Over the last few years, I’ve worked to support elementary teachers across several states with the teaching and learning of mathematics. Many times, the most meaningful activities I model in classrooms are those that build fluency and number sense. Almost everyone believes that learning how to read and being able to read fluently with comprehension are extremely important. Although I am not an expert on the teaching of reading, I do know that to be able to read, I must know the letters of the alphabet and how they are put together to form words that have meaning. Fluency with numbers and having number sense are every bit as important as reading fluency and comprehension. In fact, research shows that early academic skills in reading and math are significant predictors of future academic success (Torgesen & Burgess, 1998; Watts et al., 2014). Students who struggle with math coming out of the primary grades continue to struggle with math the rest of their school careers.
Within all states’ standards there are specific fluencies with numbers and operations to be accomplished at each grade level K–6. Fluency is much more than memorization of facts and procedures. In Adding It Up (2001), the National Research Council describes procedural fluency as “knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently” (p. 121). Additionally, standards indicate an understanding of what we call “number sense” as critical for developing mathematical proficiency. Gersten and Chard (1999) describe number sense as “fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.”
For number sense and fluency, students must learn numbers. They must make sense of numbers—how numbers are put together to have meaning. For example, the decomposition of the word cat is /c/, /a/, /t/. When the letters are put together in that order and sounded out phonetically, the word cat is formed. Numbers are much the same way. If I have the number 258, I need to make sense of the digits used to form the number: 2 means two hundreds; 5 means five tens; and 8 means eight ones. Hence when put together in that order, the numbers represent a value of 258—to describe the number of objects being counted. Of course, 258 can be thought of in different ways; for example, 258 can be described as 25 tens and 8 ones, or 258 ones. This is having a sense of numbers and how they work together in a base 10 number system. Being able to compose and decompose numbers fluently with understanding opens the doors for students to build conceptual understanding and procedural fluency in operations with numbers, all of which lead to greater opportunity for success with higher-level mathematics (algebra and beyond).
In reading, without the knowledge of letters and sounds and how they both work together, written words have little or no meaning to students. This is true of numbers as well. Students who are fluent in numbers and operations and have a sense of how they all work together have much greater success with middle and high school mathematics. Therefore, meeting the fluency standards at each grade level and having a strong sense of numbers promote success in future mathematical learning.
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33(1), 18–28.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Torgesen, J. K., & Burgess, S. R. (1998). Consistency of reading-related phonological processes throughout early childhood: Evidence from longitudinal-correlational and instructional studies. In J. Metsala & L. C. Ehri (Eds.), Word recognition in beginning literacy (pp. 161–188). Hillsdale, NJ: Lawrence Erlbaum and Associates.
Watts, T. W., Duncan, G. J., Siegler, R. S., & Davis-Kean, P. E. (2014). What’s past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43(7), 352–360.