Math Fluency-Is There a Speed Limit?

When I was in elementary school in the 1950’s there was a reading program called SRA. Looking back after all these years, the intent of this program, it seems to me, was to increase reading speed and comprehension. My buddies were a level ahead of me, so I tried to read faster to catch up with them, but my comprehension suffered. The faster I tried to read, the more frustrated I became. As a result, during my career as a high school math teacher, I was very apprehensive of anything that even hinted at doing something fast.

Presently, working with the Common Core Mathematics Curriculum, the idea of fluency combined with the ideas of conceptual understanding and modeling, have been used to define the term “rigor”, which is used in relation to both curriculum & assessment. Fluency has somehow been connected to work that is timed, which causes me to shudder. Fluency has also been defined in the proposed New York State Revised Standards as follows:

“The word fluent is used in the Standards to mean “fast and accurate.” Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns and knowing some answers from the use of strategies.”

I am not totally in agreement with this definition. I think certain tasks become automatic through repetition, and, as a result, students develop an ease and facility with these tasks. Of course, as students gain a facility with these tasks, they will begin to do them faster. However, I think this speed is a by-product of becoming more comfortable with the tasks at hand, and should not be part of the definition.

In Common Core workshops that I have been involved with, I have brought up the idea that, in my mind, fluency has nothing to do with speed. If I am fluent in a language, that doesn’t mean I speak rapidly. By definition, it means that I speak the language smoothly and with ease. The response that I usually get is that the students, who are completing fluency worksheets, are not being timed in relation to other students, but in relation to their own previous times. However, they are still being timed, and I am right back to my SRA reading experience. I have also been told that when they get a worksheet they should be told that they do not have to complete all problems. However, students are going to be aware of how many problems other students completed, which could again lead to frustration

Don’t get me wrong, I value mathematical fluency as an integral part of the learning experience. I just don’t think that the speed with which these tasks are accomplished affects how mathematically fluent the student is in relation to these activities or the subject as a whole.

One idea that has surfaced in this very important discussion is the idea of “working memory”. Dr. Paul Riccomini has introduced this idea in workshops that I have attended in relation to the Common Core.

Working memory, as I understand it, is the amount of memory available for the task at hand. I think of this as RAM memory as opposed to ROM memory in a computer. The more working memory that we can free up by performing some tasks automatically, the more successful we should be as problem solvers. Automaticity is the last of four learning progression stages. The first three being: Understanding, Relationship, and Fluency. I think this an excellent way to view this idea.

In an excerpt from an article entitled, Fluency: Simply Fast and Accurate? I think Not!Fast and A NCTM President Linda M. Gojak writes:

“Focusing on efficiency rather than speed means valuing students’ ability to use strategic thinking to carry out a computation without being hindered by many unnecessary or confusing steps in the solution process.”

She goes on to write:

”Our students enter school with the misconception that the goal in math is to do it fast and get it right. Do we promote that thinking in our teaching without realizing it? Do we praise students who get the right answer quickly? Do we become impatient with students who need a little more time to think? As we strive for a balance between conceptual understanding and procedural skill with mathematical practices, we must remember that there is a very strong link between the two. Our planning, our instruction, and our assessments must build on and value that connection. Fluency entails so much more than being fast and accurate!”

I agree! What do you think?

Jack McLoughlin
Math Consultant

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