Impact of mathematical reasoning on students� understanding of quantum optics

We report on an investigation in which we compare the conceptual performance of upper-level undergraduates and graduate students, who worked on two different validated Quantum Interactive Learning Tutorials (QuILTs). One of the QuILTs incorporates mathematical reasoning while focusing on helping students develop a good conceptual understanding of quantum optics using a Mach-Zehnder Interferometer with single photons and polarizers. Performance of students who engaged with this “hybrid” (integrated conceptual and quantitative) QuILT is compared with those who engaged with a conceptual QuILT focusing on the same topics without quantitative tools. We find that the posttest performance on conceptual questions of physics graduate students who engaged with the hybrid QuILT was generally better than those who engaged with the conceptual QuILT. For undergraduate students, the results were mixed.