Impact of Maple(TM) on the design, instruction and performance in an undergraduate physics mathematical methods course

A traditional undergraduate physics course on mathematical methods has been redesigned to incorporate the use of $\rm Maple\sp{\sc {TM}},$ a computer algebra program, during all aspects of the course. Topics covered were: complex number theory; series approximations; matrix theory; partial differentiation; vector algebra; and vector calculus. Five undergraduate students were enrolled, from sophomore to senior in academic class standing. A qualitative case study methodology was used to describe the changes in the course design resulting from the incorporation of $\rm Maple\sp{\sc {TM}}$ and their impact on the instruction of the course, and to determine the effects on the students\u27 learning and development of problem solving skills in physics using $\rm Maple\sp{\sc {TM}}$ as a problem solving tool. The impact of using $\rm Maple\sp{\sc {TM}}$ on the number and types of interactions is presented. The entire semester long course was included in this study. Each class session is described in detail. Examples of the $\rm Maple\sp{\sc {TM}}$ materials used are given. The use of the $\rm Maple\sp{\sc {TM}}$ program was allowed on all homework and exams with each student having their own computer during class. Constraints were made so that the assessment emphasis remained on the mathematics and the conceptual understanding of the problem solving methods. All of the students demonstrated some level of proficiency in using $\rm Maple\sp{TM}$ to solve the assigned problems. Strategies for effectively using $\rm Maple\sp{TM}$ were presented and were individualized by the students. The students reported positive and negative impacts of using $\rm Maple\sp{\sc {TM}}.$ All of the students satisfactorily completed the course requirements, receiving final course grades from B to A+. All of them continued to voluntarily use $\rm Maple\sp{\sc {TM}}$ during the following semester. Instructional methods used included various lecture techniques without $\rm Maple\sp{\sc {TM}}$ assistance, lectures and demonstrations using only $\rm Maple\sp{\sc {TM}},$ and student tasks assigned in class worked with the aid of $\rm Maple\sp{\sc {TM}}.\ Maple\sp{\sc {TM}}$ was used in one of these aspects in all but 3, out of 45, class periods. The use of $\rm Maple\sp{\sc {TM}}$ constituted about half of the overall class time