A comparison of programming languages and algebraic notation as expressive languages for physics

The purpose of the present work is to consider some of the implications of replacing, for the purposes of physics instruction, algebraic notation with a programming language. What is novel is that, more than previous work, I take seriously the possibility that a programming language can function as the principle representational system for physics instruction. This means treating programming as potentially having a similar status and performing a similar function to algebraic notation in physics learning. In order to address the implications of replacing the usual notational system with programming, I begin with two informal conjectures: (1) Programming-based representations might be easier for students to understand than equation-based representations, and (2) programming-based representations might privilege a somewhat different "intuitive vocabulary." If the second conjecture is correct, it means that the nature of the understanding associated with programming-physics might be fundamentally different than the understanding associated with algebra-physics. In order to refine and address these conjectures, I introduce a framework based around two theoretical constructs, what I call interpretive devices and symbolic forms. A conclusion of this work is that algebra-physics can be characterized as a physics of balance and equilibrium, and programming-physics as a physics of processes and causation. More generally, this work provides a theoretical and empirical basis for understanding how the use of particular symbol systems affects students' conceptualization.