According to NCTM, Principles and Standards for School Mathematics, computational fluency refers to having efficient and accurate methods for computing. 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. The computational methods that a student uses should be based on mathematical ideas that the student understands well, including the structure of the base-ten number system, properties of multiplication and division, and number relationships.
Developing fluency requires a balance and connection between conceptual understanding and computation proficiency.
– Computational methods that are over-practiced without understanding are forgotten or remembered incorrectly.
– Understanding without fluency can inhibit the problem solving process.
- Is an important component of proficiency, along with factual knowledge and procedural facility
- Is an essential component of the knowledge needed to deal with novel problems and settings
Should you use Fact Drills?
Meaningful practice is necessary to develop fluency with basic number combinations and strategies with multi-digit numbers. However, practice should be purposeful and should focus on developing thinking strategies and a knowledge of number relationships rather than drill isolated facts.
Students should not be subjected to fact drills unless the student has developed an efficient strategy for the facts included in the drill.
Drills can strengthen strategies with which students feel comfortable—ones they “own”—and will help to make these strategies increasingly automatic. Therefore, drill of strategies will allow students to use them with increased efficiency, even to the point of recalling the fact without being conscious of using a strategy. However, Drills without an efficient strategy present offers no assistance to students.
Teaching to Memory or Automaticity
The State of North Carolina passed the law where students are now required to receive instruction in cursive writing and the memorization of multiplication tables. This new law requires that we hold our students accountable for knowing the multiplication tables. Our desire should be automaticity. The only way to acheive this goal is to attach a strategy to the skill.
For more information go to http://maccss.ncdpi.wikispaces.net/Webinars