Developing Computational Fluency

Note: The following article was shared with participants at TTT workshops presented at the 47th Annual NW Conference in Oct. 2008

      Many teachers have shared concerns with Teacher to Teacher professional development facilitators  about allowing students to create their own mathematical processes and understandings instead of teaching students "standard" or the most commonly accepted ways of solving routine computations. The concern is expressed something like this: "If I do not teach my student the standard methods for solving computational problems, I may be doing him or her a disservice when the student is then required to participate in standardized testing. If students are too slow in their solution processes or too divergent in the ways they interpret tasks, they may do poorly on these standardized tests."

      Making Sense of Problem Solving assumes the primary goal of mathematics instruction is to develop conceptual understanding along with developing a variety of tools to apply that understanding in problem solving situations. By engaging in the tasks presented in each grade level book, students will develop the ability to reason and make sense of the mathematical concepts in the contexts of the problems. However, setting conceptual understanding as the primary goal does not mean that teachers ignore computational skill development. In order to be mathematically powerful, students need to be flexible and fluent with numbers.

     Just knowing the basic facts is not enough. We  need to help students develop the ability to quickly and accurately understand the relationships between numbers. They need to make sense of numbers as they find and make strategies for joining and separating quantities. A significant part of mathematics education is  encouraging students to develop positive habits of mind such as patience and perseverance as they solve difficult problems. As students learn to look to themselves to justify their own solutions, their motivation for becoming mathematically powerful will come from within, not from external sources.             

  It is true that any kind of drill can strengthen a student's ability to retrieve information. It's important to remember, however, that making sense of the  mathematical operations must precede any attempts to drill students for mastery of the basic facts.  Drill should  reinforce number sense, the powerful underpinning of a student's mastery of basic facts.

     To prepare students for life in the 21st Century, it is imperative that we educate students who are creative, divergent, and competent problem solvers. Finding the balance between how much time should be spent on developing conceptual understanding and how much time should be devoted to developing computational skill is part of the art of teaching in today's classrooms.