In 1974 the Swedish pop group ABBA had their first hit with a tune called Waterloo. While the song is written and performed in English, only two of the group spoke English at the time. The two female singers (and the two A’s in the group’s name), Agnetha and Anni-Frid, had very little understanding or ability in English when they recorded the song. Bjorn and Benny were fluent English speakers and wrote the lyrics, then trained the ladies how to sing the song phonetically. The song made them international stars, and by the time they released the smash hit Dancing Queen was released a few years later, Agnetha and Anni-Frid were much more fluent English speakers.
This situation raises some questions I’ve been pondering a lot lately. What does it mean to be fluent in a language? What is math fluency? What are the connections between linguistic and mathematical fluency? When students seem to be fluent, could they be just mimicking procedures the way Agnetha and Anni-Frid were singing? And why are those sappy ABBA songs so catchy?
Not surprisingly there is a lot of debate and strong emotion surrounding these questions. A recent New York Times opinion piece called for more drill and, seemingly, less fun in the classroom to increase fluency. This article drew heated rebuttal, but also support. I recently sat with a group of teachers who were wrestling with the idea of fluency as a school site. As we talked, I heard very familiar concerns. If we don’t practice math fact fluency, can kids perform necessary procedures? How do we encourage speed without turning students off to math? Does speed even matter; is that what fluency means?
Out of curiosity, I combed through the Common Core State Standards. What I found was that procedural fluency is consistently listed as something separate from conceptual understanding. Is that even possible? A 2015 article by Dr. Jo Boaler argues that number sense, conceptual understanding, and fluency are inextricably intertwined.
There are a few things I know for sure and will argue about passionately. First, using a stopwatch in math to measure student learning is a reprehensible and damaging practice which has nothing to do with fluency or math understanding. Second, number sense comes from mathematical experiences, not from repetitive drills. Thirdly, Dancing Queen is a mighty fine pop song. Other than that, I still have a lot of questions about how to define and best encourage mathematical fluency among students. What are your thoughts? I would love to hear them.