Katrina E. Black

Procedural Resource Creation in Intermediate Mechanics

A problem in resource theory is describing the creation of new, high‐level resources. We model resource creation by analyzing four student groups separating variables during a group quiz on air resistance. We assess each group’s fluency and two observables: use of overt (such as divide, subtract, equals) and covert (such as moving, bringing, or pulling over) mathematical language and use of accompanying gestures (such as circling, grabbing, or sliding). For each group, the type of language and gesture used corresponds to how easily they carry out separation of variables. We create resource graphs for each group to organize our observations and use these graphs to model the creation of the procedural resource Separate Variables.

Students’ Use of Symmetry with Gauss’s Law

To study introductory student difficulties with electrostatics, we compared student techniques when finding the electric field for spherically symmetric and non‐spherically symmetric charged conductors. We used short interviews to design a free‐response and multiple‐choice‐multiple‐response survey that was administered to students in introductory calculus‐based courses. We present the survey results and discuss them in light of Singh’s results for Gauss’s Law, Collins and Ferguson’s epistemic forms and games, and Tuminaro’s extension of games and frames.

When basic changes to a solution suggest meaningful differences in mathematics

When solving two integrals arising from the separation of variables in a first order linear differential equation, students have multiple correct choices for how to proceed. They might set limits on both integrals or use integration constants on both or only one equation. In each case, the physical meaning of the mathematics is equivalent. But, how students choose to represent the mathematics can tell us much about what they are thinking. We observe students debating how to integrate the quantity dt. One student seeks a general function that works for everyone, and does not wish to specify the value of the integration constant. Another student seeks a function consistent with the specific physics problem. They compromise by using a constant, undefined in value for one student, zero in value for the other.