What exactly is fluency? With languages, fluency is the ability to clearly express thoughts without having to grope for words. With mathematics, fluency refers to a student simply knowing a fact or procedure, without having to stop and think about it. Many first-graders can instantly tell you that 2 + 2 = 4. But too many older students hesitate with say, 9 + 5.

If the students’ minds are burdened with having to go back and reestablish 9 + 5, when they should be free to think about more complicated concepts (x + 9)(x + 5), their progress will be hampered. Their feelings about math in general will take on an aura of stress and clutter, and the feelings of curiosity, the joy of discovery and confidence will fade away. Tasks such as homework and tests will take longer than they should.

The first graders and older students may understand the concept. While understanding provides a basis for fluency, it does not automatically produce it. What enables learners to acquire fluency? Practice. But practice of the right sort is required. See our post, A Model for Using Guided Discovery in a Math Lesson.