Abstract: I will discuss results from an exploration of how students construct and employ meanings for multiply-quantified relationships. We analyzed a series of task-based interviews with graduate students taking a real analysis course as they work to understand and prove the Arzelá-Ascoli Theorem. I will present our categorization of foregrounding and backgrounding actions these students employed to focus their attention as quantification operationalizations or “quantops.” Finally, I will discuss ways in which the students’ quantops interacted with their evolving goals and problem-solving.
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