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

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.

Figure 1

Tuminaro’s schematic diagram for the recursive plug-and-chug epistemic game. From Ref. [9].

Figure 2

The interview problem on temperature.

Figure 3

The interview problem on electrostatics.

Figure 4

Components of the analytical derivation epistemic game.

Figure 5

Example of the analytical derivation epistemic game for solving the temperature problem.

Figure 6

Kara’s analytical derivation game to solve the temperature problem.

Figure 7

Example of the analytical derivation epistemic game for solving the electrostatics problem.

Figure 8

Kara’s initial, recursive plug-and-chug solution to the electrostatics problem.

Figure 9

Kara’s version of the analytical derivation game to solve the electrostatics problem.

Figure 10

Joe’s version of the analytical derivation game to solve the electrostatics problem.