  Modeling the creative mathematical sensemaking that characterizes expert
thinking in physics is typically a struggle for new learners. To help students
learn to reason this way, we created a set of supplemental activities called
Physics Invention Tasks (PITs)*. PITs engage students in quantification, the
process of mathematically generating quantities central to modeling in physics.
PITs depict a scenario in which students need to engage in decision-making
associated with creating quantities in order to resolve a problem. Students
make decisions about the arithmetic construction, the magnitude and associated
unit, and in some cases spatial direction of a new quantity. The design of PITs
is informed by Inventing with Contrasting Cases, an instructional approach
shown to foster generativity, i.e., creativity with mathematical structures. In
this paper, we describe the theoretical foundation of PITs, and their structure
and implementation. We share preliminary observations of the impact of PITs in
one course, averaged over two years, as measured by the FCI and CLASS. We see
an improvement in the FCI normalized gain corresponding to the introduction of
PITS and we see CLASS pre- to post-test gains that may be the highest reported
from a large enrollment calculus-based physics course. We discuss future
research into the learning mechanisms and instructor influence associated with
PITs.
  *available at http://inventiontasks.physics.rutgers.edu
