Tutorials And In Class Activity For Improving Student Performance In A First Year Engineering Course

An important factor in student satisfaction and retention in engineering courses is their prerequisite knowledge. We seek to address the needs of these students who are not calculus-ready upon entering our first year engineering program by introducing self-paced video tutorial modules that deliver background in basic engineering mathematics, and an in-class activity applying those mathematical concepts. We are focusing on logarithms and trigonometric functions, as they are used ubiquitously in engineering, and have been identified as particularly problematic for students in our classes. Because future engineering classes will demand frequent recall of these mathematical concepts, the modules and demonstration focused on tying these concepts to prior knowledge in hopes of reducing cognitive load. The objective of this study is to examine the effects of having first year engineering students use these resources in terms of student performance and their perception of their own learning gains. We based the design of the resources on social constructivist theory, allowing students to build on what they already know. The video modules on trigonometric functions take students from very basic definitions and relationships to solving equations using these terms. Through an inclass activity using sine functions, students observe real objects in cyclic motion, collect data from them, manipulate the data, interpret it, and make predictions about how related systems will behave. This essentially moves students through the levels of Bloom’s taxonomy from knowledge to synthesis. The experimental design consisted of comparisons between three main groups: 1) controls, 2) those who viewed the tutorials, and 3) those who viewed the tutorials and participated in the in-class activity. Student performance on preand postcontent tests, and self-assessments of learning gains were compared. We report on results of these assessments, and their implications for affecting change in student success, especially for students with weak pre-requisite skills. Introduction Students entering our first year engineering course arrive with different levels of mathematics preparation, which is of critical importance to their academic success. In our program, students scoring below a proficiency level on an institution-wide mathematics placement test are enrolled in a first semester course with an additional one-hour session (“recitation”) for content review and practice. However, even with this support, 53% of these students earned a D or F, or withdrew from the course (DFW rate). This is over twice the DFW rate of 20% for all other first year engineering students. The US is one of the few industrialized nations that do not have national mathematics standards 1 . Seventy-two percent of the states require three or less mathematics courses for a high school diploma, while twenty two percent require four mathematics credits. Consistent across states is P ge 14284.2 the college preparatory coursework offerings of Algebra I, Geometry, Algebra II, Pre-Calculus, and Calculus. To assure that students in our program have achieved a mastery level in basic mathematics skills necessary to move on to more complex topics in engineering, they are required to pass a mathematics mastery test. The test draws from high school mathematics content (60% PreCalculus, 10% Algebra I, and 30 % Algebra II). Sample test questions are listed in the Appendix. Students are given three attempts to pass the test with a passing grade of 80% or higher on a tenitem test. We have administered this test for six years, and have observed a high failure rate in spite of the fact that nearly all incoming engineering students have taken Pre-Calculus and Algebra I/II in high school. For the students entering our program in Fall 2008, 83 % had taken Calculus (and in some cases, Calculus II) in high school, yet only 40 % of all students passed the mathematics mastery test on the first attempt. A summary of high school mathematics preparation is shown in Table 1. Students who were not calculus-ready based on a university-wide mathematics placement test are particularly prone to high failure rates on this test. Engineering students scoring below a certain level on this test are placed in Pre-Calculus. All other students taking Calculus during their first semester enrolled in a two-credit introductory engineering course (CES 102). Students taking Pre-Calculus enroll in a similar course, with an additional credit hour of “recitation” for reviewing basic skills and practicing engineering problem-solving (CES 101). In order to help students in these courses master the required basic mathematics, we have developed supplemental course materials that they can access at a self-regulated pace outside of class. Table 1. Summary of mathematics courses for which students in the first year engineering courses earned high school credit. Students taking Pre-Calculus during their first semester in college were enrolled in CES 101; those taking Calculus were enrolled in CES 102. First Year Engr Course Section Algebra 1, Geometry Algebra 1, Geometry Algebra 2 Algebra 1, Geometry Algebra 2, Statistics Algebra 1, Geometry Algebra 2, Pre-Calculus Algebra 1, Geometry Algebra 2, Pre-Calculus, Statistics Algebra 1, Geometry Algebra 2, Pre-Calculus, Calculus (+) All CES 101 1 0 1 25 12 56 95 CES 102 0 2 0 49 7 440 498 All 1 2 1 74 19 496 593