Development of a framework for graph choice and construction.

COLLECTING, understanding, and interpreting data are key skills that all students should master (8, 12, 22, 33). Research on graph interpretation and basic construction is extensive, and student difficulties, primarily in K-12 type settings, have been well documented [e.g., graph choice (30, 32, 45), labels for axes (30, 32), variables (45), and scaling axes (1, 7, 32, 34)]. Although many instructional books exist on graphing (5, 20, 28, 47), they do not focus on the complex reasoning behind graph choice and construction. It is insufficient to choose an appropriate graph for data (e.g., bar graph for categorical data) without evaluating the advantages and disadvantages of using a particular graph. Metarepresentational competence (MRC) refers to the knowledge required for successful construction and reasoning with external representations, which includes graphs (14). MRC has several components that reveal students’ ability and inability with graph choice, construction, and critique (15). Specifically, these areas are invention, critique, functioning, and learning or reflection (Table 1) (15). The first area, invention, reveals students’ underlying skills and abilities that allow them to conceive novel graphical representations from data (15). The second area, critique, exposes students’ critical knowledge that is essential for assessing various types of graphs and their strengths and weaknesses (15). The third area, functioning, unearths students’ reasoning for understanding the purpose of different types of graphs and the usage being dependent on the type of data present (15). The final area, learning or reflection, reveals students’ awareness of their own understanding of graphs (15).