Abstract:

Our department was recently faced with designing a new calculus sequence for five new engineering majors beginning in the fall of 2011. This paper presents the initiatives that we applied to the single-variable calculus sequence along with the feedback that we received, and outlines the changes we plan to make to the program in the coming year. All engineering students were required to start in Engineering Calculus I, even if their placement test score suggested a lower start. To facilitate learning for this diverse group of students, we administered a midterm Gateway Exam on differentiation with a minimum passing score of 80%, and weekly laboratory exercises involving undergraduate peer-led instruction.

Our laboratory investigations took several forms. Some allowed students to develop concepts, such as the numerical exploration of limits through guided discovery, prior to their being introduced in class. Others allowed students the time to explore deeper applications from civil, electrical, biomedical, or mechanical engineering. Still others were designed to allow students to teach themselves particular topics, such as Newton’s method, by reading and analyzing technical documents. These investigations used a variety of technologies including Excel and graphing utilities.

At the mid-semester point, students at risk of failing the course were offered the option of beginning a ``Reboot'' which consisted of a hybrid intersession course which met in person during term and was fully online during break. The students took the final exam in person during the first week of the spring term. Students who passed the Reboot course were able to enroll in Engineering Calculus II on schedule.

For Engineering Calculus II, we used a second midterm Gateway Exam on methods of integration with a minimum passing score of 70% and weekly peer-led recitation sessions in the evening based on a supplemental instruction model. For overall assessment of success, all sections of each course administered a common final exam.

Our “Gateway” examinations are designed to assess our students’ readiness for subsequent courses. These contained the essential skills necessary for continuation and students were required to master them at an given level. Students who did not meet that level of proficiency retook the examination until they reached the required level of mastery.

Keywords:

Calculus, engineering, peer-instruction, hybrid.