Building Fluency and Number Sense

I think the most important thing elementary school teachers can do in math class is to build students’ fluency with rational numbers.  The research shows that weak number sense and fluency underlies many difficulties students have with math (Geary, Bow-Thomas, & Yao, 1992).

Just to be clear, I don’t mean having students memorize their multiplication tables or race to answer questions the fastest.  I mean having them be fluent with numbers similar to the way we think about being fluent in a language.

Here’s a definition of fluency from NCTM’s Principles and Standards for School Mathematics: “Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently” (p. 152).

To me, that means I need to ask:

• Can they work flexibly with numbers?  Can they decompose and recompose different numbers easily and in a variety of ways?
• Can they use mental math to solve problems or do they always need to resort to pencil and paper and a traditional algorithm?
• Do they have efficient ways to solve problems?

I’ve heard a lot of complaints recently about attempts to teach fluency to students–mostly related to complaints about the common core. Parents don’t understand why we are teaching students these new ways to add or subtract instead of the just showing them the traditional algorithm they learned in school.

The thing is that many of these strategies aren’t new. Students who have strong number sense and fluency have been developing these strategies on their own. What’s new is that we are now explicitly teaching all students these strategies. A parent who attended one of my workshops explained it nicely:

• This makes more sense to me than to me than how I learned math.  I am an Engineer with 5+ years of calculus and I find the thought process to solve the problems the kids are working on is much closer to how I think, but I had to figure it out on my own.

I’ll talk more about some of the ways we can develop fluency in students, but if you want to read about it now, check out:

O’Loughlin, T. (2007). Using Research to Develop Computational Fluency in Young Mathematicians. Teaching Children Mathematics, 14(3), 132-138.