This paper provides a summary of the development and evaluation of a componential model of graph reading called the Mixed Arithmetic-Perceptual (MA-P) model. A review of the history underlying the development of the model begins the paper. The second section describes the research used to test the predictions from the model and to further develop it. The third section integrates the research to produce a single omnibus version of the MA-P model. Finally, the fourth section projects the future of the MA-P modeling approach, for specific versions of the model, additional research, as well as applications.
HISTORICAL BACKGROUNDThe purpose of this paper is to summarize the research that I have done, often with colleagues, related to a model of how people read graphs to perform quantitative tasks. Twenty years ago, I was working for Lockheed Engineering and Sciences Company on issues related to the user interface for the Space Station. While conducting a task analysis of Space Station activities, Bob Lewis, an intern from Rice University at that time, and I became interested in the tasks that scientists on the Space Station would perform and the role that quantitative tools, such as graphical displays would play in those tasks. That interest led us to look for empirically-based models of reading graphs to solve quantitative problems. We found no models of graph reading at that time that we believed would be helpful, so we embarked on research that we hoped might lead us to such a model. (Several models did enter the literature during the time that we conducted our research -such as, Lohse, 1997 --but we had already begun what we considered to be a fruitful approach, so we continued.)We started investigating graph reading by interviewing the people around us --mostly scientists, engineers, and graduate students, as well as some undergraduate students at Rice -to discover the problems that they used graphs to solve and to describe how they interacted with graphs. Later, we became more systematic by providing other participants from these groups with simple graphs and basic tasks based on the ones that our initial participants had described, then asking them to think aloud or to write down what they thought about as they solved the problem using the graph. These qualitative data suggested to us that (1) people used a number of perceptual and cognitive processing components in order to perform quantitative tasks using graphs, and (2) people applied these processing components in systematic sequences that were similar across the various individuals and groups.The qualitative data that we collected served as the basis of a modeling approach which we came to call the "Mixed Arithmetic-Perceptual (MA-P Model); so named because some of the processing components involved sensory/perceptual processing (e.g., visual search and height comparison) and other components involved mental arithmetic (i.e., addition, subtraction, division) on values of the