We present a visual language for strategies in game theory, which has potential applications in economics, social sciences, and in general science education. This language facilitates explanations of strategies by visually representing the interaction of players’ strategies with game execution. We have utilized the cognitive dimensions framework in the design phase and recognized the need for a new cognitive dimension of “traceability” that considers how well a language can represent the execution of a program. We consider how traceability interacts with other cognitive dimensions and demonstrate its use in analyzing existing languages. We conclude that the design of a visual representation for execution traces should be an integral part of the design of visual languages because understanding a program is often tightly coupled to its execution.

Abstract. Subsetability is the ability to decompose programming languages and environments into a hierarchy of subsets, each of which can be used by students to create complete, meaningful computer programs. This paper argues that a programming language/environment's subsetability positively affects its learnability and teachability. The argument is supported by citing relevant theoretical research, little of which is grounded in empirical studies. Then the paper goes on to argue that subsetability may be a new "cognitive dimension of notational systems, " as defined by Green and Blackwell. It does so by analyzing subsetability in terms of Blackwell's criteria for dealing with new cognitive dimensions. 1