Procedural Fluency

This topic skates around the edges of the calculator post. The biggest thing to remember about teaching mathematics at any level is that each topic, concept, chapter, or course is part of a continuing story. The exploration and discovery is rooted in time and never complete. In order to share that story effectively with our students, yes, we must rely on the procedural fluency because it becomes part of the larger topics of number sense and reasoning. If students cannot perform basic operations independently, mentally, then they have an even greater challenge of making sense of the story. How is it that the operations can be boiled down to addition and multiplication? Yes, you need to understand and be effectively using procedural fluency to investigate this. But think  about the kinds of problems you would have students consider as they investigate. Would they be the longest, most-trying, paper and pencil problems so that students get lost in the procedures instead of the concepts? Or would they be carefully arranged problems that allow for all types of exploration and visualization to better develop that number sense? Yes, we are going to need to teach mathematical procedures in our classrooms. But not every one and not every day. Some of them need to be discovered by the students so they can make valuable connections with the teacher's orchestration.

When I think of the eras of testing that I have seen in my career so far, I remember that, for less confident mathematics students, teaching procedure after procedure didn't allow students to remember how to solve math problems. They simply taught a list of steps that students were supposed to memorize. Can you even imagine having to memorize a new list of steps a day, a week? No wonder kids can't keep the "tricks" straight. I was a good student but because I studied really hard, and it didn't make me more knowledgeable about the concepts and connectedness of math. If my father didn't show me exactly the way the teacher had in class, I was lost. I only learned how to teach math, to myself and my students, by planning and teaching math to my students. Through their eyes, I was able to understand my own struggles.

So procedural fluency? Important, but not nearly as important as conceptual understanding. And tools should be provided to aid in the discovery of the wonderful story of mathematics.

Look at all of the connections to other math concepts in this short video.

http://www.youtube.com/watch?v=DK5Z709J2eo