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All About the Number Line

Derek Stiffler, Jessica Hofer, & Stephen Brazelle

A high percentage of U.S. students lack conceptual understanding of fractions, even after studying fractions for several years; this, in turn, limits stu dents ’ ability to solve problems with fractions and to learn and apply computational procedures in volving fractions. (Siegler et al., 2010). Millions of students across the United States strug gle with numbers and number sense, which directly leads to a struggle with concepts related to rational numbers and negative numbers. When students struggle with whole numbers and operations, that struggle then carries over to rational numbers and negative numbers. One of the most useful representations to show a number is on the number line. The number line is important as it can show the connection between decimals, fractions, and other types of numbers and to develop a sense of relative size among the num bers. It is an especially important representation because, unlike many other representations and models used in teaching, the number line plays an important role in mathematics to the most ad vanced levels. It is used for measuring scales and Cartesian axes, as well as embodying the abstract set of real numbers. (Widjaja, Stacey, & Steinle, 2011) The number line promotes conceptual understand ing of rational numbers. From an early age, stu dents are directed to using a number line to count whole numbers, compare whole numbers, and

model early elementary operations such as addition and subtraction. At some point during their later elementary math journey, some teachers tend to shift their focus to procedural fluency, rather than maintaining a focus on number sense and the num ber line. Number lines form strong connections to students ’ learning and understanding when com paring rational numbers starting in primary grades, through upper elementary, into their middle school years and beyond. Why are number lines so helpful for rational num bers? Number lines can show “... the continuity as pect of rational numbers, ” (Diezmann & Lowrie, 2006). From elementary, focus on whole numbers to upper elementary and middle school focus on fraction, decimal and percentages, to the higher level courses in upper middle school that focus on scientific notation and other aspects of the rational number system: students ’ knowledge of the num ber line can only help build their vocabulary and knowledge of these number sets. The number line helps to connect to other models used with the ra tional number system such as the array and set model to show there are multiple ways to show these numbers that have multiple forms. The un derstanding of the number line can be crucial for students in the younger grades and will continue to add on to their math knowledge when more subsets of the rational number system are added to their mathematical vocabulary.

Virginia Mathematics Teacher vol. 47, no. 2

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