Pre-Service Elementary Teachers' Understanding of Geometric Similarity: The Effect of Dynamic Geometry Software

Article excerpt

Since the use of technology in mathematics classrooms has increased dramatically during the past few decades, critical issues such as the role of technological advances in the learning and doing of mathematics need to be addressed (Balacheff & Kaput, 1996; Leitzel, 1991; National Council of Teachers of Mathematics [NCTM], 2000). Connell (1998) reported that a technological environment can enhance construction of knowledge and influence learning. Computers are able to aid in visualizing abstract concepts and to create new environments that extend beyond students' physical capabilities. Dynamic software is often employed as a fertile learning environment in which students can be actively engaged in constructing and exploring mathematical ideas (Cuoco & Goldenberg, 1996; Garry, 1997).

Software such as the Geometer's Sketchpad[R] [GSP] (Jackiw, 1995) and Micro Worlds LOGO[TM] (LOGO Computer Systems, Inc., 1996) provide a flexibly structured mathematics laboratory that supports the investigation and exploration of concepts at a representational level, linking the concrete and the abstract. Mathematical ideas can be explored from several different perspectives in an efficient manner, resulting in deeper conceptual understanding (Kaput & Thompson, 1994). Through repetitive experiences of exploring and mathematizing, problem solving skills and one's ability to assimilate ideas are enhanced (Cooper, 1991). In addition, the interactive mode supports active learning--a necessary component for effective construction of mathematical knowledge.

Purpose of the Study

The goal of the study was to determine the extent to which a dynamic geometry learning environment affects proportional reasoning. This study explored the role in the learning of mathematical concepts of the pre-service elementary teachers' classroom environment.

The necessity of requiring pre-service teachers to learn mathematics content and methods of teaching in an environment where technology is an integral component seems clearly evident (Abramovich & Brown, 1996). Students must be given the opportunity to construct and thoroughly develop a deep, interconnected understanding of fundamental mathematics in an environment similar to the mathematics classroom they will oversee (Ma, 1999; Simon & Blume, 1992). Research on rational numbers and multiplicative structures suggests that many K-8 teachers do not have the understanding required in proportional reasoning (Cramer & Lesh, 1988; Harel & Behr, 1995). Hence, based on the assumption that teachers need to be taught in a manner similar to the way they are expected to teach, this study investigated the effect of a dynamic geometry learning interface on performance in the context of similarity tasks. Furthermore, the research sought to better understand whether such an environment assists learning and reasoning, given its ability to efficiently display a variety of mathematical situations.

Theoretical Framework

The theoretical foundation for using a dynamic learning interface emphasizing inquiry and exploration is based on the Piagetian theory of learning as well as the role of repetitive experiences according to Cooper (1991). Current research on teaching from a constructivist perspective follows Piaget's biological metaphor of development and characterizes mathematical learning as a process of conceptual reorganization. The basic tenets of a constructivist epistemology have a direct implication upon pedagogy; that is, acceptance of these premises implies a way of teaching that acknowledges learners as active knowers (Brindley, 2000; Noddings, 1990).

The role of experience is to generate or modify the organization of the relevant cognitive space. As conceived by Cooper (1991), the role of repetitive experience, repeated interaction with the environment, is to create, enhance, and/or reorganize cognitive space. The possibility that repetition induces reorganizations of knowledge, not just of skills, is the rationale that Cooper (1991) gives for use of the term "repetitive experience" rather than "practice. …