Looking for Linearity: Integrating Graphing for First-Year Chemistry Students

Abstract

Based on our observation that the general literature does not provide an organizing principle for the graphs that science students encounter, an approach called “Looking for Linearity” has been described. This approach is based on the hypothesis that when scientists look at their data and begin to represent it, they initially look for linearity. This is to say that scientists use Occam’s Razor; variables are used and transformed in such ways that when plotted against each other, the simplest representation—the straight line—is produced. A brief review of the topics typically covered in the first year of chemistry reveal a substantial number of relationships either expressed in the form of a straight line (gas laws, free energy, rate laws) or in terms of ratios that when graphed produce straight lines (density, specific heat capacity, stoichiometry). “Looking for Linearity” is an approach to graphing that serves four purposes for teaching first year chemistry students: 1) it weaves a common theme or thread through the entire year of General Chemistry, 2) it allows students to work like scientists, 3) it connects an important mathematical construct with chemical concepts, and 4) it provides a method to process data in other scientific fields like physics. The linearity heuristic is represented in what is called a Graphing Decision Tree. This tree shows, in simplified terms, how linearity can be used to organize different types of graphs found in the first year of chemistry. The Decision Tree is hierarchically structured from simple to increasing graphing complexity. Straight lines were listed as being the simplest to interpret, followed by exponential curves and then non-exponential curves; exponential curves were second because they could be converted to straight lines by using logarithms. Each pathway ends with examples of some of the different types of graphs our students will encounter in the first year of chemistry.