What is Fluency?

Fluency is...

• ‘knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems.’ (Parish 2014, p 159). Whether or not we believe that fluency requires more than the recall of math facts, research evidence points in one direction: The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense (Boaler, 2015).

• “Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. It is important to push sensitively and encouragingly toward fluency of the designated numbers at each grade level, recognizing that fluency will be a mixture of these kinds of thinking which may differ across students.” (CC/OA Progression, p. 18)  

• Fluency comes about when students develop number sense, when they are mathematically confident because they understand numbers (Boaler, 2015). 

• Fluency is NOT performing quickly and accurately under timed pressure.

The Truth about Isolated Fact Memorization

• What research tells us is that students understand more complex functions when they have number sense and deep understanding of numerical principles, not blind memorization or fast recall (Boaler, 2009). 

• Mathematics is the leading cause of students’ anxiety and fear and the unnecessary focus on memorized math facts in the early years is one of the main reasons for this (Boaler, 2015).

The Truth about Speed and Mathematics

• Sian Beilock and her colleagues have studied people’s brains through MRI imaging and found that math facts are held in the working memory section of the brain. But when students are stressed, such as when they are taking math questions under time pressure, the working memory becomes blocked and students cannot access math facts they know (Beilock, 2011; Ramirez, et al, 2013). As students realize they cannot perform well on timed tests they start to develop anxiety and their mathematical confidence erodes. 

• Timed tests at an early age are directly linked to math anxiety.

Required Core Fluencies 

Kindergarten: Add and Subtract Within 5 (K.OA.5)

First Grade: Add and Subtract Within 10 (1.OA.6)

Second Grade:

• Single-digit sums and difference from memory (2.OA.2)

• Add and Subtract Within 100 using strategies (2.NBT.5)

Third Grade:

• Single-digit products and quotients from Memory (3.OA.7)

• Add and Subtract within 1,000 using strategies (3.NBT.2)

Fourth Grade: Add and subtract within 1,000,000 (4.NBT.4)

Fifth Grade: Fluently multiply multi-digit whole numbers with the standard algorithm (5.NBT.5)

Sixth Grade: Multi-digit division with the standard algorithm (6.NBT.2) 

(Source: Utah Core & AchievetheCore.org)