Student understanding of quantum mechanical expectation values in two different curricula

As part of ongoing research to better understand how students relate Quantum Mechanics concepts to formalisms, we are studying student understanding of expectation values as well as the variety of mathematical representations they use for formalizing them in two different teaching paradigms. Analyzing students' written responses to a series of open-ended research questions has given us some insight into students' common interpretations of this concept, as well as the frequency of the various mathematical formalisms they use to represent expectation values. The results show some common patterns between students in Spin First (SF) and Position First (PF) curricular, as well as some differences.