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March 2001, Volume 32, Issue 2

FEATURES

Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications
Susan N. Friel, Frances R. Curcio, George W. Bright
Our purpose is to bring together perspectives concerning the processing and use of statistical graphs to identify critical factors that appear to influence graph  comprehension and to suggest instructional implications. After providing a synthesis of information about the nature and structure of graphs, we define graph comprehension. We consider 4 critical factors that appear to affect graph comprehension: the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics. A construct called graph sense is defined. A sequence for ordering the introduction of graphs is proposed. We conclude with a discussion of issues involved in making sense of quantitative information using graphs and ways instruction may be modified to promote such sense making.

Professionals Read Graphs: A Semiotic Analysis
Wolff-Michael Roth, G. Michael Bowen
Graph-related practices are central to scientific endeavors, and graphing has long been hailed as one of the core "general process skills" that set scientists apart. We use two case studies from a large study among scientists to exemplify our findings that graphing is not a context-independent skill. Rather, scientists' competencies with respect to graph interpretation are highly contextual and are a function of their familiarity with the phenomena to which the graph pertains. If graphing practices are not general but are tied to embodied understandings and familiarity with representation practices, then there are implications for teaching graphing in school mathematics and science settings.  

Abstraction in Context: Epistemic Actions
Rina Hershkowitz, Baruch B. Schwarz, Tommy Dreyfus
We propose an approach to the theoretical and empirical identification processes of abstraction in context. Although our outlook is theoretical, our thinking about abstraction emerges from the analysis of interview data. We consider abstraction an activity of vertically reorganizing previously constructed mathematics into a new mathematical structure. We use the term activity to emphasize that abstraction is a process with a history; it may capitalize on tools and other artifacts, and it occurs in a particular social setting. We present the core of a model for the genesis of abstraction. The principal components of the model are three dynamically nested epistemic actions: constructing, recognizing, and building-with. To study abstraction is to identify these epistemic actions of students participating in an  activity of abstraction.