2.03.03.01 Aspects of Graph Interpretation
Previous reviews of graph comprehension and interpretation (e.g., Friel et al., 2001; Shah & Hoeffner, 2002) provide a sense of the wealth of previous research, and an indication of the aspects commonly considered as factors in graph
comprehension. Friel et al. (2001) structured their review by first defining graphs, in general, as using spatial characteristics to represent quantity. They listed structural components of graphs as including the framework (e.g., axes, scales), specifiers used to represent data values (e.g., lines, bars), and labels. They defined graph
been described by a number of studies (Carswell, 1992; Curcio, 1987; McKnight, 1990; Wainer, 1992):
1. an elementary extraction of information,
2. an intermediate level of reading data to find relationships, and
3. an overall interpretive level that moves beyond the data to include, for example, topic knowledge or inference.
Friel et al. (2001) suggested that critical factors affecting comprehension include (a) purposes for using graphs, (b) characteristics of graph decoding, judgment tasks, and context, (c) characteristics of the discipline, such as variation, data types and graph complexity, and (d) characteristics of graph readers. Shah and Carpenter (2002) described the three broad factors involved in graph comprehension as (a) visual characteristics of the graph, (b) knowledge about graphs, and (c) the topic content of the graph. Visual characteristics considered have generally concerned the form of the representation (e.g., line graph, bar graph, or tabular forms) and the structuring of complex data, particularly involving more than two variables.
Pinker (1990) suggested that graph comprehension divides at the most fundamental level into (a) comprehension of the axis framework and scale, and (b) comprehension of the data elements. The scale is necessary for reading numerical values, whereas the data cases without the scale permit trend identification and qualitative comparison of cases. This is the basis for the distinction between skills of Numerical Graph Interpretation and Verbal Graph Interpretation sustained in this study, and parallels the balance between graphs locally representing specific data values and globally representing general trends or relationships in the data, as
Ben-Zvi & Arcavi, 2001; Gerber, Boulton-Lewis, & Bruce, 1995; Leinhardt et al., 1990).
Graph interpretation has been described (Curcio, 2001) as having various purposes including reading data values, reading beyond the data by prediction based on global trends, and an intermediate level of reading between the data, such as comparing values. When constructing graphs, students’ responses may be influenced by their beliefs about these purposes for the representation more than by any lack of ability to represent a given graph form (Roth & McGinn, 1997). Similarly, when interpreting graphs, the purpose of the tasks and the graph provided may influence students’ responses in relation to local or global features more than their ability to engage these features. Curcio (1987) found predictors of graph comprehension included reading achievement, mathematics achievement, and prior knowledge of the topic, mathematical content, and form of the graph. McKnight (1990) considered different levels of data-based tasks including (a) observation of facts in a graph such as extracting a numerical value, (b) observation of relationships in graphs such as “the curves tend to increase,” (c) interpretation of relationships in the real-world context, and (d) critical evaluation of inferential claims. For open-ended tasks, Gerber et al. (1995) interviewed students aged 8, 11, 14, and 16 years using multiple maps and graphs of data about fictitious countries, and identified stages in which students (a) interpreted graphs as drawings, (b) interpreted features of the individual graphs in a global or local sense, (c) identified patterns in single graphs, and (d) related patterns in graphs to other data or prior beliefs about relationships. Preece (1983b) asked 122 students, aged 14-15 years, to explain what a graph is, and found that 59% believed a graph was a useful way of displaying information, 16% said it was like a picture, 11% thought it was like a table, and only 11% indicated a graph
shows the relationship between two variables. Across a number of tasks, she identified four levels applicable to both graph interpretation and construction: (a) a graph is viewed as a picture, (b) points are interpreted, (c) comparisons across intervals are considered, and (d) continuous changes in gradient are interpreted. She found that quantitative questions were more often answered correctly than qualitative questions involving the context and the data.
2.03.03.02 Local Data Values and Global Trends
Graph interpretation tasks, and students’ abilities on tasks, differ according to the degree to which they consider graphs either locally to represent values or
globally to represent general trends or relationships in the data (e.g., Bell & Janvier, 1981; Ben-Zvi & Arcavi, 2001; Gerber et al., 1995; Guthrie, Weber, & Kimmerly, 1993; Leinhardt et al., 1990). Many early studies of graph interpretation concerned aspects of information design to improve the readability of graphs (Anscombe, 1973; Culbertson & Powers, 1959; Feliciano et al., 1963; Hermann, 1973; Kirk, Eggen, & Kauchak, 1978; MacDonald-Ross, 1977; Malter, 1952; Thomas, 1933; Washburne, 1927; see also Meyer, 1997). Studies by Vernon (1946, 1950) suggested that a logical system or statement concerning relationships between variables was important in underpinning graph interpretation.
Various studies have concluded that students construct and read graphs as individual numerical points rather than a global whole (e.g., Bell et al., 1987a; Brasell & Rowe, 1993). With respect to reading individual points using the scale, Bryant and Somerville (1986) found many students as young as 6 and 9 years can read coordinates from either axis with reasonable accuracy. The tendency to consider graphs as a global whole, however, may depend on appropriate task design. When a variety of tasks were compared, Meyer, Shinar, and Leiser (1997) found trend
judgments from line graphs and bar graphs were performed faster and more accurately than tasks (a) to read values, (b) to compare values from the same data series for different X values (X comparisons), (c) to compare values from different data series with the same X value (series comparisons), or (d) to identify the maximum. These findings may be because verbal trend interpretations generally involve reading the data series, whereas numerical interpretations also require reading the scales (Pinker, 1990). Principles of perceptual grouping support the reading of values in bar graphs, and the reading of trends in line graphs (Pinker, 1990; Zacks & Tversky, 1999).
2.03.03.03 Confusing Features of the Graph
At a basic level, some students interpret graphs as if they were pictures (Bell, Brekke, & Swan, 1987a; Janvier, 1978; Swan 1985). A graph involving changing speed over time, for example, might be perceived as a picture of a roller-coaster, that is of changing height over horizontal space. A number of studies, particularly
involving kinematics graphs, have documented the confusion of value, denoted by position, and rate, denoted by slope of a continuous graph (Beichner, 1994; Brasell & Rowe, 1993; Hermann, 1973; Hitch, Beveridge, Avons, & Hickman, 1982;
McDermott, Rosenquist, & van Zee, 1987; Padilla, McKenzie, & Shaw, 1986; Thompson, 1994b; Tobin & Capie, 1981; van Zee & McDermott, 1987; Wainer, 1980; Wavering, 1984, 1985). Exposure to teaching, particularly using computers to produce the graphs in real-time with the situational context, supported improvements in graph interpretations and construction skills (Adams & Shrum, 1988, 1990;
Avons, Beveridge, Hickman, & Hitch, 1983; Brasell, 1987; Jackson, Edwards, & Berger, 1993; Linn, Layman, & Nachmais, 1987; Mokros & Tinker, 1987; Testa, Monroy, & Sassi, 2002).
The scale of graphs is well known to affect interpretations (Ben-Zvi, 1999, 2000). Other features, such as depth or area, can interfere with reading accuracy compared to simple features such as position, length, or angle (Carswell, 1992; Zacks, Levy, Tversky, & Schiano, 1998), and even with strong skills in reading two- dimension graphs, reading data involving a third variable proves challenging
conceptually (Shah & Carpenter, 1995).