Images of Fractions 'as' Processes and Images of Fractions 'in' Processes

Within the large range of potential theoretical perspectives on fractions, this paper considers one particular interpretation: fractions' duality as process and object. By considering the number-fractionbar-number composite symbol as simultaneously representing division and rational, some process-object theories imply that fraction-as-process and fraction-in-process should be highly related. Our research studied the images evoked in these two situations across a wide range of learners and shows that while students attempted post-hoc justifications of their fraction-in-process calculations using their fraction-as-process images, these images were rarely compatible with the process of addition. Thus, we suggest that the routes to seeing the fraction symbol as process and as object may be cognitively separate. [For complete proceedings, see ED489597.]