| Abstract: | A study was conducted to determine the logical reasoning necessary to construct line graphs. Three types of line graphs were used: a straight line with a positive slope, a straight line with a negative slope, and an exponentially increasing curve. The subjects were students in grades six through twelve enrolled in a laboratory school. The responses were classified into one of nine categories. The categories ranged from no attempt to make a graph to a complete graph with a statement of a relationship between the variables. Subjects in grades six through eight exhibited behaviors mainly in the first four categories, ninth- and tenth-grade subjects scored in the middle categories, and eleventh and twelfth graders scored mainly in the upper categories. These response categories also showed a close fit with Piagetian concrete operational structures for single and double seriation and formal operational structures for proportional reasoning and correlational reasoning. |
