Analytical derivation: An epistemic game for solving mathematically based physics problems

Abstract

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Characterizing mathematical problem solving in physics-related workplaces using epistemic games

“…Bajracharya and Thompson adapted epistemic games to analyze how students derive equations using symbolic manipulations and routine mathematical operations (i.e., procedural resources) in the context of solving problems involving temperature or electrostatics [45]. While observing introductory physics students solving problems that were rich in algebraic and graphical representations, they documented another specific epistemic game (i.e., analytical derivation epistemic game).…”

“…By synthesizing the prior research that utilized epistemic games, we summarize the primary characteristics of epistemic games in Table I, which are the epistemic form, entry and ending conditions, moves, constraints and other contextual features, and knowledge base [17,44,45]. The epistemic form is often an external representation that helps guide inquiry during an epistemic game.…”

Analyzing students’ reasoning about the inverse-square law through the lens of dual processing theories

“…The understanding and implementation of physics concepts often involve the application of relevant mathematical knowledge and skills. Students lacking and/or failing to apply relevant mathematical knowledge and skills have shown difficulties with reasoning and/or solving problems in physics contexts [1][2][3]. For example, Meltzer showed using a physics concept survey that there was a significant correlation between normalized learning gain and students' pre-instruction mathematics skill [1].…”

Students’ strategies for solving a multirepresentational partial derivative problem in thermodynamics

“…To solve thermodynamics problems in multiple representations, students need deep conceptual understanding and representational fluency in addition to procedural skills. Although it is possible to present problems involving partial derivatives using various representations-such as symbolic [e.g., ð∂P=∂VÞ T , geometric (3D surfaces), graphical (contour maps), and numerical (data)-many traditional thermodynamic problems exclusively involve symbolic manipulation, also known as analytical derivation [1]. We define analytical derivation as a process by which an unknown physical quantity is expressed in terms of known physical quantities as an equation using relevant mathematical and physical knowledge.…”