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Computational Fluency, Algorithms, and Mathematical Proficiency

learningDuring a recent webinar, Computational Fluency, Algorithms, and Mathematical Proficiency were discussed.  Below you will find some important key notes from the webinar.

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.

Conceptual Understanding:

  • 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.

The kinds of experiences teachers provide clearly play a major role in determining the extent and quality of students’ learning. Students’ understanding can be built by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Procedural fluency and conceptual understanding can be developed through problem solving, reasoning, and argumentation.

Teaching to Memory or Automaticity

Teaching for Memorization refers to committing the results of unrelated operations to memory so that thinking is unnecessary, while
Teaching for Automaticity refers to answering facts automatically, in only a few seconds without counting, but thinking about the relationships within facts is critical.

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.


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