Helping Instructors Prepare Students in Prerequisite Math Courses

During discussions in SIMPLE meetings, a concern that came up early in the Fall 2015 semester was how prerequisite mathematics classes are not homogeneous, which means students have varied levels of preparation, and in some unfortunate circumstances, students are not completely ready for their current course.  Since instructors can get behind, or that classes are sometimes canceled (e.g., snow days), we considered which topics could be listed as optional in Calculus 1 and 2, and we discussed the possibility of providing instructors of these courses with target schedules. Little discussion happened in the SIMPLE meetings regarding the course which many students place when they enter GMU: Precalculus Mathematics.  Consequently, I decided to collect, create, refine, and organize resources for future instructors of Precalculus.

The first time I taught Precalculus was in Fall 2015, and the only reason I managed to cover all of the required topics was because colleagues with experience teaching this course provided me with a suggested schedule.  In the fall, I made minor adjustments to the schedule I had been given, but before the Spring 2016 semester, I was worried because Trigonometry, the topic with which students struggle the most, was covered at the very end of the semester.  Since trigonometry cannot be cut short, in the Spring 2016 semester, I experimented with teaching trigonometry in the middle of the semester as Unit 2 (after linear functions and quadratics, but before rational, exponential, and logarithmic functions).  This change meant that I had to introduce some topics differently than laid out in the textbook.  For example, vertical asymptotes are first encountered in detail with the tangent, secant, cotangent, and cosecant functions, not rational functions.  While it would be difficult to define, and even more so measure, success of this idea quantitatively, there are two benefits.  I realized that in addition to getting through all of the required sections on trigonometry, this new concept map meant that I also covered trigonometry at a time in the semester when students had more mental energy than they do in the last two weeks of the semester. 

Because students are expected to be familiar with how technology may aid in solving mathematical problems, I wrote assignments for my precalculus students to complete in Mathematica, a popular computer algebra system.  These assignments were also used by at least one colleague.  This semester, I rewrote most of the assignments to expose students to more commands in Mathematica and applications of the mathematical concepts.

A colleague and I also put together a suggested syllabus to help encourage uniform policies (e.g., whether calculators are allowed on assessments) so students have similar levels of expectations and preparations in prerequisite courses.

To bring all of the above together, I consulted with yet another colleague about a good way to establish a repository for the materials we now have for precalculus instructors.  For now, we decided to use a Blackboard group to host the materials.  As this semester draws to a close, I will place the administrative resources I have noted along with the exams and quizzes I used for the last two semesters in this Blackboard group.  I hope that these recourses will be beneficial to future instructors of precalculus who are daunted by the volume of material that needs to be covered and the need to have a technology component.  My organization is already continuing to other courses: I have drafted a target schedule for my section of Calculus 1 in the Fall 2016 semester.