## INTRODUCTION

[A]

concrete conceptionof commodity . . .coincideswith thetheoretical understandingof the entire totality of the interacting forms of economic life. (Il'enkov, 1982, p. 105, emphasis added)

Graphs and graphing, which emerged during the Renaissance period, are quintessential to the nature of science: Without these, the sciences as we know them today would not exist (Edgerton, 1985). In the production of scientific knowledge, graphs play an important role because they depict, at a sufficiently abstract level, general tendencies in the relation of two or more variables (Latour, 1987). It comes as little surprise, then, to find graphs and graphing among the fundamentals to be taught in science (e.g., National Research Council, 1996). From prekindergarten to high school, curricula are to enable students to formulate questions, collect and organize data, and display them such as to provide answers to the questions posed. Students are to learn how to develop and evaluate inferences and make predictions based on their data. Curricula should enable students to “create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena” (National Council for Teaching of Mathematics, 2000, p. 66).

Educational research and practice tend to assume that scientists are experts at graphs and graphing. But even scientists are frequently at a loss even when asked to interpret introductory-level graphs in their own field (Roth & Bowen, 1999a, 2003). The same scientists however tend to be knowledgeable when it comes to graphs from their own work. This raises questions about the nature of the expertise that tends to be ascribed to scientists when science (and mathematics) educators list graphs and graphing among the core “scientific process skills.” This study was designed to better understand the process by means scientists come to understand their data and associated graphs for the purpose of informing science educators about implications for research and practice. The purpose of this paper is to show how scientists, prior to their ultimate discoveries, indeed struggle to understand their own data and the graphs that they give rise to when these are apparently independent of context. I present an exemplifying analysis of scientists before they have arrived at the final understanding of their data and graphs that they ultimately publish. At this early point in their work, scientists still articulate many things that do not hold up in the end.