Many upper division students take linear algebra and differential equations from math departments. Sometimes the courses are separate, sometimes the two topics are linked. Often they are taught in multi-section format - Sometimes in lecture/recitation format, sometimes many smaller classes. Often they are required by many partner disciplines. Math faculty and recitation instructors may be unfamiliar with the applications. Many students from STEM majors want to see the applications. Thus the PD for lecturers and recitation instructors should involve faculty from partner disciplines who can introduce common misconceptions and explain sample problems for math people who may be unfamiliar.
Math people like generality and abstraction to facilitate a variety of applications. The folks I have talked to in STEM and Econ point out that their students are not familiar with the processes by which sample problems lead to general statements or the process by which abstract results can be specialized to applied problems.
Conversations will help as will concrete examples. Here is one from chemical engineering: Many situation are modeled as systems of linear equations. However the unknowns are usually denoted by letter suggesting the quantities they stand for and the coefficients may be called parameters not coefficients. The matrix of coefficients will likely not appear as doubly indexed letters Similarly the constants on the right-hand side may not appear as letters y with single subscripts. This difference of notational convention seems to be a major obstacle for the engineers. This is especially a problem for engineer who too an “integrated” ODE and Linear Alg course, where the emphasis may have been on single linear and non-linear ode’s rather than on systems of linear equations. CRAFTY publishes on these issues. Huge number of instructional staff in doctoral and masters universities may not be familiar with MAA at all or CRAFTY documents. Face to face PD discussions may be needed at least every other year to advance the trans-cultural understanding.