Computational Fluency

  • What Is Computational Fluency?

    Computational fluency is described as the ability to compute with accuracyflexibility, and efficiency (Adding It Up, 2001). Computational fluency for every individual is developed over time. Fluency is not a fixed ability. Rather, it grows and develops through ample opportunities to practice and discuss strategies. We demonstrate fluency when we estimate solutions, use mental mathematics, use pencil and paper, and even when we decide to use calculators. The strategies we use are often dictated by the numbers we need to compute. The way that we think about numbers and computation is as unique as our fingerprints. Even so, there are strategies for computation that many of us share.

    How is it developed?

    Computational fluency is developed over time. It begins before we enter school and is developed throughout a lifetime. In elementary grades, we learn about the four operations, the properties of the operations, and strategies used to perform the operations. We apply this understanding to make computation more efficient. We learn that the numbers we are trying to calculate help us determine what strategy would be most efficient. It is developed through concrete models (blocks), drawings, and then symbols (numbers). Teachers model strategies and tools students can use to acquire understanding. Teachers facilitate discussion to exchange ideas and perspectives when working with computation.

    Important Notes for Parents and Teachers

    • Computational fluency is not fixed. Students can develop and improve their fluency through exposure, experience, and discussion.
    • Basic fact fluency supports computational fluency but frequently the two are co-developed.
    • Students are exposed to different strategies to develop flexibility and efficiency.
    • Students are not required to solve a problem with a particular strategy or multiple strategies.
    • Students should have freedom to choose the most efficient strategy for them.
    • Students should be able to explain how they found their solution. Explanations should not be required for every calculation. But these explanations are useful as fluency is developed so misunderstandings can be corrected.
    • Algorithms can be an efficient method of computation. This is especially true when numbers are large or unfriendly. Use of paper/pencil and/or algorithms is connected to the numbers being calculated and the strategies of the individual. For example, 199 + 82 may be more efficiently solved mentally by taking 1 from 82 to make a new problem 200 + 81. Other examples such as 14,325 + 9,180 may be better solved with an algorithm.
    • Read more about standard algorithms here.