This article describes two studies which assess the benefit of using the specificity principle as a criterion for choosing between alternative graphical representations in teaching and learning. The specificity principle was interpreted as a metric called the information enforcement metric. This is simply a ratio between the total number of states a representational system can support and the number of states or referents in the material being presented. The value of the metric is tested by comparing ratios for several representational teaching systems, with the learning outcomes achieved by subjects using interactive software based on those systems. Counting the states in a representational system is complex, however it is made more simple for some systems by using an intermediate representation. Results show that while the specificity principle is able to predict learning outcomes at a course grain of analysis, that is between systems which are highly expressive and those which are far more specific, between systems of similar specificity the principle interpreted in this way is not validated. A second study shows that students' difficulties in understanding lexical conventions are more pronounced in the least specific of the systems evaluated. This casts further doubt on the value of the specificity principle as a guideline for designing interactive graphical systems for teaching and learning. Several suggestions are offered for developments of this work.