Comparing different levels of interaction constraints for deriving visual problem isomorphs

Interaction and manual manipulation have been shown in the cognitive science literature to play a critical role in problem solving. Given different types of interactions or constraints on interactions, a problem can appear to have different degrees of difficulty. While this relationship between interaction and problem solving has been well studied in the cognitive science literatures, the visual analytics community has yet to exploit this understanding for analytical problem solving. In this paper, we hypothesize that constraints on interactions and constraints encoded in visual representations can lead to strategies of varying effectiveness during problem solving. To test our hypothesis, we conducted a user study in which participants were given different levels of interaction constraints when solving a simple math game called Number Scrabble. Number Scrabble is known to have an optimal visual problem isomorph, and the goal of this study is to learn if and how the participants could derive the isomorph and to analyze the strategies that the participants utilize in solving the problem. Our results indicate that constraints on interactions do affect problem solving, and that while the optimal visual isomorph is difficult to derive, certain interaction constraints can lead to a higher chance of deriving the isomorph.