>>12181240>I once asked a colleague of mine why he so liked word problems, and his answer was: “I likethem because one can assign good problem sets.”
>My colleague’s error consisted of believing that the more testable the material, the more teachable it is. A wider spread of performance in the problem sets and in the quizzes makes the assignment of grades “more objective.” The course is turned into a game of skill, where manipulativeability outweighs understanding
>The word problems that we find in differential equations textbooks are shameful. They areartificial, dishonest, unrealistic, contrived, repetitive, and irrelevant. I cannot see how a student can
learn anything by being forced to solve snowplow problems or Rube Goldberg flows of salt water
in communicating tanks.
>What can we expect students to get out of an elementary course in differential equations? Ireject the “bag of tricks” answer to this question. 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, and the justifications
I have heard of it, citing poor preparation of the students, their unwillingness to learn, and the
possibility of assigning clever problem sets, are lazy ways out.
>In an elementary course in differential equations, students should learn a few basic concepts thatthey will remember for the rest of their lives, such as the universal occurrence of the exponential
function, stability, the relationship between trajectories and integrals of systems, phase plane analysis, the manipulation of the Laplace transform, perhaps even the fascinating relationship between
partial fraction decompositions and convolutions via Laplace transforms. Who cares whether the
students become skilled at working out tricky problems?
