Why Don't We Count Zero?: Understanding Number Lines

On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of length. In addition, transitioning from counting a set of objects to quantifying iterated lengths on a number line can be confusing for students. In the authors' work with students, they draw students' attention to recognizing what units mean and how units are used on a number line. The authors found that after first defining a unit of length (e.g., from 0 to 1) when measuring or creating a length, students are able to make sense of number and quantity on a number line This article describes the authors' experiences with developing students' understanding of concepts underlying the number line within a measurement context. Using carefully sequenced lessons, the students described how the number line showed the iteration of the same unit. This provided a basis for understanding more sophisticated concepts, such as how a smaller unit will need to be iterated more frequently than a larger unit to measure the same quantity. If students are struggling, reflect on how to introduce the number line and take the time to facilitate a discussion that focuses student attention on the units and lengths, rather than on the tick marks. Use measurement vocabulary, such as unit and length, when discussing the number line. This will help students build a robust and flexible understanding of the mathematics concepts underlying this tool.