An Application of Methodological and Notational Comparisons

During mathematics and engineering studies, students are often presented several methodologies to solve certain types of equations.Often, these processes are presented as a means of finding a solution for a specific form of an equation.An interesting study occurs for students when they are challenged to apply different problem solving techniques to the same equation.This approach allows for self discovery of the nuances inherent in each method as well as a comparison of the accuracy of the results.This paper provides a firsthand account of just such a self-study and discusses the student's results as it pertains to the research.The information included is used to illustrate the types of discoveries that may be made in order to motivate other instructors into providing a similar educational process.The latter portion of this paper compares the different type of notations that are used in mathematics for the same equation.A self-study example is again presented to illustrate the comparisons along with a brief discussion.While some of these notations may be presented briefly during coursework, they are not becoming ingrained into students due to lack of repetition.The purpose of including this comparison is to suggest to educators that regular usage of several notations could provide for broader recognition.