Work in progress: What calculus do students learn after calculus?

Clinical interviews were held with students in senior level electrical engineering and methods of teaching secondary mathematics classes. These students had all completed a 4-semester calculus sequence including differential equations. Engineering students had then taken advanced classes applying mathematical ideas in real-world contexts while mathematics education students had taken a similar amount of coursework in advanced mathematics courses. Students were interviewed to determine how their conceptual understanding of function and accumulation (integration) had grown or regressed during work after calculus. Back-transfer, where later learning improves conceptual understanding of earlier material, was observed.