|Title||Teaching Relative & Overall Phase with the Arms Representation|
|Year of Publication||2021|
|Authors||Hahn, Kelby T., and Gire Elizabeth|
|Keywords||ARMS, Quantum Mechanics|
The Paradigms @ OSU team developed a kinesthetic representation for complex numbers where individual students use their arms to embody an Argand diagram. This representation can be expanded to have groups of students working together to represent complex-valued state vectors in quantum mechanics. We conducted group teaching interviews about the relative and overall phase of 2- and 3-element state vectors to uncover how students understand geometric relationships using the Arms Representation. We interviewed nine students in the second week of a junior-level, spins-first quantum mechanics course after they had been introduced to complex numbers via the Arms Representation, but before quantum mechanical state vectors had been addressed in class. This poster will discuss how the Arms Representation supported students in understanding that an overall phase does not change the relative phase. In particular, we will attend to the conceptual support offered by the Arms Representation, the geometric interpretations of phase, and the ways students translate between the Arms Representation, Argand diagrams, and algebraic notations.