When are we ever gonna use this?

By Jennifer Bay-Williams
October 21, 2016

Before reading on, think about the first words that come to your mind when you hear this phrase. Hold that thought while we look at two examples.

1. Solve 5009 – 2995 = ?  This could be solved by regrouping (standard algorithm) or using a mental strategy (e.g., they are 2000 apart, plus another 14 apart, so the distance/difference is 2014). The challenge is to know when you want to use a mental strategy and when you want to use a standard algorithm. Our question to students: When are we ever gonna use this (mental strategy)? Perhaps when the numbers are close benchmarks.

2. Solve 4 × 2 1/3 = ? Recently a student explained it to me this way: I thought of it as  (3 × 2 1/3) + 2 1/3. Then, 3 twos is 6, three thirds is one more, so 7, and 7 plus 2 1/3 is 9 1/3. I asked, why did you do it this way and she explained that it is easier to multiply 1/3 by 3. Many students don’t understand when they can take a number apart (e.g., changing 4 into 3 + 1) and when they would want to (e.g., avoiding messy fractions). They are then stuck with a standard way to compute, an accurate way, but not always efficient (and prone to errors). 

Procedural fluency includes four components: accuracy, flexibility, appropriate strategy selection, and efficiency. The examples here illuminate the difference between knowing algorithms and having procedural fluency. These students not only have a repertoire of strategies, they have an idea of when one of those strategies is a good choice. 

How do you help each and every student develop this flexibility? Share a worked example and discuss for what situations will that strategy be an efficient option. In other words, ask, “When are we gonna use this?” I hope you now have new words come to mind with this age-old question – words like flexibility, number sense, higher-level thinking, and reasoning. 

When are you going to learn more ways to support student development of procedural fluency?

Be sure not to miss Jennifer's session at the 2017 NCTM Annual Meeting in San Antonio:

Pathways to Procedural Fluency

This session zooms in on the PtA Teaching Practice "Build procedural fluency from conceptual understanding" taking a look at research and connecting that research to instructional strategies that provide pathways to procedural fluency.