Tracking Time: Representing Elapsed Time on an Open Timeline

Abstract

Elapsed-time problems are notoriously difficult for children (Monroe, Orme, and Erickson 2002). Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM 2006). This absence of instruction may be due to a position held by some mathematics educators that telling time and determining elapsed time are life skills rather than skills delegated to mathematics instruction. (See Editor's note.) However, time is addressed in the Principles and Standards for School Mathematics (NCTM 2000) Measurement Standards for both the pre-K–2 and 3–5 grade bands. And regardless of one's perspective on the delegation of time as a discrete content area, determining elapsed time is encountered during mathematics instruction by most children at some point and is often met with frustration. This is especially true when the start or end time falls between the hour and half hour. Children find it challenging to keep track of unit changes between hours and minutes. On a national assessment, only 58 percent of eighth-grade students were able to correctly identify that 150 minutes equals 2 1/2 hours (Jones and Arbaugh 2004). Elapsed-time instruction often focuses on converting units and keeping track of those conversions rather than on counting up or back from one time to another. This article examines how students are able to make sense of elapsed-time problems when instruction is connected to open number-line strategies. Adapting this technique–typically used for recording addition and subtraction counting strategies–provides a method for supporting students' thinking about elapsed-time problems.