  Mathematical reasoning flexibility across physics contexts is a desirable
learning outcome of introductory physics, where the math world and physical
world meet. Physics Quantitative Literacy (PQL) is a set of interconnected
skills and habits of mind that support quantitative reasoning about the
physical world. The Physics Inventory of Quantitative Literacy (PIQL), which we
are currently refining and validating, assesses students proportional
reasoning, covariational reasoning, and reasoning with signed quantities in
physics contexts. In this paper, we apply a Conceptual Blending Theory analysis
of two exemplar PIQL items to demonstrate how we are using this theory to help
develop an instrument that represents the kind of blended reasoning that
characterizes expertise in physics. A Conceptual Blending Theory analysis
allows for assessment of hierarchical partially correct reasoning patterns, and
thereby holds potential to map the emergence of mathematical reasoning
flexibility throughout the introductory physics sequence.
