Development of a framework for graph choice and construction

Abstract

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).

Reflecting on Graphs: Attributes of Graph Choice and Construction Practices in Biology

“…Our previous findings (see Figure 1 in Angra and Gardner, 2016 ) on the steps taken during a pen-and-paper graphing construction task by expert professors resembled the four steps of Polya’s problem-solving cycle in mathematics ( Polya, 1945 ). Polya’s problem-solving model has been adapted based on the data and trends that have emerged from our work to explain expert graph-construction behavior and can be distilled into three phases: planning, execution, and reflection (for a detailed description, see Angra and Gardner, 2016 ). During the planning phase, before the graph is constructed, data to be plotted are evaluated, understood, and characterized.…”

“…Before constructing the graph, the graph constructor should have a clear purpose in mind, along with an adequate understanding of variables and graph types ( Berg and Smith, 1994 ; Friel and Bright, 1996 ; Clase et al. , 2010 ; Grunwald and Hartman, 2010 ; Angra and Gardner, 2016 ). For a graph to be an effective communication piece for both the creator and the observer, four main components should be considered: 1) data form, 2) graph choice, 3) graph mechanics, and 4) aesthetics and visuospatial aspects.…”

“…Owing to its complexity, choosing and constructing an appropriate graph for data can be considered a problem-solving task ( Angra and Gardner, 2016 ). Our previous findings (see Figure 1 in Angra and Gardner, 2016 ) on the steps taken during a pen-and-paper graphing construction task by expert professors resembled the four steps of Polya’s problem-solving cycle in mathematics ( Polya, 1945 ).…”

“…Owing to its complexity, choosing and constructing an appropriate graph for data can be considered a problem-solving task ( Angra and Gardner, 2016 ). Our previous findings (see Figure 1 in Angra and Gardner, 2016 ) on the steps taken during a pen-and-paper graphing construction task by expert professors resembled the four steps of Polya’s problem-solving cycle in mathematics ( Polya, 1945 ). Polya’s problem-solving model has been adapted based on the data and trends that have emerged from our work to explain expert graph-construction behavior and can be distilled into three phases: planning, execution, and reflection (for a detailed description, see Angra and Gardner, 2016 ).…”

“…Specifically, decisions on the purpose for graphically displaying the data are clarified, ways to organize the data on the graph are considered, decisions on data transformation are made, and a graph type is chosen ( Friel and Bright, 1996 ; Ainley et al. , 2000 ; Patterson and Leonard, 2005 ; Angra and Gardner, 2016 ). During the execution phase, the graph is constructed with appropriate elements of graph mechanics for clear communication (e.g., descriptive title, variables on axes, scales appropriate for data, key, etc.)…”