  One desired outcome of introductory physics instruction is that students will
develop facility with reasoning quantitatively about physical phenomena. Little
research has been done regarding how students develop the algebraic concepts
and skills involved in reasoning productively about physics quantities, which
is different from either understanding of physics concepts or problem-solving
abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL)
as a tool for measuring quantitative literacy, a foundation of mathematical
reasoning, in the context of introductory physics. We present the development
of the PIQL and evidence of its validity for use in calculus-based introductory
physics courses. Unlike concept inventories, the PIQL is a reasoning inventory,
and can be used to assess reasoning over the span of students' instruction in
introductory physics. Although mathematical reasoning associated with the PIQL
is taught in prior mathematics courses, pre/post test scores reveal that this
reasoning isn't readily used by most students in physics, nor does it develop
as part of physics instruction--even in courses that use high-quality,
research-based curricular materials. As has been the case with many inventories
in physics education, we expect use of the PIQL to support the development of
instructional strategies and materials--in this case, designed to meet the
course objective that all students become quantitatively literate in
introductory physics.
