Language Fluency gives insights into Procedural Fluency
2017 NCSM Annual Conference
Session date/time: 4/5/17 at 10:00 am
By Jennifer Bay-Williams
If you have learned a language and tried to speak it in your travels, or to others who speak it fluently, you may have found yourself lacking the words you need to say something, and instead using a less desirable way to try to communicate your ideas. This has certainly happened to me in my attempts to communicate in Spanish, where I have wished I had more options available to communicate my ideas accurately, efficiently and in the way I want to present the idea. In the same way that language fluency opens up more and better ways to communicate, procedural fluency provides access to more and better ways to do mathematics. In the sections here, I use language as a launch into understanding the ‘basics’ of procedural fluency.
- Accuracy. Certainly we want to have the right word choice! I recall in high school wanting to say I was embarrassed and guessed I should use the Spanish word embarazada. My Spanish teacher was quite surprised to hear I was pregnant! In mathematics, we want to be sure we pick correct algorithms for the situation and employ them flawlessly. Students recognize a situation that calls for multiplication, for example, and can employ a strategy to get to the right answer.
- Efficiency. If you have tried to keep up with someone fluent in a language you are learning, you can appreciate one aspect of efficiency – speed. But, efficiency is more than speed – it is also about how many words you pick to convey your idea. Why say, “If you are thinking about where you might find the nearest coffee house, then I think you should go to the one that is two blocks down Central Avenue,” if you can say, “The nearest coffee house is two blocks down Central Avenue.” In mathematics, efficiency is not just speed with a strategy, it is also choosing an efficient strategy. Students’ first thought when they see a new problem needs to be, “Which strategy might be the most efficient for this problem?”
- Appropriate Selection & Flexibility. Think of how many ways you can say something like “I’m hungry” it in your first (fluent) language. In your fluent language, you not only know a lot of ways, but you likely select a different option when you are at work, with family, or out with friends. Compare this to how you say the same phrase in a language in which you are not fluent. Similarly, if students know only one way to do a problem type (or if they think they are supposed to use a particular way the teacher demonstrated), they are not procedural fluent. A student with procedural fluency has access to a collection of ways to do a problem, and decides on the ‘best fit.’ These last two aspects are critical to procedural fluency, and they take time and explicit attention for them to develop.
How do we help each and every student develop procedural fluency? We make sure that through our leadership we provide forums that move the focus on fluency beyond speed and accuracy with standard algorithms, to the complete package of accuracy, efficiency, appropriate strategy selection and flexibility. We will explore procedural fluency in more depth, and connect these ideas to concrete classroom actions and activities. Hope to see you there!