Recommendations for Lecturer in Mathematics

March 1, 2002

We are delighted to have you as an lecturer of the Department of Mathematics at Central Washington University.

Aim high!
By virtue of your appointment as a lecturer, you represent the Central Washington University Mathematics (CWU) Faculty. Therefore, in teaching Cornerstone mathematics courses, you are expected to faithfully and expertly complete the course material with your students. More importantly, at the end of the course, your students should be as well-prepared on average as CWU students taking the same course.

Remember, part of the Cornerstone experience is bridging for your students the cultural gap between high school and college. You should provide them with a course at or above the level of difficulty of a "typical" college level course of the same type. If you fail to do this, your students will pay the price of under-preparation in their first college mathematics courses. On the other hand, providing your students with a rigorous precalculus or calculus course gives them a solid head start in their pivotal first college year.

Use texts such as Contemporary Precalculus by Thomas Hungerford or Single and Multivariable Calculus by Hughes-Hallet, Gleason, MaCallum, et al. The CWU mathematics department faculty strongly recommends that you use the same texts that they use. The Hungerford and Hughes-Hallet texts are sound pedagogical tools that bridge the gap between traditional and reform texts. Those texts were chosen by faculty members at CWU, because they best represent the department's beliefs about precalculus and calculus teaching and learning. In any case, you must secure at least one copy of the recommended text for a course, so that you may use it for reference.

Employ The Rule of Three.
A modern approach to teaching mathematics would be remiss without a modern goal: students should learn mathematics via the "Rule of Three." This means that nearly every pre-calculus or calculus concept has multiple conceptualizations: graphical, symbolic, and numerical. You are expected to teach precalculus and calculus using the Rule of Three as a caveat, liberally employing technology to aid conceptualization as well as computation. While it is difficult, given tight pedagogical time frames, to know how much time to devote to a particular conceptualization, at least one research outcome is clear: students who learn by the Rule of Three connect the material in a very meaningful way.

The spirit of the Rule of Three demands that students learn to employ the best problem-solving strategy based on a combination of accuracy and efficiency. This means that a simple algebraic solution could by valued higher than a simple numerical or graphical solution by virtue of accuracy. On the other hand, numerical and graphical strategies drive applications in the real world, since many problems are not otherwise amenable to solution. Help your students learn elegance and sophistication in their problem-solving by repeatedly comparing and evaluating different strategies.

Use the list of Student Outcomes provided with this packet.
You should have been provided with a list of learner outcomes for each Cornerstone mathematics course you teach. These outcomes are inextricably tied to the recommended text for that course, and at CWU exams and other assessments are written with these outcomes in mind. Use the list of outcomes to check that course content has been well-learned.

Use a variety of types of assessment.
The CWU mathematics department uses a variety of assessment types, including group projects and presentations, as well as the more traditional "big three": homework, quizzes, and tests. You are encouraged to do the same. We also suggest that you give your students a substantial comprehensive final examination, since that is the accepted practice at CWU. For each Cornerstone mathematics course, a sample examination from the Department of Mathematics has been provided with this packet. The final examination should be one and one half to two hours in duration and should well cover the course material. You must keep copies of students' graded final exams for at least one year after they have completed their Cornerstone course. You may be required to submit these to the Cornerstone Mathematics Coordinator. You may also be asked to gather other data from your students for the purpose of Cornerstone program assessment.

Again, we are delighted you are teaching Cornerstone mathematics courses. Your dedicated participation in this program benefits your students, the relationship between your school and CWU, and you! Call us if you have questions.