Defining Fluency

Last week we had the pleasure of hosting Cathy Carroll, a Senior Research Associate with WestEd and our state President-elect of the California Mathematics Council, as she facilitated a colloquium  to investigate “fluency” in mathematics.  She also followed up with a podcast to delve deeper into what it means to be fluent.  I have been thinking about this since she left…

After 30+ years in the field of mathematics education, I know that many people still equate fluency with knowing math facts. I have seen many teachers pull out their timed tests and explain them as a way to build fluency. But, is that really what fluency means?

I looked up the word fluency on Google and found this definition: “the ability to express oneself easily and articulately.” Wow! I cannot see how knowing math facts could help me to express myself in mathematics. I think I need much more than that… And, Cathy talked about a much broader definition.

In 2001, the National Research Council spearheaded an effort to compile a meta-analysis of the current research in mathematics education to recommend how teaching, curricula, and teacher education should change to improve mathematics learning during the pre-K through 8th grade years. The National Academy Press published their report in a landmark book entitled, Adding It Up, Helping Children Learn Mathematics.  In it, a new vision for mathematical proficiency was defined in chapter four.

Mathematical proficiency, as we see it, has five components, or strands:

  • conceptual understanding—comprehension of mathematical concepts, operations, and relations
  • procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
  • strategic competence—ability to formulate, represent, and solve mathematical problems
  • adaptive reasoning—capacity for logical thought, reflection, explanation, and justification
  • productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

The most important observation we make here, one stressed throughout this report, is that the five strands are interwoven and interdependent in the development of proficiency in mathematics.”

This is what I believe fluency in mathematics really means. And… NRC laid it out for us 16 years ago! To be able to use mathematics to describe the world around me, to be able to express myself easily and articulately in today’s world, I need to be fluent in mathematics. We need to help our students become truly fluent in mathematics. This is more important today than ever before.


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