no longer valued.  Efficiency is valued, we don’t want students to get bogged down by the steps in a problem.  We also want students to be able to think deeply and flexibly about numbers.  This does not come just by memorizing facts. 

I also want to note that one does wake up one day and suddenly have computational fluency.  The deep number sense that is described comes from lots of work, over time in a variety of situations and with different types of problems.  Each day we are building a piece of that foundation.