Offering Honors Course Option Within An Ordinary Mathematical Course For Undergraduate Students In Engineering Majors
Hong Liu · 2020
Abstract NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Offering Honors Course Option within an Ordinary Mathematics Course for Undergraduate students in Engineering Majors Abstract In order to attract talented students, many selective small universities have established honors programs in recent years 10,13 . However, because it is difficult for those small universities to schedule enough honors program students to fill all the seats of a regular-sized class, it is often too costly to offer sufficient honors courses for students in an honors program alone. A cost effective solution to this problem is to allow students who are not in the honors program to take any seats that may remain after the honors students have registered. An alternative is to offer an honors course option in a regular non-honors course by asking the honors program students who take that course to learn some extra content and do some extra work. With either solution the act of mixing a significant number of honors students with non-honors students usually results in a bi-modal distribution based on the students’ level of academic preparation. To teach such a class, instructors often face more challenges balancing the content so that the strong honors students can be adequately motivated without intimidating the other relatively weaker students. This paper reports on the first year’s experience offering an honors course option within an ordinary mathematics course that had a mix of both honors and non-honors engineering students. 1. Introduction Typical calculus or differential equation courses teach students to work on well-defined and oversimplified problems. Average college students believe that the solution to all problems simply implies finding the right formulas and plugging data into those formulas. Consequently, the learning of mathematics comes down to remembering formulas. Given application problems where the solutions are not based on formula association, most students do not know how to start their work. With the increasing complexity of postmodern technology, bridging the gap between real-world problems and problems in textbooks becomes an increasingly critical pedagogical issue. Berkey and Vernescu 1 presented an extensive survey about the curriculum reform effort of project-oriented education in 30 years. Many articles, projects, and books addressed the issue, but no magic remedy existed to solve the problem 9, 2,7 ,3 . In 2003-2004, the author participated in three summer workshops of the National Computational Science Institute 8 (NCSI) on computational science education and appreciated the pedagogical value of teaching an application oriented mathematics module on mathematical modeling. Such an approach can help students understand that mathematics is a language for accurately describing complex natural and artificial phenomena in science and engineering. While teaching courses in ordinary differential equations over the past three years to engineering students, the author introduced modifications to these courses by adding a Mathematical Modeling Module (MMM) of 8 hours. The feedback from student participants was mixed and bi- polarized. The reason behind the disparate feedback became clear after a couple of years. The ability to reach the appropriate level of abstract thinking was critical for correctly modeling complicated problems 11, 4 . The author observed that there were two main groups of students,