Emergence of Graphing Practices in Scientific Research

Graphing has long counted as one of the quintessential process skills that scientists apply independently of particular situations. However, recent expert/expert studies showed that when asked to interpret graphs culled from undergraduate courses of their own disciplines, scientists were far from perfect in providing interpretations that a course instructor would have accepted as correct. Drawing on five years of fieldwork, the present study was designed to investigate graphs and graph-related skills in scientific research. In addition to the fieldwork, a think-aloud protocol was used to elicit scientists’ graph interpretations both on familiar and unfamiliar graphs. The analyses show that graph-related skills such as perceiving relevant graphical detail and interpreting the source of this detail emerges in the research process and is related to the increasing familiarity with the research object, instrumentation, and an understanding of the transformation process that turns raw data into graphs. When scientists do not know the natural object represented in a graph and are unfamiliar with the details of the corresponding data collection protocol, they often focus on graphical features that do not pertain to the phenomenon represented and therefore do not arrive at the correct interpretations. Based on these data, it is proposed that graphs are not only the outcomes of scientific research but, in important ways, constitute representations that bear metonymic relations to the research context, most importantly to instrumentation, natural phenomenon, and the mathematical transformations used to produce the graphs from the raw data. I draw on the semantics of symbolic systems for articulating competencies and breakdowns in scientists’ graphing-related practices. Emergence of graphing 1 In the history of science, visual representations other than text in general and graphs more specifically contributed to the increasingly rapid development of science and scientific knowledge (Edgerton, 1985). It is therefore not surprising to find many such representations in scientific journals: surveys of journals in biology (Roth, Bowen, & McGinn, 1999) and physics (Lemke, 1998) revealed that there are, on average, 14.8 and 12 visual representations, respectively, per 10 pages of scientific text, of which 4.2 and 10, respectively, were histograms, scatter plots, and line graphs. Upon seeing a graph as part of some printed materials, some individuals directly relate it to a specific situation. In the workplace, experienced people no longer distinguish between graphs and the phenomena they stand for—graphs have become transparent (Roth, 2003a; Williams, Wake, & Boreham, 2001). However, when individuals are unfamiliar with graphs, they have to engage in more elaborate processes of interpretation. From a cognitive psychological perspective, graph interpretation is a process of translation from graphs to situations and verbal descriptions; processes that translate a graph into another graph or a situation (verbal description) into another situation (verbal description) are referred to as transpositions (Janvier, 1987). Taking account of the fact that structures are relative to particular lifeworlds (Agre & Horswill, 1997), Figure 1 presents a model for the semantics based on translations and transpositions. Such a model constitutes a step toward a more adequate framework for the analysis of cognition during situated scientific activity and reasoning (Greeno, 1989; Latour, 1993). In Figure 1, the process of interpretation, that is, a translation from graphs to situations (verbal descriptions) is denoted as Φ. (Scientific research would be characterized by an arrow in the reverse direction.) During this process, symbolic structures are mapped onto structures of the lifeworld. Janvier’s (1987) transpositions within the symbolic and lifeworld domains are denoted as Ψ and μ. For example, the physicists and theoretical ecologists in my database often translated a population graph into some other graph (Ψ); they also understood a decreasing birthrate with increasing Emergence of graphing 2 population density in terms of crowding a cage of rats (μ). The model further distinguishes between the raw materials that underlie symbolic and lifeworld structures; viewing the material world and the structured way it appears in lifeworld processes as a (dialectical) unit leads to a non-dualistic notion of sociocultural and cultural-historical practices (Leont’ev, 1978; Sewell, 1999). Thus, different transformations of the type Θs were involved when some scientist focused on the slope whereas others focused on the height of a graph at one or more values (Roth & Bowen, 2003). Similarly, different (experience-based) transformations of the type Θd led vision biologists to perceive the same cell on a microscope slide first as a “ultraviolet cone” then as a “a broken rod” (Roth, 2003a). Figure 1. A classical view of the semantics of interpretation, which involves a translation of a symbolic structure into the natural world or a description thereof. (Symbols are those proposed by Greeno [1989].) It is widely assumed that scientists are experts with respect to graphs and graphing generally and to translating them into situations and descriptions specifically (Tabachneck-Schijf, Leonardo, & Simon, 1997). It may therefore come as a surprise that experienced scientists performed much less than stellar in a recent expert-expert study, although the graphs for the interpretation tasks had been culled from or modeled on those found in undergraduate courses and textbooks of their own domain (Roth & Bowen, 2003). There was also a statistically detectable difference between university-based scientists and those working for an agency or company outside: the professors, who Emergence of graphing 3 taught undergraduate courses in the field, had a much higher success rate than the nonuniversity research scientists. At the same time, scientists in that study were highly competent when it came to familiar graphs. There was no difference in competence between university-based and other scientists when they explained graphs directly or indirectly related to their own work, where scientists were familiar with the methods of inquiry, instrumentation, natural environment or specimen, and so forth. These results are consistent with those of cognitive anthropological studies of arithmetic, which show that people may be highly competent in everyday settings while failing to solve structurally equivalent school-like paper-and-pencil tasks (Lave, 1988; Saxe, 1991; Scribner, 1984). This suggests that rather than being context independent, graphing (and arithmetic) competencies are tied, at least in some aspects, to familiarity with the setting (process of construction) and the phenomena represented. Competent graph reading may involve a dialectic process Φ2, whereby symbolic and familiar phenomenal worlds mutually constitute one another (Figure 2). Figure 2. Dialectical view of semantic processes underlying competent performance. In the past, cognitive deficit has often been used to explain the performances of students and laypeople on science and mathematics related representations (e.g., Leinhardt, Zaslavsky, & Stein, 1990). However, given that all the scientists in the expert/expert study had been successful in their careers (i.e., publication rates, grants, scholarships, or awards), a deficit model appears inappropriate. A different approach to Emergence of graphing 4 the performances relative to scientific and mathematical representations focuses on graphing as practice (Roth & McGinn, 1998), which requires a different methodology for studying how scientists know and learn mathematical representations. It has therefore been suggested that to understand graphs and graphing in science, we need to move toward a cognitive anthropology of graphing (Roth, 2003b). In the present study, I use materials from a study of ecologists at work to exemplify the results of my ongoing research regarding the emerging graph-related competencies of scientists during their research. Over the past five years, I have conducted several ethnographic studies of graphing in scientific research (laboratory, field) and at a variety of workplaces (farm, fish hatchery). I have also asked 37 research scientists in thinkaloud protocols to interpret graphs from introductory courses and textbooks in ecology. The present study was designed to gain an understanding of how graphing practices (skills) emerge in the process of scientific research, that is, how the function Φ2 (Figure 2) arises from and comes to be established in everyday scientific practice. I was further interested in the relation between scientists’ structuring Θd of their lifeworlds (phenomenon, instrumentation, research methods) and the corresponding structuring Θs in the symbolic domain (e.g., variables used). Here, I present and analyze both the thinkaloud (un/familiar graphs) and fieldwork data (emergence of graphs) in a case study pertaining to the same scientist.