Unpacking structural domain of mathematics to aid inquiry in physics: a pilot study

Abstract

Abstract Analysing graphs, formulating covariational relationships, and hypothesizing systems’ behaviour have emerged as frequent objectives of contemporary research in physics education. As such, these studies aim to help students achieve these objectives. While a consensus has been reached on the cognitive benefits of emphasizing the structural domain of mathematical apparatus in physics instruction, the question remains open on how to accomplish this task in school practice. This study contributes to this discussion. It attempts to determine how high-school physics students perceive formulas as a means to understand covariational relationships of natural phenomena. It also explores the hypothesis that including more structural domains of mathematics makes physics content more attractive for students. A sample of 25 advanced high-school physics students was taught kinematics, dynamics, and energy sections considering functional representations of some laws and principles traditionally covered in those sections. At the concluding phase, these students were invited to contrast formulas and their covariational embodiments as a means of providing conceptual understanding. The analysis revealed that students considered formulas as algebraic tools to attain a specific value to a particular application or carry out algebraic algorithms to solve a physics problem. They found formulas converted to covariational relationships a better fit for the learning of general phenomenon behaviour and extracting new information, especially from a graphical representation of these relationships. These findings generated the conclusion that the structural domain of mathematics can aid physics understanding by alternatively presenting formulas as mathematical entities that are transferrable to functions. It was further concluded that such parallelism would benefit not only the depth of inquiry in physics but also a general students’ STEM disposition.