Scale construction for graphing: An investigation of students' resources

Graphing is a fundamental part of the scientific process. Scales are key but little-studied components of graphs. Adopting a resources-based framework of cognitive structure, we identify the potential intuitive resources that six undergraduates of diverse majors and years at a public US research university activated when constructing scales, and identify classes of resources that share similar characteristics. The students constructed scales for data sets that range over 10 or more orders of magnitude, and were interviewed in depth about their scales. The data were analyzed using the constant comparative method. We identified four classes of resources: (1) “prior drawing experience” resources that include show all elements and what you see is what you get; (2) “wide range” resources that are used to make sense of a data set with widely varying values, such as zoom in, ratio, and conversion; (3) “prior graphing experience” resources that draw from previous work with graphing, including powers-of-ten scales and linear scales; and (4) “fundamental knowledge” resources, such as halving. These resources, while identified among undergraduates, may indicate promising educational approaches to graphing in middle and high school. Secondary school science curricula and instruction that acknowledge and build on student resources will likely result in deeper understanding of conventional scales and graphs among students at this age and thus allow for more effective instruction at the undergraduate level. Instructional activities that might activate and build upon the resources identified are presented.