Using Incorrect Worked Examples to Investigate the Consistency of First and Third Graders’ Measurement Conceptions

Elementary students demonstrate conflicts when measuring with rulers as well as measuring with discrete units. Their conflicts often lie in their focus on counting tick marks or focusing on the endpoint of objects on rulers or ignoring spaces with discrete units. In this study, we also investigated another area of conflict: students’ conceptions on where measurements should start on a ruler. Across two time points, 32 first graders and 37 third graders responded to a series of measurement tasks in the form of incorrect worked examples meant to expose students to these common conflicts of where the measurement starts and how to determine the overall length. Although students often said the objects should start at one, they were more likely to indicate that the object should be aligned with zero the closer the object was positioned to zero. However, many students said starting at the edge of the ruler (before zero) was okay, effectively equating the edge with either zero or one. Interestingly, on two related worked examples, their continuous and discrete measurements were not associated with each other. The incorrect worked examples helped illustrate important areas for further instruction, especially around their conceptions of rulers’ edges and the impact of spaces with discrete units.