Ten lessons I wish I had learned before teaching differential equations (1997) [pdf]
I couldn't agree with the last point more.<p>> A course taught as a bag of tricks is devoid of educational value. One year later, the students will forget the tricks, most of which are useless anyway. The bag of tricks mentality is, in my opinion, a defeatist mentality...In an elementary course in differential equations, students should learn a few basic concepts that they will remember for the rest of their lives...<p>I hated the DE cleass I took in college and it was largely because I felt like it was nothing but a bag of tricks.  I very distinctly remember one problem that seemed unsolvable until the teacher showed that you had to substitute a "2" with "1/2 + 3/2".  And then, to make matters worse, he put the exact same problem on the test.  So we were being rewarded, not for really understanding the core basic concepts, but for memorizing the tricks needed to solve specific problems.