Applying Structural Mathematics in Physics: Case of Parallel Connection

Abstract

Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires employing only students’ technical skills, the structural domain requires activating students’ algebraic reasoning and applying it to learn more about physical systems beyond evaluating formulas. Students’ technical skills in mathematics do not convert into structural skills automatically, and this is perceived as an obstacle that prevents complete appreciation of physics knowledge. There can be various ways to activate or to develop students’ mathematical structural domain in physics. Most common are: (a) mathematical modeling that involves experimental activities concluding with algebraic relations; (b) stimulating students to work with symbols in limiting situations; or (c) developing the understanding of physics formulas (e.g., see Ref. 5). While all these methods are valuable, students still face difficulties with transferring their structural math skills to physics, thus new attempts are made. The process of developing students’ algebraic structural skills proposed in this paper is a combination of the current approaches; however, as a means of developing mathematical reasoning, a mathematical structure is used that is derived from a physics formula. More specifically, this paper presents an attempt to interpret formula for the equivalent resistance of a parallel electric circuit using the properties of a rational function. Such formulated aim reflects not only recommendations of the physics education research community but also mathematics because it guides students in how to merge mathematical knowledge with the behavior of a physical system to learn more about the system.