Revision of Freshman Calculus To Improve Success of Engineering Undergraduates
We describe a program to improve the success of engineering students in two Freshman-year Calculus courses which are a foundational gateway to success in subsequent technical courses.
The primary goal of the project was to reduce the number of students with poor performance in the Calculus I & II courses taken by all engineering and science students in their Freshman Year as evidenced by the number of students with grades of D, W (Withdraw) or F (Fail). The project, which was initiated as a pilot then fully scaled, involved modularizing the two courses and also introducing a flipped classroom pedagogy model as an evidence-based approach shown to enhance student engagement.
The two 4-credit Calculus I & II courses were split into into four half-semester modules with a remedial half-semester module for at-risk students, thus providing better flexibility to match studentsﾒ progress. A diagnostic test administered to incoming Freshmen is used for initial placement in modules, particularly for those with poor preparation and also those who can advance through prior AP knowledge. Course content was reduced to allow for workshops to involve group work with less lecturing or ﾓteaching to the testﾔ. A gate system was incorporated on key topics that students must pass to progress or drop back to repeat the module or take the remedial module. Some lectures were placed online for students to view before class, especially those associated with gate topics. Class time is used more for problem solving and especially for modeling activity using authentic problems from science and engineering to address concepts, rather than just learning manipulations and algorithms for solving mathematics in the abstract. More recently an advanced, adaptive online tutoring tool, developed in-house, has been implemented in support of the online component of the pedagogy. It provides personalized, timely feedback to students to facilitate learning, responsive to the varying paths that students may take to solutions and to their common misconceptions and mistakes.
The impact of the overall changes has been dramatic with the number of students with the grades of D, Withdraw or Fail dropping from approximately 33-36% of all students before the interventions to 15-17% after full scale-up of the pilot. We are extending this approach to the sophomore-level core mathematics courses.
The Calculus courses that are the subject of this report are typical of those found in undergraduate engineering and science programs nationwide. Our results therefore have the potential for informing a broad constituency of educators on ways to improve student learning and with the prospect for positively impacting persistence in STEM programs.
Some faculty members who considered themselves good teachers and had historically received good student evaluations of their teaching found their ratings dropped when they implemented the evidence-based approaches to teaching of the project. This required a very supportive department chair and the Dean to provide encouragement to persist with the interventions.