Introducing a spiraling construction to traditional courses such as Calculus 1, Calculus 2, Calculus 3 and Ordinary Differential Equations is quite challenging. This is primarily due to the fact that the University of Colorado DHSC is located in a major metropolitan area where students transfer in and out of our institution on a regular basis. In addition our state has a general transfer agreement between institutions, so that our institution must accept transfer credit from other in-state institutions. Thus our program must accommodate students who transfer in after Calculus 1, or even after Calculus 3.
As a result we have introduced spiraling only for a few basic ideas which seem to be common throughout engineering and science: differential equations and modeling. In Calculus 1 we use an ILAP to introduce both of these concepts via a major interdisciplinary project (see Interdisciplinary Lively Application Projects). The ILAP in Calculus 1 takes quite a bit of time and effort on both the instructor and students part. Differential equations are formally introduced in the third week of Calculus 2. By this time students have been through one ILAP and they find the ILAP in Calculus 2 significantly easier. In Calculus 3 students get introduced to an ILAP involving electrical and magnetic fields so that vector calculus becomes more meaningful. And by the time students take Ordinary Differential Equations (which is almost completely motivated by modeling real-world problems) it is hoped that students can solidify and appreciate the connections between a variety of disciplines.