2019 NC Council of Teachers of Mathematics Conference: Unpacking Mathematical Fluency

December 20, 2019

Last month, I had the opportunity to join Heart Program Director, Cydney Kramer and Program Manager, Emily Aleski, in attending the North Carolina Council of Teachers of Mathematics Conference (NCCTM) in Greensboro, NC. We joined hundreds of other math teachers, facilitators, and researchers from across the state to explore this year’s topic of Mathematical Mindsets for All. We were inspired by and thankful for the opportunity to connect with other math educators, all grounded in a commitment to equitable math instruction for all students.  As a Heart Tutoring team, we had many of our current practices validated, and we also learned even more ways to provide equitable support for our students and families! We’ve summarized some of our findings below.

What is Mathematical Fluency?

Mathematical fluency is typically defined as the ability to solve math problems accurately and efficiently. Unfortunately, this definition often translates to a disproportionate emphasis on speed. Many of us have encountered this imbalance in our own math experiences. (If you’ve ever felt anxious about a timed multiplication tables quiz, then you probably know what I mean!) The challenge with math fluency is that we too often interpret efficiency to mean speed, resulting in students memorizing facts without foundational understanding. In order to become efficient problem solvers, students first need the opportunity to build authentic understanding of number concepts so that they can then use that knowledge in a way that makes sense to them. Learn more about defining (and redefining) mathematical fluency here.

Firing and Wiring Our Brains

Once students have grounded their thinking in understanding, then they can begin building efficiency and speed through meaningful repetition. Keynote speaker, Valerie Faulkner, calls this “firing and wiring our brains.” She argues that, when done strategically and consistently, practicing speed does not have to be inherently stressful for students. To keep stress levels low and strategic learning at the forefront, Faulker recommends regularly linking speedwork to the conceptual work needed for students to gain understanding. She also notes the importance of valuing student effort over correct answers, setting the purpose for speed-based practice, and providing opportunities for students to review and celebrate their individual progress. These strategies can shift fluency practice away from tasks that are anxiety-inducing and instead transform them into meaningful moments that are confidence-boosting!

The Power of Precise Feedback

As our students work hard to strengthen all these mathematical skills, a huge part of our role as tutors is to provide encouragement and feedback. The more precise our feedback, the more impactful. Precise feedback sounds like taking that extra minute to offer students specific language that celebrates the work they are doing and the way they are doing it. For example, rather than saying “Great job,” we might say, “I see how you organized the cubes into trains of ten to help you solve! Great thinking!” We might even ask an additional question like, “I see that you organized the cubes into trains of ten. Can you explain to me how you used those trains to solve the problem?” Precise feedback acknowledges student thinking and gives them the opportunity to reflect on that thinking themselves. To learn more, check out this six-minute video, which shows elementary students learning how specific feedback enhances outcomes.