Scaffolding methods for systems of equations encountered in introductory physics courses

Abstract In the first semester calculus-based introductory physics course, the majority of problems that require mathematical methods use methods associated to solving systems of equations rather than methods of calculus. However, this is rarely explicitly stated, which is misleading to incoming students and gives them an unnecessary layer of fear with the “calculus” branding. Without explicit focus on the primary mathematical requirement, students can get the impression that there are hundreds of distinct problems presented in standard textbooks, which in fact rely primarily on just two types of systems of equations: linear and linear-quadratic systems. To address this, we developed a general system of equations method for introductory physics that places additional emphasis on setting up a system of equations, determining its type, performing a test to assess possible solutions and interpreting the problem geometrically. This method uses mathematics and concepts standard to high school curriculum and provides scaffolding to students as there are several ways in which they can demonstrate understanding of the problem before attempting to solve for an unknown. The scaffolding of this approach, combined with limiting the apparent scope of possible problems students can face and increased general understanding of the possible solutions, is sufficient to offset the additional steps that are expected of students in the problem solving process. We give common introductory physics problems as examples of the implementation of our methodology for both linear and linear-quadratic systems. Discussion of the various benefits and variations of this approach is also presented.