In Pursuit of Fluency-Part 6: Operations Beyond Basic Facts

Because we have been talking a lot about fluency in the past few blog posts, it suddenly occurred to me the other day that I can see a surprising connection between our efforts to help students develop fluency and my experiences becoming a successful high school sprinter. Let me explain.

When I was in high school, I loved running the quarter mile, and I made it to the state track meet every year. The mile relay was my absolute favorite event on the track – four young women working tirelessly to perfect our individual races in order to combine our skills to claim the final prize of the meet. We each played an important part in creating that final success:

1. We worked on our form and rigorously built our individual skills (using the starting blocks, perfecting our just-right paces, engaging in distance running, sprinting shorter distances, etc.), all the while receiving immediate and continuous feedback from our coach.
2. We honed and customized our individual races by putting together our own well-practiced skills.
3. And then we took that last, important step — we combined our efforts into a longer, collaborative race, blending the traits of our individual races into a more complex and challenging final event.

So here’s the connection to math fluency…Just as my coaches helped me and my teammates achieve success through a prescribed sequence of skill-building activities, we, as teachers and coaches, can use the same strategies to help our students build the skills necessary to achieve fluency.

1. I equate students’ development of number sense and math-fact fluency with the smaller, individual skills we sprinters developed (our sprints, form drills, and the like).
2. Then, students’ fluency with number sense and math facts become the building blocks to fluency with multi-digit operations, just as we sprinters individually put together our running skills to design our full races.
3. Eventually, operational fluency supports problem solving (the “more complex and challenging event” that is the goal of fluency) by enabling students to invest their thinking in the problem-solving process without getting stuck in the mire of operations.

So here we are, having developed number sense and math fact fluency with our students, laying the groundwork for them to perform more complex operations with multi-digit base-ten numbers (and fractions). Ensuring that students achieve operational fluency is critical…and how we get there can be a challenge. Below are the five steps I have found to be most important in helping students gain operational fluency.

1. Continue to reinforce conceptual understanding. Using tools such as KP Ten-Frame Tiles to reinforce and describe what’s happening in the procedures will continue to support procedural understanding (Akin & Rimbey, 2017).
2. Understand that speed and fluency are not synonymous. Fluency combines accuracy, efficiency, flexibility, and appropriateness. An over-emphasis on speed alone increases math anxiety (Boaler, 2018).
3. Support fluency by giving relevant, immediate feedback. If you simply give students arithmetic worksheets with problems to practice over and over, they will not thrive because there is no opportunity for them to receive necessary and meaningful feedback.
4. Build fluency in a fun and motivating atmosphere (Boaler, 2018). Provide opportunities for students to work on their skills through interactive games and online activities where meaningful feedback is possible. Something as simple as having students work side-by-side with models and with white boards, one “acting out” while the other records the operation, can make these practice sessions more meaningful.
5. Make math fluency meaningful. All along the way, provide students with authentic opportunities to experience application of their math skills so they can see first-hand how fluency is an asset (Akin & Rimbey, 2017).

Had my mile-relay team neglected to rigorously build our individual skills, had we not had the opportunity to practice together toward a cohesive outcome, had we not focused on our common goal, we would not have been successful in seeing our vision become reality. So it is with math fluency – students must actively build their competence with number sense and math fact fluency, put these skills together as they practice toward cohesive strategies for operations, and apply these skills as they successfully engage in deep and meaningful problem solving.