From an essay, several years old, by Linda Gojak when she was president of NCTM, in which she speaks out against equating fluency with math facts, with speed. She quotes the NCTM standards to bolster her point:
“Principles and Standards for School Mathematics states, “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” (p. 152). What a wonderful description of fluency! It reminds us that a student cannot be fluent without conceptual understanding and flexible thinking.”
Right. And we’ve seen this in action. Jo Boaler being one of the adherents to this philosophy, and saying that memorization is NOT the key to learning the times table. There are strategies one can use, everyone knows that. But the NCTM standard goes beyond all that and uses the word “understand” and “explain”. And therein lies the tales we’ve been reading and hearing about. Students being made to explain problems so simple they defy explanation. And then of course, there is the poster child of “understanding” : fractional division–i.e., being able to “explain” why the invert and multiply procedure works.
Some things lend themselves to easy explanation; others take more time. I myself don’t push certain things as I’ve written about here. But the above standard (which has served as the means by which the Common Core standards are being interpreted) causes more problems than it solves. Unfortunately, the words of Gojak are living on and NCTM has not gone away. They are incarnate within the CC standards.