Scholars interested in the function of language in mathematical learning often draw on Vygotsky, whose early work on word meaning has shaped many research studies. However, near the end of a rather short life, Vygotsky heavily critiqued his own previous work and began to sketch a radical theory revision, which overturns much of what he had done…

In most epistemologies, practical actions and speech are the consequences of thought. In this study, I provide three case studies of highly educated scientists producing aspects of graphs only to erase these as soon as they have been drawn. The case studies are consistent with an alternative approach, already formulated by L. S. Vygotsky and M.…

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

In the social studies of science, visuals and graphical representations are theorized by means of the concept of inscription, a term that denotes all representations other than text inscribed in some medium including graphs, tables, photographs, and equations. Inscriptions constitute an intrinsic and integral part of scientific practice; their…

This study analyzes the interpretive activities of scientists related to familiar and unfamiliar graphs. The analyses show that when scientists were familiar with a graph, they read it transparently and thereby leapt beyond the material basis to the thing the graph is said to be about. In contrast, when scientists were less familiar with the…

The power of mathematical inscriptions, such as graphs, is often attributed to the fact that they summarize a lot of information independent of their contextual particulars. There is evidence, however, that even quintessential experts and scientists have difficulties interpreting graphs when they are unfamiliar with the entities represented and…

Inscriptions are central to the practice of science. Previous studies showed, however, that preservice teachers even those with undergraduate degrees in science, generally do not spontaneously produce inscriptions that economically summarize large amounts of data. This study was designed to investigate the production of inscription while a group…

The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

Reports on a study designed to find out what scientists and science students actually do when they are reading familiar and unfamiliar graphs. Describes changes in ontologies of scientists and science students as they engage in the reading tasks assigned to them. Theorizes a transition of graphs from things to signs that come to stand for natural…

Presents an alternative perspective that conceives of graphing as observable practices employed to achieve specific goals rather than as knowledge represented in students' minds. Highlights the nature of graphs as semiotic objects, rhetorical devices, and conscription devices. Illustrates the plausibility and fruitfulness of the new perspective in…

Examined cognitive complexities when graphs were used in lectures by observing 39 lectures, 36 seminars in which students solved problems, and 14 sessions of scientists interpreting graphs. Findings show that lectures present a scanty image of the use and interpretation of graphs. Discusses the analytic method, which relies on semiotics and…

Past research has shown that many scientists, when asked to interpret unfamiliar graphs that have nevertheless been culled from introductory undergraduate courses in their own field, experience problems and cannot give the standard answer accepted in the field. Yet, these same scientists turn out to be highly competent when it comes to graphs from…

Presents the results of a series of studies on the production, transformation, and interpretation of graphical representations from grade 8 to professional scientific practice in formal testing situations (inside) and in the course of field/laboratory work (outside). (Author/CCM)

Microanalyzes graph use in lectures drawn from artifacts compiled from videotaping all lectures and seminars in a 13-week ecology course. Focuses on both the text and the gesture-related references made in the reading of a graph in an ecology lecture. Contains 36 references. (DDR)

Investigates the use of mathematical representations in 3 grade-8 general science classes (n=65) that engaged in a 10-week open inquiry about the correlations between biological and physical variables in the environment. Demonstrates the use of representations as conscription devices, and illustrates how the use and understanding of inscriptions…