June 20, 2010
June 20, 2010
June 23, 2010
15.239.1 - 15.239.11
Bridging mathematics concepts to engineering contexts: Just-in- time review modules
The basic problem addressed in this paper is that many engineering students do not remember the essential mathematics skills and concepts they learned in earlier math courses when they enter higher level engineering courses, and yet they need to apply these earlier math abilities to advanced engineering coursework. The challenge facing the instructor is how to bring all students up to mathematical mastery level as quickly as possible at appropriate points during the semester when core mathematical skills are needed, including during the first week of class, so that they can be successful in achieving the required learning outcomes in engineering courses. It is a challenge because the typical response by the instructors to poor pre-test scores is to lose valuable class time doing review of the pre-requisite material.
In a junior level biomedical engineering course, students were given a diagnostic pre-test covering essential math skills and concepts on day one of the course. This focused on functional substitutions, graphing equations, complex algebra, and evaluating improper integrals. It was found that very few students achieved a passing grade on this test as they entered the engineering course. After the pre-test, students were directed to a set of review materials for them to study to refresh their knowledge and skills. They then undertook a second in-class test a week later. The overall results, detailed results by test question and student responses to a set of survey questions will be reported in this paper. We will also compare the performance of this group of students on a selected final exam question with the performance of students from previous years, on a similar question.
These experimental data show that providing students with review material at the beginning of a semester helps them to achieve mastery in essential mathematical knowledge and skills. Using this study as the prototype, we started to develop a series of just-in-time mathematics modules which will provide a bridge between targeted mathematics concepts and applied engineering problems. Students will complete these modules prior to encountering these topics in engineering courses. The starting point would be to assess their entry level of mathematical competence on specific topics and then, as appropriate to their level of competence to provide individualized mathematical review material (quizzes, video, review notes, animations practice problems, etc) in an interactive online system. So, we are looking at designing a process of test, individualized review, and re-test. Students would be expected to demonstrate mathematical competence after reviewing the material by taking an in-class test. The elements and functionality of such a technological tool will be described in the paper.
Key Words: Math for engineering, Calculus, Math review, student performance, pre-requisite knowledge and skills.
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