The Focusing Effect of Technology: Implications for Teacher Education

When technology is implemented in classrooms, students often form ideas that are unexpected and unwanted by the teachers and the designers of the technology. This article advances the notion of the focusing effect of technology as a way of systematically accounting for the role of technology in such situations. A focusing effect refers to the direction of students' attention toward certain properties of the subject matter domain over others, brought about by the use of particular technological tools. Technology focuses students' attention in ways that are often not anticipated in advance and can have unintended consequences for students' conceptions. Vignettes are presented from two research studies, one involving graphing calculators and one involving mathematics software called SimCaic Mathworlds. The research findings are synthesized and reinterpreted in order to illustrate and develop the notion of the focusing effect of technology. The significance of this construct lies in the connection that it afford s between individual students' conceptions and the way technology is used in the instructional environment. Implications for teaching and for the preparation of teachers in the use of technology are discussed. ********** A number of researchers have critiqued the idea that computer software or devices such as graphing calculators can embody, in a transparent manner, the subject matter concepts that designers so carefully try to embed in the technology (Holyes & Noss, 1992; Lesh, Post, & Behr, 1987; Meira, 1998; Teasely & Roschelle, 1993). In fact, students routinely form ideas and interpret technological environments in ways that vary widely from what teachers and designers expect. Researchers relying upon a constructivist perspective explain why students "see" technology differently from adults by pointing to the role of prior knowledge and experiences (Bowers & Nickerson, 2000; Kieren, 1994; Noble, Nemirovsky, Tierney, & Wright, 1999). In an oft-cited example, Goldenberg (1988) illustrated how students view representations of functions in a graphing software environment differently from mathematically sophisticated adults. If one is familiar with graphs of linear functions, then he or she will expect the graph of the line y -5x-1 to move up vertically when they-intercept is changed from -1 to +1. However, beginners lack such algebraic sophistication and are more likely to perceive that the line segment moves diagonally from the bottom left corner of the computer screen to the top right corner. This article argues that inherent features of technology also play a critical role in situations in which students form unintended ideas. The notion of the focusing effect of technology is advanced in this article. A focusing effect refers to the regular direction of users' attention toward certain properties or patterns in the subject matter domain, which is brought about by the use of particular technological tools. Technology can focus students' attention in ways that are often not anticipated in advance but which may have unintended consequences for students' conceptions. The construct of focusing effects emerged from a synthesis of a series of studies conducted as part of an ongoing research project, the Generalization of Learning Mathematics in Multimedia Environments. The purpose of this article is to characterize the focusing effect of technology, identify the theoretical roots of this notion, illustrate the focusing effect of technology with two examples from research studies, and explicate the significance of this notion for teaching and teacher education. The examples presented here are drawn from two larger studies: (a) an investigation of a high school classroom implementation of a reform mathematics curricula in which graphing calculators were used regularly; and (b) a teaching experiment conducted with secondary school students using simulation software called Mathworlds (1996), which was developed for the SimCalc Project (directed by James Kaput). …