In District 205 we use the definition of Mathematical Fluency used in Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics.
"Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose,understand and can explain these methods, and produce accurate answers efficiently"
According to Susan Jo Russell (2000),
Efficiency implies that children do 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 sub-problems 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 numbers involved, and also be able to use one method to solve a problem and another method to check the results.
Fluency is not simply memorization of facts. It is all three components described above. We can use any number of fluency activities and games to assess student fluency in the area(s) critical to each grade level. Each is a standard at the grade, although not all are currently reported to parents.
Gojak, Linda M. (Nov, 2012). Simply Fast and Accurate? I Think Not!. Linda M. Gojak.
McClure, Lynn. (Apr, 2014). Developing Number Fluency: What, Why, and How? Nrich Maths.
Russell, Susan Jo. (May, 2000). Developing Computational Fluency with Whole Numbers in the Elementary Grades. In Ferrucci, Beverly J. and Heid, M. Kathleen (eds). Millenium Focus Issue: Perspectives on Principles and Standards. The New England Math Journal. Volume XXXII, Number 2. Keene, NH: Association of Teachers of Mathematics in New England. Pages 40-54.
National Council of Teachers of Mathematics. (Nov, 1999). Principles and Standards for School Mathematics.