Frank A. Cerreto, Jung Lee, and Wondi Geremew Abstract The purpose of this study was to investigate what, if any relationship exists between graph construction ability and interpretation ability. Sixty-seven college students completed two graphing tasks, one involving construction and the other interpretation of graphs, both based on actual data. Statistical analysis of the scores showed no significant correlation between total scores on the two tasks and no significant relationships between specific components of graph construction ability and graph interpretation ability. These results suggest that the two abilities are distinct from one another. The study’s findings add to our understanding of graph construction ability and have practical implications for teaching and learning. Keywords graph construction, graph interpretation, graphing data, graphical literacy Introduction Graphs are ubiquitous in textbooks, scholarly journals, popular magazines, and newspapers, as well as on the Web (Lewandowsky and Behrens, 1999; Shah, Mayer, & Hegarty, 1999), due to their potential to help viewers understand numerical information (Winn, 1987). Graphs provide a visual medium for identifying patterns and relationships in numerical data and are used extensively when people make decisions (Raschke & Steinbart, 2008). At the same time, if graphs are wrongly designed or interpreted, they could affect our perception of the actual situation and our resulting judgments. Tufte (1983) presented many examples of graphs that lead to data misinterpretations. Tractinsky and Meyer (1999) argued that misleading graphs may sometimes be created deliberately, and Beattie and Jones (2002a, 2002b) also added that such graphs could reduce decision quality. Especially, these days when creation of graphs is as easy as a couple of clicks, people often produce incomplete, biased, or wrong graphs. In school, students are often involved in interpreting graphs and constructing graphs. For example, teachers often present results from science lab graphically to ease the complexity and to allow patterns and relationships between scientific variables to be understood (Hardy, Schneider, Jonen, Stern, & Möller, 2005), and students are also expected to make graphs (Shah & Hoeffner, 2002). Thus, graphs are considered a strong communication tools for teachers and students, and graphical interpretation and representation of information are important quantitative literacy skills. There is a wealth of research on the difficulties viewers have comprehending graphs (Carpenter & Shah, 1998; Cleveland & McGill, 1985; Gattis & Holyoak, 1996; Guthrie, Weber, & Kimmerly, 1993; Leinhardt, Zaslavsky, & Stein, 1990; Maichle, 1994; Shah & Carpenter, 1995; Shah, Mayer, & Hegarty, 1999, Wang, Wei, Ding, Chen, Wang, & Hu, 2012), as well as their implications for the classroom (Friel & Curcio, 2001; Glazer, 2011; Sharma, 2006). However, as Amodeo & Wizner (2012) and Leinhardt and her associates (1990) pointed out, few studies focused on graph construction. Yet, research studies have found some differences between graph interpretation and construction ability. Leinhardt and her associates (1990) stated, “Construction is quite different from interpretation. Whereas interpretation relies on and requires reaction to a given piece of data, construction requires generating new parts that are not given (p.12)”. Berg and Smith (1994) found widespread lack of graph interpretation and construction abilities of high school science students. Tairab and Al-Naqbi (2004) found that high school students’ interpretation of graphs was much better than their ability to construct graphs. However, there is a lack of study focusing on the relationship between the specific skills and understandings underlying these two abilities. Cerreto and Lee (2012) focused on college students’ graph construction ability, and showed that graph construction ability is a well-defined construct that is separate from general mathematics and verbal ability. In that study, moderate to strong correlations were found between all pairs of five graphing task components, establishing the validity of the graph creation construct. Purpose and Research Questions The purpose of this study is to investigate possible relationships between graph interpretation ability and graph construction ability. We tried to answer the following two research questions: To what extent is general graph construction ability related to graph interpretation ability? To what extent are specific components of graph construction ability related to corresponding components of graph interpretation ability? Participants and Method The participants in this study are 67 students who were enrolled a four-year, public, comprehensive university in New Jersey. The students were enrolled in one of three classes: a precalculus course, an intermediate algebra course, and a freshman seminar that was not related to mathematics. The students were given two tasks: graph construction (see Appendix A) and graph (Appendix B) interpretation. Students took the graph construction test first in order to avoid a chance to see any graphs in the interpretation test. In the construction test, they were given numerical data about the populations and land areas of three countries. Provided with rulers, protractors, calculators and pencils, they were asked to create graphs that could be used to answer three questions about these countries. The first question asked them to make a comparison, the second, express parts of a whole, and the third, describe a trend. After constructing each of the three graphs, the students were asked to describe their findings. The graphing task was untimed; most students finished within 45 minutes. After submitting the first test, the second, interpretation, test was given to the student. The graph interpretation test consisted of 12 multiple-choice questions based on given bar graphs, line graphs, and pie charts. It was also untimed; most students finished in 15 minutes. In order to rate the graph construction, we used rubrics for each of five components: the appropriateness of the created graph to the question (Type), the quality and completeness of the labeling of the graph (Labels), the correctness of the axis scales (Scales), the accuracy of the drawing (Accuracy), as well as the correctness and thoroughness of the written response to the question (Explanation). For each of the three questions, two raters independently assigned a score. Scores of four, three, two, or one, represent excellent, good, fair, or poor, performance, respectively. Off-topic or blank responses received a score of zero. Sum scores, ranging from zero to eight, were used for all subsequent analysis.